FINANCIAL STRESS in an ADAPTIVE SYSTEM: from EMPIRICAL VALIDITY to THEORETICAL FOUNDATIONS by MIKHAIL V. OET Submitted in Partia

FINANCIAL STRESS IN AN ADAPTIVE SYSTEM: FROM EMPIRICAL VALIDITY TO THEORETICAL FOUNDATIONS

MIKHAIL V. OET

Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Weatherhead School of Management

Designing Sustainable Systems

CASE WESTERN RESERVE UNIVERSITY

May, 2016 CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

Mikhail V. Oet

Candidate for the degree of Doctor of Philosophy. *

Committee Chair

Kalle Lyytinen, Ph.D., Case Western Reserve University

Committee Member

Lucia Alessi, Ph.D., European Central Bank

Committee Member

Agostino Capponi, Ph.D., Columbia University

Committee Member

Myong-Hun Chang, Ph.D., Cleveland State University

Committee Member

Corinne Coen, Ph.D., Case Western Reserve University

Date of Defense

March 5, 2016

*We also certify that written approval has been obtained for any proprietary material contained therein.

To my family.

In every systematic inquiry (methodos) where there are first principles, or causes, or elements, knowledge and science result from acquiring knowledge of these; for we think we know something just in case we acquire knowledge of the primary causes, the primary first principles, all the way to the elements. It is clear, then, that in the science of nature as elsewhere, we should try first to determine questions about the first principles. The naturally proper direction of our road is from things better known and clearer to us, to things that are clearer and better known by nature; for the things known to us are not the same as the things known unconditionally (haplôs). Hence it is necessary for us to progress, following this procedure, from the things that are less clear by nature, but clearer to us, towards things that are clearer and better known by nature. ——Aristotle, Phys. 184a10–21

Table of Contents List of Tables ...... v List of Figures ...... vii Abstract ...... x Executive Summary ...... 1 Problem of Practice ...... 1 Research Motivation and Goals ...... 5 Research Design ...... 8 Conceptual map ...... 8 What methods are appropriate? ...... 9 Research plan ...... 11 Chapter Outlines ...... 14 Chapter 1: The Problem of Financial Stress in Adaptive System ...... 25 1.1. Theoretical Framing ...... 25 1.1.1. Issues framed by research in financial system complexity ...... 25 1.1.2. Issues framed by research in financial system stability ...... 30 1.2. Research Precedents ...... 31 1.2.1. Financial system stress construction ...... 31 1.2.2. Stress factor decomposition ...... 33 Chapter 2: Does Financial Stability Matter to the Fed in Setting the US Monetary Policy? ...... 37 2.1. Introduction ...... 38 2.2. Conceptual framework ...... 41 2.3. Data and methodology ...... 45 2.3.1. Content analysis: FOMC discussions of monetary policy ...... 46 2.3.2. Taylor guide to monetary policy ...... 59 2.4. Thematic and Tri-mandate Monetary Policy Models ...... 66 2.4.1. Main results ...... 66 2.4.2. Sign expectations ...... 69 2.4.3. Significance ...... 74 2.5. Discussion ...... 82 2.5.1. Counterarguments ...... 82 2.5.2. Methodological limitations ...... 85 2.5.3. Implications ...... 86 Chapter 3: How to Evaluate Measures of Adverse Financial Conditions? ...... 89 3.1. Introduction ...... 89 3.2. Literature review ...... 92 3.3. Methodology ...... 97 3.3.1. Classification problem ...... 98 3.3.2. Multi-dimensional signaling ...... 99 3.3.3. Comparison of identification properties ...... 100 3.3.4. Comparison of early warning properties ...... 104 3.4. Case Study: Measures of US Systemic Conditions (1976-2014) ...... 105 3.4.1. Data and sampling ...... 105 ii

3.4.2. Results ...... 109 3.5. Conclusion: Implications and limitations ...... 122 Chapter 4: Stress in Heterogeneous Financial Agents: Validity and Dynamics ...... 126 4.1. Introduction ...... 126 4.2. Theoretical Foundation ...... 128 4.2.1. Motivation ...... 128 4.2.2. Hypotheses ...... 129 4.2.3. Micro-level stress in agents and instruments:A conjecture ...... 134 4.3. Empirical Comparison ...... 142 4.3.1. Empirical identification of micro-level stress ...... 146 4.3.2. Empirical macro-level stress in a set of representative markets ...... 146 4.3.3. Exploratory factor analysis ...... 148 4.3.4. Dynamic factor analysis ...... 151 4.4. Discussion ...... 176 Chapter 5: Connecting the Micro and Macro Levels of Financial Stress ...... 180 5.1. Agent Choices and Transmission Dynamics ...... 180 5.1.1. Dynamic analysis of agent stress ...... 181 5.1.2. Agent preferences ...... 182 5.1.3. The stress transmission process ...... 183 5.2. Methodology ...... 185 5.2.1. Revealed preference analysis ...... 185 5.2.2. Stress dynamics ...... 190 5.3. Results ...... 192 5.4. Integrated Research Findings ...... 199 5.5. Conclusion ...... 200 Appendix 1: Chapter 2 Regime Sampling ...... 204 A1.1 Regime Sampling ...... 204 A1.2 Descriptive Statistics ...... 206 A1.3 Robustness ...... 206 Appendix 2: Chapter 2 Content Analysis Methodology ...... 208 A2.1 Target of Content Analysis and Data ...... 208 A2.2 Unitizing and Coding ...... 209 Appendix 3: Chapter 2 Content Analysis Validity ...... 212 A3.1 Face Validity ...... 212 A3.2 Social Validity ...... 213 A3.3 Empirical Validity in Content Sampling and Semantics ...... 213 A3.4 Empirical Validity in Structure and Function ...... 214 A3.5 Empirical Validity in Relations to Other Variables ...... 214 Appendix 4: Chapter 3 Robustness Testing ...... 216 Appendix 5: Chapter 4 MIMIC Factor Model Specification ...... 220 A5.1. MIMIC Identification ...... 220 A5.2. MIMIC Estimation ...... 224 Appendix 6: Chapter 4 Longitudinal Factor Analysis ...... 229 Appendix 7: Chapter 4 Dynamic Factor Analysis ...... 238 A7.1. Motivations for dynamic factor analysis ...... 238

iii

A7.2. Insidious problems and remedies for longitudinal analysis ...... 240 A7.3. Two perspectives of dynamic processes ...... 244 A7.4. Model estimation ...... 251 A7.5. Empirical algorithm ...... 254 References ...... 256

iv List of Tables

Table 1 Outline of Theory Building, Methods, and Data by Research Questions ...... 13 Table 2 Financial Stress Index Construction ...... 32 Table 3 Descriptive Statistics of Themes Discussed at FOMC Meetings (1990–2012) ....48 Table 4 Granger Causality of FOMC Discussions and Monetary Policy (1990M2– 2012M6) ...... 54 Table 5 Results ...... 65 Table 6 Model Horse-Race over Regime Samples ...... 68 Table 7 Summary Statistics for the Stress Series and Benchmark Volatility Series Calculated for Monthly Data between June 2000 and February of 2014 ...... 109 Table 8 Comparison of Interventions and Multi-Dimensional Market Signals under Level Perspective ...... 112 Table 9 Comparison of Interventions and Multi-Dimensional Market Signals under Difference Perspective ...... 112 Table 10 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV ...... 115 Table 11 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV ...... 116 Table 12 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on ...... 117 Table 13 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on ...... 118 Table 14 Accuracy of Forecasts ...... 121 Table 15 Usefulness of In-Sample Data Compared to Out-of-Sample Forecasts ...... 121 Table 16 Hypothesis Testing ...... 133 Table 17 Rotated Factor Pattern (Standardized Regression Coefficients)...... 150 Table 18 Reliability of Five-Factor Stress Measure ...... 150 Table 19 Unit Root Tests of Quarterly Financial Stress ...... 156 Table 20 Cholesky Decomposition ...... 162 Table 21 Granger Causality of FX and Equity Observations with Financial Stress ...... 164 Table 22 Dynamic Parallel Factor Analysis for Quarterly Data ...... 167 Table 23 Factorability Analysis for Quarterly Data ...... 168 Table 24 Dynamic Four-Factor Extraction ...... 169 Table 25 Four-Factor Correlation Matrices (Lagged 0 through 4) ...... 170 Table 26 Factor Reliability ...... 170 Table 27 Goodness of Fit Summary ...... 173 Table 28 Analysis of Violations Revealed with Various Price Functions: Observed Price, Expected Return, Risk Premium, and Adjusted Risk Premium ...... 196 Table 29 Granger Causality among Violations Based on Adjusted Risk Premium with 12-month Memory ...... 198 Table 30 Bai-Perron Structural Break Test Results ...... 205 Table 31 Descriptive Statistics of Manifest Variables (1990M2–2012M6) ...... 206 Table 32 Two-Tailed Test of the Mean for Statistical Power (95% Confidence) ...... 207

v Table 33 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV ...... 216 Table 34 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV ...... 217 Table 35 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on ...... 218 Table 36 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on ...... 219 Table 37 Serial Correlation Testing of the Weighted Components of CFSI, the Differenced Spreads, and the Differenced Weighted Components ...... 230 Table 38 Normality Testing ...... 232 Table 39 ANOVA Deviation from Linearity F-Test ...... 234 Table 40 Correlation Matrix ...... 236 Table 41 Communality ...... 241 Table 42 KMO and Bartlett’s Test...... 241 Table 43 Anti-Image Correlation Matrix ...... 241 Table 44 Summary Nomological Comparison of Process and Shock Dynamic Factor Models ...... 251

vi List of Figures

Figure 1 Research Plan by Strand ...... 9 Figure 2 Conceptual Model: Early-Warning Policy Use in Adaptive Financial System ...... 27 Figure 3 Conceptual Model of Financial System’s Stress ...... 33 Figure 4 CFSI Components ...... 34 Figure 5 Decomposition of Stress: Components of the Markets ...... 36 Figure 6 Situational Map of Monetary Policy Themes ...... 47 Figure 7 Relative Theme Importance over Time ...... 49 Figure 8 Cross-correlograms of intentions and impact functions for FOMC discussions and monetary policy (1990M2–2008M1) ...... 53 Figure 9 Financial Stability Factors Deliberated in Setting Monetary Policy (Exploratory Analysis, 1993M1–2012M6) ...... 55 Figure 10 Financial Stability Factors Deliberated in Setting Monetary Policy (Algorithmic Analysis, 1990M2–2012M6) ...... 58 Figure 11 Comparison of Standard Taylor and Taylor-type Rules (Table 5 Columns 1–4) with Fed Funds Rate (Regimes 1–4) and Average SSR (Regime 5) ...... 60 Figure 12 Comparison of Thematic (Discussion-Augmented Taylor-Type) Model (Table 5 Column 8), Tri-Mandate Model (Table 5 Column 9), and Benchmark Taylor-Type (1999) Model (Table 5 Column 4) with Fed Funds Rate (Regimes 1–4) and Average SSR (Regime 5) ...... 64 Figure 13 Percentage of Total US Financial Assets Held by Financial Intermediaries (1952‒2013) ...... 90 Figure 14 Multidimensional Signal Compared to Several Measures of Adverse Systemic Conditions ...... 107 Figure 15 Optimal Matching of Interventions and Multi-Dimensional Market Signals ...... 111 Figure 16 VEC Forecast Results ...... 120 Figure 17 Hypotheses ...... 133 Figure 18 Conceptual Diagram of the Adaptive System Solution ...... 135 Figure 19 Comparative Theoretical Stress for Heterogeneous Agents ...... 140 Figure 20 Comparative Theoretical Stress for Heterogeneous Instruments ...... 141 Figure 21 Comparison of CFSI and Comparative Theoretical Stress ...... 142 Figure 22 Comparison of Five-Factor Stress and Comparative Theoretical Stress ...... 144 Figure 23 Comparison of Process Factor Model Stress and Comparative Theoretical Stress ...... 145 Figure 24 Comparison of Shock Factor Model Stress and Comparative Theoretical Stress ...... 145 Figure 25 MIMIC Identification of Latent Micro-Level Stress ...... 146 Figure 26 Stages and Steps of Empirical DFA ...... 152 Figure 27 Quarterly Time-Series of US Financial Stress ...... 154 Figure 28 Correlogram of Quarterly Financial Stress ...... 156 Figure 29 Stylized Block-Diagonal Toeplitz Matrix ...... 157 Figure 30 Toeplitz Intensity and Symmetry Pattern for Quarterly Financial Stress ...... 158

vii Figure 31 Correlogram of Weekly Financial Stress ...... 165 Figure 32 Process Factor Model of Quarterly Financial Stress ...... 172 Figure 33 Shock Factor Model of Quarterly Financial Stress ...... 174 Figure 34 Weak Axiom of Revealed Preferences ...... 188 Figure 35 Initial Revealed Preference Testing for All Agents ...... 193 Figure 36 Detailed Revealed Preference Testing for Heterogeneous Agents ...... 194 Figure 37 Testing Price, Expected Return, Risk Premium, Adjusted Risk Premium to Explain Agent Choice ...... 197 Figure 38 Testing Agent Memory to Explain Choice ...... 197 Figure 39 Contagion Network ...... 199 Figure 40 MIMIC Factor ...... 224 Figure 41 Scatterplot Matrix of CFSI and Market Stress Variables ...... 233 Figure 42 Outlier Boxplots of Market Stress Variables...... 235 Figure 43 Process Factor Analysis Model: PFA (1,0) ...... 247 Figure 44 Process Factor Analysis Model: PFA (0,1) ...... 247 Figure 45 Shock Factor Analysis Model: SFA (1) ...... 249

viii Acknowledgements

I am indebted to my wife Inna, my family, and Stephen Ong for making this

journey possible and for their encouragement and advice while travelling with me.

I am deeply grateful to Dr. Kalle Lyytinen, my dissertation supervisor, for his guidance in shaping my research from its very beginnings, and Dr. Lucia Alessi, Dr.

Agostino Capponi, Dr. Myong-Hun Chang, and Dr. Corinne Coen, for pushing me to strengthen and extend the boundaries of this research.

I would like to thank the faculty at Case Western Reserve University doctoral program in Designing Sustainable Systems, particularly Dr. Richard Boland, Dr. Jagdip

Singh, Dr. Eileen Doherty-Sil, and Dr. Lee Hoffer, for their intensity in expanding my research horizons.

I am grateful for the insightful critiques received from Dr. Joseph G. Haubrich,

Dr. Ben R. Craig, Dr. Charles T. Carlstrom, Dr. O. Emre Ergungor, Dr. James B.

Thomson, Dr. Owen F. Humpage, Dr. Edward S. Knotek II, Dr. Filippo Occhino, Dr.

Mark Schweitzer, Dr. Mark S. Sniderman, Saeed Zaman, John M. Dooley, Jack W. Liu,

Amanda Janosko, and Tim Bianco. To John, Jack, Amanda, and Tim, I am also deeply grateful for research assistance.

I would like to thank Sue Nartker and Marilyn Chorman, the Directors of the

Doctor of Management program, for making my time at Case Western Reserve

University a memory to treasure for a lifetime.

ix Financial Stress in an Adaptive System:

From Empirical Validity to Theoretical Foundations

Abstract

MIKHAIL V. OET

A review of financial system stress measures reveals not only the absence of theory on financial stress, but also the absence of search for theory. To remedy this gap, this study conducts a rigorous investigation of the empirical validity and dynamic properties of financial stress measurement in the context of financial system complexity. We provide and validate four contributions to literature.

First, we establish the relevance and comparative quality of macro-level stress

measurement for the financial system relative to alternative measures of system

conditions.

Second, we establish theoretical foundations for measuring financial stress across multiple units of analysis. This measure builds on the understanding of stress origins and drivers and incorporates price, quantity, and behavioral variables to explain the pattern of

apparently irrational choices of financial agents. At the macro-level, stress is supported

empirically by hypotheses of association between behavioral aspects of heterogeneous

financial agents and overall financial system stress. At the micro-level, we apply

abductive inference to the empirical results to propose a new theoretical stress measure

x for heterogeneous agents and instruments. Defining financial stress theoretically allows

continual measurement of financial stress at the level of the various heterogeneous

partitions of the financial system (e.g. agents and instruments) as these partitions evolve

through structural changes and financial innovations.

Third, we build a theory of stress transmission across micro-level of sectoral

agents to the macro-level of the financial system. This theory describes a process of stress

transmission across financial intermediaries and the process by which its agent stress escalates to the financial system.

Fourth, we examine the process by which unusual conditions in the financial

markets manifest as critical states of financial system stress.

Keywords: financial stress; heterogeneous agents; empirical validity; factor analysis;

dynamic factors; stochastic analysis; content analysis

xi Executive Summary

Problem of Practice

People view and economists study financial tsunamis as distinct and unique events. During the roaring nineteen-twenties, financial system was “lightly regulated”1

and people believed the stock market would rise forever. Uninformed people borrowed

heavily to speculate. When the stock market collapsed in the Great Crash of October of

1929, it dragged many banks to bankruptcy. Millions of depositors in these banks were

unprotected and lost everything. As purchases shrank, manufacturing withered leading to

massive layoffs and economic collapse known as the Great Depression which ravaged the

country for the next ten years.

At the opening of 1980s, the interest rates skyrocketed to about 20%. The small

savings and loan banks, which were prevented by regulations2 from paying market rates,

lost millions of deposits as savers withdrew their funding to seek higher returns from

money market mutual funds. To remedy this, financial deregulation of 19803 lifted the

rate ceilings on deposits. The savings and loans institutions rushed in to chase the

depositors, and then followed to finance the costly deposits by chasing high yields in the

real estate markets. As real estate prices collapsed, so did the banks. From 1981 to 1995,

over 1,043 institutions holding $519 billion in assets—close to half of U.S. savings and

loan banks—collapsed.4

1 Acharya et al. (2010: 13). 2 Sherman, M. (2009). 3 The 1980 Depository Institutions Deregulation and Monetary Control Act (DIDMCA). 4 Curry and Shibut (1986), Spilimbergo et al. (2009).

1 For several years in the mid-1990s, an unregulated U.S. hedge fund5 called Long-

Term Capital Management (LTCM) enjoyed tremendous reputation and success. Run by two 1997 Nobel Laureates, Myron Scholes and Robert Merton,6 the fund borrowed heavily from some of the most significant U.S. financial institutions and accumulated

$1.3 trillion of derivative exposures, or about 32% of all U.S. commercial bank assets.7

When global investors ran for the safety of U.S. Treasuries, following the 1997-1998 fiascos of the Asian and Russian currencies, they created unusual price discrepancies in the value of the dollar. In the course of four months, LTCM exposures quickly lost $4.6 billion dollars, threatening to topple the U.S. financial system.8

On June 22, 2007, “Bear Stearns Companies, the investment bank,9 pledged up to

$3.2 billion in loans … to bail out one of its hedge funds that was collapsing because of bad bets on subprime mortgages. It [was] the biggest rescue of a hedge fund since 1998 when more than a dozen lenders provided $3.6 billion to save Long-Term Capital

5 Paredes (2006). 6 Scholes and Merton won a Nobel Prize for a new method to value financial derivatives, payment contracts that depend on future values of an underlying asset. 7 Summers et al. (1999: 29): “The notional amount of LTCM’s total OTC derivatives position was $1.3 trillion at the end of 1997 and $1.5 trillion at the end of 1998. LTCM’s balance sheet leverage was 28- to-1 at the end of 1997.” For comparison, “At the end of 1998, for instance, commercial banks had $4.1 trillion in total assets; mutual funds had assets of approximately $5 trillion; private pension funds had $4.3 trillion; state and local retirement funds had $2.3 trillion; and insurance companies had assets of $3.7 trillion.” (Ibid.: 1-2). 8 LTCM strategy was based on the idea that the value of U.S. dollar 30 years from now should be very close to the value of the U.S. dollar 29.75 years from now. However, this turned out to be false in 1998. Following a wave of speculative attacks in May 1997, the Thai Bhat tumbled, sparking off a chain reaction of dropping currency and asset prices throughout Asia. Then, in August 1998, Russia defaulted on its international obligations. As global investors ran for cover, dumping Asian and Russian assets, they fled to the safety of the U.S. dollar, clamoring for the most liquid U.S. treasuries and creating unusual price discrepancies in the value of the dollar. 9 As a consolidated entity, Bear Stearns was a part of the voluntary “Consolidated Supervised Entities (CSE) program, created in 2004 as a way for global investment bank conglomerates that lack a supervisor under law” (Securities and Exchange Commission, 2008). Also see Ryback (2015: 3). Coffee and Sale (2009: 736-737) discuss that “A key attraction of the CSE Program was that it permitted its members to escape the SEC’s traditional net capital rule, which placed a maximum ceiling on their debt to equity ratios, and instead elect into a more relaxed “alternative net capital rule” that contained no similar limitation.”

2 Management.”10 Across the Atlantic, on August 9, 2007, “BNP Paribas SA, France's

biggest bank, halted withdrawals from three investment funds because it couldn't “fairly”'

value their holdings after U.S. subprime mortgage losses roiled credit markets.”11 So

innocuously began the 2007 subprime mortgage crisis, which so far has cost the U.S.

taxpayers in excess of $3 trillion including the $356.2 billion in the Trouble Assets Relief

Program, $1.5 trillion in Federal Reserve rescue efforts, and $577.8 billion in Federal government stimulus programs.12

The notion that our lives are punctuated by these exceptional financial crises is

not new. Writing about the U.S. unregulated era,13 Wesley C. Mitchell (1923) observed

that “Fifteen times within the past one hundred and ten years, American business has

passed through a “crisis”…Further, no two crises have been precisely alike and the

differences between some crises have been more conspicuous than the similarities. It is

not surprising, therefore, that business men long thought of crises as “abnormal” events

brought on by some foolish blunder made by the public or the government. On this view

each crisis has a special cause which is often summed up by the newspapers in a

picturesque phrase “the Jay Cooke panic” of 1873, “the railroad panic” of 1884, “the

Cleveland panic” of 1893, “the rich man's panic” of 1903, “the Roosevelt panic” of

1907.”14

Furthermore, modern financial system links different types of financial

intermediaries by a sophisticated network of multilateral exposures where various risky

10 Creswell and Bajaj (2007). 11 Boyd (2007). 12 Goldman (2009). 13 The regulatory era of the United States financial system is here considered to start with the creation of the Federal Reserve regulatory system in December 23, 1913 by the Federal Reserve Act. 14 Mitchell (1923: 5).

3 activities of some institutions are financed using funds borrowed from others.

Specifically, small financial intermediaries use customer deposits to make loans to large universal intermediaries that depend on wholesale short-term funds to finance a gamut of risky activities. As the value of financial assets falls, financial institutions experience increased difficulty in repaying current obligations, raising funds, and remaining solvent and liquid. Furthermore, through these linkages, failed obligations of some institutions lead to distress and losses in other institutions, markets, and economic sectors (Acharya and Yorulmazer, 2008; Iyer and Peydro, 2011; Tedeschi et al., 2012).

The problem of contagion in the financial system has been established as a source of significant levels of systemic risk (Freixas et al., 2000; Allen and Gale, 2000; Furfine,

1999) well before the Global Financial Crisis of 2007. However, the problem is compounded viciously by structural changes occurring in the system. As the system structure changes, so does the pattern of systemic risk generation (Nier et al., 2007;

Battiston et al., 2012; Lenzu and Tedeschi, 2012; Georg, 2013; and Sachs, 2014).

Consequently, policies targeted at mitigating systemic risk need to account for the evolving system structure. We refer the reader to Allen and Gale (2007), Teteryatnikova

(2009), Acharya et al. (2012), and Capponi and Chen (2013) for a more complete discussion in this regard. Hence, financial system connections constitute an important source of systemic risk (Rochet and Tirole, 1996) and need to be carefully analyzed.

4 Research Motivation and Goals

We are motivated by a particularly vicious problem of stress in the financial system. Both the experiential and theoretical evidence for this problem suggest that financial system is a complicated and dynamic phenomenon prone to significant risks and potential failure.

The present state of knowledge of financial system’s stress displays few well- understood areas where theory is validated by empirical information. At the same time, a review of extant measures of financial system conditions reveals not only the absence of theory on the measurement of system’s conditions, but also the absence of search for such theory. In current context, our knowledge of financial stress is particularly poorly across multiple units of

analysis: the macro-level of the financial system, the micro-level of the financial system’s

agents and instruments, and the meso-level of the processes by which these agents and instruments interconnect and participate in the propagation of stressful conditions across the financial system and from one level to the others. These three challenges of stress measurement at the micro-, meso-, and macro- levels of the financial system are framed within the fundamental puzzle of system complexity.

First, there is a micro-level stress problem: As stress is experienced by some financial assets, they fall in value. The stress in the particular financial assets is also experienced by the financial institutions which hold these assets directly. They experience difficulty in repaying obligations, raising funds, and remaining solvent and liquid.

Second, there is a macro-level stress problem: As some financial institutions experience direct stress, it is transmitted indirectly through the various linkages of these institutions in the financial system. These linkages include ties that are contractual and

5 strong, when failed obligations of the stressed institutions lead to disruptions in expected payments, distress and losses in other institutions, markets, and economic sectors. The linkages also include ties that are tenuous and weak, when stressed values in specific instruments and firms affect the conditions of other institutions and instruments that share some similar characteristics and are re-valuated by other financial system participants less favorable. Thus, stress can also propagate indirectly through the contagion of suspected weaknesses.

Third, there is a meso-level stress problem. Since stress can be transmitted in a number of ways, both direct and indirect, it is possible for stress “to pile-up,” accumulating redundantly. Clearly this affects all levels of stress measurement: same institution that is stressed because of failed obligations of one of its counterparties may also be additionally stressed by association because some of its assets bear resemblance to other stressed assets. At the larger units of analysis, entire markets can become tainted with stress in multiple ways. For example, as residential mortgage backed securities experience stress, stress can transfer to other types of securitized products like auto loans and to other markets like other real estate instrument in the real estate market or the consumer durable sector of the equity market. When the levels and changes in stress are moderate, it may take a number of conditions to change so that the change in the financial system stress is experienced as critical. However, under some extreme levels and changes of stress, a disaster in a single market like equity or a small cluster of institutions like high-powered banks or hedge-funds can quickly bring the entire financial system to its knees.

6 The fundamental puzzle of stress lies in the simple fact that things change. As the financial system’s structure changes, so does the pattern of stress generation. Thus, any solution to the micro problem, to the macro problem, or the meso problem that is conditioned on the historical facts is bound to eventually outgrow its usefulness.

At the macro-level, our knowledge confronts the innate vulnerability of the financial system to change like falling asset values. At the micro-level, we don’t well understand how stress affects the choices of financial agents. At the meso-level, we have difficulty in identifying the process of stress transmission and the conditions under which stress leads to critical states when policymakers must intervene. Any hope that we have to the meaningful understanding and measurement of financial stress has to confront the following six major research questions.

First, given the evidence of financial system complexity, how can the financial stress be theorized to enable the policymakers and researchers to understand it as the system undergoes change? Specifically, to the extent that stress feeds on the aspects of system’s complexity, like uncertainty, how does system complexity condition financial stress? Second, why has financial stress has become relevant to the policymakers? Third, how can we evaluate the quality of the stress measure relative to alternative measures of financial system conditions? Fourth, how can macro-level stress be defined, reliably measured, and identified in the context of an evolving financial system? Fifth, given the complexity in the pattern of stress formation at the micro-level of analysis, can agent- and instrument- stress be described functionally in a way that remains meaningful and empirically reliable as the agents undergo change? Sixth, how does stress in set of agents or instruments transfer to another set of agents or instruments?

7 The first three research questions involve advancing our knowledge of measurement of system conditions in the context of adaptive change in the system. The next three research questions involve building multi-level theory of financial stress in the adaptive context. With the last research question, we tie both areas of inquiry together by seeking to understand the causation mechanisms by which financial stress propagates across the levels of analysis. It is our intent to develop an empirically sound and theoretically insightful understanding of financial stress in order to measure it at the various units of analysis as the system undergoes change.

Research Design

Conceptual map

Because of the dual—empirical and experiential—nature of these research questions, we pursue our questions in a sequential multiple method design. We pursue the empirical questions by a number of qualitative and quantitative methods that are appropriate to the research questions posed in each chapter. For the first study of system complexity and stress, we use qualitative methods of narrative analysis. For the second study of relevance of stress, we use content analysis of policymakers’ discussions. For the third study of comparative evaluation of information quality in alternative measures of system conditions, we use a general purpose evaluation framework for that combines standard two-class classification task methods with utility-augmented time-series methods. For the fourth study of macro-level stress, we use factor analytic methods, including dynamic factor analysis. For the fifth study of micro-level stress, we propose to use the microeconomic method of revealed preferences. For the sixth study of stress transmission across multiple units of analysis we use to augment the time-series method

8 of Granger causality. Figure 1 shows the conceptual map of the research plan. As shown, we propose to structure this research sequentially, incorporating the results from one study into the next.

Figure 1 Research Plan by Strand

What methods are appropriate?

To address the multiple process study questions, the study needs to include a multi-strand sequential mixed method approach (Caracelli and Greene, 1993; Creswell &

Plano-Clark, 2010, Creswell et al., 2002; Johnson & Onwuegbuzie, 2004). This mixed- method design of each strand starts with a narrative (qual) and proceeds with empirical

(Quant) development. In addition, because, as described below, the study adapts a quota sampling strategy and confronts some ecological validity challenges, we pursue a quasi- experimental approach (Shadish, Cook & Campbell, 2003). In our implementation of this

9 approach, we will apply multiple repeated quasi-experiments with pre-test and post-test treatments for quarterly for 41 financial agents from 1970 to 2014. We will extract a hold-out sample for subsequent out-of-sample testing of financial stress for ecological validity.

Sampling Strategy. It is clearly a nearly impossible task to include the census population of over 7000 banks, and thousands of other financial system agents and instruments. We also consider that randomization approaches may introduced an unwanted bias, since the distribution of the population is highly skewed: there are very few very large institutions that hold the majority of the financial assets, an absolute majority of very small institutions that collectively have a tangible share of assets.

Importantly, there is a small important of significant and critical regional financial intermediaries that in may financial product markets play an intermediary role between to facilitate the transactions between the very small and the very large agents. Because of the skewness, a random sample may introduce large distortions into the sample data that may subsequently fail the representative ecological and predictive validity tests.

Therefore, we propose to a convenience sampling approach, improved through the quota sampling approach. In this approach our sample will be constructed to reflect the relative representative structure in the relevant agent types (e.g. a representative quota sample of the 3 banking tiers).

Validation Strategy. In order to support generalizability claims of this research, the alternative study needs to include a comprehensive approach to validity (Campbell,

1957; Bryman, 2012) and specifically recognize the questions of experimental validity

10 that are integral to supporting the quasi-experimental design validity concerns (Shadish,

Cook & Campbell, 2003).)

Specifically, the study should demonstrate face validity in building its narratives qualitatively during the abductive theory building phase. The face validity concerns will need to address extant behavioral conceptions of stress in agents and instruments. The construct validity should be demonstrated against the sample data in the empirical analysis. The convergent validity will be compared by aggregating the meso level constructs of agent and instrument stress to the macro level of system stress. This comparison can be seen as an initial attempt for greater generalization, and thus a form of external validity. Finally, the empirical analysis needs to test the developed stress measures to test ecological validity of the measures, that is, whether these measures can reproduce the patterns the patterns of agents in natural settings. To test ecological validity, the study will reserve an out-of-sample dataset not used in the analysis, and compare the supported measures of stress to this sample to verify how well the measures of stress developed in-sample can support the “natural” out-of-sample facts.

Research plan

The seven research questions in this study aim to cycle from empirical validity research to theory generation. The reason for this broad scope is the vicious problem of adaptive heterogeneous agents in a complex evolving financial system. The dual nature of the research calls for a sequential mixed method design that combines the empirical and experiential research streams in a single study. For the empirical stream, there are additional compelling reasons to combine qualitative and quantitative components in an embedded research process. This is due to the fundamental difficulty in longitudinal

11 factor research: in order for the latent factors to be identified quantitatively, the researcher must be able to support their qualitative interpretation. Specifically, since our unit of analysis includes distinct heterogeneous agents within an identifiable financial sector, we must support deductive inference of factors and agent groups over time. To pursue this, we choose multiple quantitative data sources with purposive sampling. We use maximum variation sampling to identify extreme observations and homogeneous sampling to maintain relevant agent groups. With regards to quantitative methods, we choose multiple quantitative methods (dynamic factor analysis, structural equations modeling, time-series analysis, and stochastic modeling) to support the inductive interpretation of factors and agent groups over time. In order to support the interpretation validity of the quantitative measures we choose qualitative content analysis as a principal triangulation method. In turn, we substantiate the content analysis by choosing multiple qualitative data sources including the transcripts of the Federal Reserve discussions and the text of financial news. Table 1 provides an outline of theory building, methods, and data for each of the five research questions.

12 Table 1 Outline of Theory Building, Methods, and Data by Research Questions

ID Research questions Theory building Method Sample data Chapter

What is the evidence for the financial system complexity, and how can Multiple Qual i. the financial system →Inductive sources Chapter 1 observation distress be studied by the (1976-2014) policymakers going forward?

FOMC transcripts, Is financial system stress Mixed financial →Inductive→ ii. relevant to the (embedded): news→ Chapter 2 Deductive policymakers? → Qual→Quant Multiple sources (1991-2014)

How can we evaluate the quality of the stress Multiple measure relative to iii. →Deductive Quant analysis sources Chapter 3 alternative measures of (1976-2014) financial system conditions?

What is system-level stress? How can system Multiple and agent stress and iv. →Deductive Quant analysis sources Chapter 4 financial instability be (1976-2014) defined and reliably measured?

Is there some way to Multiple Chapter 4 remedy our understanding →Abductive → v. Quant analysis sources and of the functional form of Deductive (1976-2014) Chapter 5 financial stress?

How does stress in set of Multiple Mixed agents or instruments →Abductive→ sources vi (embedded): Chapter 5 transfer to another set of Deductive (1976-2014), → qual→Quant agents or instruments? Flow of Funds

We consider the first question, what is the evidence for the financial system complexity, and how can stress be studied by the policymakers going forward, in Chapter

1. Here we detail the dimensions of the problem of study and draw on the extant literature to establish the epistemological precedents for the study. We position our research critically in reference to existing literature. We study the second question, is financial system stress relevant to the policymakers, in Chapter 2, by validating the measure of financial system stress against the incidents of policymakers’ discussions of financial system conditions during their discussions in the Federal Open Market Committee

13 meetings. We study the third question, how can we evaluate the quality of the stress measure relative to alternative measures of financial system conditions, in Chapter 3, by testing the quality of alternative measures of US financial system conditions. We consider the fourth question, what is macro-level stress, in Chapter 4, by testing hypotheses of stress toward systemic stress measurement against US financial system data. We consider the fifth question, is it possible to reconcile our understanding of micro-level stress with the observations of apparent irrationality in the choices of financial agents, in Chapters 4 and 5, by testing alternative explanations of agent choices, e.g. prospect theory, memory, cognitive dissonance, to improve explanation of individual agent choices toward an adjusted functional form of stress able to improve reconciliation of individual agent and instrument stress with systemic stress. We consider the sixth question, how does stress in set of agents or instruments transfer to another set of agents or instruments, in Chapter 5, by analyzing the transmission process stochastically. We do this by examining the causal relationships between the violations of weak axiom of revealed preference under a variety of price functions and alternative memory spans in heterogeneous representative financial agents.

Chapter Outlines

The idea that ties together the various aspects of this dissertation is the search for empirically-valid theory of financial stress. Thus, a robust investigation of validity of financial stress measurement is essential for the building of financial stress theory.

Supporting measurement validity involves testing of several types of validity. In Chapter

2, we consider face validity for the measurement of financial system stress. We support system stress prima facie since this concept has relevance in the actual decision making

14 processes of policymakers and is consistently important for their assessment of financial system conditions and financial stability. In Chapter 3, we consider comparative validity of alternative measures of financial conditions seeking to study the quality of the alternative measures of financial stress. In Chapter 4, we consider internal validity of the system stress measure by examining the reliability of components in explaining the observed variance in the series of selected financial system indicators.

After establishing a valid system-level measure of stress, to enable stress measurement at other units of analysis, it is essential to define a theoretically sound measure of agent- and instrument-level stress. In Chapter 5, we consider predictive validity of financial stress measurement. Here we test alternative definitions of agent- level financial stress to minimize the variance between stress measured at multiple units of analysis. Specifically, we seek to refine a functional form of stress measured at the agent- and instrument-level, so that measurement error between the aggregated agent- level financial stress and the aggregate system level financial system is minimized. Upon empirically valid and theoretically supported agent level financial stress, the advancement of further stress theory involves theorizing about the processes by which financial stress at the agent level propagates across agents to the system level stress. Put differently, we seek to explain the processes by which stress propagates across multiple units of analysis. Accordingly, to advance financial stress theory, we investigate three types of stress propagation processes: 1) agent preference and choice, 2) transmission, and 3) conditions.

Chapter 1: System complexity and distress. In Chapter 1, we discuss the evidence for classifying financial systems as complex rather than simply complicated. We review

15 the weaknesses and strengths of different theoretical positions in explaining the processes of emergence for such outcomes. We discuss the need for multi-level dynamic explanations and their potential value in explaining financial system risks.

In this chapter, we provide an integrative theoretical review across knowledge domains and multiple-levels of analysis to review various conflicting viewpoints and discuss an integrative path forward. This path lays the generative understanding of the financial system as a complex adaptive system, where we explain the emergent dynamic phenomena through the ability to reproduce the observed structures, functions, and behaviors across its agents by establishing simple rules for their interaction. In particular, we focus on the emerging role of financial distress as a potential tool for policymakers concerned with understanding and influencing financial system conditions and outline a research agenda relevant in the context of financial system complexity.

Chapter 2: Face validity. In Chapter 2, we address face validity by examining whether financial system conditions matter to the Fed? This entails qualitative analysis of policymakers’ discussions. We find that financial conditions matter significantly to the

US policymakers and that they can be proxied by an aggregate measure of financial system stress. Quantitatively, the measure of system stress that is found to be similar to the discussion-based series on system stability and conditions is a conjectural construct composed of representative indicators and weighted dynamically by the changing relative share of broad financial sectors in the overall US economy. Thus, this conjectural aggregate measure of stress that serves as a starting point of my research has some validity, specifically face validity. This measure is also an aggregate measure of US

16 financial system stress. Of course, many assumptions went into it, and additional types of validity remain to be addressed.

Chapter 3: Comparative validity. The intent of comparative validity is to assess the relative quality of alternative empirical measures of financial system conditions, in order to choose the optimal basis for building financial stress theory. We examine the quality of the system-level stress measure, e.g. its composition with selected representative financial indicators, by comparison of this measure against alternative measures of system conditions. While it is useful to know that a measure of aggregate financial system stress provides a good proxy for the underlying conditions of the system and its stability as captured in the policymakers' discussions, we don't know what particular measure of system stress is optimal. Choosing the best of the alternative measures of financial stress enables us to narrow and support the choice for the definition of stress at the individual unit of analysis (agent and instrument).

An initial comparison of alternative measures may begin by the comparison of correlation of alternative measures of system conditions with each other and the reference series (e.g. a reference series of financial system conditions as discussed by the policymakers or a benchmark series of outcomes). However, this approach is inadequate in comparison the relative quality with which the various alternative measures capture the dynamic aspects of critical system outcomes. The correlation is not adequate in describing the dynamic pattern of system outcomes as they occur. When critical outcomes occur, does a conditions measure identify the same period? Does the measure similarly indicate the duration of these periods? Does the measure accurately capture the pattern of outcome effects across system markets? Thus, it is desirable to compare the

17 alternative measures by the extent with which they capture the severity, persistence, and pervasiveness of market conditions. This is a more insightful comparison of alternative measures than a simple correlation. The severity aspect describes the relative magnitude of system outcomes relative to historical precedent. The persistence aspect describes the extent to which an unusual high market condition persists in that market. The pervasiveness aspect describes the extent to which an unusually high set of market conditions is present across several markets. Specifically, we seek compare the alternative measures as follows: When disturbances of particular severity occur in particular markets, which of the measures are able to better describe the effect pattern in system for both persistence and pervasiveness. Taken together, the comparison is founded on the summary quality of the comparison in these three dimensions among the alternative measures.

Chapter 4: Internal validity—static and dynamic analysis. Thinking of stress as a function of prices and quantities at the agent and instruments enables a straightforward, but unvalidated, quantification of stress at the agent- and instrument-level and its aggregation across agents and instruments. This quantification can be done, revealing the time series of agent and instrument stress and allowing for the time pattern of agent and instrument stress to be "observed." However, the quality of this quantification remains unsupported without two additional forms of validity testing: internal and predictive. In the internal validity tests (static analysis, we make modest improvements in the composition and the reliability of the macro-level stress. In the ensuing predictive validity tests (dynamic analysis), we make additional improvements in understanding the

18 time pattern of stress generation process and find that recognition of memory effects is important to varying degree across financial system markets.

Static analysis: Internal validity testing helps us to establish the reliability of the aggregate financial stress measure itself. In Chapter 4, we examine internal measurement reliability of the system-level measure by factor-analytic techniques. Being rigorous about the way the aggregate variance is explained through the selected set of markets

(factors) and the particular set of indicators chosen to represent each market, allows us to improve the internal reliability of the system-level stress measure.

Dynamic analysis: We may question the absence of behavioral effects in the definition of stress. Specifically, we observe that at the system- and market-level, the pattern of stress exhibits some stickiness (persistence and pervasiveness) properties. To the extent that the definition of stress at the individual unit of analysis fails to incorporate an explanation for this memory pattern, we fail to explain how this stickiness in aggregate emanates from the individual units of analysis. Our own heuristic rules by which the system stress is signaled include sticky properties of persistence and pervasiveness. It is reasonable that these properties have both an empirically-based and theoretically supported expression in the way that individual unit stress is defined and measured. Methodologically this means that the static factor analysis of Chapter 4 should be amended by dynamic factor analysis.15 Applying dynamic factor analysis, we find

interesting and valuable adjustments to the understanding of the dynamic properties of

the aggregate financial stress. Specifically, we find that the dynamic effects differ across

15 In the same vein, static factor rests on the absence of violations of serial correlation. Given presence of serial correlation in the results, e.g. observed in sticky time results, the dynamic effects need to be investigated through dynamic factor analysis.

19 markets: presenting short memory in highly active markets (equity and foreign exchange) and long memory effects in less active markets (credit and securitization, interbank funding, and real estate). Thus, we find that the incorporation of memory is important.

However, despite the incorporation of a series of beneficial adjustments to the aggregate financial system stress, a discrepancy remains between the system level stress and the aggregated individual level stress.

Chapter 5: Predictive validity—dynamics, preferences, and agent choice.

Despite a rigorous effort to establish an optimal macro-level measure of financial stress, clearly some variables in addition to prices and quantities are needed to explain both the pattern of apparently irrational agent choices and the apparent discrepancies between the micro- and macro-level stress. In this chapter, we advance agent-level stress theory. We examine its predictive validity by examining whether the proposed functional form of agent-level stress aggregates as expected to the system-level. Specifically, does the agent stress that is measured as conjectured integrate across all system agents to the system- level stress? If our definition of stress at the micro-level (agent and instrument) is correct, then the integration of the micro-level stress should yield the macro-level (system) stress.

Our initial literature-supported abductive conjecture is that micro-level stress is defined as a function solely of prices and quantities. Testing this, we find that macro-level

(system) stress does not equal the summation of micro-level (agent) stress and observe substantial differences between the two.

The advancement of micro-level definition of stress requires us to theorize functional form supported by literature-based hypotheses of stress and the available empirical evidence. Initially, the inference is abductive. Because we observe a reliable

20 measure of macro-level stress as a function of prices and quantities of representative indicators, we infer that stress at smaller units of analysis, e.g. agents and instruments, can be measured as a function of prices and quantities of relevant instruments which fully describe the exposure of the financial agents.

Dynamic analysis for agent stress: To make further progress, we need to critique the agent level definition of stress. The remaining reason that the aggregate stress does not equal the sum of agent stress is that the agent stress is not adequately measured. We already know that memory is important in system level stress, yet, memory is absent from agent level stress definition. The initial conjecture of agent stress includes only prices and quantities. To the extent that agents act rationally, then prices and quantities should be the only variables that explain the agent choices. In this chapter, we consider the choices across all system agents and find that using an aggregate representative agent as a unit of analysis, the allocation choices can be considered rational, with very small number of rationality exceptions (2% or less). Thus, the assumption of rationality is reasonably supported across all agents, confirming that agent allocation choices are substantially explained by prices and quantities. However, when individual agents are considered, significant number of allocations appear irrational, with violations of rationality evidenced in forming the agents’ price and quantity bundles. Thus, individually, the agents appear to be making irrational allocations. In fact, a significant number of violations exist for specific agents and appears associated with the periods of high system stress. This leads us to the idea that the functional form of agent stress is incorrectly specified and requires the incorporation of variables other than prices and quantities.

Accordingly, in this chapter we seek to recognize and include the variables missing from

21 the definition of stress. We do this, by testing alternative theories of agent preference, seeking to find the set of variables that minimizes the number of violations of agent rationality in allocating the agent choices.

Agent preferences: For the choice process, we seek to explain the pattern of apparent irrationality in agent choices and to understand the process by which the pattern of choice violations becomes system stress. This analysis is accomplished by examination of agent revealed preference and the causal pattern tying the apparent violations of rationality and financial system stress. In this chapter, we also investigate alternative variables in the definition of agent-level financial stress. The first two variables, price and quantity, form the basis of stress agent-level stress as established through the agent rationality assumption, where agent allocations among instrument bundles are determined solely on the basis of rational preferences among instrument prices and quantities. When agent choices are conditioned solely by the observations of prices and quantities of financial instruments, we observe that violations from historical rationality tend to occur during particular times—the time of high distress. Naturally, we would like to examine whether there are any relationship patterns in the transmission of stress that involve these violations. Thus, we seek to extend the specification of agent-level stress with additional variables to investigate whether they can help to explain and minimize the number of apparent violations. We expand the functional specification of agent-level stress with additional variables that provide useful information to explain actual agent choices. The variables we test come from behavioral theories of agent choice, including prospect theory, cognitive dissonance, memory (animal spirits), and liquidity preference. The

22 inclusion of additional variables completes the micro-level definition of stress and minimizes its discrepancy with macro-level stress.

The stress transmission process: In Chapter 5, we also explore the empirical pattern of connections between the violations of rationality in various sectors and financial stress. We find evidence that a set of sectoral allocations influences the transmission of financial stress from sector to sector.

Using our empirical findings, we extend financial stress theory with theory of the stress transmission process. Starting with the narrative stories of contagion in the extant literature, we advance the idea that agent choices and stress propagation are conditioned by building asset bubbles. Agents make violations of apparent rationality in choosing certain price and quantity bundles. As these violations are made, there is a snowballing effect. It becomes more profitable for agents to herd, and that is a story evidenced and tested in the data. As a bubble in asset j inflates, as indicated by the presence of apparent violations in price and quantity bundles, it becomes reasonable for agents to change their allocations to profit from short-term expectations in asset j. As the instrument j inflates, it offers a higher term short-term return and attracts increasing number of agents. Through the adjustment of instrument choices, the change in allocation is manifested as the motion of stress across agents. The asset bubble is then observed by the co-alignment of violations across sectoral agents. In this co-alignment, a number of agents make

23 violations from some sectoral agents to other sectoral agents. Put simply, asset bubbles travel through financial sectors inducing agents to realign their choices and resulting in relative adjustments of agent preferences toward other available bundles of instruments.

The apparent violations in price and quantity bundles of the bubble instruments lead to the relative valuation effects in other instruments. Thus, stress experienced in a particular sector agent or instrument can propagate.

24 Chapter 1: The Problem of Financial Stress in Adaptive System

1.1. Theoretical Framing

1.1.1. Issues framed by research in financial system complexity

The context of the economy as an adaptive16 complex system was pioneered by

Holland (1975, 1988) in his work on adaptive nonlinear networks and has been significantly extended in the past four decades. 17 Following Holland (1988: 117-118), the global economy forms an adaptive system through the following seven features: 1) interaction of many interdependent agents, 2) scarcity of global controls that allow competitive, as well as coordinated yet shifting agent associations, 3) multilevel hierarchical agent associations with asymmetric interactions across levels, 4) system adaptation through a continual recombination of agent interactions as the system accumulates experience, 5) the presence of niches exploitable by particular agent adaptations, 6) continuous creation of niches through technological innovation, and 7) suboptimal performance due to the continual thriving of niche interactions.

Nicolis and Prigogine (1977: 464) show that relative instability is a continuous dimension of adaptive systems. The main reason for the onset of an adaptive shift is that an adaptive “system is necessarily undergoing instabilities, and hence is capable of

16 Some researchers use the term self-organizing interchangeably with the term adaptive to emphasize the emergence of coordination among agents in the process of adaptation. In this study adaptive is preferred, as it refers to a more general set of interactions, including coordinating interactions. 17 See Arthur (1995) and Arthur et al. (1997) for applications of adaptive network modeling to financial markets. Brock and Hommes (1997, 1998) study financial markets as adaptive belief systems. Hommes (2001) extends this approach to markets as nonlinear adaptive evolutionary systems. See Aghion and Howitt (1992) and Howitt et al. (2008) for complexity-based macroeconomic models. See Farmer (2002) and Farmer et al. (2005) for complexity-based modeling of financial markets. See Beyeler et al. (2007), Bech and Atalay (2010), and Soramäki et al. (2007) for studies on topology and contagion in specific financial markets. See Farmer (1990) and Brock and Durlauf (2001) for critical methodologies.

25 amplifying certain disturbances including some of its own fluctuations.”18 Put differently,

a continuous state of relative financial instability is an integral aspect and an integral

problem of an adaptive financial system.

Figure 2 (Source: Oet et al., 2013) shows the conceptual model guiding this

research, supported in literature. The model suggests that macroprudential policy in

adaptive financial systems is necessarily a continuously changing process due to

perpetual financial system transformation. In this process, macroprudential policy is

repeatedly adjusted to suit its objectives through reconsideration of its functions, through

redesign of its forms, and through its methodological evaluation.

18 Nicolis and Prigogine (1977: 465). 26 Figure 2 Conceptual Model: Early_warning Policy Use in Adaptive Financial System

The conceptual model reflects the evolving relationship between the financial system and its risk policy objectives, functions, forms, and evaluation. Financial stability can be viewed as the ability to control one’s choices in adaptive systems in order to regulate preferential outcomes,

19 effectively placing financial stability within the risk management and prudential

purview. Borio (2003) and Nier (2011) consider the co-existence of microprudential

(aggregate risk is exogenous, independent of individual institution behavior) and

macroprudential (aggregate risk is endogenous, dependent on financial system behavior)

perspectives. This leads us to consider policy objectives in terms of the process through

which risk aggregates in the system over time and across the system participants.20 Policy

in the time dimension is concerned with aggregate risk evolution over time and the

adverse amplification between the financial system and the real economy

(procyclicality).21 Furthermore, the time dimension objectives form a dual set of long-

term and short-term goals. In the long run the objective is “to avoid macroeconomic costs

linked to financial instability,” while in the short run, the objective is to “limit financial

system-wide distress.”22 Similarly, policy in the cross-sectional dimension is concerned with a complementary dual set of issues: common exposures and interconnections among institutions. Accordingly, the cross-sectional macroprudential objectives include the common exposure imbalance-based goal to limit severity of failure, common exposure

19 Schinasi (2004: 8) proposes a related definition of financial stability as a continuous range where “A financial system … is capable of facilitating (rather than impeding) the performance of an economy, and of dissipating financial imbalances that arise endogenously or as a result of significant adverse and unanticipated events.” 20 IMF (2011: 8). 21 Borio (2003: 11). 22 Borio (2003: 2).

28 imbalance-based goal to limit probability of failure, and interconnectedness-based goal to strengthen infrastructure resilience.23

Macroprudential policy functions follow the consensus view expressed by Borio

(2006: 3413) that macroprudential policy contains two strategic dimensions: “first,

improving measurement of systemic conditions, and second focusing on limiting build-up

of imbalances.” The intrinsic functions involve identification of systemic conditions,

forward-looking and forecasting capacities, identification of systemic imbalances,

differentiation of excessive exposures, and sensitivity to systemic risk posed.

Policy forms follow the findings of Lim et al. (2011a, 2011b) and Galati and

Moessner (2013). Using established forms of macroprudential tools,24 Lim et al. (2011b)

find evidence that most tools are capable of reducing procyclicality, although their

usefulness “is sensitive to the type of shock facing the financial sector.” Specifically, they

propose that macroprudential efficacy is increased when implementation includes 1)

multiple tools, 2) targeted tools with higher ability to differentiate among exposures, 3)

time-varying tools that can be adjusted through the range of financial conditions, 4)

dynamic tools accompanied by clear rule-based communication, 5) tools that coordinate

well and reinforce associated policy initiatives.

Classic literature on policy evaluation suggests that in the context of the adaptive

financial system, the uncertainty in macroprudential policy can be addressed adaptively

(Lucas, 1976), incorporating the behavior of economic agents (Lucas, 1976; Sabatier,

1991), as a continuous dynamic process (Sabatier, 1991), and considering the

23 Cross institution differentiation between common exposures and interconnectedness is based on Bijlsma et al., (2010) who distinguish between direct and indirect interconnectivity mechanisms. 24 Including early warning systems, asset price models, stress testing, and microprudential feeds. 29 policymakers’ loss function (Brock et al., 2003) with the corresponding and ongoing

(Leeper and Sargent, 2003) robust analysis of model uncertainty space. Following Brock et al. (2003), the evaluation approaches can include expected loss calculations, model uncertainty aversion, local robustness analysis, and robustness with multiple models.

1.1.2. Issues framed by research in financial system stability

This work grounds on and is framed by the six theoretical and empirical elements developed in our prior qualitative and quantitative research on financial system stability.

First, we develop a methodology to measure overall financial system stress (Oet et al.,

2015a). Second, we enable the decomposition of the overall financial stress construct into its constituent factors across multiple markets of the financial system (Oet et al., 2015b).

Third, we demonstrate the existence of a significant association between institutional imbalances, system structure, and financial market stress and to explain this association

(Oet et al., 2013). Fourth, we discern agent structure within the banking sector (Oet et al.,

2016). Fifth, we determine the factors of financial intermediation within the interbank funding market (Oet et al., 2016). Sixth, we critically survey the feedbacks theory to develop a comprehensive understanding of the interaction of financial stress, financial instability, and the banking system factors (Oet and Pavlov, 2014).

Accordingly, there are three important epistemological aspects of the research problem that remain unknown and require discovery. First, we have not considered the implications of the fundamental problem of financial system complexity to financial stress measurement. Second, we lack an empirically-valid theory of stress measurement across multiple units of analysis in the context of an evolving financial system. Third, we do not understand the process by which to financial stress propagates across the financial

30 system and leads to critical states. These gaps in knowledge lead us directly to the formation of the specific research questions pursued in this study.

1.2. Research Precedents

1.2.1. Financial system stress construction

Building on the research precedent of Illing and Liu (2003, 2006), Oet and Eiben

(2009), and Oet et al. (2011), in a precedent-framing paper, Oet et al. (2015a) define systemic risk as a condition in which the observed movements of financial market components reach certain thresholds and persist. They develop the financial stress index in the US (CFSI) as a contemporaneous and continuous measure. The CFSI is created utilizing daily publicly observable data from the following components covering a wide spectrum of financial sectors (Table 2):(1) financial beta, (2) bank bond spread, (3) interbank liquidity spread, (4) interbank cost of borrowing, (5) corporate bond spread, (6) commercial paper–T- bill spread, (7) liquidity spread, (8) treasury yield curve spread, and

(9) stock market crashes, (10) commercial real estate spread, (11) residential real estate spread, (12) asset-based securitization spread, (13) commercial mortgage-backed securitization spread, (14) residential mortgage-backed securitization spread, (15) currency crashes, (16) covered interest spread. There are many weighting techniques available and utilized in indexing financial stress, such as equal weights, variance weights, principal component, and market size weights. Such techniques were tested in turn and the approach selected to minimize false alarms is a variation of a market size weight called the “credit weights” method. This method utilizes Flow of Funds data and measures the amount of credit outstanding in the four broad financial markets that make up the 11components. This allows for a dynamic weighting methodology where weights

31 change as conditions in financial markets shift (Oet and Eiben, 2009; Oet et al., 2011).

Bianco et al. (2012: 1–2) highlight that these components, mainly spreads, provide significant coverage of the US financial system markets. While stress in any of these markets could carry over into the broader financial system, the combined information contained in the stress components gains value as “systemic stress-related events are more likely to affect spreads in multiple markets. Observing conditions in a number of markets allows for the potential identification of a common factor, that is, financial stress.” The variables for each of the six financial markets and their construction are outlined in Table 2.

Table 2 Financial Stress Index Construction Financial Financial Calculation Notes Market Product Financial Beta |,| r is banking sector share prices (S&P 500 Financials), m is overall stock market (FB) | share prices (S&P 500), (t, t-1) are observations from time t to one year prior Bank Bond 10A refers to 10-year A-rated bank bond yields (Bloomberg C07010Y Index) and 10 10 Spread (BBS) 10TB refers to 10-year treasury yields Funding Interbank 3mo L is 3 month LIBOR rate and 3mo TB is 90-day treasury bill secondary Market Liquidity Spread 3 3 market rate (ILS) Interbank Cost of Borrowing 3 3mo L is 3-month LIBOR and FFR is the federal funds target rate Spread (ICOB) Corporate Bond 10CB is the 10-year Moody’s Aaa rated corporate bond yield and 10TB is the 10 10 Spread (CBS) 10-year treasury yield Commercial 90day CP 90-day is financial commercial paper (CP) rate and 3mo TB is 90-day Paper T-Bill 90 3 treasury bill secondary market rate Spread (CPTBS) Credit Market Liquidity Spread 1 moving average is calculated over the previous thirty trading days (LS) 30 2 Treasury Yield 1 thirty-day moving average of the difference between three-month t-bill yields Curve Spread 10 3 30 (3mo) on a bond equivalent basis with 10-year constant maturity yields (10yr) (TYCS) This is calculated for each of the nine subsectors of the S&P500 including Stock Market Equity Market consumer staples, consumer durables, energy, financials, health care, Crashes (SMC) ∈ | 0,1, … ,364 industrials, information technology, materials, and utilities. Commercial Real CMBS is the yield on commercial mortgage-backed securities and 7TB is the Estate Spread 7 yield on a 7-year treasury note Real Estate (CRE) Market Residential Real RMBS is the yield on agency residential mortgage-backed securities and 7TB is Estate Spread 7 the price of a 7-year treasury bond (RRE) ABS Spread ABS is the asset-backed bond yield (SYCAAB@USECON) and 5TB is the yield 5 (ABS) on a 5-year treasury note Securitization Commercial MBS CMBS is the yield on commercial mortgage-backed securities and 7TB is the 7 Market Spread (CMBS) yield on a 7-year treasury note Residential MBS RMBS is the yield on agency residential mortgage-backed securities and 7TB is 7 Spread (RMBS) the price of a 7-year treasury bond Where x is the exchange rate between the US dollar and a foreign currency. The Currency exchange rate is quoted such that it measures the price of one foreign currency Crashes (CC) ∈ | 0,1, … ,365 in USD. This calculation is performed for: AUD, CAD, EUR, GBP, JPN, MXN & ZAR. FX Market F is the 90-day forward USD-foreign currency exchange rate S* is the spot USD-foreign currency exchange rate Covered Interest ∗ r is the 90-day U.S. treasury bill rate 1 ∗ 1 Spreads (CIS) r* is the 90-day foreign treasury bill rate This calculation is performed for: Australia, Canada, Eurozone, Great Britain, Japan, Mexico and South Africa.

32 1.2.2. Stress factor decomposition

Oet et al., (2015b) extend recent research contributions to financial stress measurement (Hakkio and Keeton, 2009; Hatzius et al., 2010; Kliesen and Smith, 2010;

Brave and Butters, 2011; Oet et al., 2011; Holló, Kremer, and Lo Duca, 2012; Carlson,

Lewis, and Nelson, 2012; and Lo Duca and Peltonen, 2013) to allow a reliable decomposition of overall financial stress construct into component factors. They show that the deconstructed stress measure, adequately reflects the situation in core segments of the financial markets. Methodologically, in the formulation of financial stress the necessary elements include determining the financial system’s markets, the variables that describe market activity, and the transformation and aggregation of these variables.

Figure 3 displays the conceptual design of the stress construct.

Figure 3 Conceptual Model of Financial System’s Stress

Financial System Financial Markets Financial Products

Currency crashes Covered interest spread FX Market Financial beta Interbank liquidity spread Interbank cost of borrowing spread Funding Market Bank bond spread

Corporate bond spread Credit Market Liquidity spread Financial Treasury yield curve spread Stress CP T-Bill spread Real Estate Market Residential real estate spread Commercial real estate spread Equity Market Stock market crashes

Securitization RMBS spread Market ABS spread CMBS spread

The factor-based stress measure is constructed as a continuous stress variable,

using relative difference (spreads and spread-like) measures instead of volatility

33 measures. It is assumed that spreads will be specifically affected by increased uncertainty in the market. Conceptually, increased systemic stress should affect spreads in all markets. This means that a measure of underlying systemic financial stress has to consider spreads from a variety of different markets. By definition, we expect little correlation between the widening of spreads in separate markets if stress is non- systematic, whereas events due to systematic stress ought to affect spreads across multiple market sectors. Since spreads in each market carry some amount of market- specific idiosyncratic noise, considering aggregate spreads across different markets and over time would tend to reduce idiosyncratic noise. Put another way, considering multiple spreads in each market together reduces the likelihood of idiosyncratic causes spuriously commoving and increases the likelihood that spreads move due to a common factor, which can be interpreted as systemic financial stress.

Figure 4 CFSI Components Units of CFSI 90

0 1992 1995 1998 2001 2004 2007 2010 2013

Real Estate Market Funding Market Foreign Exchange Market Credit Market Equity Market Securitization Market

Figure 4 shows the movements of specific markets within the weekly CFSI, providing insight into the amount of stress that the six distinct markets contributed to the overall stress series. Measures from all markets tend to contribute significantly to the 34 overall financial stress. Their contributions in periods of financial stress tend to rise and fall together, amplifying overall changes on the financial stress.

Observations from individual components of the financial stress index offer insight into stress generation. Each panel of Figure 5 decomposes stress in a different market of CFSI. The first two panels of the figure document the components of the funding and credit markets. The funding market contributed the most to overall financial stress during the recent financial crisis. The contributions of the credit market to CFSI remain relatively constant with time. Panels C and D of Figure 5 decompose overall financial stress in the equity and foreign exchange markets. The equity market contributed most significantly to stress during the Dot-Com Bubble. Contributions from the foreign exchange market were largest more recently in conjunction with the European debt crisis. The final two panels of Figure 5 decompose stress in the securitization and real estate markets. Securitization markets contributed to stress most significantly during the financial crisis but have since been reduced.

35 Figure 5 Decomposition of Stress: Components of the Markets Panel A: Funding market Panel B: Credit market Panel C: Equity market

Units of CFSI Units of CFSI Units of CFSI 12 18 33

8 12 22

4 6 11

0 0 0 1992 1995 1998 2001 2004 2007 2010 2013 1992 1995 1998 2001 2004 2007 2010 2013 1992 1995 1998 2001 2004 2007 2010 2013 Corporate Bond Spread Liquidity Spread Consumer Durables Consumer Staples Financial Beta Interbank Cost of Borrowing Energy Financials Health Care Industrials CP - T-Bill Spread Treasury Yield Curve Spread Interbank Liquidity Spread Bank Bond Spread Information Technology Materials Utilities

Panel D: Foreign exhange market Panel E: Securitization market Panel F: Real estate market

Units of CFSI Units of CFSI Units of CFSI 15 27 15

10 18 10

5 9 5

0 0 0 1992 1995 1998 2001 2004 2007 2010 2013 1992 1995 1998 2001 2004 2007 2010 2013 1992 1995 1998 2001 2004 2007 2010 2013 Australia Canada Europe Great Britain Japan Mexico South Africa RMBS Spread ABS Spread CMBS Spread Commercial Real Estate Residential Real Estate

36 Chapter 2: Does Financial Stability Matter to the Fed in Setting the US Monetary

25 Policy?

The Taylor rule presents a traditional approach to guiding and evaluating contemporary monetary policy as a function of inflation and economic slack. While the responsibilities of the Federal Reserve (Fed) include price stability and long run growth, its mission has grown to include financial stability. Surprisingly, the question whether financial stability ought to be considered as part of monetary policy is hotly contested.

This study aims to determine whether policymakers’ discussions of financial stability and other factors systematically explain deviations of observed policy rates from the Taylor- rule-implied rates. To this end, we conduct content analysis of the Fed's monetary policy discussions to discover actual topics that enter into policy. There are two main findings: first, we find that discussion themes extracted from released Federal Open Market

Committee (FOMC) meeting minutes provide explanatory power beyond standard Taylor rule variables. Second, additional explanatory power is provided by a tri-mandate policy rule that accounts for changes in the economic and financial system as moderated by the evolving preferences of the policymakers. We show that a discussion-based thematic model with financial stability dominates Taylor-type rules during normal times.

Moreover, the tri-mandate policy model with financial stability dominates Taylor-type rules in zero lower bound conditions. Taken together, these findings reveal that financial stability has mattered to the Fed continuously and remains critical in setting monetary policy in zero lower bound.

25 An updated version of this chapter is forthcoming as Oet et al., (2016a). 37 2.1. Introduction

When the Fed was founded by Congress in 1913 as the central bank of the United

States, it was “to provide the nation with a safer, more flexible, and more stable monetary and financial system” (Board of Governors, 2013). The goals of US monetary policy are generally linked to the Fed’s responsibilities as defined by Congress in The Federal

Reserve Reform Act (1977: 1), where “The Board of Governors of the Federal Reserve

System and the Federal Open Market Committee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy's long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices, and moderate long term interest rates.” Policymakers sometimes refer to the first two of these three areas, employment and prices, as Fed’s dual mandate. Throughout the Fed’s one-hundred-year history, some have viewed financial stability as a part of the

Fed’s task to promote stable prices and maintain long run growth. Others have taken a narrower view that price stability is distinct from financial stability.

It was not until The Wall Street Reform and Consumer Protection Act of 2010

(Dodd-Frank, 2010: Title VIII) that the Fed’s mission was formally expanded to include financial stability responsibilities. Bernanke (2011) affirmed that “The crisis has forcefully reminded us that the responsibility of central banks to protect financial stability is at least as important as the responsibility to use monetary policy effectively in the pursuit of macroeconomic objectives.” Most people agree that the mission of the Fed has clearly evolved with the transformation of the US financial system and currently includes

“maintaining the stability of the financial system and containing systemic risk that may arise in financial markets” (Board of Governors, 2013).

38 Paradoxically, despite the massive distress brought on by occasional financial shocks, the questions whether financial stability should be reflected, and how important it might be in a good monetary policy rule are hotly contested. Despite affirming the importance of financial stability, Bernanke (2011, 2012) still segments financial stability from monetary policy and provides no analysis about their interaction. For Bernanke, monetary policy tools are still firmly connected to macroeconomic stability while financial stability remains distinct and involves using non-monetary policy tools including liquidity provision, financial regulation, and supervision.26 In summary, financial stability is a stated mission and recognized responsibility of the Fed which

affects and is in turn dependent upon monetary policy; yet, monetary policy is often

considered too blunt an instrument to efficiently promote financial stability. Thus, the

question remains whether financial stability enters into the Fed’s deliberations and

influences its setting of monetary policy.

In this article, we pursue three positive questions. To what extent are changes in

monetary policy explained by the material considered and discussed during the Federal

Open Market Committee (FOMC) meetings? Do financial stability considerations matter to the Fed in setting the US monetary policy? Do discussion-based models with financial stability provide superior explanation of Fed’s monetary policy over time?

Our study makes two claims. First, we claim that the Fed’s monetary policy is explained significantly by the themes discerned from policymakers’ discussions after accounting for inflation and economic slack. Second, we claim that additional

26 Yellen (2011: 5) has similar reservations, emphasizing that “Monetary policy cannot be a primary instrument for [financial stability]. First, it has its own macroeconomic goals on which it must maintain sharp focus. Second, it is too blunt an instrument for dealing with [financial instability].” 39 explanatory power is provided by a tri-mandate policy model that accounts for changes in the economic and financial system as moderated by the evolving preferences of the policymakers. These claims are founded on the economic data characterizing monetary policy regimes (Appendix 1), content of policymakers’ discussions of monetary policy during the FOMC meetings from 1990 to 2012 (Appendixes 2 and Section 3), and regression results (Section 4).

To support the first claim, we connect five arguments. First, we demonstrate that our derived themes of discussion are valid (Appendix 3). Second, we show that the causal inference between FOMC discussions and monetary policy is partially supported (Section

3). Third, we show that the signs exhibited by the regressed themes meet theoretical expectations (Section 4). Fourth, we show that our results are consistent with authoritative prior investigations of individual effects (Section 4). Fifth, we show that the results are generalizable to provide insight on monetary policy even in zero lower bound conditions (Section 4). The Fed Funds rate serves as monetary policy instrument before

October 2008. Shadow short rate serves as monetary policy instrument starting in

October 2008.

We support our second claim by three arguments. First, we demonstrate that discussions of financial stability are representative of actual financial stability conditions

(Section 3). Second, we establish that the state of financial stability can be measured with

financial stress (Section 3). Finally, we confirm that discussion-based models with

financial stability dominate Taylor-type rules both during normal times and in zero lower

bound conditions (Section 4).

40 The rest of this chapter is structured as follows: Section 2.2 describes the conceptual framework for monetary policy. Section 2.3 examines the dataset of FOMC discussion themes and Taylor rules which frame this study in the context of five distinct monetary regimes. Section 2.4 hypothesizes, tests, and interprets the statistical and economic significance of the thematic and tri-mandate models. In the concluding Section 2.5, we discuss the impact of this research, including its counterarguments and limitations.

2.2. Conceptual framework

The studies of Taylor (1993) and Henderson and McKibbin (1993) famously expressed interest-rate instrument reactions to “the gap between actual and desired values” of output growth rates and inflation rates within a monetary policy feedback rule.

Because the Taylor rule has explained historical interest rates reasonably well using just these two factors it is frequently used to judge monetary policy decisions as good, when the actual interest rates fit the rule, and bad, when they do not. Since output is mediated by employment and inflation by prices, Taylor’s rule parallels the so-called “dual mandate” interpretation of the Federal Reserve System’s mission to maintain maximum employment and stable prices.

We suggest that the themes discussed during FOMC meetings are relevant to monetary policy alongside current or recent economic observations such as output and inflation, in addition to which they serve as component channels through which monetary policy shapes desired economic outcomes.

Two perspectives can be distinguished in the relationship of monetary policy with economic conditions: one formed by observations and another framed by expectations.

The first, ex-post, perspective drives the intentions reaction function (Khoury, 1990: 27)

41 of monetary policy, defined as “linking the movements in real GDP and inflation… to the short-term interest rate (Taylor, 1995: 14).” The second, ex-ante, perspective motivates the impact reaction function (Khoury, 1990: 27), defined as “the linkage from short-term interest rates to exchange rates and long-term interest rates, and finally to real GDP and inflation” (Taylor, 1995: 14). As Khoury (1990: 27-28) notes, “Much of the disagreement about the [monetary policy] results from a failure to distinguish between these two types of reaction functions.”

Taylor (1995: 14) further emphasizes the link between these two perspectives in that “the links of the monetary transmission actually form a circle, [beginning with the intentions function] and with the circle being closed by [the impact function].” Literature refers to this circular process as a feedback rule and defines it as “the monetary transmission mechanism: the process through which monetary policy decisions are transmitted into changes in real GDP and inflation” (Taylor, 1995: 11).

Khoury (1990) reviews some 42 distinct impact function models that explain a variety of monetary policy variables27 including combinations of explanatory variables

such as the unemployment rate, inflation rate, balance of trade, interest rate, exchange

rate, deficit, debt, and growth. Mishkin (1995) includes financial stability implicitly

through a set of relative asset price channels. For the intentions function, many

alternative explanatory variables have been proposed using a variety of additional factors

ranging from asset and oil prices to financial imbalances and the federal debt. Clerc and

Pfister (2003: 192) classify the financial factors within the transmission channel into two

27 Khoury (1990, Appendix Table 3.1) summarizes the impact reaction functions using some twenty-five distinct dependent variables from M1 to Federal-funds rate. 42 groups: “the first includes asset prices (shares, property); the second is derived from the existence of an external funding premium and credit constraints; this category is at the origin of the credit cycle.” Borio and Zhu (2012) (BZ) discuss additional financial channels in the transmission mechanism including among others: balance sheet channel, bank lending channel, interest rate channel, bank capital channel, and risk-taking channel.

In particular, BZ (p. 237) argue that “significant aspects of the overall shape of the transmission mechanism can potentially be missed if the risk-taking channel is not incorporated in the central bank’s reaction function. The argument is that there is an endogenous interaction between the reaction function and the cumulative strength and shape of the transmission chain.”

To the extent that financial stability has been considered in the monetary reaction function, it is involved as a factor of financial intermediation by which innovations in monetary policy become real. Thus, financial stability is reflected as input to inflation.

This point of view is captured by Bernanke and Gertler (1999: 18) who conclude that

“the inflation targeting approach dictates that central banks should adjust monetary policy actively and preemptively to offset incipient inflationary and deflationary pressures.

Importantly, for present purposes, it also implies that policy should not respond to changes in asset prices, except insofar as they signal changes in expected inflation.”

Cecchetti et al. (2005: 428) emphasize the positive nature of their dissent, showing that

“central banks can improve macroeconomic performance by reacting to asset price misalignments… [and not saying] that policymakers should target asset prices.” The shift towards embracing the importance of financial stability is expressed by Bernanke (2011) and FOMC (2013) who imply the need to include financial stability in the Fed’s reaction

43 function by noting that “… the Committee should explore ways to calibrate the magnitude of the risks to financial stability so that those considerations could be more fully incorporated into deliberations on monetary policy.”

If financial stability is on par with the standard Taylor rule factors of output and inflation, does this in fact change the reaction function of the Fed? Given the increased awareness of the importance of financial stability, does this have implications for monetary policy? Building on this conceptual foundation, this study applies qualitative content analysis to examine a set of positive questions about the relevance of financial stability to the Fed in setting monetary policy.

A loosely similar textual analysis approach has led Hayford and Malliaris (2004:

387) to “find no empirical evidence that the Federal Reserve policy attempted to moderate [financial stability] during the late 1990s.”28 This result contrasts with Baxa et

al. (2013: 117), who find that in the last thirty years central banks tend to change

monetary policy rates nonlinearly in response to financial instability: “When a financial

system is stable … financial stability considerations enter monetary policy discussions

only to a limited degree”; yet, when financial instability is tangible (e.g. evidenced by financial imbalances), “central banks often change policy rates, mainly decreasing them in the face of high financial stress.” We will examine whether analysis of FOMC discussions supports the absence or presence of financial stability considerations in setting the US monetary policy.

28 Hayford and Malliaris (2004) focus their study on stock market valuations during the Greenspan era. 44 2.3. Data and methodology

According to Krippendorff (1989: 403), “content analysis is a research technique for making replicable and valid inferences from data to their context.” Stemler (2001) defines it as a systematic methodology “for compressing text into content categories based on explicit rules of coding.” This study applies Krippendorff (2012) methodological recommendations for a systematic and replicable application of six stages of content analysis: design, unitizing, sampling, coding, analysis, and validation.

From the design perspective, the importance of analyzing the text of the FOMC meetings, where the policy is being debated and formed, is self-evident. Here, the strength of textual analysis as a research method lies precisely in its ability to uncover how the Fed makes decisions and what topics enter as elements into the monetary policy considerations. Its principal challenge is the empirical support for inferential validity of its results. Its principal limitation rests on the fundamental assumption that the frequency of textual occurrence of a certain idea reflects the relative importance of this idea among others. Among two methods of textual analysis, latent semantic analysis (LSA) and content analysis, we chose the latter, because it allows a dual exploratory and algorithmic approach, enabling methodological cross-validation. By contrast, the alternative LSA method (Deerwester et al., 1990) is purely an automated dimension reduction technique.

In addition, as shown by Boukus and Rosenberg (2006), LSA reflects FOMC theme correlations through component cross-loadings, complicating interpretation of factors and reducing the possibility of parsimonious factor analysis.

Our data consists of the FOMC meeting minutes. To enable cross-validation, we chose two units of analysis: paragraph for the initial exploratory analysis of discussion

45 themes and phrase for the subsequent algorithmic analysis.29 To establish the discussion

themes, we sample the FOMC discussions in their modern form which began in 1993

(Danker and Luecke, 2005). For the algorithmic analysis, we extend the sample to span

the period from February 1990 to July 2012 to align the sample with the supported proxy measure of financial system stability (Oet et al., 2012). Appendix 3 outlines the data preparation stages. Appendix 4 details the validity stage, directed to the epistemological challenge of recognizing meaning which lies at the core of content analysis as a scientific method (Krippendorff, 2012). The dataset is summarized below.

2.3.1. Content analysis: FOMC discussions of monetary policy

Significance of discussion themes. The dataset revealed by the analysis of FOMC discussions displays surprising variability in the composition and relative importance of themes. Figure 6 presents the situational map (Clarke, 2003) for themes that emerged during the exploratory analysis of FOMC discussions at the paragraph level.

29 Appendix 3 provides additional details for these two methods known respectively as emergent coding and selective coding. 46 Figure 6 Situational Map of Monetary Policy Themes OUTPUT FINANCIAL SYSTEMS STABILITY Consumption (household consumption); Retail sales/ Durable Goods (Motor United States financial regulation system vehicles and parts, Home appliances) / Non-Durable Goods (Food, Clothing, Regulatory authorities (US Securities and Exchange Commission (SEC), Oil/gasoline, Pharmaceuticals); Financial Industry Regulatory Authority (FINRA), Commodity Futures Trading Services; Commission (CFTC), Federal Deposit Insurance Corporation (FDIC) Household saving rate; [(Liquidity Guarantee Program (TLGP)], Office of the Comptroller of the Investment / Business investment (Investment in equipment and software, Currency (OCC), National Credit Union Administration (NCUA), Office of Other business investment, Business sentiment) / Construction (Residential Thrift Supervision (OTS), Consumer Financial Protection Bureau (CFPB), construction, Housing starts, Non-residential (commercial) construction) / Federal Reserve [Term Asset-Backed Securities Loan Facility (TALF), Changes in inventories; Troubled Asset Relief Program (TARP), Term Securities Lending Facility Government Spending; (TSLF), Term Auction Facility (TAF), Term Deposit Facility (TDF), Primary Net Export (Imports, Exports, US trade deficit); Dealer Credit Facility (PDCF), Asset-Backed Commercial Paper Money Industrial production and capacity utilization (Manufacturing; Mining; Utilities; Market Mutual Fund Liquidity Facility (AMFL), Commercial Paper Funding Purchasing managers index) Facility (CPFF), Money Market Investor Funding Facility (MMIFF), Supervisory Capital Assessment Program (SCAP), Asset-Backed EMPLOYMENT Commercial Paper Money Market Mutual Fund Liquidity Facility (AMLF)]; Hiring (Nonfarm payroll employment); Unemployment (Unemployment rate, Treasury; Government National Mortgage Association (GNMA); Fed’s target unemployment rate, Unemployment insurance claims); Congressional regulatory laws [Financial Svc Modernization Act ’99, Banking Compensation/wages/salaries; Labor force participation Act ’33] Foreign central banks INFLATION European Central Bank (ECB); Bank of England; Bank of Japan; Bank of Consumer prices, Consumer Price Index (CPI); Survey of Consumer Canada; Swiss National Bank; Bank of Mexico Confidence Sentiment; Producer prices; Personal Consumption Expenditures Price Index (PCE) IDIOSYNCRATIC EVENTS FOREIGN ECONOMIC ACTIVITY Hurricanes (Hurricane Katrina, Hurricane Sandy, Unidentified hurricane); Europe (after 1999: Euro area) (Spain, Germany, Portugal, Italy, France, Drought; 2011 Tohoku earthquake and tsunami; Unusual temperatures Greece, European sovereign debt crisis, United Kingdom (UK); (Unusually warm weather, Unusually cold weather); 2001 terrorist attacks Asia (1997 Asian financial crisis, China, Japan, Collapse of the Japanese asset price bubble (1990), India, Korea, Singapore, Indonesia, Malaysia, LOGISTICS Hong Kong); Attendees; Disclosure policy / communications; Implementation of monetary Latin America (Latin American debt crisis, Brazil, Mexico); policy (Short term rates [Open market operations, System open market Canada account (SOMA), Federal reserve asset purchases, Discount rate/target federal funds rate, Interest on excess reserves (IOER), Reserve FISCAL POLICY requirements], Long term rates) Federal budget; Taxes; Fiscal stimulus; Federal spending sequester

MONEY SUPPLY M1; M2; M3

The descriptive statistics from exploratory analysis (Table 3, Panel A) provide evidence for six of the nine major themes from Figure 6. On average, the output theme is the most significant, with 40% of all themes, followed by financial stability (28%), inflation (16%), employment (10%), money supply (4%), and fiscal policy (1%). An additional theme of foreign activity arises through algorithmic analysis (Table 3, Panel

B). The table includes stationarity statistics of the significant themes for both types of content analysis. Tested in level form, only the financial stability and output themes do not exhibit a stationary process. After differencing, all the series exhibit stationary processes at the 1% level, indicating that the FOMC did not drastically change the content of their discussion from one meeting to another. Rather, the change in the importance of each theme from meeting to meeting is gradual. The differences between

47 the relative importance of the dominant themes in exploratory analysis and algorithmic analysis are statistically significant.

Table 3 Descriptive Statistics of Themes Discussed at FOMC Meetings (1990–2012) Financial Money Panel A: Exploratory analysis, 1993–2012M06 Output Inflation Employment Fiscal policy stability supply

Observations 21 21 21 21 21 21 Mean 28.1% 40.2% 16.3% 9.7% 4.4% 1.3% Standard deviation 11.1% 10.5% 3.5% 2.5% 1.8% 1.5% Median 23.8% 41.6% 15.7% 9.7% 4.3% 0.8% Maximum 50.0% 55.2% 24.0% 16.3% 7.2% 5.9% Minimum 15.2% 20.8% 11.0% 5.9% 0.4% 0.0% ADF T-Statistic (Levels) 0.14 -0.79 -3.00* -3.31** -2.08 -2.26 ADF T-Statistic (1st Difference) -6.48*** -4.07*** -5.30*** -6.20*** -3.99*** -5.83*** Financial Money Foreign Panel B: Algorithmic analysis, 1990M02–2012M06 Output Inflation Employment Fiscal policy stability supply activity Observations 269 269 269 269 269 269 269 Mean 22.3% 40.3% 19.5% 11.7% 1.7% 0.6% 4.0% Standard deviation 8.2% 8.8% 5.6% 2.6% 3.4% 0.7% 1.3% Median 19.5% 41.9% 17.9% 11.5% 0.1% 0.3% 4.0% Maximum 45.6% 56.7% 38.4% 19.5% 14.2% 2.8% 8.4% Minimum 10.1% 14.7% 9.2% 4.1% 0.0% 0.0% 1.3% ADF T-Statistic (Levels) -2.48 -2.71* -2.65* -4.33*** -3.39** -3.73*** -1.65 ADF T-Statistic (1st Difference) -11.19*** -10.95*** -15.57*** -7.71*** -5.13*** -10.20*** -5.98*** Note: Results of emergent coding at paragraph unit of analysis are summarized in annual statistics, whereas results of selective coding at phrase unit of analysis are summarized in monthly statistics. The units of summary statistics are relative percentage of theme usage per observation. p < 0.01***; p < 0.05**; p < 0.10*.

Moreover, considering the relative weights of dominant FOMC discussion themes for both types of content analysis (Figure 7), we find that the portion of each meeting’s discussions ascribed to each theme changes over regime samples (Appendix 1).30

Exploratory analysis (Figure 7, Panel A) suggests an overall pattern of increased importance of financial stability associated with a decline in the importance of output.

Algorithmic analysis (Figure 7, Panel B) suggests a richer variation, supporting a dominant role for financial stability in the first regime, its relatively constant importance in regimes 2, 3, and 4, and its substantial rise in importance during regime 5 coinciding with the Great Recession. This data suggests that the themes of inflation and financial

30 As described in Appendix 1, structural break testing of the effective Fed Funds rate time series identifies four structural breaks (January 1994, January 2001, July 2004, and February 2008) that define the following regime samples: regime 1 (1990M21993M12), regime 2 (1994M12000M12), regime 3 (2001M12004M6), regime 4 (2005M72008M1), and regime 5 (2008M22012M6).

48 stability tend to move in opposite directions of importance. During the last two regimes, their relative weights have separated distinctly for the first time since the early 1990s.31

Figure 7 Relative Theme Importance over Time Panel A: Exploratory analysis (1993M1-2012M7) Panel B: Selective Coding (1990M2-2012M6) Regime 2 Regime 3Regime 4 Regime 5 Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 60% 60%

50% 50%

40% 40%

30% 30%

20% 20%

10% 10%

0% 0% Feb-90 Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Feb-11 Feb-12 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Financial stability Output Financial stability Output Inflation Employment Inflation Employment Money supply Fiscal policy Money supply Fiscal policy

Cross-correlogram data between the FOMC discussions and the monetary policy provides additional information on the pattern of their relationships. As shown in Figure

8, Panel A, over time, the cross-correlations between discussions of financial stability and monetary policy exhibit asymmetric feedback between the leads and lags of the changes in financial stability discussions and changes in monetary policy. Consider the intentions function correlogram ⋆ between lagged discussion of financial stability and the ensuing monetary policy . A rise in financial stability (↗, measured by a drop in financial stability discussions (↘), tends to be associated with subsequent tightening of monetary policy (↗ increases of Fed Funds rate) with a convex cross- correlation reaching -21% one year later. However, as shown by the impact function

31 This changing data pattern supports the idea that the key themes in the FOMC discussions shift meaning. This suggests the potential relevance of Blumer’s (1969) “symbolic interactionism”—the idea that the Fed’s policymakers continue to shape monetary policy in response to the evolving meaning from relevant economic factors, their own actions in response to this information, and through the discussions and interaction with their peers on the FOMC. 49 correlogram ⋆ between lagged monetary policy instrument and the ensuing discussion of financial stability , tightening monetary policy (↗) tends to be associated with subsequent financial instability (↘) reflected in increased

discussions ↗ ) with a concave cross-correlation reaching 10% one year later:

↗ ↘ ↗ | ⋆ ≅ 21% (1) ↗ ↘ ↗ | ⋆ ≅ 10%

Put another way: a decrease in the Fed funds rate tends to be associated with

subsequent increases in financial stability, reflected in decreasing discussions of this topic

(impact function). However, a rise in financial stability tends to lead to a tightening

policy (intentions function), which in turn tends to lead to financial instability. The data

shows that pattern is asymmetric, where the cross-correlations of increasing financial

stability discussions with the subsequent loosening of monetary policy are stronger than the cross-correlations of a tightening policy with subsequent discussions of financial

stability. Of course, correlation is not causation, and a stronger understanding of the interaction between financial stability and monetary policy is needed to obtain further insights. For considerations of brevity, we follow the notation introduced above to summarize the remaining correlograms in Figure 8, Panel A for the period from 1990M2 to 2008M1. This sample includes the first four regime samples, using effective Fed Funds rate as MPI. It excludes regime 5 that is characterized by zero lower bound and the loss of normal functionality of the Fed Funds rate as MPI (see section 3.2). The correlograms

for the FOMC discussions of inflation (), output (), employment (), foreign

activity (), fiscal policy (), and money supply () show that the policymakers’

50 talk tends to have a tangible asymmetric and frequently nonlinear relationship with monetary policy:

↗ ↗ | ⋆ ≅ 31% (2); ↗ ↘| ⋆ ≅ 44%

↗ ↘ | ⋆ ≅ 17% (3); ↘ ↗| ⋆ ≅ 27%

↗ ↘ | ⋆ ≅ 11% (4); ↘ ↗ | ⋆ ≅0% ↘

↗ ↘ | ⋆ ≅ 11% (5); ↘ ↗ | ⋆ ≅9% ↘

↘ ↗ | ⋆ ≅ 43% (6); ↗ ↗| ⋆ ≅ 38%

↗ ↗ | ⋆ ≅1% ↘ (7). ↗ ↘| ⋆ ≅ 48%

Further support to the causal interpretation for the FOMC thematic content is

provided by the significant one-way Granger causality from the FOMC discussions of

financial stability, inflation, and employment to the monetary policy instrument (Table

4). Analysis of mutual precedence patterns of the discussions of financial stability and

monetary policy shows that, over the sample period, FOMC discussions of these topics

unidirectionally Granger-cause the subsequent monetary policy actions. Put differently,

these findings support the ideas that through the sample period from 1990M2 to 2012M6:

1) Financial stability entered the policymakers’ intentions function;

2) Discussions of inflation and slack in employment entered the policymakers’

intentions function;

51 3) Discussions of monetary aggregates entered the policymakers’ intentions

function;

4) Monetary policy had an impact on the ensuing fiscal policy, but not

conversely.

52 Figure 8 Cross-correlograms of intentions and impact functions for FOMC discussions and monetary policy (1990M2–2008M1) 0.6 52%

0.4

Financial 0.2 7% stability 0

-0.2 0 3 6 9 1215182124 0.5 31%

Inflation -0.5 -44%

-1 0 3 6 9 12 15 18 21 24 0

-0.1

-0.2 Output -17% -0.3 -27% -0.4 0 3 6 9 1215182124 0.3 0.2 0.1 0% Employment 0 -0.1 -0.2 -11% 0 3 6 9 1215182124 0.3 0.2 0.1 Foreign activity 0 -0.1 -9% -10% -0.2 0 3 6 9 1215182124 0

-0.2

Fiscal -0.4 policy -38% -0.6 -43%

-0.8 0 3 6 9 1215182124 0.6 48%

0.4

Money 0.2 supply 0 -1% -0.2 0 3 6 9 1215182124 Note: indicates impact function cross-correlation between lagged monetary policy instrument in Panel A (lagged manifest variable in Panel B) and ensuing discussion of a particular theme; indicates intentions function cross-correlation between lagged discussion of the corresponding theme and the ensuing monetary policy instrument in Panel A (lagged manifest variable in Panel B). The period from 1990M2 to 2008M1 includes 4 regime samples with effective Fed Funds rate used as MPI and excludes regime 5 which is characterized by zero lower bound when monetary policy instrument is better represented by average short shadow rate.

53 Table 4 Granger Causality of FOMC Discussions and Monetary Policy (1990M2–2012M6)              

Obs 180 180 180 180 180 180 180 180 180 180 180 180 180 180 F- 1.539 0.001 14.383††† 0.053 10.865††† 0.401 6.238††† 0.118 0.482 0.954 5.073††† 1.195 2.124† 0.005 Statistic Prob. 0.216 0.973 0.000 0.818 0.001 0.527 0.013 0.732 0.488 0.330 0.026 0.276 0.147 0.944 Note: Lags = 1 for all statistics. Average shadow short rate serves as proxy for the Federal Reserve monetary policy. The significance of Granger causality at 20%, 10%, and 5% is shown by †, ††, and ††† respectively.

Financial stability discussions. The complex and evolving nature of FOMC

discussions is supported by the substantial variation over time of each theme’s

composition. Consider a decomposition of financial stability viewed through the

exploratory analysis of Figure 9. Until 1998, the discussion of financial stability focuses

predominantly on financial market factors. The most significant aspects considered in the

financial markets include general observations, foreign exchange market, and real estate

market. After 1998, considerations of specific financial instruments grow stronger. The financial instrument factors are dominated by credit instruments with supplemental consideration of the money market, Treasury securities, bonds, and stocks. Over time the importance of the foreign exchange market may have waned, while that of the capital market and real estate market appears to fluctuate.

54 Figure 9 Financial Stability Factors Deliberated in Setting Monetary Policy (Exploratory Analysis, 1993M1–2012M6)

55 Algorithmic analysis yields additional insight on the pattern of these changes

(Figure 10). During the first regime (1990M2 to 1993M12), considerations of financial stability are dominated by five phrase factors: financial market, financial condition, foreign exchange, value of the dollar, and non-financial debt. During the second regime

(1994M01 to 2000M12), the factors of financial stability roughly double, emphasizing ten aspects: financial market, financial condition, equity price, foreign exchange, value of the dollar, stock market, mortgage rate, balance sheet, non-financial debt, and mutual fund. During the third regime (2001M1 to 2004M6), five additional phrase factors are consistently considered: market condition, equity market, mortgage interest rate, financial institution, and market price. This period is particularly marked by the emergence of financial instrument considerations. During the fourth regime (2004M7 to 2008M1), the fundamental phrase factors of the previous two regimes grow in importance, supplemented by the new market and institutional factors including corporate bonds, treasury securities, and liquid deposits. The most striking aspect of the fifth regime

(2008M2 to 2012M7), is the increased granularity of financial instruments and financial markets, coupled with greater emphasis on the consideration of US regulatory system and its international setting.

Figure 10 also suggests that as new financial stability factors emerge they tend to command considerable attention of the Fed in its discussion of monetary policy. These emergent factors may appear marginal when considered by their overall historical rank.

Yet, they carry a critical importance in each distinct regime. These critical factors include: non-financial debt in the first regime, mutual fund and market interest rate in the

56 second, market price in the third, liquid deposits in the fourth, and financial institution, commercial paper, and credit condition in the fifth.32

32 This finding suggests potential relevance of “punctuated equilibrium” to monetary policy discussions. The “alternation between long periods when stable infrastructures permit only incremental adaptations, and brief periods of revolutionary upheaval” observed by Gersick (1991: 10) in corporate policy deliberations parallels the evolving complexity of the financial stability factors. The parallel is evocative and suggests there may be something fundamental about the policymakers’ distributed cognitive processes that holds across contexts. 57 Figure 10 Financial Stability Factors Deliberated in Setting Monetary Policy (Algorithmic Analysis, 1990M2–2012M6) Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 14% 85 LIQUID DEPOSIT Lehman collapse Bear Stearns MARKET PRICE Subprime rescue MARKET INTEREST RATE Crisis begins Global $5T 12% stimulus MUTUAL FUND 1990-1991 LTCM 75 TREASURI YIELD Crisis Recession MORTGAG INTEREST RATE FINANCI INSTITU 10% US debt downgrade EQUITI MARKET 65 Early 2000s Stock Market Eurozone FUND MARKET Recession Downturn Crisis Dot-com STOCK PRICE 8% Crisis Global Bond COMMERCI PAPER Market Reversal MONEI MARKET 55 Bond CREDIT CONDITION Market Asian 6% Crisis Crisis NONFINANCI DEBT BALANC SHEET MORTGAG RATE 45 CORPOR BOND 4% STOCK MARKET MARKET CONDITION

35 VALU OF THE DOLLAR 2% FOREIGN EXCHANG EQUITI PRICE FINANCI CONDITION

0% 25 FINANCI MARKET CFSI Feb-90 Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Feb-11 Feb-12 Aug-90 Aug-91 Aug-92 Aug-93 Aug-94 Aug-95 Aug-96 Aug-97 Aug-98 Aug-99 Aug-00 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10 Aug-11

Frequency (t) 1 observation lag / lead (t-1, t+1) 2 observations lag / lead (t-2, t+2) Observations Correlation Observations F-Statistic Prob. Observations F-Statistic Prob. Financial stability theme ↛ 181 0.678 180 3.924 0.049 179 3.618 0.029 US financial stress (CFSI) US financial stress (CFSI) 9.525 0.002 2.752 0.067 ↛ Financial stability theme Note: White vertical lines indicate episodes of US financial stress. Black vertical lines indicate structural breaks in the effective Fed Funds rate series that determine the regime samples (Appendix 1). Black dashed line indicates the financial stress measure (CFSI, Oet et al., 2012) that is supported as a proxy for financial stability. The statistical comparison of correlation and Granger dependence of the financial stability discussions and CFSI is provided below and is discussed in Appendix 3. ††† – indicates Granger causality with 95% or better confidence. 58

2.3.2. Taylor guide to monetary policy

The Fed has been using the Taylor rule unofficially for probably as long as the rule has been in existence. It always had many fans among the Fed economists as a guidepost—a starting point of monetary policy considerations, perhaps because of its simplicity (Judd and Rudebusch, 1998; Carlstrom and Fuerst, 2003). Yet, clearly the

Taylor rule is a rough guide to actual monetary policy, as seen in the Figure 11. Among other candidate measures, the figure compares two popular versions of the Taylor rule,

Taylor (1993) with output gap as a measure of economic slack (1993) and Taylor

(1999) with unemployment gap as a measure of economic slack (1999), against the effective Fed Funds rate as monetary policy instrument. On initial review, it appears that the two versions of the rule track each other reasonably up to November 2008, when they separate. A closer comparison against the Fed Funds rate MPI reveals that in fact they track it fairly crudely from 1990M2 through 2008M11. Specifically, during regime 1,

1999 predicts a policy rate below the MPI by as much as 2.6%, while 1993 fluctuates and ends up predicting a higher-than-actual MPI by 1.7%. During regime 2, both Taylor rules fluctuate about the actual MPI. 1993 swings from being 1.7% below to being 2.0% above the MPI. 1999 oscillates from being 2.4% below to

being 1.9% above the MPI. The discrepancies of Taylor rules ( Δ and Δ ) with the Fed Funds MPI does not improve with time, becoming particularly poor in regime 5:

2.4% Δ 0.8% | 3 (8); 1.4% Δ 1.1%

1.1% Δ 0.9% | 4 (9); 2.1% Δ 0.3% 59 2.1% Δ 1.6% and | 5 (10). 7.8% Δ 1.3%

Figure 11 Comparison of Standard Taylor and Taylor-type Rules (Table 5 Columns 1–4) with Fed Funds Rate (Regimes 1–4) and Average SSR (Regime 5) Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 10.0

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0 Jun-91 Jun-93 Jun-95 Jun-97 Jun-99 Jun-01 Jun-03 Jun-05 Jun-07 Jun-09 Jun-11 Oct-90 Oct-92 Oct-94 Oct-96 Oct-98 Oct-00 Oct-02 Oct-04 Oct-06 Oct-08 Oct-10 Feb-90 Feb-92 Feb-94 Feb-96 Feb-98 Feb-00 Feb-02 Feb-04 Feb-06 Feb-08 Feb-10 Feb-12

Average SSR Taylor (1993) (column 1) Taylor (1999) (column 3) Fed Funds rate Taylor-type (1993) (column 2) Taylor-type (1999) (column 4)

Why would the Taylor rules provide such a wide swath of rates for predicted

monetary policy? Specifically, how can the policymakers be effectively and consistently

guided by a rule that can be so uneven in its recommendations from one form of

measurement to another? Our study is not the first by far to make these observations. A substantial body of literature examines the question whether the unmodified Taylor rules

() should serve as the benchmark for monetary policy. The answer is “probably not.”

There are at least five reasons to depart from as benchmark. First, the equilibrium real Fed Fund rate might not be constant (Laubach and Williams, 2003).

Second, does not account for the lower bound on the Fed Fund rate (Benhabib et al.,

2001; Eggertsson and Woodford, 2003). Third, does not account for Fed’s desire for

60 interest-rate smoothing in monetary policy (Rudebusch, 2006). Fourth, is not robust to minor variations in data sources (Orphanides, 2001) and rule specifications (Kozicki,

1999; Elias et al., 2014; Bosler et al., 2014; Carlstrom and Jacobson, 2015). Fifth,

variants of Taylor rule can fit the Fed Funds rate better (Carlstrom and Fuerst, 2012;

Clark, 2012; Carlstrom and Zaman, 2014). To address these critiques, we test an

alternative Taylor-type policy rules () as improved monetary policy benchmarks.

Our approach partially remedies the shortcomings of the standard by

including empirical estimation (critiques one and four), real time data (critique four) and

improved measures of economic slack (critique five) (Erceg and Levin, 2014; Bosler et

al., 2014). Estimated this way, explicitly addresses critiques one, four, and five

above. Regarding critique three, we opt not to estimate inertial Taylor-type rules based on the following reasoning. With our research questions we are fundamentally seeking to determine to what extent the inclusion of omitted variables, related to FOMC discussions, into the policy reaction function provides additional explanatory power in a simple rule.

From this perspective, inertial Taylor-rules are objectionable, as the inclusion of the lagged policy rate partially encompasses the variation due to the omitted variables.33

Therefore, we fix the reaction coefficients to those proposed by Taylor (1993, 1999), and those commonly used in the Taylor-type models in other studies—an approach that is similar to Clark (2012). Lastly, we address critique two in two ways. First, we recognize the appropriateness of using an alternative shadow rate monetary policy instrument

33 In fact, the statistical power and practical popularity of the inertial rules can be seen as a parsimonious way to account for omitted variables in the MPI rate through the known lagged observation of the MPI rate itself.

61 (Krippner, 2012; Wu and Xia, 2013; Lombardi and Zhu, 2014) after zero lower bound when the nominal effective Fed Funds rate is no longer informative of the real policy rate.34 Accordingly, we use the average shadow short rate (average SSR) to represent

MPI in the zero lower bound environment, estimated from monthly data provided by

Krippner (2012), Wu and Xia (2013), and Lombardi and Zhu (2014).35 Second, our

regime sampling strategy (Appendix 1) distinguishes four regimes from 1999M2 to

2008M1, when the use of effective Fed Funds rate as MPI is appropriate. During this

timeframe, we test the performance of candidate model specifications against the Fed

Funds rate in-sample. We reserve the fifth regime, starting in 2008M2, for testing the

candidate models in the zero lower bound environment out-of-sample and against the

average SSR.

Table 5, columns 1 through 4 provide the results of testing candidate and

rules as benchmarks for monetary policy that are also shown graphically in Figure 12.

The results show that the in-sample power of both Taylor (1993) rule and Taylor (1999)

rule can be improved by empirically-estimated Taylor-type models, as expected. The best

in-sample fit among these candidate benchmarks (see Table 5, Panel A, columns 1

through 4) is achieved by the employment-based Taylor-type (1999) model (Table 5,

34 While zero serves as a boundary for the nominal rate that banks charge each other for overnight borrowing (the Fed Funds rate), it does not bind the real monetary policy instrument rate (Dupor, 2015). When monetary policy rule indicates positive rate, this suggests the use of standard monetary policy instrument, the federal funds rate (Tallman & Zaman, 2012). When the rule indicates negative rate, this suggests the use of additional stimulative tools (Carlstrom & Fuerst, 2012; Yellen, 2012; Bernanke, 2015, April 15). 35 Monthly SSR estimates from Krippner (2012) are available at http://www.rbnz.govt.nz/research_and_publications/research_programme/additional_research/5655249 .html. Updated SSR estimates from Wu and Xia (2013) are available on the J.C. Wu’s website at http://faculty.chicagobooth.edu/jing.wu/. We obtained current SSR estimates to accompany Lombardi and Zhu (2014) from the authors.

62 column 4) with a coefficient of determination () of 87%, and a sizable mean absolute

percentage error () of 19.1%.

The out-of-sample results (Panel B, columns 1 and 3) show that both standard

Taylor (1993) and Taylor (1999) rules tend to lose power. The substantial loss of power

by the unemployment-based Taylor (1999) is particularly interesting and is in line with

36 Bosler et al. (2014). The best out-of-sample fit of 82.1% is reached by the

output-based Taylor (1993) rule. As expected, the use of Taylor-type rules (columns 2

and 4) provides tangible improvement, particularly is to no avail out-of-sample, as both

of these candidate models fail to improve the explanation of monetary policy out-of-

sample, with output-based Taylor-type (1993) rule reaching 84.1% and the

employment-based Taylor-type (1999) rule with 83.3%.

36 Bosler et al., (2014) attribute the loss of fit to the measurement errors stemming from the difficulty of differentiating between cyclical and structural changes in unemployment in the aftermath of the Great Recession. 63 Figure 12 Comparison of Thematic (Discussion-Augmented Taylor-Type) Model (Table 5 Column 8), Tri-Mandate Model (Table 5 Column 9), and Benchmark Taylor-Type (1999) Model (Table 5 Column 4) with Fed Funds Rate (Regimes 1–4) and Average SSR (Regime 5) Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 10.0

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

Average SSR Taylor-type (1999) (column 4) Tri-mandate Taylor-type (column 9) Fed Funds rate Thematic Taylor-type (column 8)

64 Table 5 Results Models (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Taylor Taylor-type Taylor Taylor-type Thematic Thematic Thematic Thematic Tri-mandate Communications

(1993) (1993) (1999) (1999) Taylor (1993) Taylor-type (1993) Taylor (1999) Taylor-type (1999) Taylor-type Taylor-type

output unemployment Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Ω 0 Intercept 3.75 3.9 4 4.09 15.137*** -39.464*** 10.202*** -42.024*** 45.248*** -23.567*** 20.018*** -11.478*** 18.955** -10.440*** 15.929*** -15.567*** 1.5 1.37 1.5 1.69 1.5 1.37 1.5 1.69 1.69 1.69 0.5 0.58   0.5 0.58     -0.448*** 0.057***   2 1.39     2 1.39 1.39 1.39 -0.024*** -0.004*** -0.165*** 0.384*** -0.106*** 0.414*** -0.424*** 0.291*** -0.150*** 0.174*** -0.150*** 0.174*** -0.150*** 0.174*** -0.172*** 0.421*** -0.118*** 0.453*** -0.458*** 0.249*** -0.178*** 0.175*** -0.178*** 0.175*** -0.178*** 0.175*** -0.080© 0.395*** -0.031** 0.389*** -0.428*** 0.209*** -0.103*** 0.010*** -0.103*** 0.010*** -0.103*** 0.010*** -0.175*** 0.398*** -0.153*** 0.398*** -0.465*** 0.214*** -0.194*** 0.155*** -0.194*** 0.155*** -0.194*** 0.155*** -0.135*** 0.389*** -0.099** 0.460*** -0.618*** 0.010© -0.199*** 0.156*** -0.199*** 0.156*** -0.108*** 0.409*** 0.059*** 0.549*** -0.252*** 0.460*** -0.070*** 0.201*** -0.070*** 0.201*** 0.007*** -0.011*** 0.013*** 0.004*** -0.022*** -0.042*** S 0.001*** 0.000** Panel A: In-sample (1990M2-2008M9). Dependent variable: Effective Federal Funds Rate.

0.833 0.838 0.752 0.873 0.940 0.937 0.802 0.948 0.886 0.956 RMSE 0.849 0.829 1.035 0.734 0.491 0.502 0.895 0.456 0.673 0.415 MAE 0.659 0.656 0.842 0.617 0.370 0.382 0.670 0.352 0.540 0.325 MAPE 0.181 0.185 0.244 0.186 0.109 0.111 0.229 0.110 0.165 0.097 Panel B: Out-of-sample (Zero Lower Bound) (2008M10-2012M6). Dependent variable: Average Shadow Short Rate.

0.821 0.841 0.233 0.833 0.818 0.893 0.072 0.860 0.951 0.930 RMSE 2.146 2.010 4.440 2.059 2.093 1.596 4.729 1.830 1.075 1.271 MAE 1.494 1.399 4.120 1.737 1.698 1.187 4.462 1.612 0.891 1.165 MAPE 0.996 0.995 3.963 1.744 1.018 0.916 4.458 2.008 1.505 1.599 Note: Statistical significance at 10%, 5% and 1% levels is indicated by *, **, and ***, respectively. © denotes constrained parameter. Unstandardized coefficients are used throughout.

Based on a similar set of theoretical and empirical critiques of the standard Taylor rules, Kozicki (1999: 24) questions the Taylor rules’ basis for guiding monetary policy as incidental: “If rule recommendations happen to match funds rate settings but do not capture the process by which the funds rate was set, then the ability of the rule to continue to match policy in the future is questionable.”37

2.4. Thematic and Tri-mandate Monetary Policy Models

This section summarizes the main results (section 4.1) from testing the

discussion-based models of monetary policy, posits their sign expectations (section 4.2),

and describes their economic and statistical significance against the Taylor-type

benchmark (section 4.3).

2.4.1. Main results

We examine whether the results of content analysis have explanatory power beyond the standard Taylor-based ( and ) rules. As shown in Table 5, columns 5–

8, inclusion of themes from FOMC discussions substantially improves fit across the corresponding Taylor and Taylor-type models (columns 1-4) both in-sample and out-of- sample. To test the explanatory power of the candidate discussion-augmented models, we add alternative explanations of monetary policy to the benchmark Taylor and Taylor-type rules, fixing the corresponding and in-sample reaction coefficients for out-of- sample testing.

37 Interestingly, Kozicki supports her query with discussion-based qualitative evidence. She refers to statements by Chairman Volcker in July 1985, Chairman Greenspan in March of 1998 and June 1994, and Governor Meyer in February 1999 that Fed’s monetary policy process was significantly guided by additional considerations that included financial strains (during 1987-1988, 1989-1993, and 1998- 1999) and foreign exchange issues (during the early 1980s). 66

Given the empirical support for the continued relevance and relative importance of financial stability discussions, we then hypothesize that interaction of principal discussion themes with the corresponding policy goals improves the explanation of actual monetary policy. This is the tri-mandate model (Table 5, column 9): policymakers care about inflation, economic slack (measured by nonemployment and output), and financial stability.38 As we drop two theme variables from the best thematic model (column 8), our

in-sample fit decreases slightly from 94.8% to 88.6%, while out-of-sample fit is

improved from 86.0% to 95.1%. This supports the tri-mandate model as optimal guide to

monetary policy. Finally, to test whether the dropping of additional themes was justified,

we put them back in (communications model, column 10). As expected, this improves in-

sample fit, but worsens out-of-sample power from 95.1% to 93.0%. We conclude that the

tri-mandate model is supported.

In the process of developing and testing the discussion-augmented models of

monetary policy, we test and support empirically two major debated assumptions from

prior literature: 1) that the policymakers' reaction functions are asymmetric; 2) that the

sign expectations in each model correspond to states of the world (deflationary and

inflationary) which are driven by real-time information.39

Fixing the coefficients in the thematic and tri-mandate models vis-à-vis the

Taylor-type benchmark allows us to verify whether they are capable of guiding monetary

policy in the spirit of a policy rule. Anchoring the models on the Taylor-type benchmark

38 Note that both output and unemployment are used to describe economic slack in the tri-mandate model, similar to Galí (2011). See also the discussion in footnote 16. 39 Coincidentally, Clarida, Galí & Gertler (1998) call this measure of real-time difference between actual policy rates and the dual-mandate Taylor rule’s rate the “stress indicator.” 67

has the advantage of treating additional influences as previously omitted variables and testing whether their influences are temporary (e.g. as headwinds) or systematic. Table 6 summarizes the horse race in explanatory performance of the Taylor-type (1999) benchmark, thematic Taylor-type (1999) model, and the Tri-mandate model40 through the

set of sampled policy regimes. As shown, the thematic model consistently outperforms

the Taylor-type (1999) benchmark in all regime samples. The tri-mandate model

outperforms the benchmark in all regimes except the first. Relative to the thematic model

which considers a larger set of economic factors, the tri-mandate model is marginally

worse in normal regimes, but is better in explaining monetary policy in zero lower bound

conditions.

Table 6 Model Horse-Race over Regime Samples Taylor- Thematic Tri- type Taylor-type mandate (1999) (1999) Taylor-type Panel A: Regime 1 (1990M2 – 1993M12) 0.929 0.971 0.859 RMSE 0.691 0.441 0.976 MAPE 0.142 0.087 0.178 MAE 0.604 0.331 0.835 Panel B: Regime 2 (1994M1 – 2000M12) 0.889 0.953 0.938 RMSE 0.728 0.476 0.544 MAPE 0.121 0.073 0.085 MAE 0.605 0.374 0.428 Panel C: Regime 3 (2001M1 – 2004M6) 0.899 0.951 0.904 RMSE 0.583 0.406 0.567 MAPE 0.314 0.209 0.317 MAE 0.501 0.336 0.473 Panel D: Regime 4 (2004M7 – 2008M1 ) 0.733 0.915 0.851 RMSE 0.766 0.431 0.572 MAPE 0.157 0.087 0.143 MAE 0.645 0.308 0.499 Panel E: Regime 5 (2008M2 – 2012M6 ) 0.826 0.866 0.950 RMSE 1.960 1.717 1.051 MAPE 1.551 1.754 1.324 MAE 1.645 1.476 0.864

40 These are specified respectively in Table 3, columns 4, 8, and 9. 68

2.4.2. Sign expectations

We hypothesize that two alternative monetary policy models—thematic model and tri-mandate model—can explain systematically the deviations of observed policy rates from the Taylor-rule-implied rates. The thematic model posits the monetary policy instrument at time t, , as a function of the Taylor-type rule implied target rate

and the policymakers’ discussion frequencies of an extended set of adverse economic conditions including inflation , output (), unemployment ), financial stability (), foreign activity (), and fiscal policy () in (11):

, ,,,,, (11).

The tri-mandate model posits as a parsimonious function of and the interactions of policymakers’ discussions of inflation, slack,41 and financial stability with the observed gaps in inflation, slack, and financial stability:

, , , ∙ , , , , (12), ,,,

41 Economic slack represents underutilized productive resources (Nelson, 1964; Garner 1994) as measured by gaps in employment, output, or other capacity-related indicators (Orphanides, 1999; Romer & Romer, 2002). Traditionally, Taylor rules have parsimoniously included a single measure of economic slack, either output or employment, but not both. The substitutability between the two measures of slack has been supported by references to Okun’s (1962) empirical law and the evidence of high negative correlation between unemployment and output (Galí, 2011). However, Friedman (1977) emphasizes the fundamental error in relying solely on unemployment as a measure of slack. Similarly, Knotek (2007: 74) finds that “Okun’s relationship between changes in the unemployment rate and output growth has varied considerably over time and over the business cycle,” while Elias et al. (2014) find that since 2012 the relationship between unemployment and output has flipped. The divergence between the various measures of economic slack compels policymakers to include more than one indicator of economic slack into monetary policy considerations (Elias et al., 2014). For example, Galí (2011, chapter 3) includes both unemployment and output into a simple Taylor-type rule finding significant optimal control coefficients for both with the unemployment coefficient 3 to 7.5 times higher than the coefficient for output (for technology and labor shocks respectively).

where ,,, and represent the respective deviations of observed variables of inflation, output, employment, and financial stability from their policy goals, while

42 , and denote the corresponding interactions of discussions with policy goals.

For both models, we expect that policymakers will react asymmetrically

(Kahneman and Tversky, 1979) to economic conditions,43 tightening its monetary policy

44 stance conditionally on real-time information (Orphanides, 2001) Ω 0 of an inflationary state, and loosening its monetary policy stance, conditionally on real-time information Ω 0 of a deflationary state. The current information Ω

(14) is equal to the gap between the observed effective monetary policy

instrument rate and the known Taylor-rule implied target rate (Clarida et al., 1998).

Sign expectations in the thematic model are dependent on the adverse conditions in the relevant aspects of economy. Fundamentally, we expect the frequency of discussions would be positively correlated with real-time adverse conditions. The

42 That is, ∶ ; ∶ ; ∶ ; ∶ (13). 43 The asymmetry of the intentions function can be explained by behavioral and economic reasoning. Behaviorally, the prospect of loss in pursuit of an objective has a greater impact on policymakers than the prospect of equally-sized gain (Kahneman and Tversky, 1979). Economically, the asymmetry is driven by the policymakers’ desire for effective control in monetary policy (Cukierman and Meltzer, 1986), where the policymakers seek to generate positive surprises in order to stimulate a deflationary economy, leaving the negative surprises for inflationary periods. In the implementation of these policy surprises, the policymakers face greater pressures to delay the tightening of monetary policy when unemployment falls than to loosen policy when unemployment increases (Blinder, 1998). Cukierman and Muscatelli (2002, 2008) find that US policymakers’ preferences are asymmetric and state- dependent. In deflationary episodes, the policymakers show recession-avoiding preferences (RAP), while in inflationary episodes, policymakers show inflation-avoiding preferences (IAP). Under RAP, policymakers show “greater precautionary demand for output expansions than for low inflation.” Under IAP, policymakers “tend to react more vigorously to positive than to negative inflation gaps.” 44 We use real-time in a sense of data that is actually available at time .

relationship of discussion frequency with the depends on the particular type of adverse conditions (e.g. deflationary or inflationary).45 During booms, adverse conditions

are inflationary, and FOMC discussions can be expected to be positively associated with

the , as the Fed would tighten monetary policy to cool off an overheating economy.

During downturns, adverse conditions are deflationary, and FOMC discussions can be

expected to be negatively associated with the , as the Fed would loosen monetary

policy to stimulate a recessed economy. These expectations are summarized in (14).

, , , , , | Ω 0 , (15) , , , , , | Ω 0

Sign expectations in the tri-mandate model are similarly dependent on the real- time information of deflationary or inflationary conditions. They also depend on the measurement of policymakers’ tri-mandate goals in inflation, economic slack, and financial stability. It is, therefore, useful to think through the model expectations with more precision.

Inflation gap π∗ (16) describes the deviation of inflation from

policymakers’ long-run goal. We measure as the difference between the estimated

real-time inflation46 π and the policymaker’s long-run inflation target ∗. Output gap

100 ln ∗ (17) describes the deviation of current real output from its estimated

45 Hereafter, for simplicity, we drop the suffix where concurrent time period is implied. 46 We use the Greenbook forecasts of real-time inflation before 2009. After 2009, we use the arithmetic average of trailing four quarters of the core personal consumption expenditures (PCE) deflator which excludes food and energy prices. We verify that the Greenbook forecasts match the actual changes in the way that the Fed policymakers considered inflation estimates: using the CPI from July 1988 to February 2000, switching to the PCE deflator until July 2004, when inflation forecasts begin employing the core PCE deflator excluding energy and food (Mehra & Sawhney, 2010). 71

current potential. We measure as percentage difference between actual GDP and

∗ ∗ an estimate of potential real GDP (Kozicki, 1999). Unemployment gap

(18) describes the deviation of current employment from its natural potential. We measure as the difference between “the Congressional Budget Office (CBO) estimate of the [unemployment] rate consistent with inflation remaining stable over time ∗” and “the actual unemployment rate [” (Yellen, 2012).

∗ Stability gap (19) describes the deviation of current financial

system conditions from their long-run stable state. We measure as the difference

between the estimated upper threshold for the long-run normal range of financial system

∗ stress and current financial system stress . During conditions of unusually high

stress ( 0,47 risk premia are high (asset prices have fallen to historically low levels).

As risk premia rise and asset prices fall, there is a loss of wealth which drives down

consumption, and, in turn, GDP (Bernanke and Gertler, 1989; Gilchrist and Leahy, 2002;

Cecchetti, 2003). Thus, in order to revive the sagging economy, policymakers are

motivated to loosen the policy instrument (e.g. by decreasing risk-free rates). Similarly,

during conditions of unusually low stress ( 0,48 risk premia are low, indicating that

asset prices are overvalued in historical terms. As risk premia fall and asset prices rise,

there is an increase in wealth which stimulates consumption, and, in turn, GDP and

inflation (Bernanke and Gertler, 1989; Gilchrist and Leahy, 2002; Cecchetti, 2003). Thus,

in order to cool down the overheating economy, policymakers are motivated to tighten

the policy instrument (e.g. by increasing risk-free rates).

47 That is, as financial system stress rises, the financial stability gap becomes more negative. 48 That is, as financial system stress falls, the financial stability gap becomes more positive. 72

In deflationary states, the adverse condition in the inflation gap is inflation running below the target ( 0, (20). The economic activity is slacked, falling below its long-run potential or target (Nelson, 1964; Garner, 1994; Romer and Romer, 2002) and producing negative gaps in output and unemployment: 0 (21) and 0

(22). Financial instability grows as the gap between the threshold for the long-run normal range of stress and the current elevated financial system stress becomes increasingly negative: 0 (23). We expect that at such times policymakers would more frequently discuss the various aspects of deflation risk, economic slack, and financial instability, and would react by loosening monetary policy to stimulate the economy. The expected MPI direction would align with the tri-mandate gaps, resulting in positive coefficients for

, , , and . The corresponding interactions of the negatively signed discussion frequencies and the positively signed tri-mandate gaps should be negative. Thus, we expect:

,,, ∙ , , , , | Ω 0 (24), , , ,

During booms, the adverse condition in inflation gap is the running of inflation

above the inflation target: 0 (25). The economic activity heats up above its long-run

potential or target. The associated gaps in output and unemployment are positive:

0 (26) and 0 (27). Financial conditions loosen as financial system stress decreases

below the threshold for the long-run normal range of stress: 0 (28). Accordingly,

we expect that at such times policymakers would more frequently discuss the various

aspects of inflationary pressures, bubble-building in economic activities, and financial

exuberance. At such times, “the Fed can raise interest rates to help cool total demand and 73

constrain inflationary pressures” (Bernanke, 2012). The expected MPI direction would align with the tri-mandate gaps, resulting in positive coefficients for , , , and .

The corresponding interactions of discussion frequencies and the tri-mandate gaps should be positive. Thus, we expect:

,,, ∙ , , , , | Ω 0 (29), , , ,

In summary, we expect that the signs for the components of the MPI tri-mandate

reaction function will depend on the real-time information of deflationary and

inflationary periods, showing sign variability in deflationary periods and remaining

positive during inflationary periods:

,,, , , , | Ω 0 ∙ , , , , (30). , , , , , , | Ω 0 , , ,

2.4.3. Significance

In this section, we discuss how the results of our analysis can be assessed in terms

of statistical and economic significance.

Statistical significance. Broadly, the results in Tables 4, 5, and 6 show that

consideration of FOMC discussions provides useful information to understand actual

monetary policy in terms of direction, significance, and causality. The causal inference

implications of FOMC discussions (Table 4) have already been discussed in Section 3.1.

Observations of the signs of the reaction coefficients for FOMC discussions (Table 5,

columns 510) reveal that our sign expectations formed in Section 4.2 are fully confirmed, while all reaction coefficients associated with FOMC discussions are statistically significant at the 1% level. This is a remarkable result, considering that the state of each monthly time period has been individually evaluated leading to the stratified, that is to say discontinuous, inflationary and deflationary samples throughout the in-sample timeframe. In addition, the magnitudes of the reaction coefficients for

FOMC discussions show partial asymmetry, supporting the hypothesis that policymakers’ preferences for the intentions function are asymmetric (Cukierman and Meltzer, 1986;

Cukierman and Muscatelli, 2008).49

Before considering the statistical significance of the tri-mandate model, it is

useful to highlight its relationship to the thematic models. First, the thematic models

support the importance of the FOMC debates and discussions in forming systematic

monetary policy adjustments relative to the wide distribution of automatic Taylor-type

rules (Bernanke, 2015, April 28). The dominant themes discussed at each FOMC meeting

convey concerns that matter in influencing the direction of monetary policy towards or

away from the Taylor rule. By contrast, the Taylor-type rules look exclusively at inflation

and output or employment, but not both, regardless of the economic pressures from

financial conditions, foreign exchange, and other relevant themes. In fact, the Fed

policymakers consider it self-evident that Taylor-type rules provide a useful starting

49 While overall asymmetric pattern is present, it is more consistent with the RAP and IAP preference differentiation of Cukierman and Muscatelli (2008). This can be seen by comparing the thematic models in columns 6 and 8. For the employment-based thematic Taylor-type (1999) model in column 8, the deflationary state reactions for employment, and foreign activity are financial stability are stronger than respective reactions for the inflationary state, consistent with Cukierman and Meltzer (1986). However, for the output-based thematic Taylor-type (1993) model, the magnitudes of the inflationary reactions are consistently stronger than the corresponding deflationary reactions (Cukierman and Muscatelli (2008). 75

point, but fail to include information that is germane to setting monetary policy in a dynamically changing economy (Greenspan, 1997; Bernanke, 2004; Yellen, 2012;

Dudley, 2012; Bernanke, 2015, April 28). The critical means for the Fed policymakers to consider this dynamic information in setting monetary policy is through the FOMC discussions. During the FOMC discussions, Fed’s policymakers continually shape monetary policy in response to the interaction (Blumer, 1969) of four classes of variables:

- the real-time information on the efficacy of their own past actions (Ω 0 or

Ω 0), - the information on observable variables in the economy , , , , … , - the discussions and interactions with their peers on the FOMC , , , , … , - the evolving meaning from relevant economic factors , , , … . The meaning of the tri-mandate model as a guide to monetary policy is that the FOMC discussions are formative in determining Fed monetary policy, interacted with the policy goals in inflation, economic slack, and financial stability.

Statistically, all the freely estimated reaction coefficients in the tri-mandate model

(Table 5, column 9) are significant at the 1% level. The signs of the thematic variables

, , , and are appropriately differentiated by the deflationary and inflationary states in line with sign expectations. Both output gap () and unemployment gap () are included to measure economic slack (Galí, 2011) with ′ coefficient fixed by the

Taylor-type benchmark and the ′ coefficient freely estimated. Interestingly, the ′ coefficient is negative and tangible.50 While significant, the magnitudes of reaction

50 It is difficult to interpret this adjustment meaningfully. However, it is interesting that a similar sign reversal has been found by Gali (2011), when both output and unemployment are included as complementary measures of slack. 76

coefficients for the interaction terms , , , and are extremely small, as one may expect and are independent of state, contrary to expectations. Given their trivial magnitudes, this is likely due to estimation issues.

Economic significance of Taylor benchmarks. To describe the economic significance of the thematic and tri-mandate models, it is useful to do so referring to their functional forms in comparison with their Taylor and Taylor-type benchmarks.

Accordingly, in this section we put into words, the policy rate projections of the unemployment-based Taylor (1999) rule (Table 5, column 4), the unemployment-based

Taylor-type (1999) rule (Table 5, column 4), the thematic model (Table 5, column 8), and the tri-mandate model (Table 5, column 9).

Taylor (1999) model.

∗ 2 0.5 2 41.52 (31)

The Taylor (1999 rule in its employment form (30) predicts that the Fed will set

its monetary policy instrument at 4% when inflation is at its target rate of 2% ( 0

and the natural rate of unemployment equals current unemployment ( 0.

Otherwise, the Fed will tighten its monetary policy stance by raising its rate, ceteris

paribus,

1) by 1.5% for each percentage point that inflation exceeds the Fed’s inflation target of 2%; 2) by 2% for each percentage point that natural rate of unemployment exceeds actual unemployment. For example, given inflation gap of 1% and unemployment gap of 1%, the model predicts

the Fed will set its instrument rate at 7.5%.

Taylor-type (1999) model.

4.09 1.69 1.39 (32)

Our Taylor-type model (2) predicts that the Fed will set its monetary policy

instrument at 4.09% when inflation is at its target rate of 2% ( 0 and the natural

rate of unemployment equals current unemployment ( 0. Otherwise, the Fed will

tighten its monetary policy stance by raising its rate, ceteris paribus,

1) by 1.69% for each percentage point that inflation exceeds the Fed’s inflation target of 2%; 2) by 1.39% for each percentage point that natural rate of unemployment exceeds actual unemployment. For example, given inflation gap of 1% and unemployment gap of 1%, the model predicts

the Fed will set its instrument rate at 7.17%.

Economic significance of thematic and tri-mandate models. To put the thematic

and tri-mandate models into words, both models predict that the Fed will asymmetrically

react to economic conditions, tightening its monetary policy stance conditionally on

information Ω 0 of an inflationary state, and loosening its monetary policy stance,

conditionally on information Ω 0 of a deflationary state.

Thematic model.

15.927 0.150 0.178 0.103 0.194 0.199 0.070 |Ω 0 (33), 15.569 0.174 0.175 0.010 0.155 0.156 0.201 |Ω 0

where Ω is determined by (14). The thematic model predicts that when the inflation gap

and unemployment gap are zero, the Fed will adjust its monetary policy instrument from

4.09% as follows.

A. Given information 0 of a deflationary state, the Fed will lower its rate relative to the benchmark rate, for each percentage point that FOMC topic discussion increases relative to other themes, ceteris paribus, by 0.15% for inflation, by 0.178% for output, by 0.103% for unemployment, by 0.194% for financial stability, by 0.199% for foreign activity, by 0.070% for money supply.

B. Given information 0 of an inflationary state, the Fed will raise its rate relative to the benchmark rate, for each percentage point that FOMC topic discussion increases relative to other themes, ceteris paribus, by 0.174% for inflation, by 0.175% for output, by 0.01% for unemployment, by 0.155% for financial stability, by 0.156% for foreign activity, by 0.201% for money supply. For example, given inflation gap of 1% and unemployment gap of 1%, and the mean levels of thematic discussion,51 the model predicts the Fed will set its instrument rate at 6.57% in a deflationary state, that is 0.60% lower than the Taylor-type model prediction of 7.17%, and to 7.62% in an inflationary state, that is 0.45% higher than the

Taylor-type model prediction of 7.17%.

Tri-mandate model.

16.955 0.150 0.178 0.103 0.194 |Ω 0 0.448 0.024 12.440 0.174 0.175 0.010 0.155 |Ω 0 0.007 0.013 0.022 0.001+ (34),

52 where Ω is determined by (14).When the inflation gap, economic slack, and financial stability gap are zero, the tri-mandate model’s corresponding reaction coefficients are identical to the thematic model that omits the themes of foreign activity and money

19.512%| 39.080%| 11.559%| 23.422%| 51 Given by ̅ , , ,̅ , 19.512%| 41.777%| 11.773%| 20.808%| 3.843%| 2.081%| , and 4.312%| 1.175%| 52 That is unemployment gap and output gap. 79

supply. The differences between the tri-mandate model and the thematic model are evidenced in non-zero gap conditions of inflation, economic slack, and financial stability.

At such times, the tri-mandate model predicts that in setting the monetary policy instrument rate the Fed primarily considers its dual mandate and its financial stability mission.53 First, for the price stability mandate, FOMC considers the inflation gap, the

importance of the inflation gap in current conditions as reflected in the meeting

discussions, and the interaction effect by which the inflation gap is moderated by the

discussions. Second, for the maximum employment mandate, FOMC considers the

unemployment and output gaps, their relative importance in current conditions as

reflected in the meeting discussions, and their interaction effect with the discussions.

Third, for its mission to protect financial stability, FOMC considers the financial stability

gap, the importance of financial stability gap in current conditions as reflected in the

meeting discussions, and the interaction effect with the discussions. Specifically, the tri-

mandate model predicts the Fed sets the monetary policy instrument as follows.

1) Considering inflation, ceteris paribus:  by raising the rate by 1.69% for each percentage point that inflation exceeds the Fed’s inflation target of 2%,  by adjusting the rate an additional 0.15% down during deflationary states and up 0.174% during inflationary states for each percentage point that FOMC discussion of inflation increases relative to other themes,  by raising the policy rate by an additional 0.007% for each 1% increase in the interaction of inflation discussions and inflation gap.

53 Confirming our findings, FOMC (2012, January 12) states that “Inflation, employment, and long-term interest rates fluctuate over time in response to economic and financial disturbances. … Therefore, the Committee's policy decisions reflect its longer-run goals … including risks to the financial system that could impede the attainment of the Committee's goals.” 80

2) Considering economic slack, ceteris paribus:

 by raising the rate by 1.39% for each percentage point that natural rate of unemployment exceeds actual unemployment, while at the same time adjusting the rate down by 0. 448% for each percentage point that output rises relative to its potential,  by adjusting the rate an additional 0.103% down during deflationary states and up 0.01% during inflationary states for each percentage point that FOMC discussion of unemployment increases relative to other themes,  by adjusting the rate an additional 0.178% down during deflationary states and up 0.175% during inflationary states for each percentage point that FOMC discussion of output increases relative to other themes,  by lowering the policy rate by an additional 0.022% for each 1% increase in the interaction of unemployment discussions and unemployment gap,  by raising the policy rate by an additional 0.013% for each 1% increase in the interaction of output discussions and output gap. 3) Considering financial stability, ceteris paribus:

 by lowering the rate by 0.024% for each percentage point increase in the difference long-run financial system stress exceeds current stress (i.e. the stability gap),  by adjusting the rate an additional 0.194% down during deflationary states and up 0.155% during inflationary states for each percentage point that FOMC discussion of financial stability increases relative to other themes.

For example, given inflation gap of 1%, unemployment gap of 1%, output gap of

1%, and financial stability gap of 1%, the mean levels of thematic discussion, the model predicts the Fed will set its instrument rate at 6.42% in a deflationary state, that is 0.75% lower than the Taylor-type model prediction of 7.17% and 0.15% lower than the thematically augmented-Taylor-type model, and to 7.59% in an inflationary state, that is

0.42% higher than the Taylor-type model prediction of 7.17% and 0.03% lower than the thematically augmented-Taylor-type model.

2.5. Discussion

Financial stability does impact monetary policy regardless of whether it “should.”

This study finds that in normal times, the Fed monetary policy-making process

systematically includes factors other than standard Taylor rule variables of inflation and

slack, principally discussions of financial stability, but also discussions of slack, inflation,

foreign activity and money supply among others. The results show that the discussion-

based thematic model with financial stability dominates Taylor-type rules during normal

times. The results also show that in zero lower bound conditions, a tri-mandate policy

model with financial stability dominates Taylor-type rules. These findings are positive:

they unequivocally claim that financial stability has mattered to the Fed in setting

monetary policy and continues to matter critically in monetary policy during the

conditions of zero lower bound.

2.5.1. Counterarguments

This study revives the old debate about whether financial system conditions

should be considered in monetary policy. There are at least four substantive

counterarguments to our claims.

First, there is an argument of monetary excesses. Taylor and Williams (2011)

(TW) contend that the aspiration of simple rules is to avoid mistakes due to pursuit of too many objectives. Against this, Taylor (1993: 197) maintains that “there will be episodes where monetary policy will need to be adjusted to deal with special factors… The Fed would need more than a simple policy rule as a guide in such cases.” Bernanke (2015,

April 28) states that given the economy’s complex dynamics, the making of monetary policy cannot be trusted to a simple rule. Inclusion of additional factors becomes critically important when the economy enters a prolonged period of cyclical displacement or undergoes a structural change. At such times, the use of simple Taylor rules produces conflicting policy recommendations that are highly sensitive to the measurement errors in the Taylor-rule variables induced by the cyclically-displaced or structurally-changed variables. When the errors produced by Taylor-type rule become systematic, the rule

becomes a biased guide to policy (Bosler et al., 2014).

Second, there is an argument of exogenous or random influences from additional

factors (TW, 2011). This argument rests on the assumption that fixing reactions in the

Taylor rule captures monetary policy systematically and without bias. This assumption is

effectively challenged by vast empirical literature (see Section 3.2). Thus, our study is

consistent with the empirical critiques of Taylor rule (e.g. Kozicki, 1999) that

demonstrate its poor fit and sensitivity to measurement issues in various regimes. In

response to critique of random influences, we provide empirical evidence that

a) deviations of monetary policy from Taylor-type rules are systematic and can be

consistently explained by the principal inclusion of financial stability in both

normal times and zero lower bound conditions.

b) far from being idiosyncratic or random, the FOMC discussions are systematically

(Bernanke, 2015, April 28) influencing the ensuing monetary policy (Table 4).

Third, there is an argument that financial conditions need to be considered only ad

hoc, when they loom large or to the extent they provide explanatory power in forecasting

inflationary or deflationary conditions (Bernanke and Gertler, 1999) (BG). BG (1999),

therefore, maintain that policymakers should consider price stability and financial stability to be mutually consistent and possible to address “within a unified policy framework.” Clearly this view does not apply in the special conditions of financial instability, specifically the 2007-2009 crisis, when low inflation has been accompanied by a prolonged rise in financial system stress. A unified monetary policy framework that is responsive to inflation alone is simply insufficient for controlling the financial stability objective, when it diverges from the price stability perspective. While BG (1999) is broadly accepted in normal conditions, there are dissents and corrections for special conditions. Bryan et al., (2001) find that omission of financial factors introduces a systematic and tangible downward bias in the inflation measure that is expected to grow

in times of distress. Similarly, Semmler (2005) finds that monetary policy distortion due

to the omission of financial conditions becomes particularly pronounced in the vicinity of

zero lower bound. Tetlow (2006) argues that financial factors are state variables in the

macroeconomic system and finds that ignoring them systematically can be costly when

changes in the financial factors are large. Bernanke (2015, April 7) states that “more

research on this issue is needed” and admits the normative “possibility that monetary

policy decisions should also take into account risks to financial stability.”

Fourth, there is an argument of trivial gains from inclusion of financial stability

(TW, 2011). In addition to restating the above contentions, TW rely on the simulation

outcomes of a macroeconomic model, where financial factors influence monetary policy

only indirectly through their influence on output and inflation, which are already captured

by a Taylor-type rule. This argument suffers from its reliance on a predetermined set of

model inputs and is vulnerable to the tests of uncertainty and dynamic change. Fuhrer

(1997) finds that monetary policy reaction functions are regime-dependent. Dudley

(2012) emphasizes that a change in the dynamic relationships between financial

conditions, monetary policy, and the economy—whether cyclical or structural—can

induce large costs for ignoring financial conditions. Brainard (1967) shows that optimal

policy under uncertainty differs “significantly from optimal policy in a world of

certainty.” An ultimate answer to the trivial gains argument is rather simple: we show

that the inclusion of financial stability significantly improves explanation of monetary

policy overall, in-sample, out-of-sample, and in every sampled regime.

2.5.2. Methodological limitations

This study examines positive questions related to explanatory models of actual

monetary policy. As such, it does not aim to address the normative question of optimal

monetary policy rule. To the extent that FOMC discussions reflect monetary policy

feedback, the frequencies of thematic discussions may include both current observations

and expectations of future conditions. This is particularly relevant under a forecast-based

monetary policy regime54. Thus, direct use of the thematic frequencies in estimation of the intentions function may be subject to bias, if the content analysis does not differentiate between thematic observations and thematic expectations. As a remedy,

future research should add an additional coding dimension that would distinguish between observations and expectations for each recording unit. This would enable a

54 See Bernanke (2004) discussion of two types of central bank monetary policies: feedback policies and forecast-based policies. Under a feedback policy regime, “the central bank's policy instrument…is closely linked to the behavior of a relatively small number of macroeconomic variables, variables that either are directly observable … or can be estimated from current information.” By contrast, “under a forecast-based policy regime, policymakers must predict how the economy is likely to respond in the medium term—say, over the next six to eight quarters—to alternative plans for monetary policy.” 85

better differentiation of thematic frequencies relevant for the estimation of the intentions function and those appropriate for the estimation of the impact function.

Critically, Mittermayer and Knolmayer (2006) point out that content analysis will not pick up numerical information and cannot account for market expectations without developing a rule-based model. They also criticize “word” as a recording unit, because of the flawed assumption that frequency of word occurrence conveys the relative importance of that word. Their critique may be relevant to the phrase and paragraph recording units used in this study since each relies upon the equivalence of a theme’s frequency with the importance of that theme.

2.5.3. Implications

This chapter contributes to the monetary policy literature by demonstrating that financial stability considerations matter in the setting of US monetary policy. By analyzing the FOMC monetary policy discussions from 1990 to 2012, this chapter finds that financial stability considerations consistently influence Fed’s monetary policy. This chapter also meaningfully contributes to the financial stability literature by analyzing factors of financial stability considered in the discussions of monetary policy. The results show these factors are dominated by the financial market concerns and have over time been supplemented by a growing set of considerations of specific financial instruments capturing the evolution and transformation of the US financial system. From the methodological viewpoint, the chapter contributes to the literature on content analysis of monetary policy by demonstrating an approach to systematically validate the analysis of text. Here, the results support the existence of a strong relationship between financial

stability factors and US financial stress. This result makes reciprocal substitution possible as a proxy for financial stability.

The findings lead to two interesting monetary policy models that incorporate the policymaking process through the FOMC discussions: the thematic and tri-mandate models of monetary policy. Both of these models include financial stability explicitly.

The thematic model is shown to provide superior explanatory power in normal conditions, while the tri-mandate model dominates in the zero lower bound conditions.

These models suggest that in normal times, the policymakers can improve on the Taylor- type rule benchmark by incorporating adjustments based on relative frequencies of thematic discussions. In zero lower bound, the policymakers can improve on the thematic model simply by including observations of gaps in financial stability and in the secondary measure of slack and by dropping the discussion variables for foreign activity and money supply.

Both models guide policymakers through transformations in the US economy and financial system. As the US economy changes over time, FOMC discussions continue to influence Fed’s monetary policy directives. Specifically, as circumstances change, Fed’s policymakers’ emphasis on certain themes adjusts monetary policy relative to the Taylor- type guideline with its parsimonious set of policy factors. In both models, significant shifts in the interaction of the economic factors are reflected in the FOMC discussions and can be observed as regime changes. The power of both models to explain monetary policy beyond the Taylor-type rules indicates that the thematic content of FOMC debates influences Fed’s adjustments in the monetary policy instrument relative to the Taylor- type projections. In the case of the tri-mandate rule, the FOMC discussions of inflation,

slack, and financial stability serve as important moderators of the respective policy goals.

As the financial system undergoes changes, the Fed spends more or less time talking about these transformations with varying impact on rate adjustments. Thus, the themes

are powerful for navigating monetary policy through changing conditions.

In summary for both models, the study shows that beyond the core Taylor-type

goals of controlling inflation and economic slack, considerations of financial stability are

included continuously. The transformation of FOMC discussions of economic conditions

also continuously improves the explanation of monetary policy beyond the Taylor-type

variables. The FOMC discussions suggest that monetary policy reevaluates the relative

importance of themes: both interweaving their composition in response to observed

conditions and reacting to their juxtapositions. In this process new meanings evolve.

Thus, understanding of policy decisions requires an appreciation of the dynamic work of the Fed for making meaning and taking action in an environment of evolution, uncertainty, and change.

55 Chapter 3: How to Evaluate Measures of Adverse Financial Conditions?

Timely identification and anticipation of adverse conditions in the financial system are critical for macroprudential policy. However, there is no consensus on how to evaluate the quality of systemic measures. This chapter provides a framework to compare measures of systemic conditions. We illustrate the proposed tests with a case study of US measures from 1976 to 2013. We find that measures which include information from multiple markets improve identification of critical system states. However, tested measures show limited capacity to anticipate critical episodes.

3.1. Introduction

The complexity of financial system continues to challenge supervisors and policymakers.56 Such challenges include not only concerns with the safety and soundness of individual institutions, they also focus on systemwide risks. Policymakers agree that the supervision of systemwide risks must recognize changes in the system. Instances of rapid financial system transformations are highlighted in Figure 1. Implementations of dynamic macroprudential policy have been suggested by the Bank of England (BoE,

2011) and the IMF (Lim et al., 2011).57 To efficiently implement prudential policies, regulators need measures that are able to identify and anticipate adverse conditions in the

55 An updated version of this chapter is forthcoming as Oet et al., (2016b). 56 The concept of the economy as a complex and adaptive system was pioneered by Holland (1975, 1988) in his work on adaptive nonlinear networks. Brock and Hommes (1997, 1998) study financial markets as adaptive belief systems. Hommes (2001) extends this approach to markets as nonlinear adaptive evolutionary systems. See Arthur (1995) and Farmer and Lo (1999) for an analysis of heterogeneity in financial markets, Hollingsworth et al. (2005) for the socioeconomic implications and Judge (2012) for analysis of complexity caused by the fragmentation of financial markets. 57 Similarly, the Basel Accords continually enhance the flexibility of banking regulation to keep pace with financial system changes. 89

financial system (Borio, 2003). The evaluation of these measures is a problem we confront in this study.

Figure 13 Percentage of Total US Financial Assets Held by Financial Intermediaries (1952‒ 2013)

Note: Vertical bars highlight episodes of change in relative ranking of financial sectors by total assets. Source: Board of Governors of the Federal Reserve System, 2014.

Multiple coincident and early-warning measures have recently been developed to assess systemwide risks.58 Substantial research effort has focused on the problem of evaluating early-warning measures (Edison, 2003; Davis and Karim, 2008; Drehmann and Juselius, 2014; Holopainen and Sarlin, 2015). However, few papers address the practical issue of evaluating coincident measures and how these measures might be used by policymakers.59 Therefore, the following questions are addressed in this chapter: First,

58 These include measures intended to continually monitor the cyclical buildup of widespread imbalances, as well as early-warning indicators of exuberance, excessive change, and misalignments. Overviews are given by Davis and Karim (2008), Gramlich et al. (2010), Babecký et al. (2013), and Holopainen and Sarlin (2015). 59 Kliesen et al. (2012) survey the composition of available coincident measures. Gallegati (2014) applies wavelet analysis to compare the early-warning properties of several coincident measures. 90

how can the suitability of systemic measures be assessed? Second, what are the empirical findings from such evaluation?

This chapter proposes a methodology to evaluate both coincident and early warning measures of systemic conditions. We apply this method in a case study of US data from

1976 to 2013. We show how the strength and consistency of association between volatility and alternative measures of US financial conditions varies. However, few of the measures considered provide reliable early-warning out of sample. Hence the available US data appears more suitable for monitoring adverse conditions than for anticipating them.

The rest of this chapter is organized as follows. Section 3.2 traces the development of evaluation methods for the binary classification problem across the literature. Section 3.3 proposes three methodological contributions to support the assessment of systemic conditions measures. First, multidimensional signal extraction enables the search for optimal systemic measurement. Second, the classification of system states is improved by considering the severity, persistence, and pervasiveness of volatility. Third, an information value statistic extends ability to assess the quality of systemic measures across a diverse range of system states. Section 3.4 applies the proposed evaluation framework to US systemic measures from 1976 to 2013. In this case study, we confirm that measures based on multiple markets identify critical states better than more narrowly constructed alternatives. In addition, we find that considerations of level and change in system conditions are relevant to policymakers’ decisions. Section

3.5 concludes with a discussion of this study’s implications. Appendix 4 provides robustness testing at multiple frequencies and across a wider subsample.

3.2. Literature review

The literature considers many measures of financial system conditions with little consensus. The measures can be generalized in two types. Coincident measures seek to identify current system conditions. Early-warning measures seek to anticipate potentially adverse conditions. Coincident measures include financial condition indexes (FCIs) and financial stress indexes (FSIs). FCIs assess the impact of deviations of asset prices from long-term trends (Bordo et al., 2000; Swiston, 2008; inter alia). The notion of FSIs varies widely from systemic excitation (Korinek, 2011) to measurement of the demand-supply imbalance for financial goods (Lo Duca and Peltonen, 2013; Borio and Lowe, 2002), to force exerted on economic agents by changing expectations (Illing and Liu, 2006). The lack of consensus is particularly evident in these coincident measures, where both policy goals and conceptual definitions vary widely. Policy goals include inter alia identification of adverse conditions (Carlson et al., 2012), differentiation from cyclical activity (Hatzius et al., 2010; Brave and Butters, 2012), guiding monetary policy (Hakkio and Keeton, 2009), and detection of system instability (Holló et al., 2012). Early-warning measures (EWMs) include macroeconomic and institutional indicators of exuberance, excessive changes, and overall build-up of imbalances. Macroeconomic EWMs detail the systemwide imbalances which lead the financial cycle toward crises (Kaminsky et al.,

1998; Borio and Drehmann, 2009; Borio, 2014; inter alia). Institutional EWMs specify leading institutional imbalances to explain the build-up of macroeconomic stress

(Hanschel and Monnin, 2005; Dridi et al., 2012; Oet et al., 2013).

Recent literature in economics (Rosser, 2013; Elsner et al., 2014), finance

(Mantegna and Stanley, 1999), and social sciences (Scott and Davis, 2015; Dopfer and

Potts, 2007; Young, 2001; Saviotti and Metcalfe, 1991) agrees that the notions of critical states, crises, instability, and distress are multidimensional concepts.60 Classic literature

on policy evaluation provides a range of means for addressing policymakers’ uncertainty:

adaptively (Lucas, 1976), incorporating the behavior of economic agents (Lucas, 1976;

Sabatier, 1991), modeling it as a continuous dynamic process (Sabatier, 1991), and considering the policymakers loss function (Brock et al., 2003), with the corresponding

and ongoing (Leeper and Sargent, 2003) robust analysis of the multidimensional model

uncertainty space. Despite this theoretical consensus, empirical measurement of financial

system conditions continues to be treated by means of binary classification (Kaminsky et

al, 1998; Edison, 2003). Recent evaluation studies have followed the suggestions of

Brock et al. (2003) and Leeper and Sargent (2003) to improve traditional binary

classification with a policymakers’ loss function (Alessi and Detken, 2011; Sarlin, 2013)

and the robust analysis of measurement uncertainty space (Holopainen and Sarlin, 2015).

However, the gap between the multidimensional systemic conditions and binary

classification of their measures remains to be addressed with a more general classification

approach.

In any classification, the measures are calibrated against the event variable of

observable critical states. Under binary classification, a unidimensional event variable is

constructed. Typically, this involves either signal extraction (Alessi and Detken, 2011),

discrete binary choice methods (Berg and Pattillo, 1999; Andreou et al., 2009;

Gerdesmeier et al., 2010), or a range of machine learning methods (Holopainen and

60 Interested readers are also referred to seminal contributions by Simon (1957, 1962, 1979, 1991), Thompson (1967), Levins (1968), and Mohr (1982). 93

Sarlin, 2015). Signaling extracts a binary event data point whenever a single reference time series exceeds a predetermined threshold. For example, Kaminsky et al. (1998) define currency crises to occur when their market-pressure index exceeds its mean with more than three standard deviations. Lo Duca and Peltonen (2013) identify systemic events when their financial stress index is above the 90th country-specific percentile. By contrast, discrete choice models apply thresholds to extract an estimated probability, as do Holopainen and Sarlin (2015) with machine learning. In prior studies, the event- variable construction has been operationalized by multiple means. Commonly, a dataset of observed crises is used (Laeven and Valencia, 2013; Holló et al., 2012). To remedy the problem of very few crisis observations in a particular system,61 researchers have also

used recessions (Hatzius et al., 2010), surveys (Illing and Liu, 2006), policy interventions

(Carlson et al., 2012), episodes of distress (Oet et al., 2013), volatility-based binary benchmarks (Oet et al., 2015b), and news (Rönnqvist and Sarlin, 2015).

Traditionally, binary classifiers are evaluated using a two-way contingency table.

This table classifies predictors by the number of four possible matches: true positive,

false positive (a Type I error), false negative (a Type II error), and true negative

(Kaminsky and Reinhart, 1999). Kaminsky et al. (1998) and Borio and Lowe (2002)

summarize this analysis with a noise-to-signal ratio (NTSR), which is a fraction of Type

II errors to one minus Type I errors. An NTSR lower than one indicates the measure is

beneficial (Kaminsky et al., 1998). Recent contributions introduce policymakers’ loss

61 For example, the list of banking crises proposed by Laeven and Valencia (2013) finds only two US episodes: 1970-1992 and 2013 (the savings and loan crisis in 1988, and the financial crisis starting in 2007). The approach can also be criticized for its focus on systemic banking crises. This inherently misses critical disturbances in the broader financial system. 94

function as a parameterized modification of the NTSR statistic. The loss-function parameters reveal policymakers’ loss aversion to misclassification (Demirgüç-Kunt and

Detragiache, 2000; Alessi and Detken, 2011; Alessi and Detken, 2014) and the costs of these errors (Bussiere and Fratzscher, 2008; Sarlin, 2013).62

Our review of the development of evaluation methods for financial system conditions would be incomplete if we did not note relevant developments in information science, empirical macroeconomics, and empirical finance. Collectively, these developments extend the means to evaluate measures of multidimensional financial system conditions.

Recent developments in information science show that partitioning the binary event variable into a multidimensional set of critical states enables the search for an optimal measurement algorithm. This literature is founded on analyzing information as a measurable quantity that differentiates one series of signals from another (Shannon and

Weaver, 1949). Information signals are transmitted by channels, generally with noise, and subject to maximum channel capacity. Thus, as additional information channels are introduced, the number of information signals (e.g., about critical states in the system)

can be expected to increase (Shannon, 1949). Wolpert and Macready (1995, 1997) show

that it is impossible to differentiate among alternative algorithms that search for and

optimize this type of signal function (e.g., crises or their costs). These findings are known

as no-free-lunch (NFL) theorems. Subsequent mathematical research (Streeter, 2003; Igel

and Toussaint; 2005) proves that NFL does not hold when the probability distribution of

62 Current literature debates which of the two approaches to policymakers’ loss function should be preferred. See Section 4 for empirical findings and Section 5 for commentary. 95

the signal function is variant (e.g., under different observation frequencies). These developments substantiate the idea that multiple channels of information (e.g., critical states in various markets) vary the probability distribution of critical outcomes with observation frequency. To generalize the evaluation of classifiers, the information- science literature introduces the information value (IV) statistic (Kullback, 1959). IV is designed to assess the quality of classification across the series by dividing it into a series of bins and quantifying the noise-to-signal properties of each. The IV statistic has been used in multinomial discrete choice models, such as credit risk scorecards, where a variety of information channels with borrower characteristics serve as classification inputs (Siddiqi, 2006).

Empirical findings in finance and macroeconomics both indicate continual changes in severity, persistence, and pervasiveness of volatility in financial markets. The macroeconomic literature contributes to the measurement of systemic conditions by building on its longstanding interest in the properties of business and financial cycles, from the classic studies of Wallis and Moore (1941), Moore (1954, 1967), and Zarnowitz

(1985) to the current contributions of Stock and Watson (2002). This stream of literature describes the cyclical properties of measures along the dimensions of severity, persistence over time, and pervasiveness across underlying system partitions (Banerji,

1999).63 Empirical-finance findings in market-volatility clustering (Fama and French,

1989; Schwert, 1989; Shiller, 1989) also contribute to the modeling of system conditions.

Fama and French (1989: 23) find that spread-based patterns of “common stocks and long-

term bonds contain a term or maturity premium that has a clear business-cycle pattern

63 Alternatively, these cyclical properties are studied as depth, duration, and diffusion (e.g. Moore, 1967). 96

(low near peaks, high near troughs).” They also find that spreads “contain a risk premium that is related to longer-term aspects of business conditions. The variation through time in this premium is stronger for low-grade bonds than for high-grade bonds and stronger for stocks than for bonds.” Shiller (1989: 1) finds that “Financial market prices, prices of stocks, bonds, foreign exchange, and other investment assets, have shown striking changes in volatility through time. For each of these kinds of assets there are years when prices show enormous unpredictable movements from day to day or month to month, and there are years of stable, uneventful markets.” Thus, the recent empirical-finance literature uses the observed linkage of volatility-clustering patterns and conditions in financial markets to explain the dynamic processes in market conditions (Lux, 2009). As a result, policymakers are particularly interested in monitoring market volatility patterns for changes in the underlying systemic conditions (Oet et al., 2015a). In this context, the policy literature recognizes that policy actions may be considered both from level and change perspectives (Carlstrom and Fuerst, 2014). Under the level view, policymakers consider how close the system conditions are to those under which policy action is warranted. Under the change view, policymakers may also consider how fast these system conditions are changing.

3.3. Methodology

This section presents a methodological framework for evaluating measures of financial system conditions. We begin by introducing evaluations as a classification problem in the policy context. We then discuss how designated tests may help supervisors select between competing financial conditions measures. Finally, we discuss how standard time-series methods are used to forecast coincident series.

3.3.1. Classification problem

Under binary classification, evaluation involves a comparison of measures of systemic conditions , with the critical states of the system . When a crisis occurs,

policy is either implemented to the benefit of the system (true positive, TP) or not

implemented with detrimental effect (false negative, FN). If a crisis does not occur, policymakers can implement an unnecessary and burdensome policy (false positive, FP) or efficiently abstain from implementing policy (true negative, TN). We assume that the costs and are non-negative while and are non-positive costs (Elkan,

2001; Sarlin, 2013). The cost of not implementing policy in times of crisis is

, and the cost of implementing policy when there is no crisis is . We

denote by the unconditional probability that there is a crisis and

1 the unconditional probability that no crisis will occur.

The use of binary classification as an approach to evaluate systemic measures can,

however, be criticized. First, it is conceptually inappropriate to evaluate measures of a

continuous phenomenon with binary classification, as it involves a loss of information.

Yet, it is worth noting that these models are most often devised to steer policy based upon

the ad hoc judgment of supervisors and policymakers, as opposed to policy set by

predetermined continuous rules. Hence, the fact that we are concerned with the

identification of events to steer discretionary policy already in itself imposes specific

needs on the evaluation tasks. Second, the no free lunch theorems of statistical inference

(NFL) (Wolpert and Macready, 1995, 1997) state that when the probability distribution of

objective function (here critical states) is invariant for all alternative measurement

algorithms, the computational cost of inference is the same for all alternative measures. 98

From this standpoint, a variability in the critical states is desirable as it supports the existence of an optimal measurement of the critical states. Our proposed method adds variance to the distribution of critical states by introducing additional system partitions with distinct volatility patterns and considering their cyclical properties. This approach follows literature in empirical finance (Fama and French, 1989; Schwert, 1989; Shiller,

1989) and empirical macroeconomics (Moore, 1954, 1967; Stock and Watson, 2002).

Because we wish to generalize the problem of classification, we propose the extension of the invariant probability distribution of critical states into a more informative set of critical states of the markets. We generalize the evaluation of classifiers with the information value (IV) statistic (Kullback, 1959) by assessing the quality of classification across the series using a division into a series of bins and quantifying the noise-to-signal properties of each. Moreover, we allow the costs of different types of errors to vary as we make use of the so-called Usefulness measures.64 Accordingly, we compare alternative measures through a three-step algorithm which involves 1) defining a multi-dimensional measure of systemic conditions, 2) comparison of identification properties, and 3) comparison of early warning properties.

3.3.2. Multi-dimensional signaling

In the first step, we extend the one-dimensional critical states series as multidimensional patterns of market signals of different severity, persistence, and pervasiveness.65 These patterns are variant at different observation frequencies.

64 This extension avoids the NFL problem and makes meaningful the search for an optimal systemic measurement algorithm. 65 Business cycle literature has historically referred to these three dimensions as depth, duration, and diffusion (Moore, 1954, 1967; Zarnowitz, 1985). 99

Therefore, the construction of , captures several characteristics of crisis. We first

determine whether to focus on an extreme level or a rapid change in systemic conditions

, (∈,). The former will identify the beginning and end of crisis while the

latter is more useful for detecting the onset of a crisis. The severity of systemic conditions

required is given by , in (36) and (37). To identify systemic crises we look for

persistence over consecutive periods in one market or pervasiveness across of the

financial system markets in (37).

, , (35) 1 ,, ,,, (36) 0 1 ,, , ,,, (37) 0 1 ,,, 1 ,,, , (38) 0

Next, a pattern of systemic conditions (e.g., patterns of volatility in the case

study) is optimally matched with the set of known one-dimensional critical states (e.g.,

interventions in the case study). The settings for severity ,, persistence , and

pervasiveness maximize the alignment with an observable one-dimensional crisis series. Optimal matching can be accomplished by standard nonparametric statistics such as and Hamming distance (Hamming, 1950).66

3.3.3. Comparison of identification properties

66 Hamming distance measures the number of observations that are different between two time series of equal length. 100

In the second step, we compare the identification properties for alternatives measures of systemic conditions against the multi-dimensional critical states using three statistics: noise-to-signal ratio (, relative usefulness , and information value

(. In the setting above, accurately encodes the occurrence and absence of crisis events. The measures support supervisors’ policy decisions by providing distinct

perspectives of the financial system. We determine how closely the conditions described

by match a history of critical states by using NTSR, IV, and collectively.

The noise to signal ratio for measure is defined as . The Type I

error indicates the proportion of crisis observations which are falsely classified as non-

crisis (1 0|1). Type II error refers to the proportion of non-

crisis periods where a crisis was mistakenly signaled (2 1|

0).

Information Value (IV) statistic has been proposed when choosing between

several regressors (Kullback, 1959; Siddiqi, 2006). Observations , are sorted and

distributed into bins ( 1,2, … , ) delimited by the 1 quantiles of measure . IV

looks at the balance between the fraction of good and bad predictions in each bin (good

and bad respectively) following equations (39)-(41).

∑ ∈, ∗ 1, 1 / (39)

∑ ∈1 , , 1 / (40)

∑ ln (41)

101

If the measure of conditions contains no relevant information, we would expect to see the same proportion of good and bad predictions in each bin leading to an information value of zero. As or approach zero, becomes very large. This makes IV a somewhat unstable metric. We select the number of bins in order to minimize the

number of measures for which the IV becomes undefined. Siddiqi (2006) provides a

guide whereby an IV of less than 0.1 is weak, IV from 0.1 to 0.3 is average, and IV from

0.3 to 0.5 is strong.

The IV and NTSR metrics do not consider the policymakers’ cost of

misidentifying critical outcomes. This offers an opportunity for improvement. Sarlin

(2013) defines the Absolute and Relative Usefulness of measure i according to (42) and

(43), respectively. represents the policymaker’s loss function (Sarlin, 2013). The

variable combines the costs , , , and into a single parameter. Specifically,

is the fraction of total costs incurred when the policymaker does not implement

policy and a crisis occurs. This construction highlights measures that minimize .

, 1 (42)

(43) ,

1 (44)

To utilize the above tests, we derive the signals from continuous indicators ,

following (45) (leveraging the notation from (35)-(37)). Crisis signals are generated when

the imbalance , for series (or the differenced imbalance) is greater than the

threshold (respectively ). The thresholds and are chosen to provide

the best match between and . 102

,, ,,, (45)

Kaminsky et al. (1998) select the thresholds for each indicator in their study (,

and , ) to minimize NTSR. However, it is generally possible to achieve a NTSR of

zero by eliminating Type II error. A sufficiently high threshold will eliminate Type II

error by achieving 0. This approach will work so long as the Type I error is less

than one, which requires only the correct identification of a single critical observation

( 0). Therefore, thresholds chosen to minimize the NTSR will focus on Type II

error at the expense of Type I error.

To achieve satisfactory IV, the measure must avoid excessive errors in each

bin. Both Type I and Type II errors cause deviation from an IV of 0.5 (which we consider

to be optimal). Therefore, selecting the thresholds , to minimize deviations of IV from

0.5 introduces less bias.

| | min 0.5 (46) ,

An alternative which incorporates the cost of Type I and Type II error is to select

and thresholds , to maximize the Relative Usefulness. Varying will determine which measures have value for differing relative cost of Type I error versus Type II

error, assuming that the policy maker is risk neutral.

max (47) ,,

The NTSR considers both Type I and II errors but it is potentially subject to

manipulation. The IV looks for consistent identification across bins. The Usefulness test considers the cost of Type I versus Type II errors. These tests allow us to compare

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against from different and complementary perspectives. Therefore, optimizing a single test we consider the remaining perspectives for supplementary evaluation.

3.3.4. Comparison of early warning properties

In the third step, comparison of early warning properties of the alternative measures can be established using standard methods of using time series analysis (Box-

Jenkins, 1970; Johansen, 1995). These time-series tests go beyond the above classification approach in predicting a window of prior adverse conditions.

Coincident measures can provide useful information for the purpose of disclosure and fast acting policies. However, the deployment of slower policies generally requires more time (Borio, 2003). Therefore, evaluation of information quality of systemic measures also calls for testing their ability to provide an early warning of adverse systemic developments. A relevant question is whether policymakers can produce useful near-term forecasts of systemic conditions using only coincident measures. To this end, the evaluation of early warning properties can consider the autoregressive properties of coincident measures. The individual measures are analyzed using the Box-Jenkins (1970) methodology. For each measure, several variations of the ARIMA (p,d,q) model are tested, given by equation (48):

Δ , ∑ Δ , , ∑ , (48).

The difference operator Δ yields the time series differenced times. Where appropriate, GARCH (p,q) methodology can be implemented to account for heteroskedasticity. The final model is selected based on properties of the residuals

(stationarity, heteroskedasticity, autocorrelation, and partial autocorrelation), and the

Bayesian information criterion (BIC). 104

Johansen (1995) method is applied to test the properties of specific data and to

select a VEC model following equations (49). This approach allows consideration of

assorted perspectives of financial system conditions provided by individual measures and

provides insight into a mechanism for the development of critical systemic episodes.

Δ ∑ Δ + (49).

This approach can be applied to a collection of coincident measures ,, where

1,…, and is the 1 vector of coincident measures. We set c as an 1

constant vector, , , , and are matrices, and is the number of lags considered for each stress measure. The number of lagged terms to incorporate is determined through consideration of the BIC.

3.4. Case Study: Measures of US Systemic Conditions (1976-2014)

3.4.1. Data and sampling

In this section, we describe the case study dataset for US systemic conditions from 1976 to 2014 and our sampling strategy. The dataset consists of three types of data: the one-dimensional series of policymakers’ financial system interventions (intervention data), the critical states indicator (signal data), and the measures of US financial system conditions (measures data).

Intervention data: We assemble a binary time series of policymakers'

interventions from prior studies (Bordo et al., 2015; FRBNY, 2013; Babecký et al., 2013;

Laeven and Valencia, 2013; Carlson et al., 2012; Kaminsky and Reinhart, 1999).67 These include foreign exchange interventions in the 1970s and 1980s, the episodes of dramatic

67 Intervention data is available from the authors upon request. 105

change in monetary policy, and regulatory interventions into established functioning of the financial system and its institutions, (e.g. forbearance, stress testing, deregulation, policy changes applied during the recent Global Financial Crisis).

Multidimensional signal data: We construct a multidimensional signal that recognizes the diverse pattern of critical conditions within US financial system markets.

The signal is sensitized to three cyclical characteristics: severity of a particular market state, its persistence over time, and pervasiveness across system markets. Accordingly, we extract signals of volatility in individual financial markets, considering six markets

(following Oet et al., 2015a): equity, foreign exchange, short-term funding, securitization, and real estate. For the equity, foreign exchange, and real estate markets we consider the rolling 30-day standard deviation of daily returns on the S&P 500, the trade weighted dollar index, and a real estate index, respectively. For the funding, credit, and securitization markets we consider the rolling 90 day standard deviation of yields on three month treasury bills, corporate bonds, and mortgage backed securities.68 Figure 14

presents a subsample of comparisons of several systemic measures with the multi-

dimensional signals of critical states under both ∈, perspectives.

68 Specifically, we use the following series from Datastream: S&PCOMP (equity), US$CWMN (foreign exchange), RLESTUS (real estate), FRTBS3M (funding), LHCCORP (credit), and LHMNBCK (securitization). 106

Figure 14 Multidimensional Signal Compared to Several Measures of Adverse Systemic Conditions Panel A: Level perspective ∈, severity , 0.6 std, persistence , 5 months, pervasiveness , 2 markets.

Panel B: Different perspective ∈, severity , 0.6 std, persistence , 1 month, pervasiveness , 1 market.

Note: The figure shows several coincident measures of systemic conditions (CFSI, NFCI, CFNAI) at monthly frequency starting in July 1976 with the multidimensional signal of critical states shaded.

107

Measures data: Our dataset includes 32 published measures of US financial conditions, at various frequencies. Each measure belongs to one of three groups: FSIs,

FCIs, and EWMs (Table 7). The first group focuses on the measures of financial system

stress. These typically incorporate variables describing core markets and functions of the

financial system which are then aggregated using a variety of weighting methodologies.

The main sample includes six measures describing the National Financial Conditions

Index (NFCI) and seven measures describing the Cleveland Financial Stress Index

(CFSI). A second group of measures (FCIs) examines the state of the financial system conditions through a set of relevant macroeconomic activities. The main sample includes

7 measures describing the Chicago Fed National Activity index. EWMs describe system conditions through market expectations of systemic risk. By contrast, select EWMs become available starting in 2000 and are only considered in our robustness sample.

Sampling: We analyze the dataset in two samples. The main sample maximizes the available length of the sample starting in 1976, while the second, robustness, sample tests the broadest population of measures available starting in 2000. Accordingly the main sample (July 1976February 2014) consists of 20 monthly, 13 weekly, and 7 daily

series. The robustness sample (June 2000February 2014) consists of 32 monthly, 23

weekly, and 16 daily series. The main sample encompasses at least five full economic

cycles (following the NBER delineation of recession periods),69 including several well-

recognized critical episodes. Our sampling strategy balances the trade-off between the

number of critical observations in the main sample and the number of indicators in the

robustness sample. Thus, the main sample enhances insight to the identification and early

69 See http://www.nber.org/cycles/cyclesmain.html. 108

warning properties of available measures. The robustness sample enhances the cross- sectional comparison between various types of measures for limited number of joint observations.

Table 7 Summary Statistics for the Stress Series and Benchmark Volatility Series Calculated for Monthly Data between June 2000 and February of 2014 Start Date Source Name Minimum Maximum Mean Variance Skewness Kurtosis (Frequency) Panel 1: Systemic Stress Series CLEVELAND FINANCIAL STRESS INDEX (CFSI) 1/19/1970(D) AUTHORS 26.35 80.67 48.60 12.90 0.41 -0.75 CFSI: CREDIT SUBINDEX 1/19/1970(D) AUTHORS 5.09 17.11 9.77 2.58 0.29 -0.38 CFSI: REAL ESTATE SUBINDEX 1/19/1970(D) AUTHORS 0.47 10.48 4.48 2.93 0.62 -0.72 CFSI: FUNDING SUBINDEX 1/19/1970(D) AUTHORS 1.14 13.98 5.25 2.62 1.37 1.93 CFSI: EQUITY SUBINDEX 1/19/1970(D) AUTHORS 4.95 28.76 16.26 7.04 0.14 -1.35 CFSI: FOREIGN EXCHANGE SUBINDEX 1/19/1970(D) AUTHORS 1.71 13.48 7.48 2.42 -0.20 -0.08 CFSI: SECURITIZATION SUBINDEX 1/19/1970(D) AUTHORS 1.47 10.60 5.36 2.11 0.65 0.01 NATIONAL FINANCIAL CONDITIONS INDEX – CHICAGO (NFCI) 1/5/1973(W) FRED -0.88 2.71 -0.28 0.65 2.52 7.28 NFCI: NONFINANCIAL LEVERAGE SUBINDEX 1/5/1973(W) FRED -1.74 2.59 0.13 1.33 0.37 -0.97 NFCI: LEVERAGE SUBINDEX 1/5/1973(W) FRED -1.80 3.69 -0.10 0.97 1.46 3.45 NFCI: CREDIT SUBINDEX 1/5/1973(W) FRED -0.86 2.53 -0.17 0.64 2.00 4.88 NFCI: RISK SUBINDEX 1/5/1973(W) FRED -0.86 2.73 -0.31 0.64 2.67 8.20 ADJUSTED NFCI 1/5/1973(W) FRED -1.30 4.26 -0.20 0.77 2.34 7.87 KANSAS CITY FINANCIAL STRESS INDEX 2/1/1990(M) FRED -0.96 5.68 0.25 1.20 2.44 7.00 ST LOUIS FINANCIAL STRESS INDEX 12/31/1993(W) FRED -1.52 5.15 -0.04 1.13 1.91 5.30 BLOOMBERG FINANCIAL CONDITIONS INDEX 1/2/1990(D) BLOOMBERG -10.29 1.26 -0.62 1.65 -2.70 10.52 BLOOMBERG FINANCIAL CONDITIONS INDEX PLUS 1/2/1990(D) BLOOMBERG -8.97 1.95 -0.19 1.84 -1.95 5.28 GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 1/2/1981(D) BLOOMBERG 98.94 103.84 100.11 0.97 1.63 2.63 GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 4/6/1983(D) BLOOMBERG 98.08 103.36 100.11 0.88 0.89 2.35 Panel 2: Economic Activity Series CHICAGO FED NATIONAL ACTIVITY INDEX (CFNAI) 3/1/1967(M) FRED -4.44 0.91 -0.37 0.85 -2.29 6.35 CFNAI: DIFFUSION INDEX 3/1/1967(M) FRED -0.87 0.47 -0.12 0.33 -0.70 -0.34 CFNAI: PERSONAL CONSUMPTION AND HOUSING 3/1/1967(M) FRED -0.40 0.19 -0.08 0.17 -0.28 -1.36 CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 3/1/1967(M) FRED -1.63 0.35 -0.17 0.37 -1.84 3.98 CFNAI: PRODUCTION AND INCOME 3/1/1967(M) FRED -1.81 0.54 -0.09 0.34 -2.00 6.53 CFNAI: SALES, ORDERS, AND INVENTORIES 3/1/1967(M) FRED -0.66 0.36 -0.03 0.16 -1.52 3.55 PHILADELPHIA'S LEADING INDEX FOR THE US 1/31/1982(M) FRED -2.67 1.91 0.85 0.96 -1.86 3.68 Panel 3: Systemic Stress Series KAMAKURA'S TROUBLED COMPANY INDEX (OVER 1%) 1/30/1990(M) KAMAKURA 5.66 42.06 16.43 8.97 0.92 -0.28 KAMAKURA'S TROUBLED COMPANY INDEX (OVER 5%) 1/30/1990(M) KAMAKURA 0.70 18.09 5.15 4.40 1.18 0.24 KAMAKURA'S TROUBLED COMPANY INDEX (OVER 10%) 1/30/1990(M) KAMAKURA 0.15 9.90 2.37 2.53 1.39 0.79 KAMAKURA'S TROUBLED COMPANY INDEX (OVER 20%) 1/30/1990(M) KAMAKURA 0.02 4.70 0.83 1.10 1.68 1.89 SRISK FROM VLAB 6/2/2000(D) NYU VLAB 24225.81 916457.07 286418.80 244535.94 0.69 -0.77

3.4.2. Results

This section empirically assesses US measures of adverse conditions. First, we

compare measures of systemic conditions against the benchmark using the full sample

between 1976 and 2014.70 The second part tests the early warning effectiveness of the

measures.

Findings from multidimensional signaling: Figure 15 compares the set of US

policymakers’ financial system interventions (shown as tan vertical bars) against the set

70 Similar results for the robust sample between 2000 and 2014 are provided in the Appendix 4. 109

of extracted market volatility signals with particular severity, persistence, and pervasiveness (shown as gray vertical bars). Tables 8 and 9 show the results of matching the extracted signals of critical states against actual interventions.

We compare the extracted signals with the set of financial system interventions at monthly frequency under two policymakers’ perspectives: the level of system conditions and their changes. We find that the rules by which the signals optimally match the interventions vary with these perspectives. Considering the level of system conditions, the best match is produced at the severity of 0.6 standard deviations and persistence of five months or pervasiveness of two markets. In other words, at the severity level above the designate threshold (of 0.6 standard deviations), historically, policymakers intervened when this level of volatility was signaled in one market for five consecutive months, or when it was signaled across two markets simultaneously.

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Figure 15 Optimal Matching of Interventions and Multi-Dimensional Market Signals

Panel A: Level perspective ∈, severity , 0.6 std, persistence , 5 months, pervasiveness , 2 markets.

Panel B: Different perspective ∈, severity , 0.6 std, persistence , 1 month, pervasiveness , 1 market.

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Table 8 Comparison of Interventions and Multi-Dimensional Market Signals under Level Perspective Conditions Pervasiveness Persistence Severity Critical states Hamming Hamming % NTSR Level 1 1 1.1 30.0% 138 30.7% 43.1% Level 1 2 1.1 31.9% 138 30.7% 43.1% Level 2 2 0.8 31.9% 144 32.0% 47.1% Level 3 2 0.8 30.2% 145 32.4% 47.7% Level 4 2 0.8 30.0% 146 32.4% 48.4% Level 5 2 0.8 30.0% 146 32.4% 48.4% Level 6 2 0.8 30.0% 146 32.4% 48.4% Level 1 3 1.1 30.0% 138 30.7% 43.1% Level 2 3 0.7 30.0% 138 30.7% 43.1% Level 3 3 0.6 29.7% 140 31.1% 44.4% Level 4 3 0.6 31.4% 141 31.3% 45.0% Level 5 3 0.6 28.1% 144 32.0% 47.1% Level 6 3 0.6 28.1% 144 32.0% 47.1% Level 1 4 1.1 30.0% 138 30.7% 43.1% Level 2 4 0.6 31.9% 137 30.4% 42.8% Level 3 4 0.5 28.5% 135 30.0% 41.0% Level 4 4 0.4 28.7% 148 32.9% 50.0% Level 5 4 0.3 31.9% 148 32.9% 49.7% Level 6 4 0.3 31.6% 149 33.1% 50.4% Level 1 5 1.1 30.0% 138 30.7% 43.1% Level 2 5 0.6 29.7% 130 28.9% 38.4% Level 3 5 0.4 28.5% 138 30.7% 43.0% Level 4 5 0.3 27.2% 135 30.0% 40.7% Level 5 5 0.3 25.9% 135 30.0% 40.4% Level 6 5 0.2 25.7% 136 30.2% 41.1% Level 1 6 1.1 30.0% 138 30.7% 43.1% Level 2 6 0.5 31.4% 137 30.4% 42.8% Level 3 6 0.3 29.3% 130 28.9% 38.30% Level 4 6 0.2 31.6% 153 34.0% 53.2% Level 5 6 0.2 28.9% 146 32.4% 48.5% Level 6 6 0.2 28.5% 148 32.9% 50.0%

Table 9 Comparison of Interventions and Multi-Dimensional Market Signals under Difference Perspective Conditions Pervasiveness Persistence Severity Critical states Hamming Hamming % NTSR Change 1 1 0.6 26.4% 140 31.1% 44.1% Change 1 2 0.6 26.4% 140 31.1% 44.1% Change 2 2 0.3 33.5% 171 38.0% 66.9% Change 3 2 0.3 25.9% 159 35.3% 60.6% Change 4 2 0.3 23.2% 154 34.2% 56.9% Change 5 2 0.2 35.0% 169 37.6% 64.6% Change 6 2 0.2 34.8% 168 37.3% 63.9% Change 1 3 0.6 26.4% 140 31.1% 44.1% Change 2 3 0.3 27.8% 157 34.9% 57.6% Change 3 3 0.2 25.1% 154 34.2% 55.9% Change 4 3 0.1 31.2% 184 40.9% 84.0% Change 5 3 0.1 23.6% 168 37.3% 74.6% Change 6 3 0.1 22.2% 167 37.1% 75.5% Change 1 4 0.6 26.4% 140 31.1% 44.1% Change 2 4 0.3 26.8% 155 34.4% 56.1% Change 3 4 0.1 35.2% 191 42.4% 85.9% Change 4 4 0.1 21.1% 171 38.0% 82.4% Change 5 4 0 36.1% 191 42.4% 85.2% Change 6 4 0 30.6% 181 40.2% 81.9% Change 1 5 0.6 26.4% 140 31.1% 44.1% Change 2 5 0.3 26.2% 152 33.8% 53.7% Change 3 5 0.1 32.7% 184 40.9% 81.3% Change 4 5 0.1 17.5% 161 35.8% 71.3% Change 5 5 0 25.3% 179 39.8% 88.2% Change 6 5 0 17.9% 160 35.6% 70.6% Change 1 6 0.6 26.4% 140 31.1% 44.1% Change 2 6 0.3 26.2% 152 33.8% 53.7% Change 3 6 0.1 32.3% 184 40.9% 81.9% Change 4 6 0 39.0% 195 43.3% 86.8% Change 5 6 0 20.0% 172 38.2% 88.2% Change 6 6 0 11.2% 148 32.9% 55.2%

Another way that policymakers consider whether or not to intervene in a critical state is to consider the changes in the system conditions. They consider whether spikes in

112

the market, events transpiring quickly are sufficiently dire to warrant intervention. In these circumstances, they are less concerned with the level of conditions and more concerned with the dramatic changes in these conditions. To study the classification from this perspective, we consider under what set of changes in the financial system policy interventions may be best matched by changes in severity, persistence, and pervasiveness.

In our case study, it turns out that using the change in volatility perspective, the best match to critical states occurs from a dramatic (severity = 0.6 std) and rapid (persistence

= one period) change in a single market (pervasiveness = 1 market). As the results show, the change-based matching is quite noisy (Figure 15, Panel B; Table 9) and inferior to the consideration of levels of system conditions (Figure 15, Panel A; Table 8). This matching pattern still produces a substantial amount of noise and is sub-optimal by comparison with an intervention rule based on observation of volatility levels.

Our results suggest policymakers obtain a superior identification of the onset and duration of critical states by considering the level of system conditions. Consideration of changes in these conditions may be justified when policymakers are particularly worried about dramatic changes in system conditions and ask whether intervention is warranted.

However, consideration of changes produces a very noisy set of signals of critical states.

Overall, we find that US policymakers get a better match between intervention and volatility when they consider the pattern in the level of volatility than the pattern in the change of volatility. Put differently, based on the known set of US financial system interventions, we find that US policymakers appear less sensitive to rapid changes in volatility than they are to the pattern of sustained volatility—persistent across time or pervasive across markets.

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Findings from comparison of identification properties: Tables 10 and 11 report

the comparative signaling results for the tested coincident measures where thresholds ,

and , are selected to optimize the information value metric IV following equation

(46). These tables should display measures with comparable IV metrics. Therefore, we

evaluate the comparative advantage of these measures in terms of the Type I (T1) error rate, Type II (T2) error rate, NTSR, and Usefulness metrics.

Table 10 displays comparative metrics when signals of crisis are based upon the level of imbalances in the volatility and stress time series. Almost every measure of stress produces a NTSR below unity at every frequency indicating varying degrees of benefit from their use. These results indicate that NFCI and CFSI produce the highest Usefulness metrics and very low NTSRs, modestly surpassing CFNAI. In Table 11 we analyze the

differenced imbalances in an effort to focus on the onset of crises instead of their

duration. There is substantial variation in the comparative advantage of each measure.

Moreover, the three tests (NTSR, IV, and ) often provide conflicting direction.

114

Table 10 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV Name , µ TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i NATIONAL FINANCIAL CONDITIONS INDEX 1.78 0.5 35 0 323 94 0.73 0 0 0.51 0.27 2-i NFCI: CREDIT SUBINDEX 2 0.5 35 0 323 94 0.73 0 0 0.5 0.27 3-i NFCI: RISK SUBINDEX 1.61 0.7 35 1 322 94 0.73 0 0.01 0.5 0.27 4-i CLEVELAND FINANCIAL STRESS INDEX 1.36 0.7 24 5 318 105 0.81 0.02 0.08 0.5 0.17 5-i CFSI: SECURITIZATION MARKET 0.77 0.7 44 58 265 85 0.66 0.18 0.53 0.5 0.15 6-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.64 0.7 43 69 254 86 0.67 0.21 0.64 0.5 0.1 7-i CFSI: REAL ESTATE MARKET 1.17 0.7 16 44 279 113 0.88 0.14 1.1 0.5 -0.02 8-i CFSI: FOREIGN EXCHANGE MARKET 0.52 0.7 43 85 238 86 0.67 0.26 0.79 0.43 0.05 9-i CFSI: INTERBANK MARKET 0.52 0.7 60 61 262 69 0.53 0.19 0.41 0.42 0.26 10-i NFCI: LEVERAGE SUBINDEX 2 0.6 10 0 323 119 0.92 0 0 0.41 0.08 11-i CFSI: EQUITY MARKET 1.48 0.7 19 33 290 110 0.85 0.1 0.69 0.35 0.04 12-i CFSI: CREDIT MARKET 0.56 0.7 53 54 269 76 0.59 0.17 0.41 0.34 0.23 13-i ADJUSTED NFCI 0.5 0.7 53 55 268 76 0.59 0.17 0.41 0.27 0.23 14-ii CFNAI: DIFFUSION INDEX 0.5 0.7 61 63 260 68 0.53 0.2 0.41 0.44 0.26 15-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.5 0.7 52 60 263 77 0.6 0.19 0.46 0.29 0.2 16-ii CFNAI: THREE MONTH MOVING AVERAGE 2 0.7 15 1 322 114 0.88 0 0.03 0.28 0.11 17-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 2 0.7 16 1 322 113 0.88 0 0.02 0.27 0.12 18-ii CHICAGO FED NATIONAL ACTIVITY INDEX 2 0.7 17 0 323 112 0.87 0 0 0.26 0.13 19-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.5 0.7 54 44 279 75 0.58 0.14 0.33 0.2 0.27 20-ii CFNAI: PRODUCTION AND INCOME 0.5 0.7 45 38 285 84 0.65 0.12 0.34 0.18 0.22 Panel 2: Weekly (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 1.36 0.6 101 16 1351 504 0.83 0.01 0.07 0.51 0.15 2-i NFCI: RISK SUBINDEX 1.33 0.6 182 10 1357 423 0.7 0.01 0.02 0.5 0.29 3-i CFSI: SECURITIZATION MARKET 0.76 0.7 204 253 1114 401 0.66 0.19 0.55 0.5 0.13 4-i NATIONAL FINANCIAL CONDITIONS INDEX 1.81 0.6 139 4 1363 466 0.77 0 0.01 0.49 0.23 5-i CFSI: REAL ESTATE MARKET 1.33 0.7 60 171 1196 545 0.9 0.13 1.26 0.49 -0.06 6-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.7 0.7 162 234 1133 443 0.73 0.17 0.64 0.43 0.07 7-i CFSI: FOREIGN EXCHANGE MARKET 0.68 0.7 195 293 1074 410 0.68 0.21 0.66 0.41 0.09 8-i NFCI: LEVERAGE SUBINDEX 2 0.6 41 0 1367 564 0.93 0 0 0.4 0.07 9-i CFSI: INTERBANK MARKET 2 0.6 26 1 1366 579 0.96 0 0.02 0.4 0.04 10-i CFSI: EQUITY MARKET 0.53 0.7 215 257 1110 390 0.64 0.19 0.53 0.33 0.15 11-i CFSI: CREDIT MARKET 0.52 0.7 253 240 1127 352 0.58 0.18 0.42 0.29 0.22 12-i NFCI: CREDIT SUBINDEX 2 0.6 153 2 1365 452 0.75 0 0.01 0.28 0.25 13-i ADJUSTED NFCI 0.5 0.7 255 213 1154 350 0.58 0.16 0.37 0.2 0.25 Panel 3: Daily (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 1.33 0.7 471 87 6825 2484 0.84 0.01 0.08 0.5 0.15 2-i CFSI: REAL ESTATE MARKET 1.36 0.7 298 795 6117 2657 0.9 0.12 1.14 0.5 -0.01 3-i CFSI: SECURITIZATION MARKET 0.74 0.7 1044 1583 5329 1911 0.65 0.23 0.65 0.49 0.12 4-i CFSI: FOREIGN EXCHANGE MARKET 0.7 0.7 918 1566 5346 2037 0.69 0.23 0.73 0.48 0.08 5-i CFSI: INTERBANK MARKET 2 0.3 92 0 6912 2863 0.97 0 0 0.45 0.03 6-i CFSI: EQUITY MARKET 0.5 0.7 1027 1364 5548 1928 0.65 0.2 0.57 0.37 0.15 7-i CFSI: CREDIT MARKET 0.5 0.7 1245 1182 5730 1710 0.58 0.17 0.41 0.32 0.25 Note: Panel 1 uses data between July 1976 and February 2014. Panels 2 uses data between 6/12/1976 and 3/22/2014. Panels 3 uses data between 6/3/1976 and 3/28/2014.

115

Table 11 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV

Name , µ TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i CFSI: REAL ESTATE MARKET 0.06 0.7 46 88 239 78 0.63 0.27 0.73 0.58 0.07 2-i CFSI: CREDIT MARKET 0.14 0.7 43 90 237 81 0.65 0.28 0.79 0.54 0.04 3-i CFSI: EQUITY MARKET 0.18 0.7 43 93 234 81 0.65 0.28 0.82 0.54 0.03 4-i NFCI: CREDIT SUBINDEX 0.02 0.7 60 108 219 64 0.52 0.33 0.68 0.53 0.11 5-i CLEVELAND FINANCIAL STRESS INDEX 0.02 0.7 61 136 191 63 0.51 0.42 0.85 0.51 0.02 6-i NFCI: LEVERAGE SUBINDEX 0.08 0.7 36 87 240 88 0.71 0.27 0.92 0.51 -0.01 7-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.02 0.7 36 162 165 88 0.71 0.5 1.71 0.51 -0.27 8-i CFSI: SECURITIZATION MARKET 0.04 0.7 65 122 205 59 0.48 0.37 0.71 0.5 0.1 9-i ADJUSTED NFCI 0.04 0.7 56 137 190 68 0.55 0.42 0.93 0.5 -0.02 10-i CFSI: FOREIGN EXCHANGE MARKET 0.02 0.7 54 162 165 70 0.56 0.5 1.14 0.5 -0.12 11-i NATIONAL FINANCIAL CONDITIONS INDEX 0.04 0.7 52 80 247 72 0.58 0.24 0.58 0.48 0.14 12-i CFSI: INTERBANK MARKET 0 0.7 68 142 185 56 0.45 0.43 0.79 0.48 0.06 13-i NFCI: RISK SUBINDEX 0.04 0.7 53 81 246 71 0.57 0.25 0.58 0.47 0.15 14-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0 0.7 75 157 170 49 0.4 0.48 0.79 0.54 0.06 15-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.46 0.7 35 82 245 89 0.72 0.25 0.89 0.52 0 16-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.22 0.7 47 84 243 77 0.62 0.26 0.68 0.5 0.09 17-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.18 0.7 43 85 242 81 0.65 0.26 0.75 0.5 0.05 18-ii CFNAI: THREE MONTH MOVING AVERAGE 0.12 0.7 40 83 244 84 0.68 0.25 0.79 0.5 0.04 19-ii CFNAI: PRODUCTION AND INCOME 0.32 0.7 43 84 243 81 0.65 0.26 0.74 0.48 0.06 20-ii CFNAI: DIFFUSION INDEX 0.16 0.7 33 91 236 91 0.73 0.28 1.05 0.48 -0.05 Panel 2: Weekly (, 0.2 and 4 bins were used for IV) 1-i NFCI: LEVERAGE SUBINDEX 0.02 0.7 155 334 1093 389 0.72 0.23 0.82 0.64 0.02 2-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0 0.7 263 861 566 281 0.52 0.6 1.25 0.64 -0.19 3-i CFSI: FOREIGN EXCHANGE MARKET 0.04 0.7 188 537 890 356 0.65 0.38 1.09 0.56 -0.08 4-i CFSI: SECURITIZATION MARKET 0.04 0.7 194 422 1005 350 0.64 0.3 0.83 0.55 0.02 5-i CFSI: CREDIT MARKET 0.06 0.7 205 454 973 339 0.62 0.32 0.84 0.53 0.02 6-i CFSI: EQUITY MARKET 0.08 0.7 203 420 1007 341 0.63 0.29 0.79 0.52 0.04 7-i CFSI: INTERBANK MARKET 0.02 0.7 215 432 995 329 0.6 0.3 0.77 0.5 0.05 8-i CLEVELAND FINANCIAL STRESS INDEX 0.08 0.7 192 404 1023 352 0.65 0.28 0.8 0.5 0.03 9-i ADJUSTED NFCI 0.02 0.7 240 526 901 304 0.56 0.37 0.84 0.48 0.03 10-i CFSI: REAL ESTATE MARKET 0.04 0.7 133 266 1161 411 0.76 0.19 0.76 0.44 0.03 11-i NFCI: RISK SUBINDEX 0.02 0.7 168 236 1191 376 0.69 0.17 0.54 0.36 0.12 12-i NATIONAL FINANCIAL CONDITIONS INDEX 0.02 0.7 160 235 1192 384 0.71 0.16 0.56 0.32 0.11 13-i NFCI: CREDIT SUBINDEX 0.02 0.7 136 208 1219 408 0.75 0.15 0.58 0.26 0.09 Panel 3: Daily (, 0.1 and 4 bins were used for IV) 1-i CFSI: SECURITIZATION MARKET 0.06 0.8 313 1000 7127 1426 0.82 0.12 0.68 0.52 0.04 2-i CFSI: FOREIGN EXCHANGE MARKET 0.16 0.8 260 792 7335 1479 0.85 0.1 0.65 0.5 0.04 3-i CFSI: CREDIT MARKET 0.14 0.8 273 997 7130 1466 0.84 0.12 0.78 0.5 0.01 4-i CLEVELAND FINANCIAL STRESS INDEX 0.14 0.8 348 954 7173 1391 0.8 0.12 0.59 0.47 0.06 5-i CFSI: EQUITY MARKET 0.14 0.8 318 958 7169 1421 0.82 0.12 0.64 0.46 0.05 6-i CFSI: INTERBANK MARKET 0.06 0.8 240 947 7180 1499 0.86 0.12 0.84 0.46 0 7-i CFSI: REAL ESTATE MARKET 0.02 0.8 220 933 7194 1519 0.87 0.11 0.91 0.46 -0.01 Note: Panel 1 uses data between July 1976 and February 2014. Panels 2 uses data between 6/12/1976 and 3/22/2014. Panels 3 uses data between 6/3/1976 and 3/28/2014.

We determine , and , based upon maximization of the Usefulness following equation (47) in Tables 12 and 13, respectively. In Table 12, all measures consistently

achieve high Usefulness metrics and low NTSR. Interestingly, determining , based upon equation (47) yields unstable results across frequencies in Table 13. In both tables the IV is generally weak.

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Table 12 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on

Name , µ TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i NATIONAL FINANCIAL CONDITIONS INDEX 0.53 0.7 61 9 314 68 0.53 0.03 0.06 0.23 0.44 2-i NFCI: CREDIT SUBINDEX 0.58 0.7 63 18 305 66 0.51 0.06 0.11 0.35 0.43 3-i NFCI: RISK SUBINDEX 0.52 0.7 61 12 311 68 0.53 0.04 0.08 0.26 0.43 4-i CLEVELAND FINANCIAL STRESS INDEX 0.5 0.7 67 31 292 62 0.48 0.1 0.18 0.23 0.42 5-i NFCI: LEVERAGE SUBINDEX 0.59 0.7 55 26 297 74 0.57 0.08 0.19 0.19 0.34 6-i ADJUSTED NFCI 0.95 0.7 45 10 313 84 0.65 0.03 0.09 0 0.32 7-i CFSI: INTERBANK MARKET 0.55 0.7 58 54 269 71 0.55 0.17 0.37 0.34 0.27 8-i CFSI: CREDIT MARKET 0.7 0.7 51 41 282 78 0.6 0.13 0.32 0.2 0.26 9-i CFSI: SECURITIZATION MARKET 1.16 0.7 39 20 303 90 0.7 0.06 0.2 0.39 0.24 10-i CFSI: EQUITY MARKET 0.53 0.7 50 54 269 79 0.61 0.17 0.43 0.22 0.21 11-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.5 0.7 62 93 230 67 0.52 0.29 0.6 0.61 0.17 12-i CFSI: FOREIGN EXCHANGE MARKET 0.89 0.7 38 53 270 91 0.71 0.16 0.56 0.11 0.12 13-i CFSI: REAL ESTATE MARKET 0.5 0.7 51 99 224 78 0.6 0.31 0.78 0.82 0.07 14-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.5 0.7 58 36 287 71 0.55 0.11 0.25 0.18 0.33 15-ii CFNAI: DIFFUSION INDEX 0.71 0.7 54 37 286 75 0.58 0.11 0.27 0.2 0.3 16-ii CFNAI: THREE MONTH MOVING AVERAGE 0.5 0.7 47 26 297 82 0.64 0.08 0.22 0.19 0.28 17-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.85 0.7 41 15 308 88 0.68 0.05 0.15 0.15 0.27 18-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.53 0.7 53 41 282 76 0.59 0.13 0.31 0.18 0.27 19-ii CFNAI: PRODUCTION AND INCOME 0.8 0.7 42 23 300 87 0.67 0.07 0.22 0.07 0.25 20-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.73 0.7 49 51 272 80 0.62 0.16 0.42 0.22 0.21 Panel 2: Weekly (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.5 0.7 319 128 1239 286 0.47 0.09 0.18 0.11 0.42 2-i NATIONAL FINANCIAL CONDITIONS INDEX 0.5 0.6 267 38 1329 338 0.56 0.03 0.06 0.19 0.4 3-i NFCI: RISK SUBINDEX 0.53 0.6 272 41 1326 333 0.55 0.03 0.07 0.42 0.4 4-i NFCI: CREDIT SUBINDEX 0.56 0.7 277 82 1285 328 0.54 0.06 0.13 0.18 0.38 5-i NFCI: LEVERAGE SUBINDEX 0.5 0.7 253 132 1235 352 0.58 0.1 0.23 0.15 0.3 6-i ADJUSTED NFCI 0.92 0.6 205 44 1323 400 0.66 0.03 0.09 0.01 0.29 7-i CFSI: INTERBANK MARKET 0.5 0.7 275 257 1110 330 0.55 0.19 0.41 0.39 0.25 8-i CFSI: CREDIT MARKET 0.59 0.7 245 216 1151 360 0.6 0.16 0.39 0.24 0.23 9-i CFSI: SECURITIZATION MARKET 1.13 0.7 178 93 1274 427 0.71 0.07 0.23 0.27 0.2 10-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.55 0.7 272 327 1040 333 0.55 0.24 0.53 0.42 0.19 11-i CFSI: EQUITY MARKET 0.67 0.7 206 211 1156 399 0.66 0.15 0.45 0.2 0.16 12-i CFSI: FOREIGN EXCHANGE MARKET 0.7 0.7 193 286 1081 412 0.68 0.21 0.66 0.39 0.09 13-i CFSI: REAL ESTATE MARKET 0.5 0.7 244 411 956 361 0.6 0.3 0.75 0.76 0.08 Panel 3: Daily (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.5 0.7 1477 583 6329 1478 0.5 0.08 0.17 0.13 0.42 2-i CFSI: CREDIT MARKET 0.5 0.7 1245 1182 5730 1710 0.58 0.17 0.41 0.32 0.25 3-i CFSI: INTERBANK MARKET 0.5 0.7 1183 1065 5847 1772 0.6 0.15 0.38 0.43 0.25 4-i CFSI: SECURITIZATION MARKET 1.21 0.7 866 468 6444 2089 0.71 0.07 0.23 0.29 0.23 5-i CFSI: EQUITY MARKET 0.62 0.7 984 1177 5735 1971 0.67 0.17 0.51 0.26 0.16 6-i CFSI: REAL ESTATE MARKET 0.5 0.7 1183 2038 4874 1772 0.6 0.29 0.74 0.82 0.1 7-i CFSI: FOREIGN EXCHANGE MARKET 0.71 0.7 909 1545 5367 2046 0.69 0.22 0.73 0.47 0.08 Note: Panel 1 uses data between July 1976 and February 2014. Panels 2 uses data between 6/12/1976 and 3/22/2014. Panels 3 uses data between 6/3/1976 and 3/28/2014.

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Table 13 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on µ Name , TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i NFCI: CREDIT SUBINDEX 0.06 0.7 51 60 267 73 0.59 0.18 0.45 0.24 0.2 2-i CFSI: SECURITIZATION MARKET 0.2 0.7 37 34 293 87 0.7 0.1 0.35 0.09 0.18 3-i NATIONAL FINANCIAL CONDITIONS INDEX 0.1 0.7 37 38 289 87 0.7 0.12 0.39 0.14 0.17 4-i NFCI: RISK SUBINDEX 0.06 0.7 47 65 262 77 0.62 0.2 0.52 0.32 0.15 5-i CLEVELAND FINANCIAL STRESS INDEX 0.32 0.7 37 45 282 87 0.7 0.14 0.46 0.14 0.14 6-i CFSI: CREDIT MARKET 0.38 0.7 25 19 308 99 0.8 0.06 0.29 0 0.14 7-i ADJUSTED NFCI 0.5 0.7 24 19 308 100 0.81 0.06 0.3 0.02 0.13 8-i CFSI: REAL ESTATE MARKET 0 0.7 75 138 189 49 0.4 0.42 0.7 0.67 0.13 9-i CFSI: EQUITY MARKET 0.38 0.7 32 45 282 92 0.74 0.14 0.53 0.08 0.1 10-i CFSI: INTERBANK MARKET 0.28 0.7 19 15 312 105 0.85 0.05 0.3 0.04 0.1 11-i NFCI: LEVERAGE SUBINDEX 0.22 0.7 14 15 312 110 0.89 0.05 0.41 0.01 0.06 12-i CFSI: FOREIGN EXCHANGE MARKET 1.02 0.7 1 0 327 123 0.99 0 0 0.03 0.01 13-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 2 0.6 0 0 327 124 1 0 0.19 0 14-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.32 0.7 34 34 293 90 0.73 0.1 0.38 0.05 0.16 15-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.28 0.7 42 63 264 82 0.66 0.19 0.57 0.26 0.12 16-ii CFNAI: PRODUCTION AND INCOME 0.56 0.7 28 34 293 96 0.77 0.1 0.46 0.06 0.11 17-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.26 0.7 33 55 272 91 0.73 0.17 0.63 0.22 0.08 18-ii CFNAI: THREE MONTH MOVING AVERAGE 0.18 0.7 31 53 274 93 0.75 0.16 0.65 0.21 0.07 19-ii CFNAI: SALES, ORDERS, AND INVENTORIES 1.48 0.7 7 4 323 117 0.94 0.01 0.22 0 0.04 20-ii CFNAI: DIFFUSION INDEX 0.84 0.7 1 0 327 123 0.99 0 0 0.01 0.01 Panel 2: Weekly (, 0.2 and 4 bins were used for IV) 1-i ADJUSTED NFCI 0.06 0.7 193 304 1123 351 0.65 0.21 0.6 0.59 0.12 2-i NATIONAL FINANCIAL CONDITIONS INDEX 0.04 0.7 107 102 1325 437 0.8 0.07 0.36 0.08 0.12 3-i NFCI: RISK SUBINDEX 0.02 0.7 168 236 1191 376 0.69 0.17 0.54 0.36 0.12 4-i NFCI: CREDIT SUBINDEX 0.02 0.7 136 208 1219 408 0.75 0.15 0.58 0.26 0.09 5-i CLEVELAND FINANCIAL STRESS INDEX 0.28 0.7 74 79 1348 470 0.86 0.06 0.41 0.06 0.07 6-i CFSI: EQUITY MARKET 0.14 0.7 166 303 1124 378 0.69 0.21 0.7 0.48 0.07 7-i CFSI: INTERBANK MARKET 0.04 0.7 162 298 1129 382 0.7 0.21 0.7 0.5 0.06 8-i CFSI: REAL ESTATE MARKET 0.02 0.7 216 443 984 328 0.6 0.31 0.78 0.57 0.05 9-i CFSI: SECURITIZATION MARKET 0.12 0.7 94 154 1273 450 0.83 0.11 0.62 0.16 0.05 10-i CFSI: CREDIT MARKET 0.12 0.7 138 275 1152 406 0.75 0.19 0.76 0.43 0.04 11-i NFCI: LEVERAGE SUBINDEX 0.06 0.7 36 53 1374 508 0.93 0.04 0.56 0.06 0.02 12-i CFSI: FOREIGN EXCHANGE MARKET 0.42 0.7 9 2 1425 535 0.98 0 0.08 0.09 0.01 13-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 2 0.1 0 0 1427 544 1 0 0.08 0 Panel 3: Daily (, 0.1 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.16 0.8 310 763 7364 1429 0.82 0.09 0.53 0.33 0.07 2-i CFSI: EQUITY MARKET 0.28 0.8 189 286 7841 1550 0.89 0.04 0.32 0.06 0.07 3-i CFSI: FOREIGN EXCHANGE MARKET 0.12 0.8 366 1071 7056 1373 0.79 0.13 0.63 0.68 0.06 4-i CFSI: SECURITIZATION MARKET 0.08 0.8 233 661 7466 1506 0.87 0.08 0.61 0.28 0.04 5-i CFSI: CREDIT MARKET 0.2 0.8 175 566 7561 1564 0.9 0.07 0.69 0.21 0.02 6-i CFSI: INTERBANK MARKET 0.1 0.8 154 564 7563 1585 0.91 0.07 0.78 0.21 0.01 7-i CFSI: REAL ESTATE MARKET 0.08 0.8 20 62 8065 1719 0.99 0.01 0.66 0.01 0 Note: Panel 1 uses data between July 1976 and February 2014. Panels 2 uses data between 6/12/1976 and 3/22/2014. Panels 3 uses data between 6/3/1976 and 3/28/2014.

Some results are common to all approaches. First, the usefulness of most series to risk neutral policymakers is maximized when Type I error is more costly than

Type II error since 0.7. Typically it is assumed that the cost of not implementing policy in the case of crisis outstrips the cost of implementing policy in the case of no crisis (0.5). Therefore, the results indicate that tested measures are in large part conducive to policymakers’ needs. This is also in line with previous findings on relative costs between errors (Sarlin, 2013; Betz et al., 2014). Second, we notice a general lack of stability (across frequencies) and agreement (between tests) when adopting a differenced

118

perspective. Third, it is interesting to note that CFSI, NFCI, and CFNAI (for which the components are also available) modestly outperform their components. This holds consistently true when we use the level perspective. This supports the use of composite methodologies and is consistent with the financial system’s property of hierarchical composition and decomposability (Simon, 1962).

Findings from comparison of early warning properties: We focus on autoregressive properties of the US coincident systemic measures. To apply the Box-

Jenkins methodology, we difference the standardized coincident measures to achieve weak form stationarity. We find that based upon autocorrelation and partial autocorrelation evidence there is no support for an autoregressive or moving average structure in the data. These results appear to support the idea that systemic conditions, as viewed by these measures individually, display characteristics of random walk between

January 2002 and June 2007. Therefore, we omit the estimation results.

We also pursue an exploratory examination of the potential for a process through which financial conditions perceived by a collection of measures may develop into stress observed by another set of measures. The VEC forecasts are presented visually in Figure

16 using an initial estimation sample from March 1992 to February 2004. The forecast is effected by estimating the parameters using all observable data and calculating the forecast one period ahead repeatedly between March 2004 and February 2014. A comparison of the forecast accuracy from out-of-sample forecasts is available in Table

14. We achieve the most accurate out-of-sample forecasts for KCFSI while CFSI ‘s forecast is the least accurate.

119

Figure 16 VEC Forecast Results

Note: Forecast—red dashed line; realized systemic conditions—solid blue line. 120

Table 14 Accuracy of Forecasts Name RMSE MAE MAPE CLEVELAND FINANCIAL STRESS INDEX 0.8740 0.6854 1.6044 KANSAS CITY FINANCIAL STRESS INDEX 0.3138 0.1910 0.4738 NATIONAL FINANCIAL CONDITIONS INDEX 0.38989 0.2606 0.8708 CHICAGO FED NATIONAL ACTIVITY INDEX 0.5919 0.4341 1.9686 PHILADELPHIA'S LEADING INDEX FOR THE US 0.4913 0.2996 1.1928 KAMAKURA'S TROUBLED COMPANY INDEX 0.4317 0.29791 0.7431 BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.6544 0.40194 2.5977 GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.6162 0.4034 4.1441

From these forecasts we generate signals of crisis where the thresholds , for each measure maximize the in-sample Usefulness metric following (13). We are interested in whether there is a difference between in-sample and out-of-sample

Usefulness (Table 15). By definition, forecasts with a uniform prediction of crisis or no crisis have a maximum Usefulness of zero. We find the NTSR, IV, and do not exhibit a great deal of stability between in-sample and out-of-sample results. Moreover, the relative rankings of these measures changes. Most of the measures perform better

(superior NTSR and ) out-of-sample than in-sample. This may be partially attributable to the prominent crisis in the out-of-sample time period.

Table 15 Usefulness of In-Sample Data Compared to Out-of-Sample Forecasts Name TP FP TN FN T1 T2 NTSR IV , (Dec.) Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1 CLEVELAND FINANCIAL STRESS INDEX 1 0.5 25 2 96 45 0.64 0.02 0.06 0.05 0.33 2 GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.55 0.6 33 20 78 37 0.53 0.2 0.43 0.49 0.23 3 KAMAKURA'S TROUBLED COMPANY INDEX 1.21 0.5 21 7 91 49 0.7 0.07 0.24 0.04 0.2 4 KANSAS CITY FINANCIAL STRESS INDEX 0.65 0.6 29 23 75 41 0.59 0.23 0.57 0.14 0.14 5 NATIONAL FINANCIAL CONDITIONS INDEX 2 0.3 6 0 98 64 0.91 0 0 0.06 0.09 6 CHICAGO FED NATIONAL ACTIVITY INDEX 1.52 0.3 3 0 98 67 0.96 0 0 0.82 0.04 7 BLOOMBERG'S FINANCIAL CONDITIONS INDEX 2 0.1 0 0 98 70 1 0 0.34 0 8 PHILADELPHIA'S LEADING INDEX FOR THE US 2 0.1 0 0 98 70 1 0 0.44 0 Panel 2: Monthly (, 0.6 and 3 bins were used for IV) 1 KANSAS CITY FINANCIAL STRESS INDEX 0.65 0.6 21 0 78 19 0.5 0 0 0.25 0.5 2 CLEVELAND FINANCIAL STRESS INDEX 1 0.5 15 0 78 18 0.64 0 0 0.34 0.36 3 CHICAGO FED NATIONAL ACTIVITY INDEX 1.52 0.3 12 0 78 23 0.71 0 0 0.1 0.29 4 GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.55 0.6 13 2 76 29 0.69 0.03 0.08 0.01 0.28 5 KAMAKURA'S TROUBLED COMPANY INDEX 1.21 0.5 10 0 78 24 0.76 0 0 0.37 0.24 6 PHILADELPHIA'S LEADING INDEX FOR THE US 2 0.1 10 0 78 22 0.76 0 0 0.24 0.24 7 BLOOMBERG'S FINANCIAL CONDITIONS INDEX 2 0.1 7 0 78 18 0.83 0 0 1.29 0.17 8 NATIONAL FINANCIAL CONDITIONS INDEX 2 0.3 7 0 78 17 0.83 0 0 1.65 0.17 Note: Panel 1 uses data from March 1990 to February 2004. Panels 2 uses data from March 2004 to February 2014.

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3.5. Conclusion: Implications and limitations

Multiple measures for systemic conditions have been developed. A major challenge is to assess their quality. Despite evidence of the multidimensional complexity of system conditions, current approaches evaluate measurement quality by methods of binary classification. The main contributions of this study are the improvements to the evaluation framework for systemic conditions and their application to a case study of existing measures. The framework is based on three incremental enhancements to prior methods. First, its event variable is constructed by multidimensional signal extraction from diverse volatility series. This introduces variance into individual probability distributions of critical states across observation frequencies. It generalizes the classification approach from binary to multinomial classification. It also enables the search for optimal systemic measurement. Second, the classification of system states is enhanced by considering the criticality of market-volatility signals as evidenced by their severity, persistence, and pervasiveness. This enhancement integrates findings from two streams of the literature: findings on patterns of volatility in financial markets from empirical finance and findings on cyclical properties from empirical macroeconomics.

Third, we apply the information-theoretic statistic of information value to assess the quality of multinomial classification across the predicted outcome distribution for each measure.

We apply this evaluation framework to the case of US systemic measures from

1976 to 2013. For this dataset, we partition the US system into six markets and assess both coincident signaling quality and early-warning performance. There are three principal findings. First, consideration of the levels and change in severity, persistence,

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and pervasiveness of market volatility is important in identifying the critical states of the

US financial system. Second, the association of market volatility with critical states varies with level and change in conditions. An efficient identification of critical states is achieved at the severity level of 0.6 standard deviations and persistence of five periods or pervasiveness across two markets. Third, measures based on multiple markets improve identification of critical states.

Implications: The conceptual implications of this study suggest that appropriateness of systemic measures to macroprudential policy hinges on their capacity to identify and anticipate adverse systemic conditions. Candidate measures must reveal these two types of information in a timely manner and across the relevant individual markets. Decomposable coincident measures tend to carry enhanced systemic information by reflecting conditions from a variety of system aspects. The case-study findings indicate that policymakers’ intervention decision is less uncertain when they consider signals from levels rather than changes in systemic conditions. This is evidenced by increased stability of the classification metrics (IV, NTSR, and Usefulness) across frequencies. Analyzing the level of systemic conditions also allows a direct study of the beginning and end of each episode, which is not possible with the difference perspective.

The case study also provides interesting empirical information in the context of the preferred quantification of policymakers’ loss function. We find that the cost-based relative Usefulness metric has three attractive features. First, it has a straightforward scaling interpretation for which higher Usefulness is better. Second, it is stable across all selections of ∈ 0,1. Third, it incorporates the necessary and intuitive aspect of policy cost versus benefit represented by the preference parameter . At the same time,

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Usefulness should not be considered by itself, but it remains a convenient and accessible metric to use for an introductory comparison of systemic measures against the NTSR and

IV statistics.

Limitations: Policymakers rely on their ability to project systemic conditions to enable the implementation of policies that take time to affect the financial system. Our analysis of US coincident measures using the Box-Jenkins ARIMA methodology indicates that these measures do not (after necessary transformation) possess sufficient structure individually. As an alternative, the VEC methodology is used with mixed results on a longer sample to determine whether systemic-conditions measures allow insight into a mechanism for the development of critical systemic episodes. The results show significant cointegration, which indicates that there are long-run relationships between several of the coincident measures. In addition, some of the forecasts exhibit moderately stable positive Usefulness out-of-sample, which is attractive to policymakers. However, even this one-period forecast radically limits the application for policy implementation.

This is a topic that requires further study using methods capable of producing robust, dynamic, and actionable forecasts.

A basic problem in identifying and analyzing systemic conditions is that they may arise from unprecedented patterns. This is particularly challenging to policymakers since a complex financial system adapts to change. Thus, past historical patterns under which critical states of the system emerge may change over time. Alternatively, assessing systemic conditions on the basis of policymakers’ loss function may lead to unrealistic assumptions. A particular challenge in applying early-warning projections for macroprudential policy is that the policy itself leads to feedbacks and unanticipated

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dynamics. Such amplification of the system’s adaptive response to macroprudential policy must be considered a major challenge of the policy itself. A further question, therefore, is to what extent policy should restrict itself to ex-post responses to the transformation of markets or direct itself ex-ante to control the sensitivity of the system’s adaptation.

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Chapter 4: Stress in Heterogeneous Financial Agents: Validity and Dynamics

A review of financial system stress measures reveals not only the absence of

theory on financial stress, but also the absence of search for theory. To remedy this gap,

this study conducts a rigorous two-stage investigation of the empirical validity and

dynamic properties of financial stress measurement. In the first stage, we propose and

empirically test hypotheses of association between micro-level stress in representative

financial agents and macro-level financial system stress. We apply abductive inference to

the empirical results to propose a new theoretical micro-level stress measure for

heterogeneous agents and instruments. Defining financial stress theoretically allows

continual measurement of financial stress at the micro-level of the various representative

heterogeneous partitions of the financial system, as these partitions evolve over time. In

the second stage, we compare theoretical micro-level stress against empirical macro-level

stress to understand whether and why they may differ. Based on the evidence of these

difference, we refine our understanding and measurement of both micro- and macro-level

financial stress. Micro-level stress is improved by incorporation of liquidity preferences

(via market liquidity spread) and time preferences (via inflation expectations). It is identified using a Multiple Indicators Multiple Causes (MIMIC) model where latent micro-level stress is predicted by observed empirically-supported variables. The reliability and validity of macro-level stress measurement is improved first by static factor analysis methods, then further by dynamic factor analysis methods.

4.1. Introduction

A review of financial system stress reveals not only the absence of theory of stress

(Gramlich et al., 2010; Kliesen et al., 2012; Oet et al., 2015b), but also the absence of

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search for theory. This dearth of theory limits our ability to evaluate stress measures

(Holló, Kremer, and Lo Duca, 2012). Thus, current measures of macro-level stress typically do not adapt to structural changes in the system such as compositional changes in its agents and instruments.

In this study, we develop a theory of financial stress from empirical foundations in two stages. First, we build upon current empirical measurement models to test several hypotheses regarding the formation of stress. Second, based on knowledge emerging from empirical observations, we evaluate stress for heterogeneous agents and instruments. By explicitly recognizing the organization of the financial system and validating the measurement of stress at a granular level, we propose that the resulting measure is robust to material ongoing transformation in the financial system.

Accordingly, in the first stage of this research, we ask: What is financial system stress? How can stress be theorized in an adaptive system? Is the measurement model sound across heterogeneous agents? These three research questions guide the development of micro-level stress theory. They build systematically by gaining insights from the systematic comparison of micro-level hypotheses with macro-level empirical measurement. The first stage of research concludes with the construction of theoretical financial stress for the US. In the second stage of the research, we compare the constructed theoretical stress with a leading coincident empirical measure of US financial stress and find a number of discrepancies between them.71 Therefore, we set out to

improve the alignment of these two measures by exploring three additional questions.

71 We conduct the empirical comparison CFSI as a leading US financial stress measure, based on the evaluation results of chapter 3. 127

What factors identify financial stress? Are the factors empirically reliable? Does inclusion of dynamic effects narrow the discrepancies between the theoretical and empirical stress measures?

This chapter is organized as follows. In Section 4.2 we propose and test hypotheses of association between behavioral aspects of heterogeneous financial agents and overall financial system stress. Supported variables are used to construct a theoretical measure of the US financial system stress. Section 4.3 explores the static and dynamic properties of empirical stress factors in an effort to shed light on the discrepancies between the empirical and the theoretical measures of stress. In Section 4.4 we close with a brief discussion of future work.

4.2. Theoretical Foundation

4.2.1. Motivation

The problem of financial stress in an adaptive system is motivated by the evidence of dramatic transformation of the financial system agents. Figure 13 shows the relative waxing and waning assets of several selected US financial system agents from

1952 to 2013 which suggests the presence of dynamic tipping points that are characteristic of complex systems. The recent financial crisis evidences one such dynamic shift. Pension funds and mortgage pools experience a sharper decline in their asset holdings than other financial institutions. ABS issuers suffer a decline in their assets earlier than most other economic agents and remain below their pre-crisis holdings. At the same time, the central bank’s balance sheet expands with the implementation of new monetary policy tools. Examining the relative asset share of these institutions over time reveals that banks hold a fairly stable 50% of assets until 1980. Then, their share begins

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to decrease until 1998, when it becomes stable at 20%. The remaining 30% market share was captured primarily by investment funds and pension funds.

4.2.2. Hypotheses

A review of selected theoretical and empirical literature strands—monetary policy transmission, structure of financial intermediation, and financial crises and cycles— provides the material from which we draw hypotheses that relate micro-level representative agents and their instrument exposures with macro-level financial stress.

Monetary policy literature generally recognizes financial stress as a latent condition of the financial system (Mishkin, 1995; Borio and Zhu, 2012). All three strands are jointly motivated by understanding the factors affecting system behavior across products and agents and by studying the factor interactions. Monetary policy transmission studies recognize factors acting in distinct mechanisms with economic conditions.72 Remarkably,

each of the mechanisms includes information about the prices of reference assets as well

as information about aggregate activity (e.g. volumes and transactions) based on these

asset prices. The literature on financial intermediation (Berger et al. 2004) brings to light

the controversial role of concentration as a factor critical to the structure of economic

systems. Literature on financial cycles and crises (Schwert, 1989; Stock and Watson,

2003, 2005) emphasizes the extent to which factors of economic conditions are generally unstable and exhibit volatility across economic systems. At the same time, behavioral economics research explains that changes in volatility are significantly affected by behavioral phenomena such as beliefs (see Barberis and Thaler, 2003, for survey), animal

72 Current literature distinguishes the following mechanisms: monetary channel, interest rate channel, credit channel, exchange rate channel, asset pricing channel, bank lending channel, bank capital channel, and consumer wealth channel (Borio and Zhu, 2012; Mishkin, 1995). 129

spirits (Akerlof and Shiller, 2010), and prospect theory and cognitive bias (Kahneman and Tversky, 1979) among others. Accordingly, we form the following direct association and interaction hypotheses concerning asset spreads, concentration, while controlling for behavioral effects.

Direct association hypotheses

Hypothesis 1: Higher risk premium, measured by expectations of yield spreads between assets and risk-free instruments of similar investment horizon, is associated with higher financial stress. Prices of financial instruments73 form an essential component in

monetary policy mechanisms (Bernanke, 1986; Greenwald and Stiglitz, 1993; Bernanke

and Gertler, 1995; Obstfeld and Rogoff, 1995; Taylor, 1995; Clerc and Pfister, 2003;

Rigobon and Sack, 2003). Empirically, Stock and Watson (1989) find that risk premium

formed as the spread between risky and risk-free reference rates contains forward-looking

information about the state of the economy. Bernanke (1990: 61) confirms the finding

and suggests that risk premium “may be useful because it summarizes available

information about the likelihood of a recession.” Freixas and Rochet (2008) emphasize

that the risk premium’s key role in various channels of monetary policy transmission

results from its amplification effect on interest rates and generating the financial

accelerator effect. Indeed, in a comprehensive empirical survey of the association of asset

prices, output, and inflation, Stock and Watson (2003) emphasize that evidence of risk

premium’s forward-looking information about expectations of future system state lies at

the heart of macroeconomics. In particular, the evidence supports the idea that market-

clearing spreads between risky and alternative risk-free instruments embed expectations

73 E.g., including short-term rates, exchange rates, equity prices, and bank deposits. 130

on the likelihood of default of the risky instrument. Thus, it is reasonable to expect that yield spreads of this type are positively associated with financial stress.

Hypothesis 2: Change in risk premium is associated with higher financial stress.

Empirical evidence finds that risky premiums tend to be sticky, as evidenced by the short-term persistence in short-term excess returns (Ball and Brown, 1968; Ball, 1978).

Bernard and Thomas (1989) investigate whether the observed drift in excess returns is due to the inherent latency of risk premium or the lag in recognition of new information for the expectations of future earnings. Ball’s (1978) analysis suggests that the mechanism is more consistent with information lag. However, Jegadeesh and Titman

(1993) find evidence that risk premia tend to persists for four quarters.

Hypothesis 3: Share of exposure is positively associated with financial stress.

Exposure describes wealth invested by a financial agent in particular asset. Share of exposure describes a share of the agent’s invested wealth relative to aggregate wealth invested in the same asset. It represents an aspect of agent net worth due to a particular asset. Cetorelli and Gambera (2001) find that the effect of asset concentration on economic growth is generally mixed and moderated by its context: positive for sectors that are dependent on external financing and negative for the banking sector itself.74

Berger et al. (2004) review similarly mixed results from theoretical studies on this topic: the “concentration-stability” view (Allen and Gale, 2000) vs. the “concentration- fragility” view (Boyd and Runkle, 1993; Mishkin, 1999; Boyd and De Nicolo, 2005).

Empirical evidence is less ambiguous. Aizenman and Pasricha (2012) find a positive

74 Note that the corresponding association of concentration with financial stress implied by the Cetorelli and Gambera (2001) findings is reversed: negative association for sectors dependent on external financing and positive for the banking sector. 131

association of concentration and financial stress in the Great Recession sample of 107 countries. Similarly, Oet et al. (2013) find a consistent pattern of positive association of exposure concentrations with financial stress in the 1991-2012 sample of the top 33 US bank holding companies.

Moderation hypotheses: interactions

Empirical studies of agent risk aversion provide mixed evidence on the interaction of wealth and risk premium with economic distress. Arrow (1971) finds that risk aversion is not affected by the share of wealth. This implies that wealth and risk premium can be considered independent. Accordingly, their interaction should not have an effect on financial stress. On the other hand, Pratt (1964) finds that the relationship between risk aversion and risk premium can be moderated by wealth. This suggests that their interaction may have a tangible effect on financial stress. Fama (1991) notes that the risk premium and wealth interaction appears to be associated with the business cycle. During times of distress, low wealth is associated with higher risk premium and signals higher future expected return.

Theoretical considerations both affirm the linkage of wealth and risk premium and raise questions about the sign of their association. First, the neoclassical notion of wealth-maximizing economic agents clearly leads to the anticipation that wealth is directly associated with agent's risk aversion. Thus, Pratt's (1964) risk premium is a function of wealth. The sign of the absolute risk aversion, and therefore, the interaction of risk premium and wealth, turns out theoretically variable and dependent on risk (or by extension the level of financial stress) (Menezes and Hanson, 1970). The time-varying risk aversion has been both supported using habit-formation arguments (e.g.

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Constantinides, 1990) and challenged empirically. In this regard, Brunnermeier and

Nagel (2008) find the allocation choices of households are not influenced by changes in wealth. Given the mixed theoretical and empirical evidence, it is reasonable to test whether the association financial stress with the interaction of wealth and risk premium is non zero.

Hypothesis 4: Financial stress is neither amplified nor attenuated by the interaction of risk premium with exposure share. Hypothesis 5: Financial stress is neither amplified nor attenuated by the interaction of change in risk premium with exposure share. Figure 17 Hypotheses

Table 16 Hypothesis Testing Variable Hypothesis Standardized Coefficient Decision Risk premium H1 0.172*** Supported Change in risk premium H2 0.026*** Supported Share of system exposure H3 0.160*** Supported Risk premium Share H4 -0.154*** Supported Change in risk premium Share H5 -0.034*** Supported Note: *** indicates significance at 1%

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These hypotheses are summarized in Figure 17 with their sign expectations. We see in Table 16 that each hypothesis is supported by appropriate signs on variable coefficients which are uniformly significant at 1%.

4.2.3. Micro-level stress in agents and instruments:A conjecture

What is the theory underlying stress applied to the adaptive financial system?

Among the many financial system dynamics, new financial instruments are introduced potentially creating entire markets, laws are changed inciting regulatory arbitrage, and financial agents may radically change their size, composition, and behavior over time.

How can we be sure that a measure which identifies stress well today will still be good tomorrow? Specifically, other than finding a particular set of spreads in various markets that seem to capture useful information (Oet et al., 2015b; Illing and Liu 2003, 2006), the question of selecting the candidate series is at best an empirical result, at worst it is theoretically opaque. Furthermore, we are concerned that when the financial system changes our empirical financial stress measure will no longer be relevant. We desire therefore to establish a theory of financial system stress that continues to be applicable both for the changing agents and instruments. Put differently, we desire a way to measure stress in a changing system—with heterogeneous evolving agents and instruments.

In theorizing the unobserved micro-level agent stress, we proceed from the empirically supported understanding of macro-level stress as force exerted on economic agents by changing expectations (Illing and Liu, 2006; Oet et al., 2015b; Holló et al.,

2012). We further form an abductive conjecture that micro-level stress should be theoretically consistent with the risk premium, change in risk premium, share of system

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exposure, and their interactions, as supported empirically by our hypotheses H1 through

H6.

Figure 18 Conceptual Diagram of the Adaptive System Solution

State at time = t State at time = t +1

Consequently, we consider a changing financial system composed of financial products 1, … , m traded by agents 1, … , such that financial instruments can be partitioned into markets ∈,…., and agents can be partitioned into various

75 sectors ∈,…, (see Figure 18). We define to be the wealth

invested in instrument i by agent j at time t which incorporates the choice of the agent to

own a quantity and the market clearing instrument price . Furthermore, let

be the risk premium, measured as yield spread between the expected return on

instrument and a risk-free product of comparable investment horizon. We now define

the momentum in instrument experienced by agent at as the product of risk

premium and share ́ of total exposure ∑ in the instrument in

75 We recognize that stress to assets and liabilities of financial agents will differ in sign. Thus, without the loss of generality in theorizing financial stress, we can treat stress separately for assets and liabilities. Henceforth, in this study, we let ∶ . 135

instrument at . Thus ∗́ , leading directly to the functional form of

economic force applied on an instrument experienced by agent at as a first derivative

of the momentum :

́ ́ (50).

We propose that the wealth of agent in instrument at time may be interpreted as a form of partitioned economic area in the financial system conceptualized in Figure 18. Accordingly, we conjecture that micro-level financial stress experienced by

agent in instrument at time can be explained as the economic force acting on .

Empirically, this conjecture means that the allocation choices revealed by the agent

should over time should be fully explained:

≞ ́ ́ (51).

We expect that an increase in the risk premium on an instrument will correspond

to a realignment of market expectations, while an increase in the quantity of an

instrument traded may also reflect changes in the market, both of which are interpreted as

positive stress. The micro-level measure of financial stress can then be aggregated to

the macro-level system stress by taking a weighted sum as

∑∑

∑∑ ́ ́ (52). ∑∑

This framework can accommodate a changing agent and instrument population

over time, as well as potentially dramatic changes in the system. However, this approach

to theoretical stress has a subtle logical flaw. While we are interested in financial stress

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experienced within various heterogeneous partitions of the financial system, the above definition lacks “memory” allowing it to consider risk premiums or quantities in a

historic context. For this reason, we modify the proposed measurement of theoretical

stress by incorporating a comparative transformation ∙:

́ ́ (53),

and (54). ||

Here, the is the cumulative distribution function (CDF) of the observed

value of . represents the probability of observing a value less than or equal to using the full time series. Applying the CDF transformation will naturally convert each series so that it is positive, avoiding a situation when raw spreads may negate each other during aggregation with misleading indication of low or nonexistent stress. At this point, we can construct measures of theoretical stress partitioned to represent observable heterogeneous financial agents and instruments as the weighted average of the CDF of instrument spreads.

By applying the CDF to each term in the definition of economic force, we not only compare each term to its historical realizations adding a layer of historic interpretation, but we also add several properties that are attractive from the standpoint of stress measurement. First, comparative force is measured on a scale of [0,1] allowing direct comparison across instruments.76 Second, since all terms of relative stress are

76 Note, that the introduction of the comparative transformation ∙ in the comparative force expression necessitates that the numerator be divided by 2 to preserve the [0,1] scale: ∶ 2 137

positive, we need not worry about situations where stress appears small despite significant activity (e.g. high stress due to large positive changes in risk premium may be neutralized by simultaneous reductions in quantity).

Comparative micro-level stress can be aggregated to macro-level system

stress stress using the same weighted sum methodology as theoretical stress without the convenient simplifications, namely

∑∑ ́ ́ (55). ∑∑

We estimate the above measure of stress using data from the Board of Governor’s

Financial Accounts of the US Z.1 Release, alongside data from Datastream, Bloomberg,

Global Financial Data (GFD), and Haver Analytics. Stress is measured quarterly for 28 sectors and 41 instruments between 1980 and 2013. The results are summarized for select sectors and instruments in Figures 19 and 20, respectively. The adaptive nature of the financial system is evident in the nonlinearities of structural, functional, and behavioral patterns exhibited by the economic agents over time. The emergent macro-patterns stem in large part from the heterogeneous agents’ micro-activities. For example, financial stress exposures and experiences of US chartered depository institutions, funding corporations, real estate investment trusts (REITs), and government-sponsored entities

(GSEs) corporations differ over time (see Figure 19). US banks are among the more complex agents covered by empirical stress; their main sources of stress stem from time deposits, residential real estate, and GSE backed securities, as well as consistently decreasing stress in checkable deposits and somewhat sporadic stress in commercial real estate (mainly during the crisis). Funding corporations have an entirely different

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structure, evidenced by the way they experience stress which arises from commercial paper (with consistently decreasing importance), followed by corporate bonds and money market mutual funds shares (each of which steadily rises in importance). For the REITs, bonds form largest source of stress followed by the commercial real estate, GSE backed securities, and after 2002 they experience growing stress from the federal funds market.

GSEs experience stress primarily due to GSE back securities and loans with minor stress from residential real estate.

We also ask whether stress can be quantified across different financial instruments. Figure 20 shows the stress contributions of different agents to stress in particular financial instruments. Shown here is a sample selection of GSE-backed securities, interbank activity, residential real estate and corporate bonds. For the GSE securities the largest participants are GSEs and mortgage pools with minor participation by life insurance, US banks, and the rest of the world. Interbank activity is due mostly to

US banks and foreign banking, with steadily decreasing participation by credit unions and sporadic participation by the rest of the world and the monetary authority. Residential real estate stress is experienced in large part by households with mortgage pools and US banks as steady minor stakeholders and GSEs entering as participants in the past 4 years.

Corporate bonds have fairly stable participation with corporate businesses, ABS issuers, and the rest of the world as primary holders while households are a minor but growing part of the market.

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Figure 19 Comparative Theoretical Stress for Heterogeneous Agents

Note: These graphs represent stress in a selected group of agents (restricted for the sake of brevity), stress series for all agents available from authors upon request. The charts represent in descending order: US Chartered Depository Inst. (US Banks), Funding Corporation, REITs, and GSEs.

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Figure 20 Comparative Theoretical Stress for Heterogeneous Instruments

Note: These graphs represent stress in a selected group of instruments (restricted for the sake of brevity), stress series for all instruments is available from authors upon request. The charts represents in descending order: GSE Backed Securities, Net Interbank, Residential Real Estate, and Corporate Bonds

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4.3. Empirical Comparison

A natural question in light of the proposed theoretical stress measure for heterogeneous agents is how this measure compares against extant empirical measures of overall financial system stress. Given the discrepancies between the two, we undertake successive modifications of the empirical stress measures to improve the alignment to

theoretical stress. First, we evaluate the comparative macro-level system stress based

on our theoretical conjecture against the empirical macro-level system stress, as measured

by CFSI (Oet et al., 2015b) which adopts the perspective of measuring system stress via a

set of representative markets. We find that there are material deviations between them

(Figure 21).

Figure 21 Comparison of CFSI and Comparative Theoretical Stress 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 Jul-86 Jul-99 Jul-12 Apr-83 Oct-89 Apr-96 Oct-02 Apr-09 Jan-80 Jun-85 Jan-93 Jun-98 Jan-06 Jun-11 Feb-81 Mar-82 Feb-94 Mar-95 Feb-07 Mar-08 Aug-87 Sep-88 Nov-90 Dec-91 Aug-00 Sep-01 Nov-03 Dec-04 Aug-13 May-84 May-97 May-10

Comparative Stress CFSI RMSE MAPE MAE Thiel U 0.111 0.085 25.4 0.068 0.141

Based on this outcome, we seek to remedy the conceptual gap in our

understanding of financial stress at both the micro- and macro-level of measurement. At

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the macro-level, we critically re-examine CFSI.77 as a reliable and valid empirical

measure of stress. This process is described in subsections 4.3.3 and 4.3.4. At the micro-

level (subsection 4.3.1), we seek to remedy our empirical understanding of stress with

additional theoretical considerations drawn from prior research.78 Furthermore, in

Chapter 5, we analyze the allocation choices revealed by the representative micro-level

agents to verify that our understanding of economic forces, acting on them can be

considered complete.

At this point, it is reasonable to preview our results. In Subsection 4.3.3., we

modify the empirical stress measure to remedy its inherent subjectivity in the selection of

markets. To this end, we apply static factor analysis to modify the markets selected in

CFSI as common factors for the CFSI component indicators (Figure 22).

77 Whereas our previous evaluation of CFSI against alternative measures of financial system conditions (Chapter 3) provide general support for CFSI, they do not examine its empirical validity critically. Our previous examination of validity of CFSI was in the context of its use as a broad proxy for financial stability considerations used by policymakers in making monetary policy decisions (Chapter 2). 78 The latent micro-level stress can also be imputed from the MIMIC model explained in subsection 4.3.1. Thus, additional insight can be gained from considering the misalignments of this imputed micro-level stress with the conjectural comparative stress . We leave this comparison for future work. 143

Figure 22 Comparison of Five-Factor Stress and Comparative Theoretical Stress 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 Jul-86 Jul-99 Jul-12 Oct-89 Oct-02 Apr-83 Apr-96 Apr-09 Jan-80 Jun-85 Jan-93 Jun-98 Jan-06 Jun-11 Feb-81 Mar-82 Feb-94 Mar-95 Feb-07 Mar-08 Aug-87 Sep-88 Nov-90 Dec-91 Aug-00 Sep-01 Nov-03 Dec-04 Aug-13 May-84 May-97 May-10

Comparative Stress 5 Sector CFSI RMSE MAPE MAE Thiel U 0.159 0.085 23.08 0.068 0.131

Next, given remaining discrepancies between the adjusted empirical and theoretical measures, we recognize the conceptual shortcoming of static factor analysis approach in failing to incorporate the dynamic idea of stress experience. Econometrically, this corresponds to the lack of recognition that static factors reflect observations stress that may be subject to serial correlation. Therefore, we extend the empirical measure further through the dynamic factor analysis (DFA) model with further improvement in alignment to theoretical stress (Figure 23 and Figure 24).

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Figure 23 Comparison of Process Factor Model Stress and Comparative Theoretical Stress 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 Oct-12 Apr-15 Oct-07 Apr-10 Oct-02 Apr-05 Oct-97 Apr-00 Oct-92 Apr-95 Jun-14 Jun-09 Jun-04 Jun-99 Jun-94 Feb-11 Feb-06 Feb-01 Feb-96 Dec-11 Aug-13 Dec-06 Aug-08 Dec-01 Aug-03 Dec-96 Aug-98 Dec-91 Aug-93

Comparative Stress Process Factor Model RMSE MAPE MAE Thiel U 0.136 0.089 23.42 0.072 0.126

Figure 24 Comparison of Shock Factor Model Stress and Comparative Theoretical Stress 0.8

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0.6

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0.2

0.1

0 Oct-92 Apr-95 Oct-97 Apr-00 Oct-02 Apr-05 Oct-07 Apr-10 Oct-12 Apr-15 Jun-94 Jun-99 Jun-04 Jun-09 Jun-14 Feb-96 Feb-01 Feb-06 Feb-11 Dec-91 Aug-93 Dec-96 Aug-98 Dec-01 Aug-03 Dec-06 Aug-08 Dec-11 Aug-13

Comparative Stress Shock Factor Model RMSE MAPE MAE Thiel U 0.150 0.084 23.26 0.071 0.126

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4.3.1. Empirical identification of micro-level stress

We identify the latent micro-level stress using a Multiple Indicators Multiple

Causes (MIMIC) factor model (Figure 25). The method allows us to systematically test the power of several alternative theoretical explanations for micro-level financial stress to complement our empirical hypotheses H1 through H6. Specifically, we test the importance of two rival explanations of financial drivers of micro-level agent choice: time preference theory (Fisher, 1930), liquidity preference theory (Keynes, 1936). We also control for behavioral effects (Barberis and Thaler, 2003). In this approach the latent

stress variable is predicted by observed empirically-supported variables. We discus three

key issues associated with MIMIC models—identification, estimation, and testing—in

Appendix 5.

Figure 25 MIMIC Identification of Latent Micro-Level Stress

4.3.2. Empirical macro-level stress in a set of representative markets

The topic of financial stress measurement has gained considerable attention since

the early 2000s and particularly since the financial crisis. In this literature, financial stress 146

typically aims to measure economic forces characterizing relative state of financial system instability (Illing and Liu, 2006; Oet et al., 2015b; Holló et al., 2012). Holló et al.,

(2012) measure the European financial system stress using five representative market segments and dynamically weigh them using asset price correlations.79 Oet et al. (2015a)

test and empirically support a conjecture that stress is identified by a function of asset

price spreads that are dynamically weighted by transactions in the economy. Oet et al.

(2015b) measure U.S. financial system stress with an index to construct CFSI, consisting of six a priori representative financial markets at time :80

∑ ∑ (56)

(57), ∑

and (58). ∑

When transaction level data is unavailable for (57) equal weights are assigned to

each measure. Accordingly, the CFSI stress construct is operationalized from

observations of six a priori market factors and thirty-seven financial components

which are dynamically weighted within and subsequently across markets according to

and , respectively. Thus, component and factor loadings of the stress measure are

time-varying according to each component’s and factor’s changing share of the economy.

Each of the thirty-seven indicators describes a different aspect of one a priori market

factors. Nine components are asset spreads of characteristic factor assets; nineteen

79 The CISS (Holló et., 2012) assumes five representative factors: money market, bond market, equity market, financial intermediaries, and foreign exchange market. 80 The CFSI (Oet et al., 2012) utilizes six a priori factors: funding, foreign exchange, credit, equity, real estate, and securitization. 147

measure the degree by which underlying series (indexes of equity and foreign exchange markets) have decreased in the past year, and seven measures the covered interest spread.

A moving average of relative bid-ask spreads and a financial beta are also included.

Figure 21 compares aggregate CFSI as calculated by Oet et al. (2015b) using credit weights to construct six a priori market factors against financial system relative stress from equation (55). With generally poor explanatory power of CFSI towards relative stress and a correlation of merely 0.33, there are material discrepancies between these series. CFSI appears to assign much lower stress to the 2003-2007 period than relative stress does. Moreover, the comparative theoretical stress appears to be more volatile than CFSI. The additional volatility may be due to the presence of the additional interaction term in theoretical stress.

4.3.3. Exploratory factor analysis

The above discrepancies between CFSI and comparative theoretical stress lead us to question a priori assumptions about CFSI’s construction. We attempt to improve the alignment between CFSI and comparative theoretical stress by examining the indicators used in CFSI to empirically support the estimation of each latent factor.

There is strong and consistent evidence that stress in distinct (possibly correlated) markets can be measured, eventually affecting the stress level of the overall financial system. This finding is supported by longitudinal exploratory factor analysis of the components of CFSI as constructed in Oet et al. (2012) with results as shown in Tables

16 and 17. Three factors explain 82% of the variance, where the credit and securitization factor explains 42%, funding factor explains 23%, and real estate factor explains 17% of the variance. Table 17 shows the three rotated factors with clean loadings. We also find

148

in this process, that two a priori market factors (credit and securitization) behaved as a single combined factor, while two remaining a priori market factors (equity and foreign exchange) were not identified because of insufficient number of components. We subsequently fix both of the unidentified factors and rerun the exploratory factor analysis

(for full results see Appendix 6). The revised equity factor consists of eight components: consumer, energy, financials, health, industrials, information, materials, and consumer durables. We also fix the foreign exchange factors to include fourteen components in relative foreign exchange rates (currency crashes) and covered interest spreads, (two sets of components for Canada, Mexico, Japan, UK, Australia, South Africa, and Europe).81

There is evidence that the empirical factor structure of CFSI is reliable and valid. Table

17 shows the findings from the reliability and validity testing of the revised factors, where in the exploratory factor analysis (EFA) five factors are found. The Cronbach’s

Alpha (CA) statistic in Table 18 consistently exceeds the recommended threshold of 0.7.

81 Inclusion of China in our analysis would be preferred due to the large volume of trade between China and the United States however the regulated nature of the USD-Yuan Renminbi (notably from 1995 through 2010) could compromise its usefulness in a currency crashes or covered interest spread measure and as a result we do not consider this data. 149

TABLE 17 Rotated Factor Pattern (Standardized Regression Coefficients) Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 BBS 0.901 CFSI 0.888 CMBSS 0.879 ABSS 0.867 CBS 0.697 LS 0.576 ILS 1.014 CPTBS 0.970 ICB 0.783 RRES 0.921 CRES 0.906 Equity 1 Equity 2 Equity 3 Equity 4 Equity 5 Equity 6 Equity 7 Equity 8 FX 1 FX 2 Note: Normalization of factor rows by rescaling to represent covariances

Table 18 Reliability of Five-Factor Stress Measure

There is strong evidence that empirical stress converges to the theoretical specification. In Figure 22 we compare the alignment between the empirical five-sector system stress based on the EFA results and relative stress between October 1991 and

September 2013.82 Although the correlation has improved to 0.399 the results are still not

satisfactory. As mentioned in Appendix 7, several limitations of static factor analysis are

not always suitable for financial data. In particular, the assumption that observations are

82 While the credit weights aggregation scheme is flexible enough to handle missing indicators, the EFA approach implemented here cannot handle missing observations resulting in a shorter comparison window. 150

independent, have no serial correlation, is not expected to hold since states of high and low stress tend to persist. We will therefore attempt to improve the identification of each factor while recognizing the persistence of stress in the next section by leveraging dynamic factor analysis (DFA).

4.3.4. Dynamic factor analysis

We estimate both the process and shock forms of the dynamic factor model using the MLE-SEM method via the Toeplitz transform (the original estimation method of

Molenaar, 1985), follow the five-stage empirical algorithm suggested by Wood (2012), and clarify the empirical stages with additional detail as illustrated in the conceptual map in Figure 26.83 Our empirical approach offers interpretive clarity, transparency, and

relative simplicity by virtue of its parallels to the classic factor-analytic stages of exploratory and confirmatory factor analysis.

We apply and detail the five-stage empirical algorithm (Wood, 2012) in the following seven steps (Figure 26: (stage 1, step 1) data suitability; (stage 1, step 2) dependency window; (stage 2, step 3) Toeplitz construction and descriptive analysis;

(stage 3, step 4) Cholesky factorization; (stage 4, step 5) parallel factor analysis; (stage 5, step 6) factor extraction; and (stage 5, step 7) estimation.

83 More information on the motivation and development of process and shock forms of dynamic factor analysis can be found in Appendix 7. 151

Figure 26 Stages and Steps of Empirical DFA

1.1 Data suitability

Stage 1: Stage 1.2 Dependency window Exploration of Exploration dimensionality

2.1 Toeplitz construction

Stage 2: Stage 2.2 Toeplitz descriptive analysis Toeplitz matrix Block-diagonal Block-diagonal

3. Cholesky factorization Stage 3: Stage Cholesky Cholesky factorization

4. Parallel factor analysis analysis Stage 4: Stage Parallel factor

5.1 Factor extraction Stage 5: Stage estimation 5.2 Estimation Adjustment and Adjustment

4.3.4.1. Exploratory analysis of dimensionality

Data suitability considerations. Wood (2012) suggests that innovations in longitudinal models enable researchers to better understand the pattern of changes over time. However, he warns that not all time-series data benefit from being modeled through dynamic factors. He suggests that the purpose of dynamic factor models is to capture not only concurrent covariation between observable variables but also the patterns of covariation over time. Wood (2012) warns that various characteristics observed in time series data (e.g. stationarity, positive and negative lag patterns, cyclicality, seasonality, etc.) should be carefully considered for appropriateness to research interest and the resulting methods—only some of which are appropriate for dynamic factor analysis.

An important reason to consider the nature of the data is to facilitate the

perception of potential patterns underlying the data. A presence of patterns may in turn 152

suggest special consideration and care in analytical choices. In some cases, DFA may not be appropriate. Specifically, Wood distinguishes seven cases: 1) random variability, 2) random positively lagged variability, 3) random negatively lagged variability, 4) random linearly trended variability, 5) random episodic variability, 6) cyclic variability, and 7) seasonal variability. To the extent that data suggests non-random variability, the researcher has to make a basic choice guided by the research objectives. If the researcher is interested in understanding the general pattern variation in the observable data that include linear or similar time effects, the researcher would choose to conduct dynamic factor analysis on unaltered data. However, if the researcher is interested in understanding the underlying structural pattern between the observed variables, the large scale time trends should be removed. Wood (2012) warns that without this adjustment, the observed variation between the variables may be partially contaminated by time trends. A simple way to remove the time component is to use only the residual remaining in the linear regression of the variable as a function of time.

Following Wood (2012) recommendations, prior to performing dynamic factor modeling of longitudinal data, we begin by verifying that that the time-series is appropriate using a dual approach: first, visual inspection of time-series data; second, examination of the stationarity properties of the time-series data.

Visual inspection. We examine the quarterly time-series of financial stress for

appropriateness to being represented via a dynamic factor model. As Wood (2012)

suggests, while random variability (unlagged, positively lagged, or negatively lagged) is

appropriate; random episodic, cyclic, and seasonal variability are not appropriate; and

random linearly trending variability may or may not be appropriate depending on the

153

research objectives. Figure 27 shows the quarterly time-series of US financial stress measured by the Cleveland Financial Stress Index (Oet et al., 2015b). Visual inspection of the time-series suggests random variability with apparent lagged effects. Specifically, it appears that when stress, measured from 0 to 100, is above the value of 50, it tends to remain above 50. Similarly, when values of stress are below 50, stress tends to remain below 50. While this type of variability can be associated with cyclic variability, the data shows that periodicity and magnitude of these pseudo-cyclic variations is likely random.

Therefore, we conclude that this initial visual evidence provides encouraging results for appropriateness of dynamic factor analysis.

Figure 27 Quarterly Time-Series of US Financial Stress

100

0 Apr-93 Apr-95 Apr-97 Apr-99 Apr-01 Apr-03 Apr-05 Apr-07 Apr-09 Apr-11 Apr-13 Dec-91 Aug-92 Dec-93 Aug-94 Dec-95 Aug-96 Dec-97 Aug-98 Dec-99 Aug-00 Dec-01 Aug-02 Dec-03 Aug-04 Dec-05 Aug-06 Dec-07 Aug-08 Dec-09 Aug-10 Dec-11 Aug-12 Dec-13

Stationarity of quarterly financial stress. The apparent random variability of the

financial stress is tested formally via stationarity analysis. Since nonstationary process may be due to a random walk, random walk with drift, or random walk with drift around a stochastic trend, we conduct several econometric tests for the three different forms 154

under three different null hypotheses:

Case 1. Test quarterly financial stress (FSIt) as a random walk:

(59)

Case 2. Test quarterly FSIt as a random walk with drift:

FSI β δFSI u (60)

Case 3. Test quarterly FSIt as a random walk with drift around a stochastic trend:

FSI β βtδFSI u (61)

Typically, the null hypothesis is that 0, that is there is a unit root and time

series is nonstationary84:

: 0 | (62) : 0 |

If the null hypothesis is rejected for case 1, then FSIt is stationary with a zero

85 mean. If the null hypothesis is rejected for case 2, then FSIt is stationary with a nonzero

mean. If the null hypothesis is rejected for case 3, then FSIt is stationary around a

deterministic trend. As Table 19 shows, quarterly FSIt can be considered stationary with

random variability and draft at 1% critical level. Thus, we conclude that the quarterly financial stress time-series exhibits random variability and is appropriate for further dynamic factor analysis.

: 0 | 84 Except that under the KPSS test, . : 1 | 85 Since quarterly financial stress is measured from 0 to 100, it clearly has a non-zero mean. Therefore, case 1(random walk with zero mean) testing is omitted for brevity. 155

Table 19 Unit Root Tests of Quarterly Financial Stress Unit Root tests: DFa ADFb PPc KPSSd ERSe NPf MZa MZt MSB MPT Test statistic -0.90(ns) -0.93(ns)

CFSIt 1% level -2.59 -2.59 critical values as a random walk 5% level -1.94 -1.94 τ 10% level -1.61 -1.61 Test statistic -3.02*** -2.70* -2.41(ns) 0.16(ns) -2.72*** -15.21*** -2.64*** 0.17*** 2.02**

CFSIt 1% level -2.59 -3.51 -3.50 0.74 -2.59 -13.80 -2.58 0.17 1.78 critical values as a random walk with drift 5% level -1.94 -2.90 -2.89 0.46 -1.94 -8.10 -1.98 0.23 3.17 τ 10% level -1.61 -2.59 -2.58 0.35 -1.61 -5.70 -1.62 0.28 4.45 Test statistic -3.04* -2.74(ns) -2.43(ns 0.15(ns) -2.82* -15.20* -2.69* 0.17* 6.41* CFSIt 1% level -3.62 -4.06 -4.06 0.22 -3.61 -23.80 -3.42 0.14 4.03 as a random walk with drift critical values 5% level -3.06 -3.46 -3.46 0.15 -3.05 -17.30 -2.91 0.17 5.48 around a stochastic trend τ 10% level -2.77 -3.16 -3.16 0.12 -2.76 -14.20 -2.62 0.19 6.67 Note: a—Dickey Fuller test, b—Augmented Dickey Fuller test, c—Phillips-Perron test, d—Kwiatkowski-Phillips-Schmidt-Shin test, e—Elliot-Rothenberg-Stock test, f—Ng-Perron test; *—significance at 10% level, **—significance at 5% level, ***—significance at 1% level, (ns)—not significant at 10% level.

Estimation of dependency window. We follow Molenaar (1985) in selecting a dependency window of size (63) 1, where is the maximum lag length of significant effects present in the data. Here, effects are considered significant at

5% level, if the autocorrelations of lagged data exceed the corresponding approximate

error bounds . As shown in Figure 28, 5 for the quarterly financial stress data; accordingly, we use the dependency window of lag 6.

Figure 28 Correlogram of Quarterly Financial Stress Lagged autocorrelation Number AC PAC Q‐Stat Prob

1 1 0.866 0.866 73.598 0.000 0.8 2 0.701 ‐0.200 122.290 0.000 0.6 0.4 3 0.549 ‐0.027 152.500 0.000 0.2 4 0.402 ‐0.092 168.880 0.000 0 5 0.239 ‐0.174 174.720 0.000 -0.2 123456789101112 6 0.113 0.047 176.040 0.000 -0.4

4.3.4.2. Construction and descriptive analysis of the block-diagonal Toeplitz matrix

Construction of the block-diagonal Toeplitz matrix. The block-diagonal matrix illustrated in Figure 29 shows a stylized structure for a DFA of four observable variables that have a two-lag window of time dependency. In the above matrix, the triangular blocks are composed of variances and covariances of matching lagged pairs of observed 156

variables: Lag 0-Lag 0 in the upper left of the diagonal, Lag 1-Lag 1 in the middle of the diagonal, Lag 2-Lag 2 in the bottom right of the diagonal. The rectangular blocks are composed of variances of non-matching lagged pairs of observed variables: Lag 1-Lag 0 in the middle of the first column, Lag 2-Lag 0 in the bottom of the first column, and Lag

2-Lag 1 in the bottom of the second column.

In the third stage of our dynamic factor analysis, we apply a similar block- diagonal approach to the study dataset of thirty-seven variables observed with a quarterly frequency and manifesting a six lag-dependency. The estimation of the rectangular

Toeplitz covariance matrix is straightforward and can be facilitated in most modern statistical packages. Because the resulting 216 216 matrix is quite large and difficult to present, we show our results are schematically in Figure 30, which illustrates the pattern of symmetry and relative magnitude of manifest covariances over the six-lag window.

Figure 29 Stylized Block-Diagonal Toeplitz Matrix Lag 0 0 Lag

Lag 0 variances/covariances Lag 1 1 Lag

Lag 1 Lag 0 Lag 2 2 Lag

Lag 2 Lag 1 Lag 0

Lag 0 Lag 1 Lag 2

157

Descriptive analysis of the block-diagonal Toeplitz matrix. Wood (2012: 581) suggests that a common property of the dynamic factor models is that effects of latent variables wears itself out over time, so that “only those latent variables found to exist in the lag 0 factor analysis may be examined for the presence of lagged effects.” We verify

that this property holds by considering whether the Toeplitz covariance is a

decreasing function: that is for any lags i, j, m, and n, (64) ⇒

86 . This property supports the idea that dynamic effects might be parsimoniously

captured by focusing on more proximate lags. Had this not been the case, it would be

quite difficult to simplify the model by focusing on near-term lags and would be critical

to capture the important relationships that happen only at longer lags, but oddly do not

manifest at short lags. Figure 30 is color-coded to emphasize that manifest variables

exhibit a symmetric and diminishing covariation with overall financial stress with the

passage of time.

Figure 30 Toeplitz Intensity and Symmetry Pattern for Quarterly Financial Stress

Lag 00 Lag 01 Lag 02 Lag 03 Lag 04 Lag 05

Lag 10 Lag 11 Lag 12 Lag 13 Lag 14 Lag 15

Lag 20 Lag 21 Lag 22 Lag 23 Lag 24 Lag 25

Lag 30 Lag 31 Lag 32 Lag 33 Lag 34 Lag 35

Lag 40 Lag 41 Lag 42 Lag 43 Lag 44 Lag 45

Lag 50 Lag 51 Lag 52 Lag 53 Lag 54 Lag 55

86 Full statistical testing of this property is for the present beyond the scope of this study. We examine the rectangular Toeplitz matrix manually to verify that it holds for most of the variables. For

example: 0.005 0.004 0.004 0.003

0.002 0.001 or 25.749

25.177 24.500 23.933 23.380

22.626 . The five-lag rectangular Toeplitz matrix is available from the authors on request. 158

4.3.4.3. Cholesky factorization

Consistently with well-established exploratory-confirmatory analytical paradigm in the P- and R- techniques of static factor analysis (Jöreskog, 2007), Wood (2012: 577) advances the combined use of Cholesky factorization and parallel factor analysis to establish exploratory analysis prior to undertaking “the fitting of dynamic factor models via confirmatory models.” To this end, Cholesky decomposition of the Toeplitz matrix of lagged covariances allows researcher “to explore the dimensionality length of time- lagged components of the model.”

In a Cholesky factorization, the a symmetric positive-definite covariance matrix is expressed as a product of the lower triangular matrix and the upper triangular matrix

. can be considered a form of the ∗∗, where (65) ∗√. Note that (66)

, where is an identity matrix representing orthogonal variables with unit

variances. It follows that Cholesky factorization represents the corresponding latent

variable model. Wood (2012: 578) points out that “When time-lagged data are considered

in a block Toeplitz matrix such as that described above, the sum of squared loadings within a block can be considered an eigenvalue associated with the latent variable represented in the row.”

It is useful to offer further discussion of Cholesky factorization to clarify its methodological purpose as a component of dynamic factor analysis. In general, a Toeplitz

matrix of covariances can be ill-formed, that is, be anything other than symmetric

positive-definite. Such a Toeplitz matrix lends itself to only one type of factor solution:

principal components, where the orthogonality of components is enforced statistically,

regardless whether they make sense as common factors. Here, the intermediate use of 159

Cholesky factorization enforces the desired symmetric positive definite properties of the

Toeplitz matrix of lagged covariances by seeking out an appropriate subset of lagged covariances. This Cholesky-reduced symmetric positive-definite subset allows a richer set of factor extraction and rotation techniques and provide researcher with more opportunities for a coordinated conceptually-meritorious and statistically-sound exploratory dynamic factor analysis.

Accordingly, we establish that the original rectangular Toeplitz matrix of covariances of order 5 is symmetric but not positive-definite. We apply Cholesky- factorization to find a symmetric positive-definite subset of order 4, consisting of 65 manifest variables, shown in Table 19.

Considering the lower triangular matrix from the Cholesky factorization shown in

Table 19, we note that the results are puzzling. The retained set of manifest variables consists of observations in the credit, real estate, and securitization markets that have already been shown to yield interpretable static common factors in our prior work. The odd aspect of the factorization is the omission of the observations from the Foreign

Exchange (FX) and Equity markets. There are two possible explanations of this fact: 1) heterogeneity of observations, and 2) scale of the dynamic processes.

The intuition for the first—heterogeneity of observations—comes from the fact that the omitted observations represent time series with little in common and cannot reasonably be expected to reflect some common latent factor. In fact, the opposite, formative causation can be hypothesized and tested, where the variance in observations exhibits Granger causality with respect to financial stress and not vice versa. The first conjecture is tested by Granger causality between the omitted manifest variables and

160

quarterly financial stress. The intuition for the second—scale of the dynamic processes— is based on the idea the dynamic relationship between latent factors in the equity and FX markets takes place at a different, faster, frequency, than the latent-manifest relationships in the credit, real estate, and securitization markets. The second conjecture is tested by

Cholesky factorization of the FX-Equity subset at several alternative frequencies: daily, weekly, bi-weekly, and monthly.

We provide results of testing the first conjecture in Table 21, Panel A. As shown, there is weak evidence for Granger causality of the quarterly manifest variables in the FX and Equity markets with financial stress. Only two variables (covered interest spreads relative to Canada and Japan), both in the FX market, lead the changes in financial stress.

By this reasoning, Granger causality testing reveals no support for the idea that financial stress can be considered a latent common factor that explains distinct movements in the

FX and Equity variables. We, therefore, move to testing the second conjecture, that the dynamic relationships between financial stress and FX and Equity observations is based on a frequency other than quarterly.

161

Table 20 Cholesky Decomposition

RE_RRE_L0 RE_CRE_L0 FD_BBS_L0 FD_IBCOB_L0 FD_FB_L0 FD_IBLS_L0 CR_CBS_L0 CR_CPTBS_L0 CR_LIQS_L0 CR_TYCS_L0 SE_ABS_L0 SE_CMBS_L0 SE_RMBS_L0 RE_RRE_L1 RE_CRE_L1 FD_BBS_L1 FD_IBCOB_L1 FD_FB_L1 FD_IBLS_L1 CR_CBS_L1 CR_CPTBS_L1 CR_LIQS_L1 CR_TYCS_L1 SE_ABS_L1 SE_CMBS_L1 SE_RMBS_L1 RE_RRE_L2 RE_CRE_L2 FD_BBS_L2 FD_IBCOB_L2 FD_FB_L2 FD_IBLS_L2 CR_CBS_L2 CR_CPTBS_L2 CR_LIQS_L2 CR_TYCS_L2 SE_ABS_L2 SE_CMBS_L2 SE_RMBS_L2 RE_RRE_L3 RE_CRE_L3 FD_BBS_L3 FD_IBCOB_L3 FD_FB_L3 FD_IBLS_L3 CR_CBS_L3 CR_CPTBS_L3 CR_LIQS_L3 CR_TYCS_L3 SE_ABS_L3 SE_CMBS_L3 SE_RMBS_L3 RE_RRE_L4 RE_CRE_L4 FD_BBS_L4 FD_IBCOB_L4 FD_FB_L4 FD_IBLS_L4 CR_CBS_L4 CR_CPTBS_L4 CR_LIQS_L4 CR_TYCS_L4 SE_ABS_L4 SE_CMBS_L4 SE_RMBS_L4

RE_RRE_L0 1.553

0.167 0.651 RE_CRE_L0

0.380 0.457 0.400 FD_BBS_L0

0.204 0.154 -0.392 0.694 FD_IBCOB_L0

0.119 -0.020 -0.410 0.269 0.675 FD_FB_L0

0.252 0.178 -0.366 0.490 -0.027 0.640 FD_IBLS_L0

0.693 0.464 0.767 -0.228 -0.050 -0.207 0.584 CR_CBS_L0

0.309 0.235 -0.643 0.657 -0.035 0.939 -0.170 0.355 CR_CPTBS_L0

0.265 0.286 0.005 -0.012 0.191 -0.238 -0.546 0.288 0.764 CR_LIQS_L0

-0.054 -0.206 -0.594 0.156 -0.286 0.915 -0.069 -0.121 0.060 0.681 CR_TY CS_L0

0.219 1.164 -0.138 0.193 0.139 0.119 -0.322 -0.069 0.220 0.172 0.492 SE_ABS_L0

0.054 0.272 0.018 -0.001 0.033 -0.036 -0.033 -0.017 0.030 -0.020 0.061 0.037 SE_CMBS_L0 LAG 0 LAG 1 LAG 2 LAG 3 LAG 4 4.737 0.514 0.159 -0.066 0.442 -0.702 0.202 -0.572 -0.169 -0.342 0.989 0.569 0.719 SE_RMBS_L0

1.316 0.010 0.147 0.218 0.143 -0.243 0.036 -0.196 0.027 -0.049 -0.205 -0.012 -0.170 0.588 RE_RRE_L1

0.134 0.633 0.045 -0.029 0.011 -0.057 0.038 -0.021 -0.021 0.034 -0.021 -0.013 -0.009 0.062 0.132 RE_CRE_L1

0.333 0.446 0.417 -0.047 0.020 -0.122 0.039 -0.051 0.018 -0.006 -0.034 -0.037 -0.063 0.087 0.064 0.156 FD_BBS_L1

0.124 0.196 -0.352 0.527 0.066 0.100 0.061 -0.071 0.094 0.088 0.032 -0.176 -0.022 0.074 0.010 -0.019 0.416 FD_IBCOB_L1

0.025 0.005 -0.441 0.283 0.519 0.013 -0.017 -0.018 0.011 -0.076 -0.022 -0.081 -0.020 0.026 0.020 0.026 0.066 0.410 FD_FB_L1 LAG 0 0.288 0.232 -0.311 0.415 -0.004 0.579 0.006 -0.126 0.008 0.098 -0.028 -0.158 -0.111 0.047 0.049 0.020 0.121 0.030 0.247 FD_IBLS_L1

0.539 0.378 0.766 -0.227 0.042 -0.435 0.501 -0.147 -0.099 -0.029 -0.145 -0.048 -0.038 0.237 0.112 0.191 -0.078 -0.037 0.038 0.291 CR_CBS_L1

0.419 0.337 -0.548 0.608 -0.032 0.861 -0.143 0.069 0.046 0.147 -0.049 -0.186 -0.126 0.047 0.043 0.052 0.116 0.022 0.359 -0.025 0.264 CR_CPTBS_L1

0.265 0.332 -0.026 -0.094 0.219 -0.271 -0.483 0.243 0.661 -0.043 0.037 0.023 -0.114 -0.010 0.016 -0.005 0.006 -0.010 -0.036 0.082 0.121 0.351 CR_LIQS_L1

0.069 -0.215 -0.497 0.131 -0.223 0.982 -0.188 -0.159 0.017 0.500 -0.021 -0.039 -0.086 0.145 0.220 -0.029 -0.116 -0.037 0.060 0.103 -0.102 -0.016 0.303 CR_TY CS_L1

0.188 1.186 0.005 0.098 0.222 0.074 -0.307 -0.129 0.165 0.190 0.359 0.040 0.005 0.141 0.200 -0.020 0.009 0.029 0.017 0.058 -0.004 0.023 0.083 0.194 SE_ABS_L1

0.039 0.271 0.036 -0.009 0.043 -0.057 -0.014 -0.023 0.020 -0.008 0.050 0.028 0.000 0.015 0.045 -0.005 -0.001 0.002 0.001 0.001 -0.004 0.002 -0.002 0.003 0.010 SE_CMBS_L1

3.820 0.542 0.803 0.767 1.012 -1.388 0.267 -1.325 -0.080 -0.423 0.108 0.546 0.102 1.877 -0.003 -0.117 0.039 0.092 -0.003 -0.038 -0.051 -0.004 -0.080 0.042 0.273 0.383 SE_RMBS_L1

0.999 -0.004 0.172 0.257 0.253 -0.462 0.103 -0.173 0.054 -0.129 -0.280 -0.130 -0.317 0.442 0.030 0.112 0.247 0.021 0.034 -0.058 -0.256 -0.017 0.102 -0.045 -0.012 -0.094 0.524 RE_RRE_L2

0.098 0.591 0.079 -0.084 0.020 -0.097 0.073 -0.007 -0.039 0.026 -0.007 -0.066 0.030 0.069 0.178 -0.003 0.011 0.012 -0.019 -0.011 -0.023 -0.007 0.031 -0.016 0.010 -0.037 0.060 0.091 RE_CRE_L2

0.260 0.419 0.414 -0.118 0.010 -0.234 0.051 -0.064 0.022 -0.059 -0.043 -0.088 -0.080 0.084 0.086 0.135 0.012 0.017 -0.044 0.037 -0.038 -0.029 -0.003 0.010 0.001 -0.038 0.094 0.052 0.132 LAG 1 FD_BBS_L2

0.045 0.213 -0.312 0.397 0.137 0.166 0.061 0.028 0.126 0.148 0.004 -0.251 0.024 0.119 0.067 0.017 0.217 -0.007 0.064 0.068 -0.203 -0.021 -0.012 0.139 -0.003 0.058 0.047 0.000 0.027 0.331 FD_IBCOB_L2

-0.060 0.053 -0.439 0.230 0.309 0.061 -0.033 0.021 0.069 -0.155 -0.004 -0.137 -0.015 0.082 -0.044 -0.043 0.130 0.410 0.044 0.004 -0.016 -0.067 -0.018 0.033 -0.049 0.098 0.045 0.009 -0.026 0.072 0.334 FD_FB_L2

0.265 0.267 -0.233 0.351 0.044 0.541 -0.027 -0.073 -0.014 0.104 -0.106 -0.242 -0.138 0.139 0.083 -0.014 0.089 0.023 0.170 0.048 -0.205 -0.049 0.042 0.090 -0.027 -0.034 0.027 0.063 0.037 0.059 0.036 0.203 FD_IBLS_L2

0.335 0.270 0.723 -0.291 0.076 -0.602 0.418 -0.186 -0.178 -0.198 -0.196 -0.158 -0.066 0.176 0.170 0.218 0.029 -0.033 -0.090 0.176 -0.084 -0.047 0.047 -0.009 0.010 -0.013 0.207 0.083 0.148 -0.080 -0.024 0.012 0.258 CR_CBS_L2

0.426 0.414 -0.459 0.598 0.036 0.819 -0.127 0.060 0.050 0.143 -0.181 -0.293 -0.117 0.183 0.066 0.001 0.070 -0.013 0.238 0.042 -0.163 0.009 0.124 0.095 -0.048 -0.129 0.013 0.055 0.106 -0.011 0.062 0.257 -0.022 0.204 CR_CPTBS_L2

0.275 0.379 -0.104 -0.160 0.206 -0.337 -0.415 0.246 0.552 -0.122 0.125 0.007 -0.131 0.022 -0.017 0.011 -0.045 0.007 -0.033 0.084 0.068 0.256 0.043 -0.020 -0.044 -0.012 -0.016 -0.009 -0.006 -0.001 -0.055 -0.008 0.068 0.127 0.310 CR_LIQS_L2

0.209 -0.220 -0.424 0.087 -0.172 0.987 -0.326 -0.158 -0.079 0.292 -0.005 -0.133 -0.148 0.136 0.261 -0.017 -0.074 -0.039 0.133 0.035 -0.136 -0.026 0.202 -0.024 -0.027 -0.086 0.143 0.172 -0.085 -0.094 -0.050 0.038 0.071 -0.056 -0.037 0.260 CR_TY CS_L2

0.136 1.180 0.129 -0.020 0.244 0.021 -0.310 -0.106 0.104 0.086 0.298 -0.017 0.024 0.165 0.281 0.004 0.017 0.113 0.015 0.013 -0.068 0.018 0.157 0.075 0.042 -0.017 0.127 0.152 -0.041 0.028 -0.019 -0.012 0.056 0.023 0.006 0.069 0.155 SE_ABS_L2

0.023 0.261 0.049 -0.030 0.049 -0.073 0.002 -0.017 0.011 -0.009 0.053 0.007 0.013 0.016 0.061 -0.002 0.004 0.012 -0.006 -0.003 -0.009 0.000 0.008 -0.002 0.012 -0.004 0.015 0.032 -0.004 -0.001 0.001 0.002 0.001 -0.002 0.001 -0.002 0.004 0.009 SE_CMBS_L2

2.660 0.483 0.983 0.869 1.342 -2.047 0.488 -1.197 0.047 -0.572 -0.129 0.085 -0.598 1.317 0.147 0.479 0.891 0.299 0.150 -0.358 -1.015 -0.058 0.240 -0.181 0.276 0.205 1.629 0.057 -0.083 0.006 0.098 0.054 -0.037 0.000 -0.032 -0.076 0.091 0.182 0.327 SE_RMBS_L2 LAG 2 0.746 -0.021 0.145 0.269 0.207 -0.645 0.125 -0.002 0.121 -0.178 -0.261 -0.252 -0.298 0.179 0.021 0.134 0.222 0.122 -0.093 0.107 -0.353 -0.206 -0.063 0.012 -0.027 -0.018 0.422 0.095 0.041 0.174 0.004 0.047 -0.044 -0.269 -0.016 0.089 0.016 -0.051 -0.104 0.416 RE_RRE_L3

0.076 0.538 0.111 -0.137 0.010 -0.125 0.097 0.008 -0.063 0.002 0.012 -0.104 0.105 0.041 0.170 -0.013 -0.014 0.033 -0.037 0.009 -0.015 -0.009 0.021 0.000 -0.009 -0.033 0.078 0.102 -0.019 0.016 -0.002 -0.007 -0.015 -0.025 -0.019 0.027 -0.005 0.015 -0.025 0.049 0.071 RE_CRE_L3

0.201 0.384 0.403 -0.188 -0.015 -0.315 0.064 -0.029 0.014 -0.104 -0.030 -0.118 -0.053 0.036 0.065 0.062 0.005 0.023 -0.103 0.061 -0.061 -0.046 -0.055 0.029 0.009 -0.032 0.118 0.052 0.077 0.016 -0.008 -0.042 0.039 -0.016 -0.040 -0.023 0.003 0.015 -0.031 0.085 0.034 0.100 FD_BBS_L3

-0.025 0.213 -0.283 0.231 0.182 0.236 -0.041 0.040 0.059 0.193 -0.107 -0.241 -0.001 0.095 0.080 0.025 0.207 0.065 0.054 0.182 -0.091 0.024 -0.104 0.161 0.099 0.009 0.112 0.123 -0.029 0.170 -0.001 0.022 0.084 -0.114 0.004 -0.051 0.146 -0.003 0.007 0.029 0.088 -0.039 0.247 FD_IBCOB_L3

-0.128 0.103 -0.402 0.177 0.186 0.058 -0.081 0.091 0.076 -0.068 -0.015 -0.131 -0.035 0.081 -0.070 -0.072 0.103 0.223 0.206 -0.006 -0.029 -0.070 -0.081 0.058 -0.028 0.169 0.048 -0.021 -0.058 0.088 0.356 0.042 0.006 0.008 -0.077 -0.018 0.038 -0.108 0.034 0.044 0.057 -0.003 0.064 0.290 FD_FB_L3

0.243 0.285 -0.165 0.232 0.082 0.505 -0.100 -0.024 -0.070 0.070 -0.193 -0.311 -0.189 0.099 0.114 -0.004 0.126 0.034 0.132 0.063 -0.149 -0.082 0.020 0.105 -0.018 -0.029 0.116 0.099 -0.057 0.071 0.004 0.101 0.010 -0.157 -0.040 0.012 0.082 -0.021 -0.016 0.011 0.088 0.029 0.027 0.036 0.167 FD_IBLS_L3

0.206 0.171 0.656 -0.399 0.012 -0.743 0.354 -0.132 -0.202 -0.285 -0.141 -0.277 0.010 0.006 0.077 0.131 0.036 0.035 -0.150 0.084 -0.098 -0.171 -0.078 -0.001 0.015 0.034 0.186 0.066 0.132 0.053 -0.063 -0.049 0.139 -0.044 -0.099 0.028 -0.007 0.018 0.016 0.213 -0.005 0.118 -0.025 -0.053 0.015 0.201 CR_CBS_L3

0.423 0.471 -0.379 0.435 0.108 0.794 -0.212 0.022 -0.044 0.069 -0.299 -0.453 -0.206 0.138 0.122 0.010 0.207 -0.005 0.174 0.115 -0.102 -0.008 0.073 0.068 -0.039 -0.038 0.161 0.061 -0.062 0.048 -0.047 0.124 -0.036 -0.123 -0.006 0.060 0.064 -0.013 -0.078 0.014 0.042 0.081 -0.016 0.072 0.190 -0.055 0.172 CR_CPTBS_L3

0.296 0.432 -0.182 -0.252 0.231 -0.362 -0.328 0.202 0.442 -0.178 0.146 0.070 -0.087 0.004 -0.114 -0.041 0.001 -0.025 -0.066 0.098 0.121 0.170 0.027 0.074 0.002 -0.074 0.023 -0.039 -0.018 -0.012 -0.038 0.011 0.066 0.080 0.200 0.059 0.016 -0.028 0.006 -0.019 -0.077 -0.031 -0.025 -0.021 -0.019 0.013 0.107 0.229 CR_LIQS_L3

0.358 -0.201 -0.332 0.105 -0.147 0.946 -0.367 -0.113 -0.120 0.116 0.026 -0.210 -0.198 0.104 0.178 -0.077 -0.136 -0.024 0.128 -0.127 -0.129 -0.073 0.145 0.042 -0.092 -0.098 0.147 0.167 -0.069 -0.048 -0.068 0.141 -0.020 -0.082 -0.070 0.178 0.003 -0.069 -0.069 0.164 0.158 -0.101 -0.106 -0.089 0.036 0.067 -0.034 -0.036 0.172 CR_TY CS_L3

LAG 3 0.119 1.168 0.201 -0.143 0.200 -0.048 -0.286 -0.080 0.065 -0.018 0.296 -0.091 0.094 0.078 0.219 0.049 -0.056 0.138 -0.019 -0.009 -0.064 -0.016 0.077 0.023 -0.003 -0.032 0.183 0.203 -0.071 0.043 0.052 0.023 0.008 -0.042 -0.029 0.130 0.075 0.042 0.001 0.109 0.131 -0.056 0.016 -0.024 -0.006 0.046 0.019 0.019 0.085 0.114 SE_ABS_L3

0.010 0.247 0.062 -0.052 0.046 -0.085 0.014 -0.011 0.002 -0.016 0.058 -0.009 0.040 0.010 0.057 -0.003 -0.006 0.024 -0.012 0.005 -0.004 -0.003 0.004 0.003 0.001 -0.003 0.019 0.038 -0.007 0.006 0.005 0.000 -0.004 -0.008 -0.006 0.007 0.003 0.011 0.000 0.010 0.026 -0.002 0.000 0.000 0.003 0.001 -0.002 0.001 -0.001 0.002 0.007 SE_CMBS_L3

1.699 0.414 0.916 0.795 1.091 -2.588 0.555 -0.588 0.321 -0.666 0.026 -0.442 -0.705 0.509 0.043 0.612 0.752 0.690 -0.292 0.285 -1.309 -0.745 -0.313 -0.031 0.191 0.330 1.240 0.442 0.234 0.641 0.222 0.315 -0.296 -0.962 -0.128 0.242 0.064 0.010 0.073 1.290 0.063 -0.028 0.084 0.052 0.129 -0.085 0.002 -0.054 -0.062 0.083 0.185 0.265 SE_RMBS_L3

0.484 -0.071 0.109 0.225 0.149 -0.764 0.104 0.077 0.223 -0.163 -0.266 -0.301 -0.240 0.126 0.136 0.114 0.280 0.079 -0.119 0.159 -0.164 -0.226 -0.286 0.141 -0.037 -0.034 0.161 0.071 0.003 0.131 0.148 -0.087 0.084 -0.320 -0.132 -0.128 0.142 -0.117 -0.091 0.269 0.221 0.087 0.054 -0.068 -0.015 0.013 -0.220 0.067 0.107 0.036 -0.052 0.006 0.272 RE_RRE_L4

0.051 0.475 0.160 -0.163 -0.009 -0.154 0.100 -0.006 -0.084 -0.012 0.005 -0.097 0.179 0.045 0.176 -0.017 -0.042 0.037 -0.027 0.001 0.019 0.004 -0.023 0.018 -0.046 -0.005 0.053 0.077 -0.036 -0.014 0.018 -0.024 0.002 -0.021 -0.010 0.005 0.028 -0.015 -0.024 0.059 0.088 -0.009 0.013 -0.013 -0.008 -0.011 -0.021 0.005 0.032 -0.003 0.006 -0.002 0.012 0.049 RE_CRE_L4

0.137 0.336 0.402 -0.218 -0.061 -0.412 0.065 -0.019 0.022 -0.112 -0.033 -0.092 0.005 0.022 0.085 0.039 -0.028 0.017 -0.068 0.039 -0.014 -0.059 -0.090 0.055 -0.047 -0.031 0.054 0.021 -0.004 0.020 -0.012 -0.079 0.061 -0.044 -0.048 -0.087 0.032 0.017 -0.020 0.093 0.031 0.064 0.026 -0.011 -0.042 0.044 -0.004 -0.011 -0.002 0.006 0.010 0.010 0.049 0.018 0.071 FD_BBS_L4

-0.057 0.213 -0.260 0.094 0.159 0.300 -0.066 0.134 0.092 0.136 -0.119 -0.280 0.028 0.096 0.072 0.038 0.052 0.114 0.040 0.036 -0.105 -0.071 0.023 0.047 -0.043 0.069 0.080 0.057 0.027 0.106 0.014 0.018 0.193 -0.082 0.009 -0.103 0.190 0.079 0.024 0.105 0.157 -0.055 0.130 -0.040 0.034 0.079 -0.097 0.025 -0.066 0.175 -0.038 0.051 0.027 0.057 -0.020 0.129 FD_IBCOB_L4

-0.192 0.137 -0.385 0.160 0.139 0.061 -0.142 0.198 -0.012 0.005 -0.015 -0.107 -0.059 0.089 -0.045 -0.007 0.061 0.054 0.179 0.024 -0.061 0.035 -0.029 0.019 -0.007 0.115 -0.007 -0.011 -0.037 0.014 0.228 0.169 -0.037 -0.033 -0.102 -0.112 0.081 -0.143 0.056 0.035 0.026 -0.004 0.107 0.284 0.036 -0.001 -0.043 -0.063 -0.038 0.082 -0.114 -0.008 0.022 0.075 0.052 0.051 0.204 FD_FB_L4

0.229 0.296 -0.110 0.209 0.032 0.443 -0.112 0.093 -0.069 0.019 -0.235 -0.343 -0.165 0.076 0.129 0.015 -0.018 0.090 0.074 -0.018 -0.173 -0.091 -0.023 0.095 -0.100 -0.089 0.096 0.104 -0.038 0.067 0.024 0.058 0.043 -0.172 -0.047 -0.007 0.129 -0.023 0.002 0.061 0.121 -0.054 0.032 0.026 0.059 0.078 -0.168 0.001 0.026 0.069 -0.006 0.044 -0.030 0.052 0.021 -0.010 0.036 0.087 FD_IBLS_L4

0.054 0.073 0.605 -0.388 -0.065 -0.861 0.304 -0.113 -0.167 -0.246 -0.196 -0.189 0.117 0.004 0.023 0.039 -0.044 0.016 -0.184 0.024 -0.038 -0.162 -0.254 0.121 -0.043 0.017 0.038 0.037 0.016 0.050 0.026 -0.112 0.062 -0.048 -0.174 -0.134 0.022 -0.001 0.050 0.166 0.067 0.097 0.062 -0.108 -0.076 0.086 -0.036 -0.059 0.020 -0.020 -0.019 0.098 0.146 -0.001 0.081 -0.077 -0.035 0.008 0.141 CR_CBS_L4

0.416 0.510 -0.343 0.413 0.035 0.695 -0.189 0.117 -0.062 -0.005 -0.379 -0.472 -0.219 0.094 0.174 0.095 -0.010 0.079 0.111 -0.047 -0.227 -0.008 -0.021 0.192 -0.167 -0.133 0.123 0.158 -0.036 0.130 0.011 0.073 0.063 -0.160 0.040 0.025 0.118 -0.055 0.010 0.093 0.112 -0.027 -0.001 0.011 0.038 0.068 -0.128 0.035 0.074 0.020 0.013 0.004 -0.047 0.002 0.050 0.049 0.063 0.093 -0.043 0.100 LAG 4 CR_CPTBS_L4

0.322 0.496 -0.208 -0.228 0.263 -0.457 -0.287 0.091 0.310 -0.138 0.106 0.171 -0.074 -0.032 -0.121 -0.050 -0.116 -0.062 -0.073 0.056 0.189 0.130 0.013 0.075 -0.012 0.028 0.012 -0.062 -0.044 0.086 0.002 0.003 0.094 0.106 0.140 0.033 0.141 0.022 -0.044 0.017 -0.103 -0.042 -0.124 0.032 -0.028 0.031 0.023 0.076 0.012 -0.041 -0.036 -0.038 0.007 -0.040 -0.029 0.034 -0.053 -0.055 -0.030 0.026 0.136 CR_LIQS_L4

0.468 -0.169 -0.191 0.228 -0.086 0.834 -0.440 -0.086 -0.174 0.062 -0.075 -0.198 -0.192 0.066 0.127 -0.150 -0.127 -0.041 0.218 -0.124 -0.130 -0.105 0.046 0.061 -0.173 -0.213 0.088 0.101 -0.112 -0.111 0.009 0.059 -0.189 -0.132 -0.026 0.090 0.083 -0.092 -0.058 0.117 0.176 -0.011 -0.087 -0.099 0.046 -0.010 -0.099 0.032 0.202 -0.020 -0.068 0.034 0.014 0.103 -0.076 -0.112 -0.070 -0.046 0.038 -0.058 -0.062 0.073 CR_TY CS_L4

0.091 1.143 0.284 -0.229 0.167 -0.132 -0.257 -0.092 0.037 -0.055 0.255 -0.076 0.159 0.060 0.191 0.027 -0.110 0.095 -0.001 -0.044 -0.016 -0.028 -0.031 0.035 -0.106 -0.005 0.093 0.142 -0.021 -0.056 0.095 -0.019 -0.033 -0.059 -0.047 0.038 0.068 -0.047 -0.026 0.162 0.217 -0.038 0.023 -0.013 0.004 -0.011 -0.044 0.021 0.142 0.015 -0.010 0.071 0.031 0.110 -0.036 0.001 -0.033 -0.014 0.003 -0.006 0.018 0.055 0.059 SE_ABS_L4

-0.004 0.229 0.078 -0.065 0.039 -0.095 0.019 -0.014 -0.009 -0.020 0.054 -0.010 0.066 0.010 0.056 -0.008 -0.017 0.026 -0.013 0.005 0.007 0.005 -0.010 0.008 -0.008 0.005 0.015 0.027 -0.012 -0.005 0.016 -0.006 0.004 -0.004 -0.006 0.001 0.012 -0.003 0.000 0.013 0.033 -0.003 0.007 0.001 0.003 -0.003 -0.006 0.000 0.010 0.001 0.006 0.006 0.000 0.019 -0.001 0.000 0.000 0.003 0.000 -0.001 -0.002 0.000 0.003 0.002

162 SE_CMBS_L4

0.735 0.225 0.864 0.558 0.852 -2.856 0.457 -0.234 0.664 -0.602 0.087 -0.666 -0.662 0.324 0.455 0.417 0.826 0.461 -0.505 0.571 -0.643 -0.865 -1.105 0.509 0.091 0.271 0.506 0.258 0.113 0.418 0.738 -0.184 0.193 -1.033 -0.561 -0.498 0.451 -0.249 -0.017 0.749 0.850 0.348 0.324 -0.069 0.203 -0.119 -0.797 0.140 0.221 0.171 -0.036 0.356 0.811 -0.013 -0.030 0.055 0.075 0.147 -0.110 0.056 -0.064 0.017 0.160 0.014 0.144 SE_RMBS_L4

In order to determine potential frequency scale that to be tested for the FX and

Equity markets, we reconsider financial stress data at the highest available frequency scales, daily and weekly. As shown in Figure 31 autocorrelation of weekly financial stress exceeds the critical value of 0.056750435 ( ) for 86 weeks (5.375 √

quarters). This is an interesting and welcome result, as it clearly supports the originally

estimated dependency window of five quarters when considering financial stress at a

higher frequency.

163

Table 21 Granger Causality of FX and Equity Observations with Financial Stress PANEL A: Quarterly dependence PANEL B: Weekly dependence PANEL C: Daily dependence Quarterly Lag 0 - 1 window Quarterly Lag 0 - 5 window Weekly Lag 0-86 window Weekly Lag 0-1 window Daily Lag 0-29 window Daily Lag 0-13 window Daily Lag 0-6 window Daily Lag 0-1 window

Variables F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation F-Statistic Prob. Interpretation FSI does not Granger Cause EQ_S5COND 0.972 0.327 (ns) 0.706 0.621 (ns) 4.082 0.044 ††† 4.082 0.044 ††† 2.927 0.000 ††† 5.992 0.000 ††† 11.443 0.000 ††† 27.237 0.000 ††† EQ_S5COND does not Granger Cause FSI 0.848 0.359 (ns) 1.072 0.382 (ns) 0.704 0.402 (ns) 0.704 0.402 (ns) 1.125 0.294 (ns) 1.005 0.443 (ns) 1.820 0.091 †† 2.621 0.106 † FSI does not Granger Cause EQ_S5CONS 0.014 0.905 (ns) 1.357 0.250 (ns) 0.014 0.907 (ns) 0.014 0.907 (ns) 1.440 0.059 †† 1.342 0.180 † 1.610 0.140 † 2.322 0.128 † EQ_S5CONS does not Granger Cause FSI 0.546 0.462 (ns) 1.375 0.243 (ns) 0.056 0.814 (ns) 0.056 0.814 (ns) 1.087 0.341 (ns) 1.409 0.146 (ns) 0.838 0.540 (ns) 1.194 0.275 (ns) FSI does not Granger Cause EQ_S5ENRS 1.303 0.257 (ns) 0.757 0.584 (ns) 1.147 0.284 (ns) 1.147 0.284 (ns) 2.076 0.001 ††† 2.441 0.003 ††† 3.579 0.002 ††† 0.419 0.518 (ns) EQ_S5ENRS does not Granger Cause FSI 1.613 0.207 (ns) 1.325 0.262 (ns) 3.832 0.051 †† 3.832 0.051 †† 1.714 0.010 ††† 1.641 0.067 †† 1.576 0.150 † 6.450 0.011 ††† FSI does not Granger Cause EQ_S5FINL 1.080 0.301 (ns) 1.200 0.317 (ns) 4.758 0.029 ††† 4.758 0.029 ††† 5.027 0.000 ††† 9.044 0.000 ††† 17.885 0.000 ††† 32.667 0.000 ††† EQ_S5FINL does not Granger Cause FSI 0.281 0.598 (ns) 1.663 0.153 † 1.259 0.262 (ns) 1.259 0.262 (ns) 1.369 0.090 †† 2.140 0.010 ††† 0.478 0.825 (ns) 1.513 0.219 (ns) FSI does not Granger Cause EQ_S5HLTH 2.144 0.147 † 0.800 0.553 (ns) 1.681 0.195 † 1.681 0.195 † 1.621 0.019 ††† 3.093 0.000 ††† 4.978 0.000 ††† 18.340 0.000 ††† EQ_S5HLTH does not Granger Cause FSI 0.712 0.401 (ns) 0.896 0.488 (ns) 0.039 0.843 (ns) 0.039 0.843 (ns) 1.172 0.240 (ns) 0.745 0.719 (ns) 1.167 0.321 (ns) 1.777 0.183 † FSI does not Granger Cause EQ_S5INDU 0.758 0.386 (ns) 0.643 0.668 (ns) 1.681 0.195 † 1.681 0.195 † 4.322 0.000 ††† 7.678 0.000 ††† 14.299 0.000 ††† 17.445 0.000 ††† EQ_S5INDU does not Granger Cause FSI 0.103 0.749 (ns) 1.212 0.311 (ns) 3.724 0.054 †† 3.724 0.054 †† 1.534 0.033 ††† 2.430 0.003 ††† 4.809 0.000 ††† 3.958 0.047 ††† FSI does not Granger Cause EQ_S5INFT 0.210 0.648 (ns) 0.707 0.620 (ns) 0.108 0.743 (ns) 0.108 0.743 (ns) 1.911 0.002 ††† 3.011 0.000 ††† 4.691 0.000 ††† 2.045 0.153 † EQ_S5INFT does not Granger Cause FSI 1.374 0.244 (ns) 0.500 0.775 (ns) 0.206 0.650 (ns) 0.206 0.650 (ns) 1.328 0.112 † 1.741 0.047 ††† 2.358 0.028 ††† 0.012 0.914 (ns) FSI does not Granger Cause EQ_S5MATR 0.190 0.664 (ns) 1.385 0.239 (ns) 0.013 0.908 (ns) 0.013 0.908 (ns) 2.799 0.000 ††† 5.114 0.000 ††† 7.603 0.000 ††† 2.506 0.114 † EQ_S5MATR does not Granger Cause FSI 0.238 0.627 (ns) 1.029 0.407 (ns) 1.584 0.208 (ns) 1.584 0.208 (ns) 1.205 0.207 (ns) 1.505 0.107 † 2.747 0.011 ††† 1.527 0.217 (ns) FSI does not Granger Cause EQ_S5UTIL 1.432 0.235 (ns) 1.707 0.143 † 0.122 0.727 (ns) 0.122 0.727 (ns) 1.117 0.304 (ns) 1.644 0.066 †† 2.565 0.018 ††† 1.137 0.286 (ns) EQ_S5UTIL does not Granger Cause FSI 0.147 0.703 (ns) 0.750 0.589 (ns) 2.186 0.140 † 2.186 0.140 † 0.694 0.889 (ns) 0.605 0.852 (ns) 1.241 0.282 (ns) 1.700 0.192 † FSI does not Granger Cause FX_CIS_AUD 0.628 0.430 (ns) 2.398 0.045 ††† 1.913 0.167 † 1.913 0.167 † 1.656 0.015 ††† 1.139 0.320 (ns) 1.304 0.251 (ns) 0.117 0.732 (ns) FX_CIS_AUD does not Granger Cause FSI 0.133 0.716 (ns) 3.815 0.004 ††† 0.189 0.664 (ns) 0.189 0.664 (ns) 0.559 0.973 (ns) 0.747 0.717 (ns) 1.139 0.337 (ns) 0.103 0.749 (ns) FSI does not Granger Cause FX_CIS_CAD 0.060 0.807 (ns) 0.485 0.787 (ns) 0.095 0.758 (ns) 0.095 0.758 (ns) 2.122 0.000 ††† 3.123 0.000 ††† 4.113 0.000 ††† 0.018 0.894 (ns) FX_CIS_CAD does not Granger Cause FSI 1.684 0.198 † 3.162 0.012 †† 0.527 0.468 (ns) 0.527 0.468 (ns) 0.571 0.969 (ns) 0.729 0.736 (ns) 0.472 0.830 (ns) 0.472 0.492 (ns) FSI does not Granger Cause FX_CIS_EUR 0.729 0.396 (ns) 1.192 0.321 (ns) 4.476 0.035 ††† 4.476 0.035 ††† 2.421 0.000 ††† 2.494 0.002 ††† 3.812 0.001 ††† 4.578 0.032 ††† FX_CIS_EUR does not Granger Cause FSI 0.046 0.830 (ns) 3.541 0.006 ††† 0.391 0.532 (ns) 0.391 0.532 (ns) 1.624 0.019 ††† 1.884 0.027 ††† 1.604 0.142 † 1.754 0.185 † FSI does not Granger Cause FX_CIS_GBP 0.053 0.819 (ns) 0.322 0.899 (ns) 0.002 0.969 (ns) 0.002 0.969 (ns) 1.629 0.018 ††† 1.759 0.044 ††† 1.564 0.153 † 0.301 0.584 (ns) FX_CIS_GBP does not Granger Cause FSI 0.397 0.530 (ns) 1.211 0.312 (ns) 0.491 0.483 (ns) 0.491 0.483 (ns) 1.469 0.050 ††† 2.395 0.003 ††† 1.315 0.246 (ns) 0.574 0.449 (ns) FSI does not Granger Cause FX_CIS_JPY 1.907 0.171 † 1.957 0.094 †† 2.412 0.121 † 2.412 0.121 † 1.140 0.276 (ns) 1.670 0.060 †† 2.008 0.061 †† 0.001 0.972 FX_CIS_JPY does not Granger Cause FSI 4.806 0.031 ††† 2.469 0.039 ††† 3.736 0.054 †† 3.736 0.054 †† 1.223 0.190 † 1.561 0.088 †† 1.209 0.298 (ns) 2.863 0.091 †† FSI does not Granger Cause FX_CIS_MXN 0.032 0.858 (ns) 0.385 0.858 (ns) 0.914 0.339 (ns) 0.914 0.339 (ns) 0.924 0.583 (ns) 1.232 0.249 (ns) 0.850 0.531 (ns) 1.799 0.180 † FX_CIS_MXN does not Granger Cause FSI 0.138 0.711 (ns) 0.341 0.886 (ns) 0.211 0.646 (ns) 0.211 0.646 (ns) 0.779 0.795 (ns) 0.710 0.756 (ns) 0.918 0.480 (ns) 0.227 0.634 (ns) FSI does not Granger Cause FX_CIS_ZAR 1.635 0.204 (ns) 1.018 0.413 (ns) 1.194 0.275 (ns) 1.194 0.275 (ns) 1.097 0.328 (ns) 1.175 0.291 (ns) 1.140 0.336 (ns) 0.297 0.586 (ns) FX_CIS_ZAR does not Granger Cause FSI 0.063 0.802 (ns) 0.880 0.498 (ns) 0.023 0.879 (ns) 0.023 0.879 (ns) 1.353 0.098 †† 1.140 0.319 (ns) 1.363 0.225 (ns) 0.001 0.980 (ns) FSI does not Granger Cause FX_CRSH_AUD 0.068 0.795 (ns) 0.887 0.494 (ns) 0.002 0.969 (ns) 0.002 0.969 (ns) 1.279 0.144 † 1.319 0.193 † 2.170 0.043 ††† 0.270 0.603 (ns) FX_CRSH_AUD does not Granger Cause FSI 0.884 0.350 (ns) 1.765 0.130 † 0.331 0.565 (ns) 0.331 0.565 (ns) 1.807 0.005 ††† 0.951 0.498 (ns) 1.144 0.334 (ns) 0.017 0.896 (ns) FSI does not Granger Cause FX_CRSH_CAD 0.746 0.390 (ns) 1.220 0.307 (ns) 0.784 0.376 (ns) 0.784 0.376 (ns) 1.165 0.248 (ns) 1.317 0.194 † 2.082 0.052 †† 1.722 0.190 † FX_CRSH_CAD does not Granger Cause FSI 1.257 0.265 (ns) 2.133 0.070 †† 0.721 0.396 (ns) 0.721 0.396 (ns) 1.653 0.015 ††† 1.232 0.248 (ns) 1.880 0.080 †† 0.006 0.940 (ns) FSI does not Granger Cause FX_CRSH_EUR 0.124 0.725 (ns) 0.230 0.948 (ns) 0.402 0.526 (ns) 0.402 0.526 (ns) 0.841 0.709 (ns) 0.434 0.958 (ns) 0.244 0.962 (ns) 0.244 0.621 (ns) FX_CRSH_EUR does not Granger Cause FSI 1.608 0.208 (ns) 0.564 0.727 (ns) 0.770 0.380 (ns) 0.770 0.380 (ns) 0.782 0.791 (ns) 0.280 0.995 (ns) 0.206 0.975 (ns) 0.354 0.552 (ns) FSI does not Granger Cause FX_CRSH_GBP 1.271 0.263 (ns) 0.923 0.470 (ns) 3.608 0.058 †† 3.608 0.058 †† 1.466 0.051 †† 1.913 0.024 ††† 0.981 0.436 (ns) 4.880 0.027 ††† FX_CRSH_GBP does not Granger Cause FSI 0.041 0.840 (ns) 0.604 0.697 (ns) 0.167 0.683 (ns) 0.167 0.683 (ns) 0.802 0.764 (ns) 0.288 0.994 (ns) 0.306 0.934 (ns) 1.139 0.286 (ns) FSI does not Granger Cause FX_CRSH_JPY 0.007 0.934 (ns) 1.137 0.348 (ns) 0.105 0.745 (ns) 0.105 0.745 (ns) 0.875 0.658 (ns) 0.457 0.948 (ns) 0.352 0.909 (ns) 0.000 0.994 (ns) FX_CRSH_JPY does not Granger Cause FSI 0.352 0.554 (ns) 0.847 0.521 (ns) 0.507 0.477 (ns) 0.507 0.477 (ns) 1.104 0.319 (ns) 0.837 0.621 (ns) 0.920 0.479 (ns) 0.255 0.614 (ns) FSI does not Granger Cause FX_CRSH_MXN 0.070 0.792 (ns) 0.563 0.728 (ns) 0.232 0.630 (ns) 0.232 0.630 (ns) 0.901 0.618 (ns) 0.868 0.587 (ns) 1.298 0.254 (ns) 0.465 0.495 (ns) FX_CRSH_MXN does not Granger Cause FSI 0.527 0.470 (ns) 0.610 0.693 (ns) 0.264 0.607 (ns) 0.264 0.607 (ns) 0.879 0.652 (ns) 1.151 0.310 (ns) 1.054 0.388 (ns) 0.221 0.638 (ns) FSI does not Granger Cause FX_CRSH_ZAR 4.088 0.046 ††† 1.061 0.389 (ns) 2.743 0.098 †† 2.743 0.098 †† 1.592 0.023 ††† 1.947 0.021 ††† 1.266 0.269 (ns) 1.581 0.209 (ns) FX_CRSH_ZAR does not Granger Cause FSI 2.928 0.090 †† 0.647 0.665 (ns) 0.265 0.607 (ns) 0.265 0.607 (ns) 1.158 0.255 (ns) 0.862 0.593 (ns) 1.244 0.280 (ns) 0.019 0.890 (ns) Note: † – indicates Granger causality with 80% or better confidence; †† – indicates Granger causality with 90% or better confidence; ††† – indicates Granger causality with 95% or better confidence.

164

Figure 31 Correlogram of Weekly Financial Stress Lagged autocorrelation Number AC PAC Q‐Stat Prob 1 0.982 0.982 1201.6 0 2 0.959 ‐0.165 2348.4 0 3 0.939 0.093 3448.2 0 1 4 0.919 ‐0.033 4502.4 0 5 0.901 0.059 5516.4 0 6 0.886 0.066 6498.3 0 0.95 7 0.874 0.043 7453.6 0 8 0.862 0.001 8383.6 0 9 0.851 0.024 9290.1 0 10 0.838 ‐0.032 10171 0 0.9 11 0.824 ‐0.033 11024 0 12 0.81 ‐0.009 11848 0 13 0.796 0.026 12644 0 14 0.783 ‐0.002 13416 0 0.85 15 0.769 ‐0.033 14160 0 16 0.756 0.025 14881 0 17 0.744 0.009 15580 0 18 0.732 ‐0.035 16256 0 0.8 19 0.72 0.026 16910 0 20 0.709 0.029 17546 0 21 0.699 ‐0.015 18164 0 22 0.687 ‐0.034 18761 0 0.75 23 0.674 ‐0.011 19337 0 24 0.662 ‐0.005 19892 0 25 0.65 0.018 20428 0 0.7 26 0.638 ‐0.007 20945 0 27 0.626 ‐0.032 21443 0 28 0.613 ‐0.034 21921 0 29 0.6 0.028 22380 0 0.65 30 0.589 0.015 22822 0 31 0.58 0.055 23252 0 32 0.572 ‐0.001 23670 0 33 0.564 0.008 24077 0 0.6 34 0.556 ‐0.021 24472 0 35 0.547 0.002 24855 0 36 0.539 0.016 25227 0 37 0.528 ‐0.049 25585 0 0.55 38 0.518 0.014 25929 0 39 0.508 ‐0.016 26260 0 40 0.499 0.041 26581 0 41 0.491 ‐0.022 26891 0 0.5 42 0.481 ‐0.05 27189 0 43 0.471 ‐0.009 27475 0 44 0.461 0.013 27750 0 0.45 45 0.451 ‐0.034 28012 0 46 0.439 ‐0.01 28261 0 47 0.428 ‐0.011 28498 0 48 0.417 ‐0.017 28724 0 0.4 49 0.407 0.048 28939 0 50 0.399 0.006 29145 0 51 0.39 ‐0.026 29342 0 52 0.378 ‐0.081 29528 0 0.35 53 0.366 ‐0.006 29703 0 54 0.353 ‐0.034 29865 0 55 0.34 0.019 30016 0 56 0.328 ‐0.006 30156 0 0.3 57 0.317 ‐0.002 30287 0 58 0.306 ‐0.021 30409 0 59 0.295 0.001 30522 0 60 0.282 ‐0.068 30626 0 0.25 61 0.27 0.024 30721 0 62 0.258 0.007 30808 0 63 0.247 0.022 30888 0 0.2 64 0.235 ‐0.051 30960 0 65 0.223 ‐0.003 31025 0 66 0.21 ‐0.029 31083 0 67 0.198 0 31135 0 0.15 68 0.186 ‐0.021 31180 0 69 0.175 0.052 31221 0 70 0.166 0.006 31257 0 71 0.156 ‐0.027 31289 0 0.1 72 0.147 0.029 31318 0 73 0.141 0.036 31344 0 74 0.134 0.009 31368 0 75 0.127 0.004 31389 0 0.05 76 0.122 0.039 31409 0 77 0.117 ‐0.02 31427 0 78 0.11 ‐0.022 31443 0 79 0.104 0.017 31458 0 0 80 0.097 ‐0.028 31470 0 1 4 7

10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 81 0.089 0.002 31481 0 100 82 0.082 ‐0.022 31490 0 -0.05 83 0.075 0.013 31497 0 84 0.069 ‐0.006 31504 0 85 0.064 0.004 31509 0 86 0.058 ‐0.024 31513 0 -0.1 87 0.052 0.03 31517 0 88 0.046 ‐0.01 31520 0 89 0.04 ‐0.013 31522 0 90 0.034 0.001 31524 0

165

4.3.4.4. Dynamic parallel factor analysis

Prior to factor extraction, parallel factor analysis is applied to answer the critical question of the number of factors to be retained. The choice necessarily involves research judgment among several methodological options suggested by prior research and common in practice (Hayton, 2004; Matsunaga, 2010). One common choice is the factor retention suggested by the Kaiser-Guttman criterion (Guttman, 1954; Kaiser, 1960), retaining all factors with eigenvalues greater than one. The intuition for the Kaiser-

Guttman criterion is simple: the only factors worth retaining are those that contribute more to the explanation of variance among latent factors than a single observed and standardized variable (z) that has a variance of one by construction. One critique of the method is the omission of sampling error adjustment in is application (Hayton et al.,

2004). Another critique in the context of dynamic factor analysis is the absence of adjustment for the lagged influences of latent factors. To compensate for the first shortcoming, a technique of parallel analysis (PA) (Horn, 1965) is utilized to adjust for sampling variance. To remedy the second shortcoming, we apply the O'Connor (2000)

PA algorithm with column-randomized Monte Carlo sampling of actual lagged variable subsets in to account for deviations of data from normality with results shown in Table

22. In this approach, the lagged variables subsets are separately column-randomized to yield lag-adjusted parallel eigenvalues. As shown by the dynamic parallel factor analysis:

1) Four factors should be retained from observations with zero lag; 2) The first two of the four retained factors exhibit dynamic effects over four time periods.

166

Table 22 Dynamic Parallel Factor Analysis for Quarterly Data CHOLESKY DECOMPOSITION PARALLEL EIGENVALUES FACTOR RE_RRE RE_CRE FD_BBS FD_IBCOB FD_FB FD_IBLS CR_CBS CR_CPTBS CR_LIQS CR_TYCS SE_ABS SE_CMBS SE_RMBS Eigenvalue Parallel eigenvalue LAG 0 EFFECTS 1 1.553 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.759 2.200 2 0.167 0.651 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.719 1.825 3 0.380 0.457 0.400 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.674 1.602 4 0.204 0.154 (0.392) 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.556 1.418 5 0.119 (0.020) (0.410) 0.269 0.675 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.779 1.286 6 0.252 0.178 (0.366) 0.490 (0.027) 0.640 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.414 1.175 7 0.693 0.464 0.767 (0.228) (0.050) (0.207) 0.584 0.000 0.000 0.000 0.000 0.000 0.000 0.319 1.054 8 0.309 0.235 (0.643) 0.657 (0.035) 0.939 (0.170) 0.355 0.000 0.000 0.000 0.000 0.000 0.273 0.968 9 0.265 0.286 0.005 (0.012) 0.191 (0.238) (0.546) 0.288 0.764 0.000 0.000 0.000 0.000 0.229 0.870 10 (0.054) (0.206) (0.594) 0.156 (0.286) 0.915 (0.069) (0.121) 0.060 0.681 0.000 0.000 0.000 0.133 0.781 11 0.219 1.164 (0.138) 0.193 0.139 0.119 (0.322) (0.069) 0.220 0.172 0.492 0.000 0.000 0.082 0.687 12 0.054 0.272 0.018 (0.001) 0.033 (0.036) (0.033) (0.017) 0.030 (0.020) 0.061 0.037 0.000 0.038 0.589 13 4.737 0.514 0.159 (0.066) 0.442 (0.702) 0.202 (0.572) (0.169) (0.342) 0.989 0.569 0.719 0.024 0.508 LAG 1 EFFECTS 1 1.316 0.010 0.147 0.218 0.143 (0.243) 0.036 (0.196) 0.027 (0.049) (0.205) (0.012) (0.170) 5.982 2.271 2 0.134 0.633 0.045 (0.029) 0.011 (0.057) 0.038 (0.021) (0.021) 0.034 (0.021) (0.013) (0.009) 2.600 1.844 3 0.333 0.446 0.417 (0.047) 0.020 (0.122) 0.039 (0.051) 0.018 (0.006) (0.034) (0.037) (0.063) 1.244 1.621 4 0.124 0.196 (0.352) 0.527 0.066 0.100 0.061 (0.071) 0.094 0.088 0.032 (0.176) (0.022) 0.903 1.430 5 0.025 0.005 (0.441) 0.283 0.519 0.013 (0.017) (0.018) 0.011 (0.076) (0.022) (0.081) (0.020) 0.680 1.273 6 0.288 0.232 (0.311) 0.415 (0.004) 0.579 0.006 (0.126) 0.008 0.098 (0.028) (0.158) (0.111) 0.429 1.165 7 0.539 0.378 0.766 (0.227) 0.042 (0.435) 0.501 (0.147) (0.099) (0.029) (0.145) (0.048) (0.038) 0.340 1.056 8 0.419 0.337 (0.548) 0.608 (0.032) 0.861 (0.143) 0.069 0.046 0.147 (0.049) (0.186) (0.126) 0.248 0.964 9 0.265 0.332 (0.026) (0.094) 0.219 (0.271) (0.483) 0.243 0.661 (0.043) 0.037 0.023 (0.114) 0.203 0.872 10 0.069 (0.215) (0.497) 0.131 (0.223) 0.982 (0.188) (0.159) 0.017 0.500 (0.021) (0.039) (0.086) 0.148 0.791 11 0.188 1.186 0.005 0.098 0.222 0.074 (0.307) (0.129) 0.165 0.190 0.359 0.040 0.005 0.106 0.707 12 0.039 0.271 0.036 (0.009) 0.043 (0.057) (0.014) (0.023) 0.020 (0.008) 0.050 0.028 0.000 0.079 0.624 13 3.820 0.542 0.803 0.767 1.012 (1.388) 0.267 (1.325) (0.080) (0.423) 0.108 0.546 0.102 0.039 0.521 LAG 2 EFFECTS 1 0.999 (0.004) 0.172 0.257 0.253 (0.462) 0.103 (0.173) 0.054 (0.129) (0.280) (0.130) (0.317) 4.897 2.334 2 0.098 0.591 0.079 (0.084) 0.020 (0.097) 0.073 (0.007) (0.039) 0.026 (0.007) (0.066) 0.030 2.762 1.853 3 0.260 0.419 0.414 (0.118) 0.010 (0.234) 0.051 (0.064) 0.022 (0.059) (0.043) (0.088) (0.080) 1.666 1.640 4 0.045 0.213 (0.312) 0.397 0.137 0.166 0.061 0.028 0.126 0.148 0.004 (0.251) 0.024 1.069 1.429 5 (0.060) 0.053 (0.439) 0.230 0.309 0.061 (0.033) 0.021 0.069 (0.155) (0.004) (0.137) (0.015) 0.809 1.270 6 0.265 0.267 (0.233) 0.351 0.044 0.541 (0.027) (0.073) (0.014) 0.104 (0.106) (0.242) (0.138) 0.550 1.165 7 0.335 0.270 0.723 (0.291) 0.076 (0.602) 0.418 (0.186) (0.178) (0.198) (0.196) (0.158) (0.066) 0.441 1.064 8 0.426 0.414 (0.459) 0.598 0.036 0.819 (0.127) 0.060 0.050 0.143 (0.181) (0.293) (0.117) 0.229 0.972 9 0.275 0.379 (0.104) (0.160) 0.206 (0.337) (0.415) 0.246 0.552 (0.122) 0.125 0.007 (0.131) 0.201 0.888 10 0.209 (0.220) (0.424) 0.087 (0.172) 0.987 (0.326) (0.158) (0.079) 0.292 (0.005) (0.133) (0.148) 0.140 0.798 11 0.136 1.180 0.129 (0.020) 0.244 0.021 (0.310) (0.106) 0.104 0.086 0.298 (0.017) 0.024 0.124 0.714 12 0.023 0.261 0.049 (0.030) 0.049 (0.073) 0.002 (0.017) 0.011 (0.009) 0.053 0.007 0.013 0.058 0.622 13 2.660 0.483 0.983 0.869 1.342 (2.047) 0.488 (1.197) 0.047 (0.572) (0.129) 0.085 (0.598) 0.053 0.524 LAG 3 EFFECTS 1 0.746 (0.021) 0.145 0.269 0.207 (0.645) 0.125 (0.002) 0.121 (0.178) (0.261) (0.252) (0.298) 5.551 2.471 2 0.076 0.538 0.111 (0.137) 0.010 (0.125) 0.097 0.008 (0.063) 0.002 0.012 (0.104) 0.105 2.067 1.866 3 0.201 0.384 0.403 (0.188) (0.015) (0.315) 0.064 (0.029) 0.014 (0.104) (0.030) (0.118) (0.053) 1.373 1.637 4 (0.025) 0.213 (0.283) 0.231 0.182 0.236 (0.041) 0.040 0.059 0.193 (0.107) (0.241) (0.001) 1.031 1.440 5 (0.128) 0.103 (0.402) 0.177 0.186 0.058 (0.081) 0.091 0.076 (0.068) (0.015) (0.131) (0.035) 0.751 1.277 6 0.243 0.285 (0.165) 0.232 0.082 0.505 (0.100) (0.024) (0.070) 0.070 (0.193) (0.311) (0.189) 0.736 1.160 7 0.206 0.171 0.656 (0.399) 0.012 (0.743) 0.354 (0.132) (0.202) (0.285) (0.141) (0.277) 0.010 0.540 1.051 8 0.423 0.471 (0.379) 0.435 0.108 0.794 (0.212) 0.022 (0.044) 0.069 (0.299) (0.453) (0.206) 0.399 0.976 9 0.296 0.432 (0.182) (0.252) 0.231 (0.362) (0.328) 0.202 0.442 (0.178) 0.146 0.070 (0.087) 0.226 0.901 10 0.358 (0.201) (0.332) 0.105 (0.147) 0.946 (0.367) (0.113) (0.120) 0.116 0.026 (0.210) (0.198) 0.145 0.818 11 0.119 1.168 0.201 (0.143) 0.200 (0.048) (0.286) (0.080) 0.065 (0.018) 0.296 (0.091) 0.094 0.100 0.736 12 0.010 0.247 0.062 (0.052) 0.046 (0.085) 0.014 (0.011) 0.002 (0.016) 0.058 (0.009) 0.040 0.069 0.646 13 1.699 0.414 0.916 0.795 1.091 (2.588) 0.555 (0.588) 0.321 (0.666) 0.026 (0.442) (0.705) 0.013 0.552 LAG 4 EFFECTS 1 0.484 (0.071) 0.109 0.225 0.149 (0.764) 0.104 0.077 0.223 (0.163) (0.266) (0.301) (0.240) 5.481 2.728 2 0.051 0.475 0.160 (0.163) (0.009) (0.154) 0.100 (0.006) (0.084) (0.012) 0.005 (0.097) 0.179 2.894 1.970 3 0.137 0.336 0.402 (0.218) (0.061) (0.412) 0.065 (0.019) 0.022 (0.112) (0.033) (0.092) 0.005 1.516 1.722 4 (0.057) 0.213 (0.260) 0.094 0.159 0.300 (0.066) 0.134 0.092 0.136 (0.119) (0.280) 0.028 1.258 1.455 5 (0.192) 0.137 (0.385) 0.160 0.139 0.061 (0.142) 0.198 (0.012) 0.005 (0.015) (0.107) (0.059) 0.658 1.267 6 0.229 0.296 (0.110) 0.209 0.032 0.443 (0.112) 0.093 (0.069) 0.019 (0.235) (0.343) (0.165) 0.519 1.120 7 0.054 0.073 0.605 (0.388) (0.065) (0.861) 0.304 (0.113) (0.167) (0.246) (0.196) (0.189) 0.117 0.296 1.027 8 0.416 0.510 (0.343) 0.413 0.035 0.695 (0.189) 0.117 (0.062) (0.005) (0.379) (0.472) (0.219) 0.138 1.006 9 0.322 0.496 (0.208) (0.228) 0.263 (0.457) (0.287) 0.091 0.310 (0.138) 0.106 0.171 (0.074) 0.099 0.974 10 0.468 (0.169) (0.191) 0.228 (0.086) 0.834 (0.440) (0.086) (0.174) 0.062 (0.075) (0.198) (0.192) 0.072 0.911 11 0.091 1.143 0.284 (0.229) 0.167 (0.132) (0.257) (0.092) 0.037 (0.055) 0.255 (0.076) 0.159 0.039 0.833 12 (0.004) 0.229 0.078 (0.065) 0.039 (0.095) 0.019 (0.014) (0.009) (0.020) 0.054 (0.010) 0.066 0.022 0.744 13 0.735 0.225 0.864 0.558 0.852 (2.856) 0.457 (0.234) 0.664 (0.602) 0.087 (0.666) (0.662) 0.007 0.607

4.3.4.5. Factor extraction and estimation

Factor extraction. The dataset analyzed above from a symmetric positive-definite

Toeplitz matrix of covariances and LL’ Cholesky factorization. It retains five sets of thirteen variables lagged from 0 to 4 periods.87 The factorability of the dataset for each

87 RE_RRE, RE_CRE, FD_BBS, FD_IBCOB, FD_FB, FD_IBLS, CR_CBS, CR_CPTBS, CR_LIQS, CR_TYCS, SE_ABS, SE_CMBS, and SE_RMBS. 167

lagged is supported by the results shown in Table 23, panels A (for lag 0) through E (for lag 4). As shown in each panel, factorability of manifest variables in each lag is supported, by the communality statistics above 0.5, overall measures of sampling adequacy above 0.5, and significance of the Bartlett’s test for the manifest correlations.

The analysis suggests that four factors should be extracted, explaining eighty-six percent of the total variance.

Table 23 Factorability Analysis for Quarterly Data RRE CRE BBS IBCOB FB BLS CBS CPTBS LIQS TYCS ABS CMBS RMBS Panel A: Lag 0 Communality 0.947 0.915 0.919 0.721 0.769 0.960 0.893 0.915 0.591 0.788 0.930 0.960 0.937 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.563

0.458 0.542 0.687 0.544 0.671 0.534 0.821 0.612 0.408 0.444 0.602 0.54 0.505 Bartlett's Test of Sphericity: Approx. Chi-Square: 1387.014, df: 78, Sig.: 0 Panel B: Lag 1 Communality 0.946 0.915 0.920 0.721 0.771 0.962 0.892 0.915 0.580 0.792 0.929 0.960 0.936 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.559

0.451 0.532 0.69 0.536 0.665 0.535 0.824 0.611 0.395 0.446 0.599 0.533 0.496 Bartlett's Test of Sphericity: Approx. Chi-Square: 1369.026, df: 78, Sig.: 0.000 Panel C: Lag 2 Communality 0.945 0.915 0.921 0.717 0.772 0.962 0.890 0.915 0.572 0.792 0.928 0.960 0.935 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.556

0.445 0.526 0.691 0.53 0.662 0.534 0.827 0.61 0.386 0.448 0.596 0.528 0.491 Bartlett's Test of Sphericity: Approx. Chi-Square: 1347.830, df: 78, Sig.: 0.000 Panel D: Lag 3 Communality 0.944 0.915 0.921 0.714 0.773 0.963 0.887 0.914 0.559 0.794 0.927 0.959 0.934 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.553

0.432 0.519 0.695 0.527 0.659 0.533 0.829 0.608 0.365 0.456 0.597 0.526 0.479 Bartlett's Test of Sphericity: Approx. Chi-Square: 1327.440, df: 78, Sig.: 0.000 Panel E: Lag 4 Communality 0.942 0.915 0.921 0.710 0.773 0.965 0.885 0.913 0.545 0.798 0.924 0.959 0.933 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.551

0.417 0.519 0.696 0.525 0.646 0.533 0.826 0.608 0.356 0.466 0.596 0.53 0.468 Bartlett's Test of Sphericity: Approx. Chi-Square: 1306.718, df: 78, Sig.: 0.000

To capture the factor correlation, we extract four factors by principal components

using oblique factor rotation with Kaiser normalization (Jennrich and Sampson, 1966;

Harman, 1976). Table 24, the rotated factor pattern, shows the dynamic loadings of

manifest variables items onto the four extracted factors for each lag. The loadings show

that ABS, CMBS, CRE, and BBS consistently load into factor 1; IBLS, CPTBS, and

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TYCS consistently load into factor 2; RRE, RMBS, CBS consistently load into factor 3; and FB and IBCOB consistently load into factor 4. The consistency of the loading pattern is a particularly welcome result that supports the loading constraints we will undertake in the construction of the measurement model to confirm the dynamic factor analysis in step

Table 24 Dynamic Four-Factor Extraction Rotated Factor Pattern (Standardized Regression Coefficients) Factor 1 Factor 2 Factor 3 Factor 4 Lag 0 Lag 1 Lag 2 Lag 3 Lag 4 Lag 0 Lag 1 Lag 2 Lag 3 Lag 4 Lag 0 Lag 1 Lag 2 Lag 3 Lag 4 Lag 0 Lag 1 Lag 2 Lag 3 Lag 4 ABS .952 .954 .955 .957 .959 CMBS .951 .951 .951 .951 .952 CRE .925 .927 .929 .931 .934 BBS .640 .639 .639 .638 .638 IBLS .921 .918 .920 .919 .924 CPTBS .875 .872 .874 .872 .877 TYCS .852 .851 .849 .845 .838 RRE .981 .983 .985 .987 .989 RMBS .944 .946 .948 .950 .952 CBS .642 .649 .650 .649 .651 FB .847 .853 .856 .861 .862 IBCOB .537 .547 .548 .555 .558

Factor 1 consists of observations of four manifest variables: asset-backed

securitization (ABS), commercial mortgage-backed securitization (CMBS), commercial

real estate (CRE), and bank bond spread (BBS). We interpret the factor as a measure of

stress in the commercial securitization market. Factor 2 reflects three manifest variables:

overnight borrowing spread (IBLS), commercial paper (CPTBS), and treasury yield

(TYCS). All three variables describe instruments in the money market. Accordingly, this

factor can be interpreted as a measure of stress in the money market. Factor 3 involves

three manifest variables: residential real estate (RRE), residential mortgage-backed

securitization (RMBS), and corporate bond spread (CBS). Based on the strongest

loadings in this factor, we interpret it to reflect stress in the credit and residential real

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estate market. Factor 4 contains two manifest variables: financial beta (FB), and interbank cost of short-term funding (IBCOB). Since beta describes a systematic, non- diversifiable risk that emanates from common movements in the financial markets, it is reasonable to interpret this factor as a measure of common systematic stress.

We find that the extracted four factors show a well differentiated correlation matrix, Table 25, demonstrated by the near independence of all factors for each lag. This provides evidence to support the discriminant validity of the extracted factors.

Table 25 Four-Factor Correlation Matrices (Lagged 0 through 4) LAG 0 LAG 1 LAG 2 Factor1 Factor2 Factor3 Factor4 Factor1 Factor2 Factor3 Factor4 Factor1 Factor2 Factor3 Factor4

Factor1 1.000 -.063 .261 .057 1.000 -.066 .255 .054 1.000 -.068 .250 .051 Factor2 -.063 1.000 -.048 .233 -.066 1.000 -.053 .230 -.068 1.000 -.059 .226 Factor3 .261 -.048 1.000 .006 .255 -.053 1.000 -.003 .250 -.059 1.000 -.013 Factor4 .057 .233 .006 1.000 .054 .230 -.003 1.000 .051 .226 -.013 1.000

LAG 3 LAG 4 Factor1 Factor2 Factor3 Factor4 Factor1 Factor2 Factor3 Factor4

Factor1 1.000 -.072 .241 .042 1.000 -.078 .231 .033 Factor2 -.072 1.000 -.065 .222 -.078 1.000 -.074 .214 Factor3 .241 -.065 1.000 -.027 .231 -.074 1.000 -.040 Factor4 .042 .222 -.027 1.000 .033 .214 -.040 1.000

Following Peterson and Kim (2013), we test the reliability of each factor by

verifying that its components exhibit internally consistency as measured by the

Cronbach’s Alpha. The results are shown in Table 26 and demonstrate adequate

reliability, as Cronbach’s Alpha of the factors ranges from 0.549 (Factor 4 lag 4) to 0.833

(Factor 1 lags 1 through 4).

Table 26 Factor Reliability Factor 1 Factor 2 Factor 3 Factor 4 Lag 0 0.832 0.824 0.686 0.593 Lag 1 0.833 0.824 0.690 0.585 Lag 2 0.833 0.824 0.693 0.575 Lag 3 0.833 0.822 0.695 0.563 Lag 4 0.833 0.820 0.698 0.549

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Estimation of alternative dynamic factor models. Finally, we estimate two alternative dynamic models using the MLE-SEM approach: a process factor model (e.g.

Nesselroade et al., 2001) and a shock factor model (e.g. Browne and Nesselroade, 2005).

In the process factor model, the structure of latent factors is autoregressive, where current manifest variables and current latent factors are influenced by past latent factors. In the shock factor model, the manifest variables are directly influenced by current and past latent factors. To estimate the process factor model, we follow Zhang et al. (2008) and

Browne and Zhang (2005). To estimate the shock factor model, we follow Molenaar

(1985) and Nesselroade et al. (2001).

We construct both process factor (Figure 32) and shock factor (Figure 33) measurement models, and estimate them using IBM SPSS Amos (Analysis of Moment

Structures) software v22.0, a covariance-based structural equation modeling technique using MLE. The nomological configuration of the process model is based on the findings of the exploratory dynamic factor analysis in stages 14. Specifically, we hypothesize

that the first two extracted process factors at time t (f and f ) follow the PFA (4,0)

process, while the last two extracted process factors at time t (f and f ) are static.

Nomologically, the model follows standard process model configuration (Appendix7:

Table 44, Figure 43). Specifically: the process factor loadings are time-invariant; lag of

zero is measured via four process factors f ,f ,f ,f ; lags 1 through 4 are measured via

two process factors f ,f , where j 1,2,3,4; process factors are intercorrelated

within lags and across lags by lag-dependent direct autoregressive relationships;

disturbances of manifest variables are correlated within variables and uncorrelated across

variables. 171

Figure 32 Process Factor Model of Quarterly Financial Stress

Table 27, column (3) reports the goodness of fit results for the process factor model of the quarterly manifest variables of financial stress.88 The results show that this particular model has less than an adequate fit evidenced by the CMIN/df of 3.722, CFI of

88 All parameter estimates were significant to 0.05 level. 172

0.782, the hypothesized model’s BCC of 3177.605 exceeding the saturated model BCC of 3050.566, and RMSEA of 0.2170.

Table 27 Goodness of Fit Summary (1) (2) (3) (4) Measure Threshold Process factor model Shock factor model ⁄ < 3 good; < 5 adequate 3.722 3.189 p-value 0.000 0.000 > 0.95 great; >0.90 good; >0.80 CFI 0.782 0.830 adequate PCFI 0.694 0.715 SRMR 0.251 0.236 RMSEA < 0.05 good; > 0.1 bad 0.170 0.153 PCLOSE > 0.005 0.000 0.000 AIC 2971.832 2559.251 BCC hypothesized 3177.605 2797.515 BCC saturated 3050.566 3050.566 HOELTER .05 28 33

The shock factor model configuration is based on the findings of the exploratory dynamic factor analysis in stages 14. Specifically, we hypothesize that the first two

extracted process factors at time t (z and z ) follow the SFA (4) process, while the last

two extracted process factors at time t (z and z ) are static. Nomologically, the model

follows standard shock model configuration (Appendix 7: Table 44, Figure 45).

Specifically: the shock factor loadings are time-varying dependent on lag j∈ 1,2,3,4;

lag of zero is measured via four shock factors z ,z ,z ,z ; lags 1 through 4 are

measured via two shock factors z ,z ; shock factors are intercorrelated within lags

only; (similarly to the process model) disturbances of manifest variables are correlated

within variables and uncorrelated across variables.

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Figure 33 Shock Factor Model of Quarterly Financial Stress

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Table 27, column (4) reports the goodness of fit results for the shock factor model of the quarterly manifest variables of financial stress.89 The results show that the estimated shock factor model has an adequate fit evidenced by the CMIN/df of 3.189,

CFI of 0.830, the hypothesized model’s BCC of 2797.515 below the saturated model

BCC of 3050.566, and RMSEA of 0.153.

We compare the aggregate system level stress index resulting from both DFA models against relative stress in Figures 23 and 24. As we had expected from the model fit statistics in Table 27, the correlation between relative stress and the shock factor model is relatively higher at 0.399 than the correlation against the process factor model

0.368. Despite the increased sophistication of the model, and recognition of factor persistence, we do not find a realized improvement against the static factor analysis results. However, it should be recognized that, unlike sections 3.1 and 3.2, the versions of

CFSI based upon DFA below do not yet incorporate equity or foreign exchange information since these factors experience persistence at a different frequency (Table 21

and Figure 31). Moreover, dynamic factor analysis was estimated using quarterly data

requiring comparison against relative stress at a more granular quarterly frequency than

the monthly frequency previously used. Given these material limitations it is quite

possible that the dynamic factor analysis approach does materially improve the alignment

with relative stress.

However, the discrepancy between CFSI’s variations and relative stress likely has

another, more fundamental, cause. By definition CFSI is calculated as the relative

deviation (CDF transformation) from relationships (indicators such as spreads, covered

89 All parameter estimates were significant to 0.001 level. 175

interest spread, drawdown, etc.) which are expected to remain relatively stable in the long term. However, the definition of relative stress also includes the volume, change in volume, change in spread, and the concentration forming a much more comprehensive set of considerations. Moreover, the distribution of CFSI is different from relative stress. The

CDF transformation will transform the distribution of any input dataset to a uniform distribution. Therefore, CFSI and its variations are a weighted sum of uniform random variables. However, the numerator of relative stress involves the product of the CDF of two indicators which will change the distribution of our output from a uniform distribution.

4.4. Discussion

A fundamental challenge to researchers and policymakers is that financial stress lacks a definition which has theoretical basis, requiring that empirical indicators are compared to various series of market volatilities (as in Oet et al., 2015b) or historical lists of crisis events. Drawing upon literature, we support eight hypotheses which aim to determine the drivers (rate spreads, transaction volume, agent exposures, etc.) of financial system stress. This allows us to construct a new theoretical measure of stress with components and architecture supported conceptually and quantitatively.

Relatively poor alignment between the theoretical measure of financial system stress and CFSI is partly explained by the different characteristics of stress incorporated.

While CFSI focuses purely on spreads, the theoretical measure also incorporates volume, transaction, and concentration information for each agent’s positions. Another distinction between the theoretical and empirical measures lies in their partitioning. The theoretical stress measure leverages a detailed decomposition of the financial system in terms of the

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instrument portfolios for a large set of heterogeneous financial agents, while the empirical measures assumes the importance of six a priori markets. Therefore, as a means of improving the discriminatory power of the empirical measure (CFSI), we support the reliability of a 5-factor version of CFSI based upon empirically tested static factor analysis and find a noticeable improvement. Furthermore, when in the subsequent dynamic factor analysis, we adjust the empirical stress to align with the theoretical notion of stress that is experienced today to reflect the persistence of stress from previous periods, we find that the fit is consistent with a static factor analysis construction.90 This is remarkable, since the process and shock factor models are handicapped by the current omission of indicators reflecting the important equity and foreign exchange factors. This suggests that further improvements in explanatory power are readily attainable, when these factors are incorporated. Beyond increasing the alignment with theoretical stress, applying dynamic factor analysis reveals that stress is best modeled as a shock process with persistence that varies by factor up to a year and a half.

This study is further motivated by the methodological challenge to the problem of financial system stress identification that stems from serial correlations of observations over time. We extend previous research on financial system stress measurement by exploring and applying the dynamic factor analytic perspective to clarify and incorporate the time dependency between financial stress observations.

In the course of this study, we make the following four contributions to the literature on financial stress measurement: 1) we carefully review the relevant insights on

90 The correlation of theoretical stress against the five factor version of CFSI based upon static factor analysis is 0.399 which is essentially identical to the correlation between theoretical stress and the shock model of 0.399. 177

dynamic factor analysis from an extended set of research traditions that include social science and psychometric contributions to longitudinal data analysis; 2) we extend an empirical analytic algorithm established in literature; 3) we consider the typology of alternative dynamic factor models and explain the distinctions between them; 4) we estimate two alternative dynamic factor models for US financial stress based on the observation dataset for the Cleveland Financial Stress Index: a process factor model and a shock factor model.

The process model explains current latent factors as direct time-dependent effects of past latent factors of stress. The shock model explains manifest variables at each time point as direct effects of extant and past shock factors. We find that the shock factor model provides a better fit to the quarterly observations of financial stress than the process factor model.

Implications for practice. Several of our exploratory findings are particularly interesting. First, the factor extraction results are encouraging and suggest that current measurement of US financial stress by the Cleveland Financial Stress is broadly consistent with extracted factors. Particularly, it appears that the current six-market approach to measurement of system stress is consistent with the number and type of extracted factors. At the same, the extracted factors suggest the need to rethink the factor composition and interpretation for markets.91

Second, our findings suggest a co-existence of mixed frequency dynamic effects,

with four dynamic factors having quarterly time dependency with a 4-lag horizon, and

91 For example, four dynamic factors acting with a quarterly effect are securitization, money market, credit/residential real estate, and funding. This adjusts the corresponding extant naïve 4-market composition of securitization, credit, real estate, and funding. 178

two additional factors having a weekly time dependency with a 4-week horizon. It would be highly interesting to extend this study by inclusion of the mixed-frequency dynamic effects.

Limitations. The results of this study should be taken with a degree of caution, given the known limitations in estimating dynamic factor measurement models via MLE-

SEM approaches. It would be useful to comprare the robustness of the obtained results using alternative software and estimation methods6)

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Chapter 5: Connecting the Micro and Macro Levels of Financial Stress

Grief does not change you… It reveals you. ― John Green, The Fault in Our Stars

Omnia mutantur nos et mutamur in illis Illa vices quasdam res habet, illa vices. ― All things are changed, and we change with them That matter changes is demonstrated by the changes in matter

5.1. Agent Choices and Transmission Dynamics

Despite a rigorous effort to establish an optimal macro-level measure of financial stress, clearly some variables in addition to prices and quantities are needed to explain both the pattern of apparently irrational agent choices and the apparent discrepancies between the micro- and macro-level stress. In this chapter, we advance agent-level stress theory. We examine its predictive validity by examining whether the proposed functional form of agent-level stress aggregates as expected to the system-level. Specifically, does the agent stress that is measured as conjectured integrate across all system agents to the system-level stress? If our definition of stress at the micro-level (agent and instrument) is correct, then the integration of the micro-level stress should yield the macro-level

(system) stress. Our initial literature-supported abductive conjecture is that micro-level stress is defined as a function solely of prices and quantities. Testing this, we find that macro-level (system) stress does not equal the summation of micro-level (agent) stress and observe substantial differences between the two.

The advancement of micro-level definition of stress requires us to theorize functional form supported by literature-based hypotheses of stress and the available

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empirical evidence. Initially, the inference is abductive. Because we observe a reliable measure of macro-level stress as a function of prices and quantities of representative indicators, we infer that stress at smaller units of analysis, e.g. agents and instruments, can be measured as a function of prices and quantities of relevant instruments which fully describe the exposure of the financial agents.

5.1.1. Dynamic analysis of agent stress

To make further progress, we need to critique the agent level definition of stress.

The remaining reason that the aggregate stress does not equal the sum of agent stress is that the agent stress is not adequately measured. We already know that memory is important in system level stress, yet, memory is absent from agent level stress definition.

The initial conjecture of agent stress includes only prices and quantities. To the extent that agents act rationally, then prices and quantities should be the only variables that explain the agent choices. In this chapter, we consider the choices across all system agents and find that using an aggregate representative agent as a unit of analysis, the allocation choices can be considered rational, with very small number of rationality exceptions (2% or less). Thus, the assumption of rationality is reasonably supported across all agents, confirming that agent allocation choices are substantially explained by prices and quantities. However, when individual agents are considered, significant number of allocations appear irrational, with violations of rationality evidenced in forming the agents’ price and quantity bundles. Thus, individually, the agents appear to be making irrational allocations. In fact, a significant number of violations exist for specific agents and appears associated with the periods of high system stress. This leads us to the idea that the functional form of agent stress is incorrectly specified and requires

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the incorporation of variables other than prices and quantities. Accordingly, in this chapter we seek to recognize and include the variables missing from the definition of stress. We do this, by testing alternative theories of agent preference, seeking to find the set of variables that minimizes the number of violations of agent rationality in allocating the agent choices.

5.1.2. Agent preferences

For the choice process, we seek to explain the pattern of apparent irrationality in agent choices and to understand the process by which the pattern of choice violations becomes system stress. This analysis is accomplished by examination of agent revealed preference and the causal pattern tying the apparent violations of rationality and financial system stress. In this chapter, we also investigate alternative variables in the definition of agent-level financial stress. The first two variables, price and quantity, form the basis of stress agent-level stress as established through the agent rationality assumption, where agent allocations among instrument bundles are determined solely on the basis of rational preferences among instrument prices and quantities. When agent choices are conditioned solely by the observations of prices and quantities of financial instruments, we observe that violations from historical rationality tend to occur during particular times—the time of high distress. Naturally, we would like to examine whether there are any relationship patterns in the transmission of stress that involve these violations. Thus, we seek to extend the specification of agent-level stress with additional variables to investigate whether they can help to explain and minimize the number of apparent violations. We expand the functional specification of agent-level stress with additional variables that provide useful information to explain actual agent choices. The variables we test come

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from behavioral theories of agent choice, including prospect theory, cognitive dissonance, memory (animal spirits), and liquidity preference. The inclusion of additional variables completes the micro-level definition of stress and minimizes its discrepancy with macro-level stress.

5.1.3. The stress transmission process

We explore the empirical pattern of connections between the violations of rationality in various sectors and financial stress, resulting in two main findings. First, we find a strong set of allocation influences from sector to sector in the financial system.

Second, we find that these influences vary distinctly across time. The first finding of causal links among violations in different sectors is supported by Granger causality analysis, revealing a set of strong unidirectional and bi-directional relationships. The second finding is supported by Markov chain analysis of violations across sections and reveals the presence of two different memory channels. In the first of these two channels, a distinct set of sector choice violations influences another set of violations in a particular set sectoral agents next period—an example of the short-memory causal influences that take place during the next time period. In the second of these channels, another set of sectoral violations influence another set of particular sectoral violations in two periods— an example of longer-term memory causal influences. The corresponding second-order

Markov analysis enables the assessment of the probability of a critical financial system stress state, when violations in instrument choices originate in certain sectors. The

Markov analysis is a stochastic process model that enables the study of two dynamic phenomena. First, we can study the likely mechanisms of stress transmission across sectors and estimate the amount of propagation time to an absorbing critical state of

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system stress. Second, we can study the comparison of probability of alternative stress propagation scenarios.

“herding” allocation choices that involve instrument j. These choices may appear irrational from the longer perspective—violations of historically rational price and quantity bundles—but are supported by the short-term expectations. Thus, the motion in stress across instruments and agents is observed through propagation of apparent violations from some sectoral agents to other sectoral agents. Put simply, asset bubbles travel through financial sectors inducing agents to realign their choices and resulting in relative adjustments of agent preferences toward other available bundles of instruments.

The apparent violations in price and quantity bundles of the bubble instruments lead to

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the relative valuation effects in other instruments. Thus, stress experienced in a particular sector agent or instrument can propagate. In the remaining chapters, we consider additional properties and effects of the processes of stress propagation.

5.2. Methodology

5.2.1. Revealed preference analysis

Revealed preference theory (Samuelson, 1938) states that underlying or latent preferences of an economic agent determine the optimal choice that the agent should make. The observed decisions of the agent tell us something about: 1) whether the agent is optimizing across choices, and 2) an optimizing agent’s latent preferences. The weak and strong axioms of revealed preference (WARP and SARP, respectively) allow us to determine whether decisions depart from optimizing behavior in an observable manner.

When no violations are present, the distinct choices of the agent provide insight into the upper and lower bounds of indifference curves.

Consider the bundle … which includes the quantities of each good that are bought as part of bundle . This bundle was bought following the

price vector …, where is the price paid for each unit of good as

part of bundle . The cost of bundle is given by ∑ . Various bundles ∈

can be bought. These bundles may be indexed in several ways, one of which is to index them by the time at which the bundle was purchased ( ∈ ⇔ ∈ 1,2, … , ).

When we observe multiple purchased bundles we can begin to address the

concerns mentioned above (decision maker’s optimizing behavior and their preference

curves). Consider the simple case where we have two goods and observe two purchased bundles. Figure 34 shows different ways the bundles and budget lines can be combined. 185

Budget surfaces have been drawn (if ∈ then the boundary is a line). If the funds

available to purchase bundle are given by then the intercept on the quantity axis of

good of the budget surface is /. The area in positive closed orthant bounded by the

budget surface (inclusive) is the convex feasible region (determined by and ).

The bundle that is actually chosen is directly observed to be preferred by the

decision maker over every bundle in the feasible region. In Figure 34(a), Bundles 1 and 2

are chosen over every alternative bundle from their respective feasible regions. If bundle

does not lie on the budget line then 1) the decision was not optimal, or 2) there are

omitted variables affecting the decision. In panels (a) and (b), both bundles lie on their

respective budget lines.

In Figure 34(b), we find that bundle 2 belongs to the feasible region of bundle 1

( ). Bundle 2 could have been bought and yet bundle 1 was selected. This

directly revealed preference for bundle 1 over bundle 2 is denoted 1,2 1.

Definition 1: , 1 if and only if bundle belongs to the feasible region

( ) and the feasible regions for and are distinct (∃ . ).

Note that bundle 1 belongs to the feasible region of bundle 2 so 2,1 1. The

conflict between 1,2 1 and 2,1 1 is essentially that between bundles 1 and 2 they cannot both be preferred to the other. This intuition is stated in the weak axiom of revealed preferences (WARP) below. Choices that violate WARP indicate a departure from optimal decisions.

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Weak Axiom of Revealed Preferences (WARP): If belongs to the feasible set of

( ) then does not belong to the feasible set of j ( )

(equivalently, , , 0).

The direct revealed preference relation , is not transitive, symmetric

(, 1 would identically violate WARP), or reflexive (since a bundle cannot be

preferred to itself). However, not all revealed preference directly observable. Revealed

preference in a more general sense is denoted by ≻ and it is transitive. In Figure 34 (c), we observe directly that 1,2 1 and 2,3 1 then it follows indirectly that ≻

(naturally, this can be extended to include many bundles in Def. 2). We call this a

chain of indirect (or implicit) revealed preference ,. Note that we have not observed

that bundle 1 would be chosen over bundle 3 since bundle 3 doesn’t belong to feasible

region 1. Therefore, while revealed preference (≻) and indirect revealed preferences

(,) are transitive, directly observed revealed preference (, ) is not transitive.

The idea of both direct and indirect revealed preferences is used in SARP by requiring

that if ≻ then we cannot have ≻.

Definition 2: , 1 if and only if , 0 and a chain of preference between bundles and exists , , …., 1.

Strong Axiom of Revealed Preferences (SARP): if ≻ (either directly

, 1 or indirectly , 1) and the situations are not equivalent (∃ . )

then we must not have ≻ (either directly , 1 or indirectly , 1).

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Figure 34 Weak Axiom of Revealed Preferences

a) No revealed preference violation b) WARP violation c) Transitivity of preference but not , Note: The bundles describe the quantities purchased in bundle 1 and 2 such that 1, 2 , and 1, 2 , .

We can locate violations of WARP and SARP without great difficulty. Suppose

that we observe bundles ∈ 1,…,. Then we calculate the matrix as

. Thus is the amount bundle j would have cost if the cost vector from

bundle was applied. Then the matrix determines whether bundle belonged to the feasible region of bundle (and consequently whether is directly revealed preferred

1, to ). That is, we define the matrix following , . 0,

WARP is violated when , , 1 which is true when ′ 1.

This violation of WARP is summarized as follows:

1⇔ & ⇔ &

To find the violations of SARP, the matrix

1, , 1 , 1 captures the presence of direct and indirect preference 0,

between bundles. SARP will be violated when 1. Unfortunately, determining

, can become computationally burdensome.

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Revealed preference implementation. To implement revealed preference analysis, we apply the Houthakker (1950) and Houthakker and Taylor (1970) six-step algorithm to implement the analysis of WARP violations over panels of prices and quantities.

Step 1) Create matrix M, where element Mij is the dot product of price vector p

from time i and quantity vector q from time j.

∙ ∙ ⋱ ∙ ∙

Step 2) Let d (T x 1) be the diagonal vector of M. Replicate d (a column vector) T times into a TxT matrix.

⋮⋮ ⋮⋮ ⋮⋮

Step 3) Create matrix R = M > D, where Rij = 1 if Mij > Dij, else 0.

Step 4) The WARP violation matrix V is given by the element-by-element

product of R and R’ (transpose of R). 1 means violation of WARP, 0 means no violation.

0… ⋱ ⋮0⋮ …0

Step 5) Compute the violation index time series u by normalizing the violation matrix

V in a rolling window of length w. For each row of V, sum up elements in index

range [d-w, d], where d is the diagonal element’s index within the row. Divide the

vector by w to derive u, a vector representing the percentage of time that violations

had took place in a rolling window of w periods.

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… , , 1 _ ⋮⋮ , …,

Step 6) For alternative measures of WARP, repeat the above steps by replacing price

data with other data such as risk premium, expected return, expected inflation, etc.

5.2.2. Stress dynamics

Current analysis. To investigate the dynamics of stress transmission across the heterogeneous representative agents, we apply the Toda-Yamamoto (1995) test for

Granger causality in the violation pattern of the heterogeneous representative agents.

Specifically, we examine whether one agent’s violations Granger cause violations in any other agent. Among the 25 agents captured in our dataset, there are 600 (25 x 24) possible pairs of bivariate relationships to examine. We apply the following 8-step algorithm to complete the analysis:

Step 1) Obtain the order of integration () for each agent’s violation index. This is done by iteratively performing first difference to the violation series if it doesn’t pass the Augmented Dicky-Fuller (ADF) test for stationarity at 1% significance level.

Step 2) For the pair of violation indices in consideration, define to be the maximum of the two series’ order of integration.

Step 3) Set up a vector autoregressive (VAR) model using the pair of indices without any differencing.

Step 4) Determine the optimal lag length for the VAR model with the Hannan-

Quinn information criterion (HQIC)92. Call the optimal lag .

92 AIC tends to give high lag lengths, while SIC tends to give very low lag lengths. HQIC’s length is in between. 190

Step 5) Add lags to the VAR model on top of .

Step 6) Compute p-value for does not cause . Use standard Wald test to compute test-statistics against the hypothesis that the first lag coefficients for are jointly zero in the equation where is the dependent variable.

Step 7) We repeat the above procedures for all 600 combinations, testing →

Granger causality to obtain a complete set of bivariate pairs. In this process, we set the

Granger-implied probability of violations in agent causing the subsequent violations in agent to

≞1, where p is the p-value given by the Toda-Yamamoto (1995) test.

Step 8) We construct the directed network edges on nodes , ) if the pair’s

probability is greater than 0.999.

Future analysis. Further insight can be gained by the application of Markov

chains to model dynamic processes among the heterogeneous representative agents

within the financial system. Such processes can be described as system states and their

transitions. By analogy to the monitoring of financial stress, the stress grade can be considered a state and the probabilities of transition from a particular grade of stress to any stress grade in the next time step are defined in the model. Thus, in the Markov state

model (MSM), the probabilities of transitions from state to state can be used to study the

dynamics of the system.

We would not be the first in thinking of stress in terms of the Markov state model

approach. For example, Holló et al. (2012) apply Markov regime switching approach to

determine the stress states (stress regimes). This is a more sophisticated approach to the

determination of stress states than the assumption of equal size in the determination of 191

stress grades,93 since it generalizes the ranges of stress space associated with certain types

of economic conditions and does not presume that the space is equally subdivided.

Given the state space regions (clusters), it is straightforward to determine the

probabilities of transitions between states given empirical data. The forward-looking

simulations can be compared with empirical data to determine, for example, whether

different stress regimes exist (as might be suggested by statistically significant structural

breaks in the system stress time series). Certainly a welcome finding might be that the

clustering does not change over time. A finding of changing clusters would make the interpretation of stress states (grades) a more difficult task. This however, would be very important for any heuristic rule that would have a policymaker sound certain alarms or trigger some policies given a particular state. The outcome would be the potential reduction in false alarms, and a more effective early warning based on this approach.

5.3. Results

Figure 35 shows results of WARP analysis as a percent count of violations in a

10-year moving window, when agent choices are explained by only observed prices and quantities. Clearly, about half the time no violations are observed, and when the violations do occur, with the exception of the financial crisis, they are really minor on the order below 2%. This is consistent with prior studies. The violations in the Financial

Crisis have been higher, reaching 7% in October 2008 and 9% in May 2012. These results, as a first approximation, provide reasonable support that the Flow of Funds

93 See also González-Hermosillo & Hesse (2011), Aboura & Van Roye (2013), van Roye, 2014, Mallick & Sousa (2013). 192

agents can be considered to make rational price and quantity choices and proceed to apply the hypothesized relationships to form a conjecture of agent financial stress.

Figure 35 Initial Revealed Preference Testing for All Agents

10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% Nov-90 Nov-91 Nov-92 Nov-93 Nov-94 Nov-95 Nov-96 Nov-97 Nov-98 Nov-99 Nov-00 Nov-01 Nov-02 Nov-03 Nov-04 Nov-05 Nov-06 Nov-07 Nov-08 Nov-09 Nov-10 Nov-11 Nov-12 May-90 May-91 May-92 May-93 May-94 May-95 May-96 May-97 May-98 May-99 May-00 May-01 May-02 May-03 May-04 May-05 May-06 May-07 May-08 May-09 May-10 May-11 May-12 May-13

However, on further testing (Figure 36), we find that the results of invariance testing of the conjectured functional form of stress support the existence of unexplained variation in agent financial stress. This becomes particularly evident, when we go beyond the first approximation of rationality among heterogeneous agents and uncover as we show in the graph, that many agents in fact appear to behave in stunningly irrational manner. Witness the funding companies shown here, where the violations of WARP reach 76% in early 2000 or the REITs that violate WARP in 23% percent of their allocation choices in July of 2010.

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Figure 36 Detailed Revealed Preference Testing for Heterogeneous Agents

FUNDING_CORPORATIONS REITS US_CHARTERED_DEPOS_INSTIT 80%

70%

60%

50%

40%

30%

20%

10%

0% Nov-90 Nov-91 Nov-92 Nov-93 Nov-94 Nov-95 Nov-96 Nov-97 Nov-98 Nov-99 Nov-00 Nov-01 Nov-02 Nov-03 Nov-04 Nov-05 Nov-06 Nov-07 Nov-08 Nov-09 Nov-10 Nov-11 Nov-12 May-90 May-91 May-92 May-93 May-94 May-95 May-96 May-97 May-98 May-99 May-00 May-01 May-02 May-03 May-04 May-05 May-06 May-07 May-08 May-09 May-10 May-11 May-12 May-13

Clearly, to make progress in understanding financial stress, the study needs to explain this apparent agent irrationality by understanding the drivers of the agent behavioral effects. Only then, we can hope to make further progress in advancing a theory of financial stress for the heterogeneous financial agents.

Table 28 and Figure 37 provide the results of analysis of violations under various price functions. These include the set of observed prices (p), the set of expected returns

(r), the set of risk premia (s), and the set of adjusted risk premia (as). In the latter case, we apply the empirically supported adjustments to account for liquidity preference and time preference. We use the market liquidity spread (Oet et al., 2015), measured by the difference between the 3-month LIBOR and the 3-month US Treasury yield. We use the

10-year inflation expectation (Haubrich et al., 2012), to describe time preference. Table

28 reports the mean percent of violations observed across agents under the various price functions. Figure 37 provides probability density estimates (kernel density estimates,

KDE) for each price function under various memory windows. Table 28 shows that violations are minimized when agent choices are considered using adjusted risk premium. 194

Figure 37 suggests that agent choices are further minimized when agents are considered to have short-term memory of the past respective price functions. This analysis is confirmed in Figure 38, which reports the mean observations of violations across the set of heterogeneous representative agents for memory of 12 months (Panel A), 36 months

(Panel B), and 120 months (Panel C).

Table 29 summarizes estimated Granger causality across agents based on the time series of their minimized violations, based on adjusted risk premium (as) with 12-month memory. Figure 39 plots the corresponding contagion network. A link from node to node in this graph is shown by a line with a bolded arrow head at node and indicates a probability higher than 99.9% that violations in nodes Granger cause violations in node .

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Table 28 Analysis of Violations Revealed with Various Price Functions: Observed Price, Expected Return, Risk Premium, and Adjusted Risk Premium Price Adjusted risk premium Expected return Risk premium Memory 12 months 36 months 120 months 12 months 36 months 120 months 12 months 36 months 120 months 12 months 36 months 120 months AGENT P_012 P_036 P_120 as_012 as_036 as_120 r_012 r_036 r_120 s_012 s_036 s_120 ABS issuers 0.06% 0.12% 0.10% 0.23% 0.10% 0.06% 0.16% 0.05% 0.10% 0.68% 0.84% 0.26% Banks in US affiliated areas 0.78% 1.03% 0.50% 0.48% 0.30% 0.11% 0.42% 0.31% 0.09% 1.16% 0.97% 0.32% Closed end funds 1.42% 3.37% 4.38% 0.13% 0.54% 0.33% 0.13% 0.22% 0.16% 2.97% 5.89% 8.88% Corporate business 0.39% 1.89% 1.60% 1.52% 2.40% 2.34% 0.81% 2.56% 6.59% 2.94% 4.45% 5.67% Credit unions 0.23% 0.11% 0.03% 0.39% 1.87% 1.76% 0.00% 1.26% 2.13% 0.19% 0.23% 0.16% ETFs 0.03% 0.01% 0.00% 0.03% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Federal government 1.71% 2.50% 4.22% 0.10% 0.10% 0.39% 0.19% 0.09% 0.26% 0.23% 0.23% 0.59% Federal pension 0.36% 0.12% 0.04% 0.16% 0.05% 0.02% 0.19% 0.06% 0.02% 0.97% 0.58% 0.17% Finance companies 0.74% 0.98% 0.55% 0.26% 0.19% 1.18% 0.06% 0.02% 0.52% 0.03% 0.13% 0.48% Foreign banking 0.81% 0.82% 1.13% 0.87% 0.57% 1.01% 0.58% 0.47% 1.20% 2.10% 3.38% 2.29% Funding corporations 0.23% 0.39% 0.16% 0.61% 1.31% 1.31% 0.58% 1.82% 1.51% 1.39% 1.27% 0.86% GSEs 0.23% 0.13% 0.04% 0.61% 0.60% 0.22% 0.42% 0.66% 0.25% 1.39% 5.78% 4.58% Holding companies 0.23% 0.15% 0.06% 0.87% 0.80% 0.79% 1.78% 1.77% 1.01% 3.65% 3.18% 2.17% Households 1.52% 3.09% 17.01% 0.26% 0.20% 0.12% 0.87% 0.54% 0.20% 1.07% 0.81% 0.84% Life insurance 1.10% 1.26% 0.46% 0.13% 0.14% 0.05% 0.06% 0.11% 0.04% 0.45% 0.52% 0.16% MMMFs 0.03% 0.05% 0.02% 0.52% 0.40% 0.77% 1.03% 0.59% 3.28% 3.71% 4.31% 4.22% Monetary authority 0.23% 0.36% 0.11% 0.32% 0.53% 0.27% 0.19% 0.47% 0.42% 0.36% 1.28% 0.64% Mutual funds 0.65% 0.45% 0.14% 0.29% 0.16% 0.05% 0.10% 0.06% 0.02% 0.84% 0.31% 0.09% Noncorporate business 0.16% 0.27% 0.16% 0.58% 1.95% 3.25% 0.52% 1.44% 2.41% 2.65% 2.77% 4.77% PC insurance 2.39% 4.38% 5.42% 0.19% 1.08% 0.44% 0.13% 0.64% 0.29% 3.55% 10.15% 8.32% Private pension 1.13% 1.46% 2.53% 0.55% 0.82% 0.37% 0.68% 1.16% 0.37% 1.26% 1.94% 1.10% REITs 0.32% 0.57% 0.99% 0.81% 1.93% 2.47% 0.52% 1.41% 3.71% 1.52% 3.65% 3.75% Rest of the world 1.74% 1.41% 0.42% 0.52% 0.55% 0.19% 0.32% 0.59% 0.24% 1.20% 1.34% 0.75% Security brokers 0.74% 0.59% 0.28% 1.39% 1.34% 0.87% 0.90% 1.41% 1.57% 3.42% 5.04% 3.57% State government 0.65% 0.43% 0.24% 0.42% 0.31% 0.28% 0.36% 0.52% 0.36% 1.49% 1.48% 1.99% State pension 1.68% 5.46% 3.42% 0.90% 1.01% 1.01% 0.71% 1.43% 0.81% 1.36% 1.96% 2.48% US chartered depository institutions 1.13% 1.34% 0.68% 0.26% 0.14% 0.04% 0.32% 0.27% 0.09% 0.29% 0.18% 0.09% All agents 2.23% 5.39% 2.79% 0.39% 0.40% 0.12% 0.26% 0.38% 0.14% 0.87% 0.86% 0.27%

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Figure 37 Testing Price, Expected Return, Risk Premium, Adjusted Risk Premium to Explain Agent Choice Panel C: Risk premium Panel A: Price Panel B: Expected return Panel D:Adjusted risk premium

Figure 38 Testing Agent Memory to Explain Choice Panel A: 12-month memory window Panel B: 36-month memory window Panel C: 120-month memory window

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Table 29 Granger Causality among Violations Based on Adjusted Risk Premium with 12-month Memory NODE AGENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 ABS issuers 22.6% 23.3% 98.3% 100.0% 99.7% 29.9% 18.5% 16.2% 52.9% 25.7% 53.9% 20.8% 35.9% 88.0% 30.4% 28.6% 32.7% 38.5% 41.8% 48.5% 100.0% 37.2% 9.9% 48.5% 2 Banks in US affiliated areas 36.3% 31.5% 16.2% 15.8% 27.3% 35.2% 100.0% 50.2% 7.0% 20.9% 99.3% 24.6% 50.3% 43.2% 30.6% 2.7% 36.1% 63.1% 97.7% 10.3% 25.3% 43.6% 39.2% 55.2% 3 Closed end funds 50.1% 17.1% 19.2% 10.0% 17.4% 22.7% 14.0% 33.1% 50.8% 70.3% 37.2% 0.0% 27.4% 26.7% 100.0% 100.0% 24.9% 29.4% 63.6% 78.3% 63.4% 28.4% 16.2% 46.1% 4 Credit unions 40.8% 15.0% 17.5% 100.0% 15.0% 100.0% 12.3% 31.9% 25.7% 68.8% 12.1% 14.4% 100.0% 47.9% 20.8% 33.4% 99.3% 21.6% 33.7% 5.9% 22.0% 96.6% 17.9% 22.7% 5 ETFs 0.0% 8.5% 10.1% 100.0% 8.7% 100.0% 7.0% 16.8% 13.7% 11.6% 28.2% 7.8% 100.0% 13.4% 11.6% 10.9% 12.5% 14.9% 53.3% 1.6% 14.3% 14.4% 8.1% 12.9% 6 Federal government 99.8% 14.8% 100.0% 16.6% 8.7% 19.7% 12.1% 100.0% 23.7% 21.4% 32.4% 0.1% 23.8% 23.2% 20.0% 100.0% 21.6% 32.6% 27.9% 77.5% 88.4% 53.2% 32.9% 99.8% 7 Federal pension 26.1% 19.1% 22.6% 100.0% 100.0% 19.5% 15.6% 36.9% 30.4% 47.2% 41.3% 17.5% 100.0% 29.7% 94.5% 24.2% 22.7% 32.8% 37.5% 98.9% 31.6% 31.7% 18.1% 28.5% 8 Finance companies 32.9% 3.0% 28.5% 13.3% 14.2% 24.7% 31.9% 45.9% 38.1% 17.2% 19.3% 100.0% 38.2% 36.1% 0.2% 49.5% 78.4% 100.0% 3.7% 75.0% 100.0% 4.4% 65.7% 91.8% 9 Foreign banking 78.2% 15.0% 54.5% 65.1% 21.5% 94.7% 46.8% 29.8% 52.0% 39.2% 90.8% 33.2% 70.5% 2.8% 59.7% 71.1% 50.9% 91.7% 63.1% 100.0% 49.4% 69.1% 100.0% 93.5% 10 Funding corporations 37.0% 29.1% 32.6% 25.9% 17.2% 29.8% 38.2% 69.7% 54.3% 47.4% 62.2% 52.0% 47.5% 81.8% 100.0% 100.0% 41.8% 14.5% 18.5% 37.7% 47.2% 47.2% 27.7% 42.8% 11 GSEs 68.2% 21.4% 23.2% 29.5% 12.2% 21.4% 26.5% 17.5% 31.2% 77.0% 10.1% 100.0% 100.0% 23.9% 29.5% 24.3% 26.2% 38.8% 34.9% 10.7% 34.2% 51.0% 100.0% 32.2% 12 Holding companies 70.0% 100.0% 39.4% 94.6% 19.5% 34.3% 43.9% 12.1% 74.7% 34.8% 63.4% 31.0% 15.7% 65.9% 92.7% 49.8% 47.8% 55.5% 81.4% 29.1% 31.3% 53.8% 14.0% 54.2% 13 Life insurance 23.4% 17.1% 100.0% 14.9% 10.0% 100.0% 22.7% 0.0% 63.9% 59.4% 28.2% 37.2% 98.5% 26.7% 23.1% 21.7% 24.9% 100.0% 32.0% 5.3% 21.6% 93.7% 24.9% 25.6% 14 MMMFs 37.8% 58.8% 32.8% 100.0% 93.9% 28.5% 100.0% 22.9% 0.1% 4.0% 13.9% 57.8% 82.6% 42.7% 97.6% 35.2% 40.1% 46.9% 100.0% 14.5% 10.4% 80.7% 9.8% 41.1% 15 Monetary authority 36.6% 27.0% 31.8% 77.1% 15.9% 27.6% 35.5% 100.0% 59.1% 42.3% 31.8% 60.6% 24.8% 42.5% 36.2% 34.1% 38.9% 45.5% 49.2% 64.3% 63.0% 58.1% 59.5% 39.8% 16 Mutual funds 31.6% 96.5% 0.7% 22.0% 13.6% 23.7% 30.6% 0.9% 2.7% 14.5% 28.3% 100.0% 21.3% 12.0% 35.8% 99.5% 33.6% 39.4% 24.1% 2.0% 59.0% 32.6% 0.9% 46.3% 17 Noncorporate business 39.3% 89.5% 57.8% 22.4% 17.2% 2.8% 38.1% 29.3% 82.8% 11.2% 26.6% 100.0% 99.6% 45.5% 44.4% 100.0% 41.7% 54.3% 3.7% 49.0% 59.7% 12.4% 89.6% 34.2% 18 PC insurance 28.6% 100.0% 24.7% 7.1% 12.3% 21.4% 23.5% 100.0% 40.2% 33.2% 30.4% 44.8% 19.2% 66.6% 32.5% 28.2% 26.5% 35.8% 52.9% 9.9% 94.4% 34.6% 40.3% 31.2% 19 Private pension 40.9% 30.3% 35.6% 34.3% 17.9% 99.9% 39.7% 100.0% 66.3% 64.0% 95.2% 12.3% 99.0% 7.2% 89.6% 40.4% 55.4% 59.8% 23.1% 82.4% 98.3% 53.3% 88.4% 100.0% 20 REITs 44.8% 94.0% 39.1% 84.5% 19.3% 34.0% 92.5% 6.3% 60.9% 100.0% 44.8% 27.1% 30.7% 98.3% 50.4% 84.6% 100.0% 45.8% 59.4% 54.2% 15.1% 95.3% 31.7% 21.7% 21 Rest of the world 97.0% 11.8% 100.0% 7.7% 3.9% 87.2% 5.2% 8.0% 91.7% 4.0% 10.6% 10.2% 10.8% 24.1% 92.8% 72.2% 6.4% 17.3% 65.0% 29.1% 28.5% 45.5% 20.0% 87.1% 22 Security brokers 8.8% 8.6% 47.7% 90.5% 25.2% 91.0% 53.9% 77.8% 68.1% 40.4% 17.9% 78.6% 100.0% 14.1% 56.2% 60.1% 34.6% 82.0% 100.0% 73.7% 63.4% 12.6% 44.1% 16.7% 23 State government 73.8% 28.7% 91.0% 67.3% 17.0% 96.7% 37.6% 4.9% 28.4% 44.7% 100.0% 15.1% 99.9% 100.0% 58.3% 5.7% 9.0% 41.1% 100.0% 23.3% 10.1% 24.0% 97.6% 98.8% 24 State pension 49.7% 52.7% 37.5% 12.7% 19.0% 61.5% 41.8% 85.0% 0.5% 19.9% 100.0% 11.6% 48.4% 22.4% 97.1% 0.4% 26.8% 14.9% 69.1% 57.0% 14.2% 86.8% 57.6% 46.7% 25 US chartered depos institutions 51.1% 69.1% 25.4% 24.3% 14.2% 24.7% 31.9% 100.0% 99.0% 38.1% 31.2% 10.4% 22.2% 38.2% 83.7% 51.7% 89.0% 34.9% 32.6% 44.4% 98.7% 9.0% 39.7% 54.7% 198

Figure 39 Contagion Network

Note: The nodes in the contagion network are coded as follows. 1 – ABS issuers; 2 – Bank in US affiliated areas; 3 – Closed end funds; 4 – Credit unions; 5 – ETFs; 6 – Federal government; 7 – Federal pension; 8 – Finance companies; 9 – Foreign banking; 10 – Funding corporations; 11 – GSEs;12 – Holding companies; 13 – Life insurance; 14 – MMMFs; 15 – Monetary authority; 16 – Mutual funds; 17 – Noncorporate business; 18 – PC insurance; 19 – Private pension; 20 – REITs; 21 – Rest of the world; 22 – Security brokers; 23 – State government; 24 – State pension; 25 – US chartered depository institutions.

5.4. Integrated Research Findings

Contributions. This research makes four contributions to current state of knowledge on financial stress measurement. First, we improve stress measurement across at the micro level of analysis of various representative financial agents. Second, we explain the patterns of apparent violations of agent choice in allocating among various

portfolios of financial assets by testing alternative price functions. Third, we explain the

dynamic stress generation processes by testing alternative theories (e.g. memory retention and mixed frequency memories).

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Validity. As a significant contribution to the literature on financial stress, we address validity comprehensively across multiple levels of analysis. Specifically, in the component studies, this research supports face validity (through narrative development), internal validity (through construct validity), external validity (through convergent and predictive validity), and ecological validity through out-of-sample testing of stress on hold-out data.

Practical usefulness and comparative advantages. By comparison with current research, this study breaks new ground for measuring financial stress dynamically not only for the overall financial system but also for the micro-level agents and instruments.

The ability to measure stress at the micro level introduced in this study permits stress measurement to evolve with the changes in the adaptive financial system.

5.5. Conclusion

Relatively poor alignment between the theoretical measure of financial system stress and CFSI is partly explained by the different characteristics of stress incorporated.

While CFSI focuses purely on spreads, the theoretical measure also incorporates volume, transaction, and concentration information for each agent’s positions. Another distinction

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between the theoretical and empirical measures lies in their partitioning. The theoretical stress measure leverages a detailed decomposition of the financial system in terms of the instrument portfolios for a large set of heterogeneous financial agents, while the empirical measures assumes the importance of six a priori markets. Therefore, as a means of improving the discriminatory power of the empirical measure (CFSI), we support the reliability of a 5-factor version of CFSI based upon empirically tested static factor analysis and find a noticeable improvement. Furthermore, when in the subsequent dynamic factor analysis, we adjust the empirical stress to align with the theoretical notion of stress that is experienced today to reflect the persistence of stress from previous periods, we find that the fit is consistent with a static factor analysis construction.94 This is remarkable, since the process and shock factor models are handicapped by the current omission of indicators reflecting the important equity and foreign exchange factors. This suggests that further improvements in explanatory power are readily attainable, when these factors are incorporated. Beyond increasing the alignment with theoretical stress, applying dynamic factor analysis reveals that stress is best modeled as a shock process with persistence that varies by factor up to a year and a half.

94 The correlation of theoretical stress against the five factor version of CFSI based upon static factor analysis is 0.399 which is essentially identical to the correlation between theoretical stress and the shock model of 0.399. 201

In the course of this study, we make the following four contributions to the literature on financial stress measurement: 1) we carefully review the relevant insights on dynamic factor analysis from an extended set of research traditions that include social science and psychometric contributions to longitudinal data analysis; 2) we extend an empirical analytic algorithm established in literature; 3) we consider the typology of alternative dynamic factor models and explain the distinctions between them; 4) we estimate two alternative dynamic factor models for US financial stress based on the observation dataset for the Cleveland Financial Stress Index: a process factor model and a shock factor model.

95 For example, four dynamic factors acting with a quarterly effect are securitization, money market, credit/residential real estate, and funding. This adjusts the corresponding extant naïve 4-market composition of securitization, credit, real estate, and funding. 202

Second, our findings suggest a co-existence of mixed frequency dynamic effects, with four dynamic factors having quarterly time dependency with a 4-lag horizon, and two additional factors having a weekly time dependency with a 4-week horizon. It would be highly interesting to extend this study by inclusion of the mixed-frequency dynamic effects.

Limitations. The results of this study should be taken with a degree of caution, given the known limitations in estimating dynamic factor measurement models via MLE-

SEM approaches. It would be useful to comprare the robustness of the obtained results using alternative software and estimation methods. In addition, a serious limitation of our approach is that financial markets transformation and the increased sophistication gained by financial agents in using the more transparent measures of stress may shift their behavior and psychology of financial agents in unexpected ways. For example, it may become easier to speculate in the markets with longer memory. The discovery of this fact may transform slow thinkers into fast thinkers (Kahneman and Tversky) and generate a wild new bunch of “animal spirits” (Akerlof and Shiller, 2010) within us as the agents in the financial system. Things change…

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Appendix 1: Chapter 2 Regime Sampling

A1.1 Regime Sampling

Given the evidence of regime transformations in the processes of monetary policy setting (Bryant et al., 1993),96 we seek to establish a representative sampling for the study

period from 1990M2 to 2012M6. To determine the regime samples, we apply the Bai-

Perron (1998) test for the presence of multiple unknown structural break points in a time

series. The test employs a sequential algorithm to search and analyze the time series for

structural breaks by comparing the goodness-of-fit statistics across the sets of possible

break points with a candidate set that includes an additional break point against the

critical values provided by Bai-Perron (2003). To avoid estimating the model with

insufficient observations, we maintain a minimum permissible length of the observation segment , where 15% is the trim parameter, and is the total number of observations. The results for the effective Fed Funds rate from 1990M2 to 2012M6 are presented in Table 30, Panel A, and indicate the presence of four structural breaks which are significant at 1%.

The four structural breaks are found in January 1994, January 2001, July 2004, and February 2008. Therefore, we support the following regime sampling strategy:

Regime 1 sample includes observations from 1990M2 to 1993M12; Regime 2 sample comprises data from 1994M1 to 2000M12; Regime 3 covers observations from 2001M1

96 Bryant et al., (1993) discuss a variety of operational processes that result in policy regime changes. These include among others changes in the ultimate target variables, changes in in the instrument choice, intermediate variables, adjustments in the loss function, changes in the policymakers’ intermediate strategies, discretionary preferences, and measurement uncertainties. The intuition for the presence of several policy regimes in this timeframe is based for the post 2008M8-presence of the zero lower bound for the Fed funds rate, multiple changes in the measurement of the inflation, output, and the evolution of the Fed’s inflation targeting strategy. 204

to 2004M6; Regime 4 lasts from 2005M7 to 2008M1; and Regime 5 contains observations from 2008M2 to 2012M6.

In addition, we test the FOMC discussions for the presence of structural breaks to examine whether the policymakers materially change their discussions across the sampled regimes. The results (Table 30, Panel B) show that only the discussions of financial stability reveal structural breaks. Interestingly both structural breaks in discussions of financial stability (1999M01 and 2007M08) precede the respective breaks in the Fed Funds rate (2001M01 and 2008M02), suggesting that possibility that the respective regime changes were conditioned by the policymakers’ discussions of the structural changes in financial conditions.97

Table 30 Bai-Perron Structural Break Test Results Break Test Date F-statistic Scaled F-statistic Critical Value** Panel A: Effective Fed Funds rate 0 vs. 1 * 2008M02 22.41 44.82 11.47 1 vs. 2 * 2004M07 9.91 19.82 12.95 2 vs. 3 * 2001M01 30.95 61.90 14.03 3 vs. 4 * 1994M01 20.82 41.63 14.85 Panel B: FOMC discussion themes Financial stability theme 0 vs. 1 * 2007M08 9.56 19.12 11.47 1 vs. 2 * 1999M01 7.86 15.73 12.95 Output theme 0 vs. 1 5.70 11.40 11.47 Inflation theme 0 vs. 1 5.33 10.65 11.47 Unemployment theme 0 vs. 1 3.39 6.78 11.47 Foreign activity theme 0 vs. 1 3.57 7.14 11.47 Fiscal policy theme 0 vs. 1 5.37 10.74 11.47 Money supply theme 0 vs. 1 5.03 10.05 11.47 Note: * Significant at the 0.05 level. ** Bai-Perron (2003) critical values.

97 The first structural break in financial stability discussions coincides with The 1999 US Financial Services Modernization Act (1999) that broke down structural barriers between commercial banking, investment banking, and insurance. The second structural break coincides the beginning of the Subprime Crisis in August 2007. 205

A1.2 Descriptive Statistics

Table 31 Descriptive Statistics of Manifest Variables (1990M2–2012M6) Money Stability Unemployment Foreign Foreign Fiscal Policy Inflation Output Output Gap Stability Unemployment Money Supply Supply Fiscal Policy Gap Gap Activity Activity Gap Gap Gap Panel A: Full Sample (1990M2 – 2012M6) Observations 269 269 269 269 269 269 269 269 269 269 269 269 269 Mean 2.22 2.14 -1.35 48.72 5.35 37.77 -0.83 -3.02 0.00 5541.58 0.00 -89.19 0.00 Std. Dev. 0.93 1.85 2.68 10.58 10.58 1.74 1.55 1.64 1.00 2001.05 1.00 130.79 1.00 Median 2.15 2.42 -0.75 47.14 6.93 37.30 -0.40 -2.95 0.04 5107.52 -0.22 -61.60 0.21 Maximum 5.16 5.11 3.10 81.45 21.27 41.80 1.21 0.64 2.23 10026.17 2.24 208.72 2.28 Minimum 0.71 -6.28 -7.60 32.80 -27.38 35.30 -4.91 -6.20 -1.94 3191.31 -1.17 -476.75 -2.96 Panel B: 1990M2 – 1993M12 Observations 47 47 47 47 47 47 47 47 47 47 47 47 47 Mean 3.57 1.39 -2.57 50.15 3.92 38.12 -1.03 -0.80 1.35 3361.57 -1.09 -65.37 0.18 Std. Dev. 0.60 1.68 1.59 5.84 5.84 0.55 0.80 0.58 0.35 80.04 0.04 26.00 0.20 Median 3.42 1.80 -3.10 48.17 5.90 38.30 -1.24 -0.96 1.25 3392.47 -1.07 -65.68 0.18 Maximum 5.16 4.66 0.60 68.93 10.18 38.80 0.68 0.64 2.23 3472.40 -1.03 -13.26 0.58 Minimum 2.60 -2.76 -4.50 43.89 -14.86 36.80 -2.12 -1.59 0.87 3191.31 -1.17 -119.77 -0.23 Panel C: 1994M1 – 2000M12 Observations 84 84 84 84 84 84 84 84 84 84 84 84 84 Mean 2.59 2.90 1.23 44.78 9.29 36.41 0.20 -2.32 0.42 4032.69 -0.75 1.69 0.69 Std. Dev. 0.49 1.01 1.17 7.20 7.20 0.71 0.62 0.97 0.59 465.58 0.23 61.06 0.47 Median 2.58 2.94 1.66 43.64 10.43 36.15 0.22 -1.86 0.70 3921.86 -0.81 -15.70 0.56 Maximum 3.45 5.11 3.10 65.67 20.06 37.90 1.21 -1.19 1.11 4949.69 -0.30 208.72 2.28 Minimum 1.65 -0.39 -1.10 34.01 -11.60 35.30 -1.15 -4.21 -0.72 3473.17 -1.03 -75.14 0.11 Panel D: 2001M1 – 2004M6 Observations 42 42 42 42 42 42 42 42 42 42 42 42 42 Mean 1.20 2.16 -1.51 51.11 2.96 37.20 -0.53 -4.29 -0.77 5674.10 0.07 -55.22 0.26 Std. Dev. 0.30 1.89 0.81 8.89 8.89 0.66 0.59 0.48 0.29 372.37 0.19 75.83 0.58 Median 1.30 2.03 -1.68 53.33 0.74 37.30 -0.70 -4.33 -0.80 5690.42 0.07 -62.57 0.20 Maximum 1.65 4.88 0.10 63.14 21.27 38.00 0.80 -3.29 -0.16 6252.04 0.36 191.90 2.15 Minimum 0.71 -2.40 -2.66 32.80 -9.07 35.60 -1.30 -5.12 -1.28 4987.98 -0.28 -171.83 -0.63 Panel E: 2004M7 – 2008M1 Observations 43 43 43 43 43 43 43 43 43 43 43 43 43 Mean 2.02 2.82 -0.26 41.89 12.18 37.15 0.13 -5.42 -1.46 6837.90 0.65 -72.84 0.13 Std. Dev. 0.28 1.13 0.67 8.49 8.49 0.30 0.34 0.49 0.30 383.46 0.19 80.59 0.62 Median 2.14 3.24 -0.04 40.03 14.04 37.10 0.30 -5.49 -1.51 6776.38 0.62 -86.25 0.02 Maximum 2.37 4.49 0.59 68.13 21.12 37.70 0.60 -4.29 -0.77 7562.84 1.01 133.30 1.70 Minimum 1.48 0.25 -1.40 32.95 -14.06 36.60 -0.50 -6.20 -1.94 6276.21 0.37 -205.03 -0.89 Panel F: 2008M2 – 2012M6 Observations 53 53 53 53 53 53 53 53 53 53 53 53 53 Mean 1.40 1.05 -5.10 57.36 -3.29 40.59 -3.31 -3.15 -0.08 8709.48 1.58 -294.55 -1.57 Std. Dev. 0.45 2.56 2.06 14.07 14.07 1.51 1.42 0.66 0.40 671.93 0.34 117.64 0.90 Median 1.24 1.84 -5.79 56.21 -2.14 41.40 -3.75 -2.95 0.04 8561.30 1.51 -320.17 -1.77 Maximum 2.43 4.58 -0.37 81.45 19.42 41.80 0.10 -2.46 0.34 10026.17 2.24 22.95 0.86 Minimum 0.76 -6.28 -7.60 34.65 -27.38 37.20 -4.91 -4.81 -1.09 7633.00 1.05 -476.75 -2.96 Note: We use the Greenbook dataset for variables before 2009. After 2009, we use Haver Analytics data as described in Section 4.2.

A1.3 Robustness

We further test the adequacy of the samples suggested by the structural break

results for statistical power to differentiate sample means relative to the population at

95% confidence. The results, shown in Table 32 generally support the suggested regime sampling strategy. However, they also highlight a pattern of limited statistical power relative to Regime 4, where the null hypothesis of identical means may be incorrectly rejected. In addition, a pattern of limited statistical power is present in the discussions of fiscal policy. These results suggest caution in interpreting the inferential analysis using the regime samples, particularly relative to Regime 4 and fiscal policy.

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Table 32 Two-Tailed Test of the Mean for Statistical Power (95% Confidence) FedFunds Ave. SSR Regime 1 100% 100% 93.8% 100% 99.5% 91.0% 100% 99.6% 100% (1990M21993M12) Regime 2 99.9% 100% 90.1% 100% 99.7% 35.2% 100% 100% 100% (1994M12000M12) Regime 3 100% 100% 97.1% 100% 100% 100% 100% 100% 100% (2001M12004M6) Regime 4 100% 5.6% 68.2% 100% 99.9% 99.9% 100% 77.7% 99.5% (2004M72008M1) Regime 5 16.2% 100% 91.4% 100% 100% 42.7% 100% 100% 100% (2008M22012M7) Note: Statistical power of incorrectly rejecting the null hypothesis that there is no difference in average values of sample relative to population at 95% confidence. Shading indicates samples with compromised statistical power.

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Appendix 2: Chapter 2 Content Analysis Methodology

A2.1 Target of Content Analysis and Data

The target of content analysis is Federal Reserve discussions of monetary policy.

According to Danker and Luecke (2005) (DL), the sources that capture this information include reports of the FOMC communications in two forms as summarized minutes

(“Published Summaries of Meetings”) and transcripts (“Detailed Internal Accounts of

Meetings”). In addition to the minutes, the FOMC

“releases a statement on the same day that policy decisions are made, the Chairman provides semiannual testimony to the Congress, and the Board submits semiannual Monetary Policy Reports, which include a summary of the economic projections of the Board members and Reserve Bank presidents. In addition, the Chairman testifies on the economy and other topics on several occasions during the year; Committee members regularly give public speeches; and a wide range of documents, including FOMC meeting transcripts, is made available after a five-year lag” (DL: 175).

The minutes were chosen because full transcripts are only available with a five- year lag. FOMC (1977) attested to high quality of the minutes document, as containing “a full and accurate report of all matters of policy discussed and views presented, clearly sets forth all policy actions taken by the FOMC and the reasons therefore, and includes the votes by individual members on each policy action.” DL distinguish three meeting regimes. From 1936 to the end of 1992, Federal Reserve summarized its discussions in the record of policy action. From June 20, 1967 to the end of 1992, the minutes of action were recorded. Beginning in 1993, modern minutes were recorded. The format of the modern minutes had in turn had some adjustments. For example, from 1993 to the end of

2003, the intermeeting conference calls were not consistently recorded and embedded within the meeting minutes, while from 2004 and onward, all intermeeting conference

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calls are recorded at the end of the next meeting’s minutes. The data chosen for this study consists of FOMC meeting minutes from 1990M2 to 2012M6.

A2.2 Unitizing and Coding

To support replicable inferences from content analysis, we employ a cross- validation strategy of dual coding, applying each form of coding to overlapping units of analysis (paragraphs and phrases). First, we use an interpretive method of emergent coding that allows exploratory investigation of text, paragraph by paragraph, and gradual establishment of hierarchical themes through consensus building by multiple human coders. Second, we employ algorithmically-aided selective coding where text is parsed into phrases, then mapped to the themes established in emergent coding.

Coding method 1: Emergent coding. Four coders were randomly assigned minutes from the sample dataset. The coders were provided with a Federal Reserve

Taxonomy,98 a list of economic themes used by the Federal Reserve Library in classifying economic research which served as the basis for an emergent coding process.

Coders read the minutes and applied the codes to each recording unit (paragraph). The

coding process was emergent, in the sense that the coders coordinated with each other to

agree on trimming or adding codes to the list and on reorganizing its hierarchical themes based on FOMC minutes content. The hierarchical interpretation of the content was based on the coders’ discussion and agreement about the broad themes or “parent codes” and their respective sub-themes or “child codes” with increasingly narrow subjects.

98 Federal Reserve Taxonomy is a private metadata classification system developed by the Federal Reserve System from 2002 to 2006. 209

The emergent coding process was completed in two passes. During the first pass, each excerpt was coded as fine as possible with one theme that encompassed the entire contents of the recording unit. The excerpts were typically confined to one complete paragraph and may have also included subsequent complete paragraphs if their contents were of the same subject. On occasion, the paragraphs discussed two or more distinct broad themes. In these cases, several applicable codes were applied to the same paragraph. During the first coding pass, all of the minutes were coded individually by the coders using the emergent themes based on the Federal Reserve Taxonomy. Concurrent with this coding, the hierarchy of the taxonomy was reorganized by collective consensus.

Consistently with Krippendorff (1989: 404), it was normal for the coders to “change their perspective as they read through large volumes of material and to be selective in support of their favored” interpretation. At the end of the first pass, the revised taxonomy was summarized into a situational map (Clarke, 2003). In the second pass, coding for the entire set of documents was consistently re-applied, guided by the situational map (Figure

6).

Coding method 2: Selective coding. Unlike the process of emergent coding, which leveraged the intuitive and rigorous manual coding of four individuals, selective coding implemented an algorithmic approach using the SAS Data Miner software. The selective coding sample was extended to the beginning of 1990 to improve the

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comparison of financial stability theme with the available time series of US financial stress.99

In this process, text of FOMC minutes was stripped of pronouns, conjunctions,

and other common words100 from the FOMC meeting minutes that were jointly identified

in a stopword list (Luhn, 1958). The intent was to remove words that do not contribute to

the information contained in the meeting minutes. Next, the remaining words were

stemmed to their semantic roots.101 After this preparation had been completed, SAS Data

Miner functions were used to parse out each sample into recording units. Unlike the

paragraph recording unit considered for emergent coding, selective coding considers

individual phrases to improve the granularity of analysis. We maintain a record of the

context and frequency of each recording unit for every meeting. This process results in

33, 292 phrases, from the most frequent (“econom activ” occurring 1060 times) to least

frequent (“tragic event” occurring twice). In the final step of selective coding we select

the 1000 most frequently observed phrases which are mapped to themes using the

situational map (Figure 6) resulting from the emergent coding.

99 See Oet et al., (2012). Data available at https://www.clevelandfed.org/en/Our%20Research/Indicators%20and%20Data/Current%20Level%20 of%20the%20CFSI.aspx 100 In addition to the conjunctions (e.g. and, but, or), prepositions (e.g. up, over, by for), the excluded words consisted of pronouns (e.g. he, she, who, them), proper nouns (e.g. names of chairmen, economists, secretaries), numbers (e.g. 1, 2, 3, etc.) and common words and phrases associated with meeting logistics (e.g. Federal Reserve, notation vote, Chairman, Mr., Mrs., Federal Open Market Committee). 101 For example, words like “walking” and “walked” were transformed to their semantic root “walk”. 211

Appendix 3: Chapter 2 Content Analysis Validity

Krippendorff (1989: 403) emphasizes that “The methodologically critical requirement of any content analysis is to justify the inferential step this involves.”

Krippendorff (2012: 334) develops a typology of validation in content analysis and distinguishes three broad types of validity: face validity, social validity, and empirical validity.102 Face validity and social validity can be established rhetorically, whereas

support for empirical validity involves a set of evidentiary standards. Here, Krippendorff

details three essential subclasses of empirical validity: content sampling and semantics,

internal structure, and relations to other variables.

A3.1 Face Validity

Plausibility serves as a test for face validity of the inference from FOMC

discussions of financial stability factors to the research question about its role in

monetary policy: “it makes sense.” Examination of the frequency of the financial stability

discussions over time reveals a number of episodes characterized with a sharp rise in

relative frequency relative to the near-time history (see Figure 10). The financial stability

factors in FOMC discussions exhibit a highly volatile pattern, marked by rapid and

tangible increases in the frequency of their use. Figure 10 shows the episodes of US

financial stress as white line disruptions in the time series of the FOMC discussions. To

an observer familiar with the history of US financial instability, the correspondence of the

time series in Figure 10 with the critical episodes in US financial history is evident.

102 Krippendorff (2012: 333) defines face validity as “obvious or common truth” and empirical validity as “The degree to which available evidence and established theory support intermediated stages of a research process and its results.” Riffe et al. (1998: 137) define social validity as “the degree to which content analysis categories created by the researchers have relevance and meaning beyond an academic audience.” 212

A3.2 Social Validity

The social validity of the inference is supported by the evidence of emerging consensus on the importance of additional breadth among public authorities when considering policy issues (Bernanke 2011, 2012; FOMC 2013; Dodd-Frank, 2010: Title

VIII). Literature has examined both the normative question “which variables should monetary policy react to?” and the positive question “which variables does monetary policy react to?” (Hayford and Malliaris, 2004). Thornton and Wheelock (2000) examine the effect of asymmetric language in FOMC directives and found that policy changes were usually in the direction of bias. Similarly, Pakko (2005) determines that the communications bias of FOMC statements can be incorporated as dummy variables interacting with the output and inflation gap series that accentuate or diminish the sensitivity to information about output and inflation. Farka (2011: 488) shows that changes in FOMC statement patterns have an impact on market response and that “the behavior of volatility around policy announcement[s] is tent-shaped.”

A3.3 Empirical Validity in Content Sampling and Semantics

There are two perspectives associated with content validity which attempt to verify that the target of analysis is representative (sampling validity) and that the hierarchical categorization makes sense (semantic validity).

The representativeness of the sample used for this study is supported in section 3.

The critical aspects affecting the selection of this sample include the timeliness of data, span of coverage, and completeness of content. The minutes are available three weeks after the meeting’s decision is released, thereby avoiding the five-year lag inherent to analysis of full meeting transcripts or other documents. These releases originate in 1936

213

and continue to be produced which easily accommodates the window of analysis necessary for this study. Finally, the meeting minutes follow a standardized form with regular release timelines which facilitates manual and algorithmic analysis, while the depth and breadth of minutes’ content is affirmed by the issuing committee (FOMC

1977). The semantic dimension of content analysis is addressed for emergent coding by the cross-validation of themes and for selective coding by the internal structure tests

(Section 5.2).

A3.4 Empirical Validity in Structure and Function

A more advanced validation of the quality of the content analysis (the themes of

FOMC) is the relevance of extracted themes to the explanation of monetary policy due to their structural patterns. Structural validity for both the emergent and selective coding methods is provided by evidence of thematic tipping points consistent with the structural breaks of the monetary policy instrument (Fed Funds rate) presented in section 4.2.

Functional validity focuses on the use of the analytical constructs rather than on their structure. It is supported by failure to reject the significant association of extracted themes to monetary policy instrument. This can be falsified by a model regressing the monetary policy instrument on thematic discussion frequencies and considering both sign expectations (equation 1) and statistical power. The analysis in section 4.1 demonstrates that the content analysis themes satisfy both sign and significance criteria (Table 5).

A3.5 Empirical Validity in Relations to Other Variables

Relational validity refers to the way that the derived content analysis series fulfill the expected relationships amongst themselves (correlative validity) and with other concepts (predictive validity).

214

Correlative validity. How do we know that the factors of financial stability are reasonably identified? The results may be validated against a time series of US financial stress (Oet et al., 2012). As shown in Figure 10, the factors of financial stability and financial stress are highly correlated with a contemporaneous correlation 0.678. In addition, the Granger causality between the two series is very strong in both directions, indicating that they move essentially in tandem. Thus, FOMC discussions of the financial stability factors may be viewed as a proxy for the US financial stress. The reverse is also relevant: the US financial stress series may be viewed as a proxy for financial stability concerns expressed during the monetary policy deliberations at the FOMC.

Predictive validity. The predictive validity of extracted themes is supported through the thematic and tri-mandate models estimated in Section 2.4.1 (Table 5 and

Table 6). The consistent improvement in adjusted upon switching from Taylor-type

rules to the tri-mandate model serves to suggest that the output, employment, inflation,

and financial stability discussion themes are able to explain deviations between monetary

policy and the Taylor-type benchmark. Moreover, the tri-mandate model exhibits lower

errors (RMSE, MAE, MAPE) and greater fit (adjusted ) in all regime samples except

for the first. All of these properties assert that themes used in the tri-mandate model

satisfy predictive validity. The thematic model also demonstrates lower errors (RMSE,

Theil U) and improved model fit over Taylor-type benchmark in all regime samples.

Finally, the high levels of significance indicated in Table 5 confirm that the themes of foreign activity, money supply, and fiscal policy also meet requirements for predictive

validity.

215

Appendix 4: Chapter 3 Robustness Testing

Table 33 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV

Name , TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i ST LOUIS FINANCIAL STRESS INDEX 2 0.2 7 0 113 45 0.87 0 0 0.13 2-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.5 0.6 24 5 108 28 0.54 0.04 0.1 1.31 0.4 3-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.91 0.3 16 0 113 36 0.69 0 0 1.24 0.31 4-i CLEVELAND FINANCIAL STRESS INDEX 0.8 0.6 32 7 106 20 0.38 0.06 0.1 0.99 0.53 5-i CFSI: REAL ESTATE MARKET 0.5 0.7 34 16 97 18 0.35 0.14 0.22 0.86 0.49 6-i CFSI: EQUITY MARKET 0.59 0.7 32 27 86 20 0.38 0.24 0.39 0.84 0.35 7-i KANSAS CITY FINANCIAL STRESS INDEX 0.83 0.6 16 1 112 36 0.69 0.01 0.03 0.75 0.29 8-i NFCI: RISK SUBINDEX 0.61 0.6 20 4 109 32 0.62 0.04 0.09 0.75 0.33 9-i NFCI: CREDIT SUBINDEX 1.36 0.6 13 1 112 39 0.75 0.01 0.04 0.52 0.24 10-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 1.64 0.6 14 2 111 38 0.73 0.02 0.07 0.5 0.24 11-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 1.36 0.3 11 0 113 41 0.79 0 0 0.48 0.21 12-i NATIONAL FINANCIAL CONDITIONS INDEX 0.56 0.6 22 4 109 30 0.58 0.04 0.08 0.48 0.37 13-i CFSI: SECURITIZATION MARKET 1.19 0.6 16 4 109 36 0.69 0.04 0.12 0.48 0.26 14-i CFSI: CREDIT MARKET 0.8 0.7 21 20 93 31 0.6 0.18 0.44 0.48 0.18 15-i NFCI: LEVERAGE SUBINDEX 1.63 0.6 9 4 109 43 0.83 0.04 0.2 0.4 0.12 16-i CFSI: FOREIGN EXCHANGE MARKET 0.67 0.7 17 26 87 35 0.67 0.23 0.7 0.37 0.05 17-i CFSI: INTERBANK MARKET 0.56 0.7 21 13 100 31 0.6 0.12 0.28 0.3 0.24 18-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.62 0.7 13 29 84 39 0.75 0.26 1.03 0.3 -0.06 19-i ADJUSTED NFCI 1.34 0.6 16 1 112 36 0.69 0.01 0.03 0.1 0.29 20-ii PHILADELPHIA'S LEADING INDEX FOR THE US 1.76 0.6 10 1 112 42 0.81 0.01 0.05 0.5 0.18 21-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.7 0.6 21 10 103 31 0.6 0.09 0.22 0.5 0.28 22-ii CFNAI: THREE MONTH MOVING AVERAGE 0.58 0.6 18 11 102 34 0.65 0.1 0.28 0.45 0.21 23-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.58 0.7 26 30 83 26 0.5 0.27 0.53 0.38 0.2 24-ii CFNAI: DIFFUSION INDEX 0.78 0.7 20 15 98 32 0.62 0.13 0.35 0.25 0.21 25-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.98 0.6 13 6 107 39 0.75 0.05 0.21 0.2 0.17 26-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.52 0.7 18 15 98 34 0.65 0.13 0.38 0.1 0.17 27-ii CFNAI: PRODUCTION AND INCOME 0.52 0.7 19 14 99 33 0.63 0.12 0.34 0.02 0.19 28-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5% 1.49 0.6 13 7 106 39 0.75 0.06 0.25 1.64 0.16 29-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 1.33 0.6 17 8 105 35 0.67 0.07 0.22 1.48 0.22 30-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10% 1.58 0.6 11 7 106 41 0.79 0.06 0.29 1.4 0.12 31-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20% 1.54 0.6 10 8 105 42 0.81 0.07 0.37 0.86 0.09 32-iii SRISK FROM VLAB 0.73 0.7 26 25 88 26 0.5 0.22 0.44 0.52 0.24 Panel 2: Weekly (, 0.5 and 4 bins were used for IV) 1-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 2 0.2 30 0 382 182 0.86 0 0 0.14 2-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 2 0.6 34 0 382 178 0.84 0 0 0.16 3-i ST LOUIS FINANCIAL STRESS INDEX 2 0.6 33 0 382 179 0.84 0 0 0.16 4-i CFSI: REAL ESTATE MARKET 2 0.5 0 0 382 212 1 0 0 5-i CLEVELAND FINANCIAL STRESS INDEX 0.64 0.6 145 12 370 67 0.32 0.03 0.05 1.28 0.65 6-i NFCI: RISK SUBINDEX 0.55 0.6 93 10 372 119 0.56 0.03 0.06 0.93 0.41 7-i CFSI: INTERBANK MARKET 0.97 0.6 69 7 375 143 0.67 0.02 0.06 0.92 0.3 8-i CFSI: EQUITY MARKET 1.27 0.6 78 8 374 134 0.63 0.02 0.06 0.52 0.34 9-i NFCI: CREDIT SUBINDEX 1.22 0.6 62 3 379 150 0.71 0.01 0.03 0.51 0.28 10-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 1.4 0.6 64 1 381 148 0.7 0 0.01 0.5 0.3 11-i NATIONAL FINANCIAL CONDITIONS INDEX 0.73 0.6 85 8 374 127 0.6 0.02 0.05 0.5 0.38 12-i CFSI: SECURITIZATION MARKET 1.17 0.6 75 10 372 137 0.65 0.03 0.07 0.5 0.32 13-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 2 0.4 35 0 382 177 0.83 0 0 0.45 0.17 14-i NFCI: LEVERAGE SUBINDEX 2 0.6 28 0 382 184 0.87 0 0 0.43 0.13 15-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.52 0.6 63 125 257 149 0.7 0.33 1.1 0.38 -0.1 16-i ADJUSTED NFCI 2 0.2 30 0 382 182 0.86 0 0 0.35 0.14 17-i CFSI: CREDIT MARKET 2 0.6 23 0 382 189 0.89 0 0 0.29 0.11 18-i CFSI: FOREIGN EXCHANGE MARKET 0.5 0.6 85 98 284 127 0.6 0.26 0.64 0.18 0.09 19-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.5 0.6 116 11 371 96 0.45 0.03 0.05 1.46 0.51 20-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20% 0.5 0.6 78 6 376 134 0.63 0.02 0.04 0.87 0.35 21-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10% 0.5 0.6 86 7 375 126 0.59 0.02 0.05 0.84 0.38 22-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5% 0.5 0.6 97 7 375 115 0.54 0.02 0.04 0.72 0.44 23-iii SRISK FROM VLAB 2 0.6 20 0 382 192 0.91 0 0 0.27 0.09 Panel 3: Daily (, 0.5 and 4 bins were used for IV) 1-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 2 0.5 148 0 1981 848 0.85 0 0 0.15 2-i CFSI: REAL ESTATE MARKET 2 0.4 0 0 1981 996 1 0 0 3-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.5 0.6 560 69 1912 436 0.44 0.03 0.06 2.07 0.52 4-i CLEVELAND FINANCIAL STRESS INDEX 0.55 0.6 722 129 1852 274 0.28 0.07 0.09 1.03 0.64 5-i CFSI: INTERBANK MARKET 0.91 0.6 369 45 1936 627 0.63 0.02 0.06 0.75 0.34 6-i CFSI: EQUITY MARKET 1.19 0.6 417 87 1894 579 0.58 0.04 0.1 0.51 0.36 7-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 1.85 0.6 199 0 1981 797 0.8 0 0 0.5 0.2 8-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 1.49 0.6 280 34 1947 716 0.72 0.02 0.06 0.5 0.26 9-i CFSI: SECURITIZATION MARKET 1.16 0.6 380 55 1926 616 0.62 0.03 0.07 0.5 0.34 10-i CFSI: CREDIT MARKET 2 0.6 108 0 1981 888 0.89 0 0 0.47 0.11 11-i CFSI: FOREIGN EXCHANGE MARKET 0.7 0.6 332 407 1574 664 0.67 0.21 0.62 0.24 0.06 12-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.5 0.6 534 94 1887 462 0.46 0.05 0.09 1.27 0.47 13-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.5 0.6 363 63 1918 633 0.64 0.03 0.09 0.95 0.32 14-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.5 0.6 463 75 1906 533 0.54 0.04 0.08 0.86 0.41 15-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.5 0.6 417 68 1913 579 0.58 0.03 0.08 0.84 0.37 16-iii SRISK FROM VLAB 2 0.6 93 0 1981 903 0.91 0 0 0.42 0.09 Note: Panel 1 uses data between June 2000 and February 2014. Panels 2 and 3 use data between 10/31/2002 and 3/28/2014 (since daily data for the Kamakura Troubled Company Indices is available starting 10/31/2001).

216

Table 34 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on IV

Name , µ TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i NFCI: LEVERAGE SUBINDEX 0.1 0.7 12 30 93 29 0.71 0.24 0.83 0.64 -0.02 2-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.06 0.7 17 29 94 24 0.59 0.24 0.57 0.59 0.11 3-i NATIONAL FINANCIAL CONDITIONS INDEX 0.02 0.7 21 27 96 20 0.49 0.22 0.43 0.56 0.23 4-i ADJUSTED NFCI 0.22 0.7 14 25 98 27 0.66 0.2 0.6 0.55 0.08 5-i ST LOUIS FINANCIAL STRESS INDEX 0.04 0.7 20 25 98 21 0.51 0.2 0.42 0.54 0.23 6-i CFSI: EQUITY MARKET 0.2 0.7 16 31 92 25 0.61 0.25 0.65 0.54 0.07 7-i CLEVELAND FINANCIAL STRESS INDEX 0.18 0.7 16 28 95 25 0.61 0.23 0.58 0.52 0.1 8-i CFSI: CREDIT MARKET 0.18 0.7 11 31 92 30 0.73 0.25 0.94 0.52 -0.06 9-i KANSAS CITY FINANCIAL STRESS INDEX 0.08 0.7 15 19 104 26 0.63 0.15 0.42 0.5 0.17 10-i CFSI: SECURITIZATION MARKET 0.16 0.7 7 26 97 34 0.83 0.21 1.24 0.5 -0.1 11-i NFCI: RISK SUBINDEX 0.04 0.7 20 26 97 21 0.51 0.21 0.43 0.49 0.22 12-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.16 0.7 20 28 95 21 0.51 0.23 0.47 0.49 0.2 13-i CHICAGO FED NATIONAL ACTIVITY INDEX 0.26 0.7 13 29 94 28 0.68 0.24 0.74 0.49 0.01 14-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 0.04 0.7 4 27 96 37 0.9 0.22 2.25 0.49 -0.18 15-i CFSI: REAL ESTATE MARKET 0.44 0.4 1 0 123 40 0.98 0 0 0.48 0.02 16-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.18 0.7 17 19 104 24 0.59 0.15 0.37 0.47 0.22 17-i CFSI: FOREIGN EXCHANGE MARKET 0.26 0.7 7 33 90 34 0.83 0.27 1.57 0.47 -0.17 18-i CFSI: INTERBANK MARKET 0.16 0.7 15 21 102 26 0.63 0.17 0.47 0.46 0.15 19-i NFCI: CREDIT SUBINDEX 0.08 0.7 13 19 104 28 0.68 0.15 0.49 0.46 0.12 20-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.06 0.7 17 27 96 24 0.59 0.22 0.53 0.41 0.13 21-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.44 0.7 15 30 93 26 0.63 0.24 0.67 0.56 0.05 22-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.16 0.7 15 31 92 26 0.63 0.25 0.69 0.52 0.04 23-ii CFNAI: THREE MONTH MOVING AVERAGE 0.02 0.7 22 59 64 19 0.46 0.48 0.89 0.5 -0.08 24-ii CFNAI: DIFFUSION INDEX 0.2 0.7 8 29 94 33 0.8 0.24 1.21 0.5 -0.11 25-ii CFNAI: PRODUCTION AND INCOME 0.36 0.7 13 30 93 28 0.68 0.24 0.77 0.49 0 26-ii PHILADELPHIA'S LEADING INDEX FOR THE US 0.1 0.7 12 23 100 29 0.71 0.19 0.64 0.46 0.05 27-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.14 0.7 14 29 94 27 0.66 0.24 0.69 0.45 0.04 28-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0 0.7 21 53 70 20 0.49 0.43 0.84 0.54 -0.04 29-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0 0.7 20 56 67 21 0.51 0.46 0.93 0.53 -0.1 30-iii SRISK FROM VLAB 0.1 0.7 7 13 110 34 0.83 0.11 0.62 0.49 0.03 31-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0 0.7 21 53 70 20 0.49 0.43 0.84 0.49 -0.04 32-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0 0.7 22 56 67 19 0.46 0.46 0.85 0.48 -0.05 Panel 2: Weekly (, 0.2 and 4 bins were used for IV) 1-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.02 0.7 65 113 333 82 0.56 0.25 0.57 0.64 0.11 2-i ST LOUIS FINANCIAL STRESS INDEX 0.02 0.7 68 87 359 79 0.54 0.2 0.42 0.63 0.21 3-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.04 0.7 71 106 340 76 0.52 0.24 0.49 0.58 0.17 4-i CFSI: EQUITY MARKET 0.26 0.7 33 71 375 114 0.78 0.16 0.71 0.55 0.02 5-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.06 0.7 66 110 336 81 0.55 0.25 0.55 0.53 0.13 6-i CFSI: CREDIT MARKET 0.1 0.7 46 84 362 101 0.69 0.19 0.6 0.52 0.07 7-i CFSI: FOREIGN EXCHANGE MARKET 0.2 0.7 20 77 369 127 0.86 0.17 1.27 0.52 -0.09 8-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.04 0.7 57 70 376 90 0.61 0.16 0.4 0.47 0.18 9-i CLEVELAND FINANCIAL STRESS INDEX 0.14 0.7 30 60 386 117 0.8 0.13 0.66 0.47 0.03 10-i CFSI: REAL ESTATE MARKET 0.04 0.7 38 68 378 109 0.74 0.15 0.59 0.46 0.06 11-i ADJUSTED NFCI 0.06 0.7 57 76 370 90 0.61 0.17 0.44 0.45 0.17 12-i CFSI: INTERBANK MARKET 0.04 0.7 52 69 377 95 0.65 0.15 0.44 0.45 0.15 13-i NFCI: RISK SUBINDEX 0.02 0.7 50 57 389 97 0.66 0.13 0.38 0.4 0.17 14-i NFCI: LEVERAGE SUBINDEX 0.04 0.7 38 62 384 109 0.74 0.14 0.54 0.37 0.08 15-i CFSI: SECURITIZATION MARKET 0.1 0.7 32 68 378 115 0.78 0.15 0.7 0.36 0.02 16-i NATIONAL FINANCIAL CONDITIONS INDEX 0.02 0.7 44 50 396 103 0.7 0.11 0.37 0.29 0.15 17-i NFCI: CREDIT SUBINDEX 0.02 0.7 42 61 385 105 0.71 0.14 0.48 0.29 0.11 18-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 2 0.4 0 0 446 147 1 0 0.28 0 19-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.02 0.7 64 137 309 83 0.56 0.31 0.71 0.58 0.04 20-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.04 0.7 40 69 377 107 0.73 0.15 0.57 0.56 0.07 21-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.04 0.7 52 75 371 95 0.65 0.17 0.48 0.53 0.14 22-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.06 0.7 39 64 382 108 0.73 0.14 0.54 0.5 0.08 23-iii SRISK FROM VLAB 0.04 0.7 35 74 372 112 0.76 0.17 0.7 0.47 0.02 Panel 3: Daily (, 0.1 and 4 bins were used for IV) 1-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.08 0.8 173 228 2200 375 0.68 0.09 0.3 0.55 0.21 2-i CFSI: EQUITY MARKET 0.18 0.8 138 348 2080 410 0.75 0.14 0.57 0.54 0.09 3-i CFSI: FOREIGN EXCHANGE MARKET 0.28 0.8 109 318 2110 439 0.8 0.13 0.66 0.51 0.05 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.04 0.8 135 194 2234 413 0.75 0.08 0.32 0.5 0.16 5-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 2 0.7 0 0 2428 548 1 0 0.5 0 6-i CFSI: CREDIT MARKET 0.14 0.8 97 323 2105 451 0.82 0.13 0.75 0.49 0.03 7-i CFSI: SECURITIZATION MARKET 0.08 0.8 86 249 2179 462 0.84 0.1 0.65 0.44 0.04 8-i CLEVELAND FINANCIAL STRESS INDEX 0.12 0.8 127 267 2161 421 0.77 0.11 0.47 0.4 0.11 9-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.06 0.8 131 169 2259 417 0.76 0.07 0.29 0.38 0.16 10-i CFSI: INTERBANK MARKET 0.04 0.8 69 199 2229 479 0.87 0.08 0.65 0.31 0.04 11-i CFSI: REAL ESTATE MARKET 0.02 0.8 43 181 2247 505 0.92 0.07 0.95 0.29 0 12-iii SRISK FROM VLAB 0.04 0.8 141 271 2157 407 0.74 0.11 0.43 0.58 0.13 13-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.06 0.8 140 287 2141 408 0.74 0.12 0.46 0.56 0.12 14-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.04 0.8 147 291 2137 401 0.73 0.12 0.45 0.54 0.14 15-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.06 0.8 126 248 2180 422 0.77 0.1 0.44 0.51 0.12 16-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.06 0.8 132 246 2182 416 0.76 0.1 0.42 0.46 0.13 Note: Panel 1 uses data between June 2000 and February 2014. Panels 2 and 3 use data between 10/31/2002 and 3/28/2014 (since daily data for the Kamakura Troubled Company Indices is available starting 10/31/2001).

217

Table 35 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on

Name , TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.5 0.7 39 16 97 13 0.25 0.14 0.19 1.07 0.59 2-i CFSI: REAL ESTATE MARKET 0.5 0.7 34 16 97 18 0.35 0.14 0.22 0.86 0.49 3-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.5 0.6 29 8 105 23 0.44 0.07 0.13 0.09 0.46 4-i CFSI: SECURITIZATION MARKET 0.55 0.7 31 13 100 21 0.4 0.12 0.19 0.24 0.45 5-i NATIONAL FINANCIAL CONDITIONS INDEX 0.5 0.6 25 4 109 27 0.52 0.04 0.07 0.38 0.43 6-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.5 0.6 24 5 108 28 0.54 0.04 0.1 1.31 0.4 7-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.56 0.7 27 12 101 25 0.48 0.11 0.2 1.28 0.38 8-i NFCI: LEVERAGE SUBINDEX 0.59 0.6 23 5 108 29 0.56 0.04 0.1 0.02 0.38 9-i NFCI: CREDIT SUBINDEX 0.52 0.6 22 5 108 30 0.58 0.04 0.1 0.33 0.36 10-i CFSI: EQUITY MARKET 0.59 0.7 32 27 86 20 0.38 0.24 0.39 0.84 0.35 11-i NFCI: RISK SUBINDEX 0.61 0.6 20 4 109 32 0.62 0.04 0.09 0.75 0.33 12-i CFSI: CREDIT MARKET 0.61 0.7 29 22 91 23 0.44 0.19 0.35 0.25 0.33 13-i ST LOUIS FINANCIAL STRESS INDEX 0.78 0.6 19 3 110 33 0.63 0.03 0.07 0.33 14-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 1.31 0.6 18 2 111 34 0.65 0.02 0.05 0.33 0.32 15-i KANSAS CITY FINANCIAL STRESS INDEX 0.61 0.6 20 5 108 32 0.62 0.04 0.12 0.75 0.32 16-i CFSI: INTERBANK MARKET 0.95 0.6 18 2 111 34 0.65 0.02 0.05 0.27 0.32 17-i ADJUSTED NFCI 1.17 0.6 18 3 110 34 0.65 0.03 0.08 0.1 0.31 18-i CFSI: FOREIGN EXCHANGE MARKET 0.59 0.7 20 27 86 32 0.62 0.24 0.62 0.3 0.1 19-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 1.84 0.1 2 0 113 50 0.96 0 0 0.12 0.04 20-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.52 0.7 24 12 101 28 0.54 0.11 0.23 0.45 0.32 21-ii CFNAI: DIFFUSION INDEX 0.58 0.7 26 18 95 26 0.5 0.16 0.32 0.17 0.3 22-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.98 0.7 24 16 97 28 0.54 0.14 0.31 0.05 0.28 23-ii PHILADELPHIA'S LEADING INDEX FOR THE US 0.53 0.7 22 13 100 30 0.58 0.12 0.27 0.5 0.27 24-ii CFNAI: THREE MONTH MOVING AVERAGE 0.94 0.6 16 4 109 36 0.69 0.04 0.12 0.25 0.26 25-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.55 0.6 19 10 103 33 0.63 0.09 0.24 0.14 0.24 26-ii CFNAI: PRODUCTION AND INCOME 1.15 0.6 14 3 110 38 0.73 0.03 0.1 0.02 0.23 27-ii CFNAI: SALES, ORDERS, AND INVENTORIES 1.51 0.1 12 0 113 40 0.77 0 0 0.06 0.23 28-iii SRISK FROM VLAB 0.8 0.7 26 17 96 26 0.5 0.15 0.3 0.29 0.31 29-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.5 0.7 25 21 92 27 0.52 0.19 0.39 1.68 0.26 30-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 1.31 0.6 16 11 102 36 0.69 0.1 0.32 1.69 0.17 31-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.71 0.7 19 19 94 33 0.63 0.17 0.46 1.63 0.15 32-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.61 0.7 18 19 94 34 0.65 0.17 0.49 1.01 0.13 Panel 2: Weekly (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.59 0.6 147 14 368 65 0.31 0.04 0.05 1.28 0.65 2-i CFSI: EQUITY MARKET 0.52 0.6 153 41 341 59 0.28 0.11 0.15 0.29 0.59 3-i CFSI: SECURITIZATION MARKET 0.52 0.6 128 20 362 84 0.4 0.05 0.09 0.25 0.54 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.5 0.6 115 11 371 97 0.46 0.03 0.05 0.51 5-i ST LOUIS FINANCIAL STRESS INDEX 0.53 0.6 107 11 371 105 0.5 0.03 0.06 0.47 6-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.5 0.6 102 11 371 110 0.52 0.03 0.06 0.45 7-i NFCI: CREDIT SUBINDEX 0.5 0.6 100 8 374 112 0.53 0.02 0.04 0.1 0.45 8-i NATIONAL FINANCIAL CONDITIONS INDEX 0.5 0.6 100 9 373 112 0.53 0.02 0.05 0.35 0.44 9-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.52 0.6 95 5 377 117 0.55 0.01 0.03 0.27 0.43 10-i NFCI: RISK SUBINDEX 0.52 0.6 94 11 371 118 0.56 0.03 0.06 0.93 0.41 11-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.53 0.6 90 11 371 122 0.58 0.03 0.07 0.09 0.39 12-i NFCI: LEVERAGE SUBINDEX 0.53 0.6 95 17 365 117 0.55 0.04 0.1 0.02 0.39 13-i CFSI: REAL ESTATE MARKET 0.5 0.6 127 66 316 85 0.4 0.17 0.29 0.39 14-i CFSI: INTERBANK MARKET 0.65 0.6 90 13 369 122 0.58 0.03 0.08 0.99 0.38 15-i ADJUSTED NFCI 0.52 0.6 85 14 368 127 0.6 0.04 0.09 0.17 0.36 16-i CFSI: CREDIT MARKET 0.53 0.6 120 68 314 92 0.43 0.18 0.31 0.08 0.35 17-i CFSI: FOREIGN EXCHANGE MARKET 0.55 0.6 83 92 290 129 0.61 0.24 0.62 0.18 0.1 18-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 1.72 0.6 5 0 382 207 0.98 0 0 0.08 0.02 19-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.5 0.6 116 11 371 96 0.45 0.03 0.05 1.46 0.51 20-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.5 0.6 97 7 375 115 0.54 0.02 0.04 0.72 0.44 21-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.5 0.6 86 7 375 126 0.59 0.02 0.05 0.84 0.38 22-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.5 0.6 78 6 376 134 0.63 0.02 0.04 0.87 0.35 23-iii SRISK FROM VLAB 1.3 0.1 64 0 382 148 0.7 0 0 0.15 0.3 Panel 3: Daily (, 0.5 and 4 bins were used for IV) 1-i CLEVELAND FINANCIAL STRESS INDEX 0.53 0.6 729 137 1844 267 0.27 0.07 0.09 1.04 0.64 2-i CFSI: SECURITIZATION MARKET 0.5 0.6 627 116 1865 369 0.37 0.06 0.09 0.19 0.55 3-i CFSI: EQUITY MARKET 0.62 0.6 677 221 1760 319 0.32 0.11 0.16 0.35 0.53 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.5 0.6 560 69 1912 436 0.44 0.03 0.06 2.07 0.52 5-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.5 0.6 492 65 1916 504 0.51 0.03 0.07 0.45 6-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.5 0.6 445 61 1920 551 0.55 0.03 0.07 0.24 0.41 7-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.5 0.6 460 87 1894 536 0.54 0.04 0.1 0.14 0.4 8-i CFSI: INTERBANK MARKET 0.68 0.6 444 67 1914 552 0.55 0.03 0.08 0.78 0.4 9-i CFSI: CREDIT MARKET 0.5 0.6 602 349 1632 394 0.4 0.18 0.29 0.2 0.37 10-i CFSI: REAL ESTATE MARKET 0.5 0.6 605 363 1618 391 0.39 0.18 0.3 0.36 11-i CFSI: FOREIGN EXCHANGE MARKET 0.78 0.6 305 344 1637 691 0.69 0.17 0.57 0.16 0.08 12-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.5 0.6 534 94 1887 462 0.46 0.05 0.09 1.27 0.47 13-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.5 0.6 463 75 1906 533 0.54 0.04 0.08 0.86 0.41 14-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.5 0.6 417 68 1913 579 0.58 0.03 0.08 0.84 0.37 15-iii SRISK FROM VLAB 1.27 0.6 323 6 1975 673 0.68 0 0.01 0.13 0.32 16-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.5 0.6 363 63 1918 633 0.64 0.03 0.09 0.95 0.32 Note: Panel 1 uses data between June 2000 and February 2014. Panels 2 and 3 use data between 10/31/2002 and 3/28/2014 (since daily data for the Kamakura Troubled Company Indices is available starting 10/31/2001).

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Table 36 Comparison of Coincident Measures’ Ability to Signal Stress when Selecting , Based on

Name , µ TP FP TN FN T1 T2 NTSR IV (Dec.)

Panel 1: Monthly (, 0.6 and 3 bins were used for IV) 1-i ST LOUIS FINANCIAL STRESS INDEX 0.08 0.7 20 16 107 21 0.51 0.13 0.27 0.18 0.32 2-i CFSI: REAL ESTATE MARKET 0 0.8 31 46 77 10 0.24 0.37 0.49 1.06 0.3 3-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.3 0.7 15 7 116 26 0.63 0.06 0.16 0.09 0.29 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.16 0.7 14 8 115 27 0.66 0.07 0.19 0.01 0.26 5-i NFCI: RISK SUBINDEX 0.06 0.7 18 17 106 23 0.56 0.14 0.31 0.21 0.26 6-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.16 0.7 15 12 111 26 0.63 0.1 0.27 0.03 0.24 7-i KANSAS CITY FINANCIAL STRESS INDEX _ OVER 1% 0.22 0.7 11 3 120 30 0.73 0.02 0.09 0.07 0.24 8-i NATIONAL FINANCIAL CONDITIONS INDEX 0.04 0.7 19 21 102 22 0.54 0.17 0.37 0.39 0.24 9-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.18 0.7 20 25 98 21 0.51 0.2 0.42 0.36 0.23 10-i ADJUSTED NFCI 0.46 0.7 11 9 114 30 0.73 0.07 0.27 0.08 0.17 11-i NFCI: CREDIT SUBINDEX 0.1 0.7 13 14 109 28 0.68 0.11 0.36 0.26 0.17 12-i CFSI: INTERBANK MARKET 0.2 0.7 14 16 107 27 0.66 0.13 0.38 0.3 0.17 13-i CLEVELAND FINANCIAL STRESS INDEX 0.26 0.7 13 16 107 28 0.68 0.13 0.41 0.17 0.15 14-i CFSI: CREDIT MARKET 0.56 0.7 6 2 121 35 0.85 0.02 0.11 0.04 0.13 15-i CFSI: EQUITY MARKET 0.32 0.7 14 20 103 27 0.66 0.16 0.48 0.19 0.13 16-i NFCI: LEVERAGE SUBINDEX 0.22 0.7 7 8 115 34 0.83 0.07 0.38 0.05 0.09 17-i CFSI: SECURITIZATION MARKET 0.8 0.7 3 2 121 38 0.93 0.02 0.22 0 0.05 18-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 2 0.3 0 0 123 41 1 0 0.12 0 19-i CFSI: FOREIGN EXCHANGE MARKET 2 0.3 0 0 123 41 1 0 0.2 0 20-ii CFNAI: THREE MONTH MOVING AVERAGE 0.2 0.7 12 9 114 29 0.71 0.07 0.25 0.09 0.2 21-ii CFNAI: EMPLOYMENT, UNEMPLOYMENT, AND HOURS 0.28 0.7 11 12 111 30 0.73 0.1 0.36 0.04 0.14 22-ii PHILADELPHIA'S LEADING INDEX FOR THE US 0.32 0.7 6 1 122 35 0.85 0.01 0.06 0.01 0.14 23-ii CHICAGO FED NATIONAL ACTIVITY INDEX 0.32 0.7 12 17 106 29 0.71 0.14 0.47 0.18 0.11 24-ii CFNAI: SALES, ORDERS, AND INVENTORIES 0.52 0.7 15 24 99 26 0.63 0.2 0.53 0.3 0.11 25-ii CFNAI: PRODUCTION AND INCOME 0.74 0.7 6 4 119 35 0.85 0.03 0.22 0.01 0.1 26-ii CFNAI: PERSONAL CONSUMPTION AND HOUSING 0.2 0.7 10 16 107 31 0.76 0.13 0.53 0.13 0.08 27-ii CFNAI: DIFFUSION INDEX 2 0.3 0 0 123 41 1 0 0.12 0 28-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.06 0.7 17 20 103 24 0.59 0.16 0.39 0.29 0.21 29-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.06 0.7 16 20 103 25 0.61 0.16 0.42 0.2 0.18 30-iii KAMAKURA'S TROUBLED COMPANY INDEX 0.2 0.7 10 7 116 31 0.76 0.06 0.23 0.13 0.17 31-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.04 0.7 15 20 103 26 0.63 0.16 0.44 0.27 0.16 32-iii SRISK FROM VLAB 0.04 0.7 18 32 91 23 0.56 0.26 0.59 0.92 0.1 Panel 2: Weekly (, 0.2 and 4 bins were used for IV) 1-i ST LOUIS FINANCIAL STRESS INDEX 0.04 0.7 50 39 407 97 0.66 0.09 0.26 0.22 0.23 2-i ADJUSTED NFCI 0.08 0.7 51 52 394 96 0.65 0.12 0.34 0.21 0.2 3-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.08 0.7 42 28 418 105 0.71 0.06 0.22 0.13 0.2 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.04 0.7 57 65 381 90 0.61 0.15 0.38 0.35 0.2 5-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.08 0.7 64 83 363 83 0.56 0.19 0.43 0.61 0.19 6-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.08 0.7 52 58 388 95 0.65 0.13 0.37 0.4 0.18 7-i NFCI: RISK SUBINDEX 0.02 0.7 50 57 389 97 0.66 0.13 0.38 0.4 0.17 8-i CFSI: INTERBANK MARKET 0.06 0.7 43 44 402 104 0.71 0.1 0.34 0.23 0.16 9-i NATIONAL FINANCIAL CONDITIONS INDEX 0.02 0.7 44 50 396 103 0.7 0.11 0.37 0.29 0.15 10-i NFCI: CREDIT SUBINDEX 0.06 0.7 26 20 426 121 0.82 0.04 0.25 0.05 0.12 11-i CFSI: CREDIT MARKET 0.18 0.7 29 36 410 118 0.8 0.08 0.41 0.12 0.09 12-i CLEVELAND FINANCIAL STRESS INDEX 0.24 0.7 20 20 426 127 0.86 0.04 0.33 0.11 0.08 13-i NFCI: LEVERAGE SUBINDEX 0.06 0.7 26 33 413 121 0.82 0.07 0.42 0.19 0.08 14-i CFSI: EQUITY MARKET 0.4 0.7 26 38 408 121 0.82 0.09 0.48 0.22 0.07 15-i CFSI: REAL ESTATE MARKET 0.02 0.7 63 125 321 84 0.57 0.28 0.65 0.77 0.06 16-i CFSI: FOREIGN EXCHANGE MARKET 0.44 0.7 6 1 445 141 0.96 0 0.05 0.26 0.04 17-i CFSI: SECURITIZATION MARKET 0.12 0.7 28 50 396 119 0.81 0.11 0.59 0.2 0.04 18-i NFCI: NONFINANCIAL LEVERAGE SUBINDEX 2 0.1 0 0 446 147 1 0 0.28 0 19-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.04 0.7 52 75 371 95 0.65 0.17 0.48 0.53 0.14 20-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.06 0.7 47 71 375 100 0.68 0.16 0.5 0.37 0.11 21-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.08 0.7 34 43 403 113 0.77 0.1 0.42 0.3 0.11 22-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.02 0.7 55 98 348 92 0.63 0.22 0.59 0.76 0.09 23-iii SRISK FROM VLAB 0.08 0.7 24 29 417 123 0.84 0.07 0.4 0.08 0.08 Panel 3: Daily (, 0.1 and 4 bins were used for IV) 1-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX 0.06 0.8 189 255 2173 359 0.66 0.11 0.3 0.7 0.23 2-i GOLDMAN SACHS FINANCIAL CONDITIONS INDEX WITH OIL 0.08 0.8 173 228 2200 375 0.68 0.09 0.3 0.55 0.21 3-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX 0.08 0.8 115 92 2336 433 0.79 0.04 0.18 0.26 0.17 4-i BLOOMBERG'S FINANCIAL CONDITIONS INDEX PLUS 0.04 0.8 135 194 2234 413 0.75 0.08 0.32 0.5 0.16 5-i CFSI: EQUITY MARKET 0.32 0.8 98 111 2317 450 0.82 0.05 0.26 0.05 0.13 6-i CLEVELAND FINANCIAL STRESS INDEX 0.16 0.8 105 157 2271 443 0.81 0.06 0.34 0.17 0.12 7-i CFSI: INTERBANK MARKET 0.02 0.8 148 471 1957 400 0.73 0.19 0.72 1.02 0.06 8-i CFSI: SECURITIZATION MARKET 0.1 0.8 72 158 2270 476 0.87 0.07 0.5 0.22 0.06 9-i CFSI: FOREIGN EXCHANGE MARKET 0.28 0.8 109 318 2110 439 0.8 0.13 0.66 0.51 0.05 10-i CFSI: CREDIT MARKET 0.16 0.8 88 265 2163 460 0.84 0.11 0.68 0.34 0.04 11-i CFSI: REAL ESTATE MARKET 2 0.7 0 0 2428 548 1 0 0.02 0 12-i SRISK FROM VLAB 0.02 0.8 195 481 1947 353 0.64 0.2 0.56 1.24 0.14 13-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 10 0.04 0.8 168 369 2059 380 0.69 0.15 0.5 0.8 0.14 14-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 20 0.04 0.8 147 291 2137 401 0.73 0.12 0.45 0.54 0.14 15-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 5 0.04 0.8 166 367 2061 382 0.7 0.15 0.5 0.77 0.14 16-iii KAMAKURA'S TROUBLED COMPANY INDEX _ OVER 1% 0.04 0.8 172 399 2029 376 0.69 0.16 0.52 0.87 0.13 Note: Panel 1 uses data between June 2000 and February 2014. Panels 2 and 3 use data between 10/31/2002 and 3/28/2014 (since daily data for the Kamakura Troubled Company Indices is available starting 10/31/2001).

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Appendix 5: Chapter 4 MIMIC Factor Model Specification

MIMIC model (multiple indicator and multiple causes) can be considered a basic building block of structural models that include causes and effects. Because MIMIC structure are so omnipresent in structural modeling, it makes sense to differentiate between a MIMIC factor (which involves a single latent factor) and MIMIC models

(which involve multiple latent factors). There are two key econometric issues associated with MIMIC models: identification and estimation.

A5.1. MIMIC Identification

Bollen & Davis (2009) focus on identification of structural equation models that have causal indicators. The presence of causal indicators is key to economic problems

(Blalock, 1964). The authors provide helpful rules of identification and show how the rules help distinguish identified from under-identified models. Specifically, Bollen &

Davis (2009) consider the following models where all exogenous variables are observed and measured as deviations from their means:

(67),

(68), with the set of latent variables , the set of effects and the set of causes . Here, is an 1 vector of endogenous latent variables; is an coefficient matrix that gives the impact of the s on each other; is an coefficient matrix that gives the impact of the s on the s, is a 1 vector of exogenous variables; an 1 vector of disturbances; and E() is zero and is uncorrelated with . They consider that vector contains the exogenous causal indicators, although other exogenous observed variables

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also could be part of this vector. Equation (67) describes a set of relationships known as behavioral equations (Spanos, 1984: 127).

In equation (68) is a 1 vector of random variables, is coefficient

(or factor loading) matrix that shows the effects of the latent variables on , and is a

1 vector of errors. Typically, contains the effect indicators of the model, but it also can contain perfectly measured latent variables. In addition, the E() is zero and the covariances of with and with are zero. Equation (68) describes a set of relationships known as measurement equations (Spanos, 1984: 127).

Bollen and Davis (2009) discuss three necessary and two sufficient conditions for identification. The three necessary rules are: (1) scaling rule, (2) t-rule, and (3) 2+ emitted paths rule. The two sufficient conditions for identification are: (1) exogenous X condition, (2) piecewise strategy.

The first necessary condition is the scaling rule, which states that each latent variable in a structural equation model must be assigned a scale for the model to be identified. One of the most common ways of assigning a scale is to set the factor loading for one of a latent variable’s effect indicators to one. This is commonly done by (a) setting path from a causal indicator to the latent variable to one, or (b) constraining the variance of the latent variable to one, or (c) setting the variance of the disturbance to one for an endogenous latent variable.

The second necessary condition is the t-rule, which states that the number of free parameters in a model, say t, must be less than or equal to the number of nonredundant elements in the covariance matrix of the observed variables in the model. Thus, the rule

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involves counting the number of free parameters and making sure that this count does not exceed the number of nonredundant variances and covariances for the observed variables.

The third necessary condition is the 2+ emitted paths rule, which states that every latent variable with an unrestricted variance (or error variance) must emit at least two directed paths to variables when these latter variables have unrestricted error variances.

The “emitted paths” are directed paths that originate with the latent variable or, equivalently, the number of equations in which the latent variable appears as an explanatory variable. These paths can be directed to observed or to latent variables. This rule assumes that the variance of the latent variable (or the error variance if the latent variable is endogenous) and the error variance of all variables directly influenced by the latent variable are free parameters.

The first sufficient condition is the exogenous X rule, proven in Bollen & Davis

(2009). The rule consists describes four states each of which must be satisfied. First, each latent variable has at least one effect indicator that loads only on it (a “unique indicator”) and their errors are uncorrelated. Second, each latent variable directly affects at least one other effect indicator and errors for these variables are uncorrelated with the errors of the unique indicators. Third, there are at least m causal indicators and () has full row rank (that is each of the m-rows are linearly independent). Fourth, the structural model relating the causal indicators to the latent variables and the latent variables among themselves (equation 67) has an identified structure.

The second sufficient condition is the existence of a piecewise identification strategy. In other words, the model as a whole is identified, if a strategy can be found to identify a model by breaking the model into smaller pieces and to establish the

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identification of one piece before moving on to the next piece. At each step of the piecewise strategy, once we establish the identification of the sub-model, we treat the covariance matrix of the latent and observed variables of that part of the model as identified. This enables us to use the identified covariance matrix to help establish the identification of the next part of the model. This process continues until the identification status of all parameters of the model is established.

Consider the MIMIC factor shown in Figure 40. Note that, according to Bollen and Davis (2009), a MIMIC factor has the following attributes:

1) Its latent variable if formatively defined by causal indicators

through , where ∈ ;

2) Its causal indicators through are considered to be observed without

error;

3) The latent variable is formed endogenously with error

4) The latent variable is reflected by its effect indicators through ,

where ∈ 1;

5) The effect indicators through are observed with respective errors

through , where ∈ 1;

6) The covariances of with and with are zero.

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Figure 40 MIMIC Factor

Examination of the MIMIC factor reveals that the necessary rules hold.

Specifically, the scaling rule is met by scaling to as represented by the 1 on the path

between these variables; the 2+ emitted path rule is satisfied because there are two or

more paths from to ; the t rule is satisfied as well. The sufficient condition of exogenous X rule holds as well, since there is one latent variable (m = 1); there are at least two effect indicators and at least one causal indicator; has full rank; the errors are

uncorrelated; and the equation has an identified structure.

A5.2. MIMIC Estimation

In this section we briefly sketch two estimation methods that are typically

encountered in estimating structural equation models in economics: maximum likelihood

and Kalman filter.

Maximum likelihood estimation. In SEM, maximum likelihood (MLE) is statistical estimation method that provides a set of model parameter values which

224

maximizes the fit of the model with observed data.103 MLE achieves this by maximizing

the likelihood function (Myung, 2003), which is itself defined as a function of the

parameters of a statistical model, such that “the likelihood of a set of parameter values, θ,

given outcomes x, is equal to the probability of those observed outcomes given those

parameter values”104:

| | (69)

Then

≝ | ∀ ∈Θ (70),

where Θ is the parameter space of . 105

Gorsuch (1983: 127) states that MLE estimate has two characteristics “first, a

maximum likelihood estimate will have the highest probability of converging to the

population parameter as the size of the ample increases toward that of the population.

Second, the estimated parameters will be the most consistent with the smallest variance

across samples.”

Gujarati (2003: 113) discusses MLE as a common “alternative to the least-squares

method,” but warns that:

“To use this method, however, one must make an assumption about the probability distribution of the disturbance term . In the regression context, the assumption most popularly made is that follows the normal distribution. Under the normality assumption, the ML and OLS estimators of the intercept and slope parameters of the regression model are identical. However, the OLS and ML estimators of the variance of are different. In large samples, however, these two estimators converge. Thus

103 Hair et al. (2010: 632) describes MLE as “estimation method commonly employed in structural equation models. An alternative to ordinary least squares used in multiple regression, MLE is a procedure that iteratively improves parameter estimates to minimize a specific fit function.” 104 Likelihood function. (2014a). Wikipedia. Retrieved October 12, 2014, from http://en.wikipedia.org/wiki/Likelihood_function 105 Likelihood function (2014b). Planetmath.org. Retrieved October 12, 2014, from http://planetmath.org/LikelihoodFunction 225

the ML method is generally called a large-sample method. The ML method is of broader application in that it can also be applied to regression models that are nonlinear in the parameters.”

To provide a better intuition for the MLE method, we provide an algebraic presentation for MLE, following Gujarati (2003). We are given “a two-variable model

1 2 (71),

where the are normally and independently distributed with mean of 1 2

2 and variance of and is a random error. As a result, the joint probability density function of ,,…, , given the preceding mean and variance, can be written as

, ,,…,| , (72)

Since is independently distributed:

,,…,| ,

| , | , …| , (73)

where is the probability density function for the normally distributed :

(74) √

Substitution of (6) into (5) yields:

, ,…, | , (75), √

which is defined as the likelihood function of observed with unknown ,, :

, , (76), √

For MLE, finding the Maximum of ,, is particularly straightforward in the log form:

ln ln ln2 ∑ ln ln2 ∑ (77),

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We differentiate (9) partially with respect to , , and (equations 76, 77, and

78, respectively) and set the first order conditions in equations 79, 80, and 81, where ,

, and denote ML estimators:

∑ 1 (78),

∑ (79),

∑ (80),

∑ 0 (81),

∑ 0 (82),

∑ 0 (83),

After simplification of (81) and (82) and substitution into (83), it is straightforward to show that

∑ ∑ ∑ (84)

This MLE estimator of variance is biased relative to the OLS estimator that is known to

be unbiased and equal to ∑ . The direction of the bias is down, confirmed by taking expectation of MLE:

∑ (85)

Therefore, as the sample size grows becomes asymptotically unbiased as well, since

lim 22 (86) →

MLE caveats. Hair et al. (2010: 661) state that MLE can “under ideal conditions” provide valid results with sample sizes “as small as 50.” With larger sample sizes “the method becomes more sensitive and almost any difference is detected, making goodness-

227

of-fit measures suggest poor fit (Tanaka, 1993). As a result, sample sizes in the range of

100 to 400 are suggested subject to the other considerations…” MLE is well defined for normal distributions, which is a common assumption in econometric and psychometric data used in SEM. However, MLE solutions may not possible or well-defined for SEM problems with non-normal data. As Hair et al. (2010: 663) state: “The potential sensitivity of MLE to nonnormality, however, created a need for alternative estimation techniques. Methods such weighted least squares (WLS), generalized least squares

(GLS), and asymptotically distribution free (ADF) estimation became available (Hayduk,

1996). The ADF technique has received particular attention due to its insensitivity to nonnormality of the data, but its requirement of rather large sample sizes limits its use.”

Kalman filter estimation. Spanos (1984: 129) shows that the MIMIC model of equations (67) and (68) can be described as a special case of a general latent variable model—the state-space model, which takes the following form:

(87),

(88),

~ ∑ ∑ (89), ∑ ∑

Where is an 1 time-varying vector of latent variables, is a 1 time-varying

vector of observable exogenous variables (causes), is a 1 time-varying vector of

observable effects of . Here ,,, are time-varying vectors of dimensions ,

, 1, and , respectively, and . Similarly to the MIMIC equations, equation (87)

describes behavioral equations, and equation (88) describes measurement equations for the state-

space system. It is easy to see, that the state-space model becomes MIMIC at each time t, when

1, 0, , . 228

Appendix 6: Chapter 4 Longitudinal Factor Analysis

The Cleveland Financial Stress Index is constructed under the assumption that indicators can be aggregated to reflect conditions in six underlying markets with conceptual importance to the financial system. Exploratory Factor Analysis (EFA) is applied to the weighted cumulative density functions of each indicator used to construct

CFSI to test this claim. Since EFA does not incorporate a priori intuition about how latent factors should be grouped it is appropriate for an initial investigation of the effect that latent factors such as stress in designated financial sectors may exert on observable measures. We will first address the suitability of EFA for the analysis of time series data and then verify our dataset satisfies the properties required.

(90)

The core assumptions of EFA (equation 90) include that factors and

idiosyncratic residuals do not exhibit serial. Referring to the assumption of serial

correlation Geweke (1977: 365) raises the point that “if the are time series this

assumption is almost always inappropriate since and will in general be

correlated.” Stock and Watson (2011 pg. 2) provide the analogy that residuals pick up on

issues unique to an individual indicator, like the impact of a salmonella scare which affects restaurant employment but not the pet store next door. Anderson (1963: 7) agrees

that shocks in the time dimension may persist across multiple time periods leading to

serial correlation issues. However, Anderson concludes that the “day-to-day correlation

may be of no greater disadvantage than if the observations were independent”.106 Table

106 Referring to Principal Component Analysis, a special kind of EFA, Bai and Ng (2008) point out that dealing “with cross-sectionally correlated errors, which is a genuine feature of an approximate factor model, remains an unresolved issue.” 229

35 shows that there is significant serial correlation for several variables used in the original CFSI construction and that even after two forms of differencing are applied this serial correlation may not be entirely corrected. However, after conducting EFA on all three datasets we find that our results are robust in that very similar factors are found from each dataset.

Table 37 Serial Correlation Testing of the Weighted Components of CFSI, the Differenced Spreads, and the Differenced Weighted Components Weighted CDFs Differenced Spreads Differenced Weighted CDFs LM Obs*R-squared H ( no serial LM Obs*R-squared H ( no serial LM Obs*R-squared H ( no serial Variable 0 0 0 (at -1 lag) correlation) (at -x lags) correlation) (at –x lags) correlation) CR_ABS 0.000(ns) cannot reject at *** 6.707(ns-2) cannot reject at *** 3.381 (*-1) cannot reject at ** CR_BBS 0.207(ns) cannot reject at *** 1.908(ns-2) cannot reject at *** 4.727 (**-1) cannot reject at * CR_CBS 0.000(ns) cannot reject at *** 1.953(ns-3) cannot reject at *** 1.038 (ns-3) cannot reject at *** CR_CMBS 2.968* rejected at ** 6.164(ns-4) cannot reject at *** 8.318 (ns-12) cannot reject at *** CR_LIQS 2.329(ns) cannot reject at *** 6.06(**-2) cannot reject at *** 7.376 (ns-12) cannot reject at *** EQ_COND 2.266(ns) cannot reject at *** 6.222(**-2) cannot reject at *** 5.872 (ns-3) cannot reject at *** EQ_CONS 0.000(ns) cannot reject at *** 4.647(ns-7) cannot reject at *** 14.132 (***-1) rejected EQ_ENRS 0.000(ns) cannot reject at *** 6.253(ns-6) cannot reject at *** 13.179 (***-1) rejected EQ_FINL 2.900* rejected at ** 9.820(ns-9) cannot reject at *** 6.101 (**-1) cannot reject at * EQ_HLTH 1.875(ns) cannot reject at *** 6.797(ns-6) cannot reject at *** 5.461 (**-1) cannot reject at * EQ_INDU 12.725*** rejected 4.640(ns-7) cannot reject at *** 7.791 (**-1) cannot reject at * EQ_INFT 16.995*** rejected 0.775(ns-2) cannot reject at *** 6.591 (**-1) cannot reject at * EQ_MATR 1.834(ns) cannot reject at *** 7.012(ns-7) cannot reject at *** 0.059 (ns-1) cannot reject at *** EQ_UTIL 0.000(ns) cannot reject at *** 0.208(ns-1) cannot reject at *** 11.018 (***-1) rejected FD_CPTBS 19.618*** cannot reject at *** 5.091(***-2) cannot reject at *** 6.155 (ns-3) cannot reject at *** FD_ICOB 0.000(ns) cannot reject at *** 10.147(*-1) rejected 1.602 (ns-1) cannot reject at *** FD_ILIQS 23.065*** rejected 4.663(*-2) cannot reject at *** 5.483 (ns-3) cannot reject at *** FX_AUD_CIS 35.682*** rejected 14.301(***-1) rejected 11.286 (***-1) rejected FX_AUD_CRSH 0.000(ns) cannot reject at *** 1.469(ns-2) cannot reject at *** 8.035 (**-1) cannot reject at * FX_CAD_CIS 33.218**** rejected 12.070(***-1) rejected 11.794 (***-1) rejected FX_CAD_CRSH 0.000(ns) cannot reject at *** 1.683(ns-4) cannot reject at *** 14.372 (ns-12) cannot reject at *** FX_EUR_CIS 50.294*** rejected 3.947(ns-4) cannot reject at *** 12.333 (***-1) rejected FX_EUR_CRSH 0.000(ns) cannot reject at *** 4.434(ns-3) cannot reject at *** 12.048 (ns-12) cannot reject at *** FX_JPN_CIS 30.677*** rejected 36.657(***-1) rejected 34.646 (***-1) rejected FX_JPN_CRSH 0.000(ns) cannot reject at *** 0.513(ns-4) cannot reject at *** 3.674 (ns-4) cannot reject at *** FX_MEX_CIS 2.759 * cannot reject at *** 4.945(*-2) cannot reject at *** 0.347 (ns-3) cannot reject at *** FX_MEX_CRSH 0.400(ns) cannot reject at *** 5.387(ns-3) cannot reject at *** 16.029 (ns-12) cannot reject at *** FX_UK_CIS 46.469*** rejected 13.583(***-1) rejected 5.559 (ns-12) cannot reject at *** FX_UK_CRSH 0.000(ns) cannot reject at *** 4.076(ns-6) cannot reject at *** 7.712 (ns-6) cannot reject at *** FX_ZAR_CIS 14.235*** rejected 11.213(***-1) rejected 9.514 (ns-7) cannot reject at *** FX_ZAR_CRSH 10.623** rejected 7.139(ns-8) cannot reject at *** 10.461 (ns-11) cannot reject at *** RE_CRE 0.000(ns) cannot reject at *** 7.930(***-1) rejected 9.146 (**-1) cannot reject at * RE_RRE 0.000(ns) cannot reject at *** 6.527(**-2) cannot reject at *** 6.176 (**-1) cannot reject at * Note: * estimated coefficients significant at 10%; **estimated coefficients significant at 5%; ***estimated coefficients significant at 1% In order to determine whether the data is suitable for factor analysis, several assumptions must be tested: 1. whether data is suitable for correlation testing; 2. whether data is normally distributed; 3. whether the relations between variables are linear; 4. whether data has outliers; 5. whether data is factorable; and 6. whether the sample size is adequate.

230

Suitability: The CFSI data is a longitudinal dataset suitable for factor analysis with variables consisting of metric data with 5436 observations for each of the 24 variables.107

Normality: Table 38 provides skewness and kurtosis statistics for the 23

continuously scaled variables in the dataset, as well as the results of the normality tests:

Kolmogorov-Smirnov, Lilliefors, Cramer-von Mises, Watson, Anderson-Darling, and

Jarque-Bera. Common to these normality tests is the null hypothesis that the sample

population is normally distributed. The significance of 0.000 in all the test statistic results

support the alternative hypothesis of non-normality. The lack of normality does not

invalidate the use of factor analysis, however, it suggests that during factor extraction,

maximum likelihood extraction may not be the optimal choice (Fabrigar et al., 1999).

107 One of the variables is a date series. 231

Table 38 Normality Testing Kolmogorov- Lilliefors Cramer-von Mises Watson Anderson-Darling Jarque-Bera Variable Skewness Kurtosis Smirnov (Sig.) (Sig.) (Sig.) (Sig.) (Sig.) (Sig.) .093 0.093 11.561 9.853 66.526 312.938 CFSI 0.537 2.523 (.000) (.000) (.000) (.000) (.000) (.000) .117 0.117 22.906 19.308 152.923 580.379 ABSS 0.771 2.573 (.000) (.000) (.000) (.000) (.000) (.000) .073 0.073 9.245 9.235 55.398 192.868 BBS 0.106 2.102 (.000) (.000) (.000) (.000) (.000) (.000) .247 0.247 81.111 74.039 435.847 876.416 CMBSS 0.933 2.377 (.000) (.000) (.000) (.000) (.000) (.000) .091 0.091 14.720 14.708 95.483 367.140 CPTBS -0.012 1.727 (.000) (.000) (.000) (.000) (.000) (.000) .043 0.043 2.848 2.747 24.160 94.805 CRES 0.235 2.555 (.000) (.000) (.000) (.000) (.000) (.000) .056 0.056 5.210 5.179 38.096 242.025 CBS -0.046 1.970 (.000) (.000) (.000) (.000) (.000) (.000) .072 0.072 6.139 5.537 53.078 210.770 CIS 0.469 2.777 (.000) (.000) (.000) (.000) (.000) (.000) .062 0.062 7.107 5.311 43.948 378.506 CM 0.645 3.081 (.000) (.000) (.000) (.000) (.000) (.000) .067 0.067 6.400 6.251 44.786 174.144 EM 0.242 2.268 (.000) (.000) (.000) (.000) (.000) (.000) .098 0.098 12.850 12.746 74.354 198.233 FB 0.211 2.165 (.000) (.000) (.000) (.000) (.000) (.000) .062 0.062 7.553 6.818 57.691 300.352 FXM 0.333 2.061 (.000) (.000) (.000) (.000) (.000) (.000) .076 0.076 6.322 5.984 46.925 230.843 ICB 0.279 2.158 (.000) (.000) (.000) (.000) (.000) (.000) .077 0.077 11.764 11.763 76.701 333.044 ILS 0.016 1.788 (.000) (.000) (.000) (.000) (.000) (.000) .056 0.056 6.731 4.363 56.002 1001.455 IM 0.923 4.006 (.000) (.000) (.000) (.000) (.000) (.000) .069 0.069 5.627 5.614 46.870 253.083 LS -0.040 1.946 (.000) (.000) (.000) (.000) (.000) (.000) .045 0.045 1.029 0.979 14.370 58.726 REM 0.163 2.610 (.000) (.000) (.000) (.000) (.000) (.000) .189 0.189 49.202 44.870 313.262 RMBSS 0.786 2.333 660.4900 (.000) (.000) (.000) (.000) (.000) .077 0.077 11.037 11.035 68.825 303.1411 RRES 0.002 1.843 (.000) (.000) (.000) (.000) (.000) (.000) .153 0.153 28.217 25.164 191.904 532.585 SM 0.695 2.351 (.000) (.000) (.000) (.000) (.000) (.000) .067 0.067 6.400 6.251 44.786 174.144 SMC 0.242 2.268 (.000) (.000) (.000) (.000) (.000) (.000) .071 0.071 9.165 9.086 68.522 333.943 TYCS -0.105 1.804 (.000) (.000) (.000) (.000) (.000) (.000) .062 0.062 7.553 6.818 57.691 300.352 WDC 0.333 2.061 (.000) (.000) (.000) (.000) (.000) (.000)

Linearity: Figure 41, Panel A provides scatterplot results comparing the CFSI dependent variable (DV) and the market stress independent variables (IVs): CM (credit market stress), EM (equity market stress), IM (funding market stress), FXM (foreign exchange market stress), REM (real estate market stress), and SM (securitization market stress). The figure suggests that the relationship of several IVs (particularly CM, EM,

FXM, IM and REM) with DV may be non-linear. Figure 41, Panels B through E show the relationship of DV with the components of market stress in credit market (panel B), interbank market (panel C), securitization market (panel D), and real estate market (panel

E). Several of these relationships appear to be possibly non-linear: particularly the relationships with CIS, CPTBS, and TYCS components in the credit market; ILS components in the interbank market; and CRES and RRES in the real estate market.

232

Many of these scatterplots are characterized by concentrated clusters of data within a wide dispersion of DV data, a pattern that may be indicative of moderating variables influencing the IV-DV relationship.

Figure 41 Scatterplot Matrix of CFSI and Market Stress Variables PANEL A: CFSI vs. market stress variables

CFSI

CM EM FXM IM REM SM PANEL B: CFSI vs. credit market stress variables

CFSI

LS CIS CPTBS TYCS CBS PANEL C: CFSI vs. interbank market stress variables

CFSI

FB ICB BBS ILS PANEL D: CFSI vs. securitization market stress variables

CFSI

RMBSS CMBSS ABSS PANEL E: CFSI vs. real estate market stress variables

CFSI

CRES RRES

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Given these results, it is useful to test linearity among the DV and IV variables and their components more rigorously. Table 39 provides results of ANOVA deviation from linearity F-test.

Table 39 ANOVA Deviation from Linearity F-Test Variable F p Linear PANEL A: CFSI vs. market stress variables CM 1705.136 .019 non-linear EM 53.561 .000 non-linear FXM 39.178 .000 non-linear IM 211.968* .000* linear* REM 7.569* .006* linear* SM 3966.186* .000* linear* PANEL B: CFSI vs. credit market stress variables LS 16.113 .000 non-linear CIS 5.664 .000 non-linear CPTBS 417.028 .000 non-linear TYCS 65.493 .000 non-linear CBS 128.195 .000 non-linear PANEL C: CFSI vs. interbank market stress variables FB 10.952 .000 non-linear ICB 22.804 .000 non-linear BBS 40.296 .000 non-linear ILS 61.905 .000 non-linear PANEL D: CFSI vs. securitization market stress variables RMBSS 1.596 .000 non-linear CMBSS 6.434 .000 non-linear ABSS 11.473 .000 non-linear PANEL E: CFSI vs. real estate market stress variables CRES 144.562 .000 non-linear RRES 11.986 .000 non-linear Note: * indicates results of pairwise ANOVA linearity F-test

Outliers: Outliers in the IVs are considered in Figure 42, panels A through E.

Two market stress variables, CM and IM, in panel A show several outliers.108 However,

no outliers are present in the various market stress components shown in panels B-E.

Thus, no data exclusion is performed.

108 Review of this data reveals the outliers mainly include the data from the financial crisis of 2008-2009 and also include odd starting values. 234

Figure 42 Outlier Boxplots of Market Stress Variables PANEL A: Market stress variables

PANEL B: Credit market stress variables

PANEL C: CFSI vs. interbank market stress variables

PANEL D: CFSI vs. securitization market stress variables

PANEL E: CFSI vs. real estate market stress variables

Factorability: Seventeen of the original twenty-three variables are retained for further analysis to avoid matrix analysis problems.109 Visual inspection of the correlation matrix (Table 40) reveals that roughly half of the correlations are larger than 0.3, suggesting that the dataset may be factorable. All communalities (Table 41) are above

109 By original dataset construction, six of the twenty-three variables were linear combinations of the remaining seventeen variables causing the resulting matrix to lose positive and definite properties. 235

0.2—a welcome result for factorability, however the communality for CFSI (the dependent variable) is greater than 1--an ultra-Heywood case. This result suggests that there is something wrong with the dataset.110

Table 40 Correlation Matrix CFSI ABSS CMBSS RMBSS CRES RRES BBS FB ILS ICB CIS LS CPTBS TYCS CBS SMC WDC

CFSI 1.000 .630 .618 .573 .130 -.066 .663 -.121 -.002 -.039 -.044 .496 -.110 -.147 .640 .737 .393 ABSS .630 1.000 .771 .438 -.312 -.311 .619 -.072 .111 -.086 -.400 .428 .016 .087 .296 .364 .342 CMBSS .618 .771 1.000 .496 -.078 -.099 .754 -.180 -.232 -.258 -.372 .786 -.337 -.359 .607 .273 .409 RMBSS .573 .438 .496 1.000 .070 -.207 .376 -.171 -.307 -.252 -.304 .597 -.456 -.040 .429 .090 .078 CRES .130 -.312 -.078 .070 1.000 .694 -.117 .184 -.270 -.114 .222 .178 -.260 -.203 .441 -.086 -.112 RRES -.066 -.311 -.099 -.207 .694 1.000 -.119 .151 .175 .152 .195 -.120 .154 -.017 .267 -.134 -.391 BBS .663 .619 .754 .376 -.117 -.119 1.000 -.252 -.084 -.202 -.172 .578 -.185 -.330 .713 .464 .318

FB -.121 -.072 -.180 -.171 .184 .151 -.252 1.000 .200 .318 .459 -.109 .218 -.050 -.134 -.278 -.084 ILS -.002 .111 -.232 -.307 -.270 .175 -.084 .200 1.000 .627 .154 -.636 .937 .516 -.298 .150 -.345 ICB -.039 -.086 -.258 -.252 -.114 .152 -.202 .318 .627 1.000 .319 -.375 .618 -.009 -.327 .075 -.280 CIS -.044 -.400 -.372 -.304 .222 .195 -.172 .459 .154 .319 1.000 -.172 .288 -.330 -.014 -.071 .032 LS .496 .428 .786 .597 .178 -.120 .578 -.109 -.636 -.375 -.172 1.000 -.682 -.644 .651 .068 .441 CPTBS -.110 .016 -.337 -.456 -.260 .154 -.185 .218 .937 .618 .288 -.682 1.000 .452 -.404 .067 -.251 TYCS -.147 .087 -.359 -.040 -.203 -.017 -.330 -.050 .516 -.009 -.330 -.644 .452 1.000 -.419 -.007 -.359 CBS .640 .296 .607 .429 .441 .267 .713 -.134 -.298 -.327 -.014 .651 -.404 -.419 1.000 .341 .182 SMC .737 .364 .273 .090 -.086 -.134 .464 -.278 .150 .075 -.071 .068 .067 -.007 .341 1.000 .139 WDC .393 .342 .409 .078 -.112 -.391 .318 -.084 -.345 -.280 .032 .441 -.251 -.359 .182 .139 1.000

Although significance for the Bartlett’s Test (Table 42) supports the sampling adequacy of the dataset for the Exploratory Factor Analysis (EFA), the Kaiser-Meyer-

Olkin (KMO) Measure of Sampling Adequacy (MSA) is below 0.5 indicating that the dataset is not suitable. Essentially, the conflicting evidence suggests that although the data is factorable, it is not very useful. Consideration of the MSAs from the diagonals of the anti-image correlation matrix provides further insight into suitability of individual variables (Table 43). As shown, all variables except for two have unacceptably low MSA

110 The reasons may include too few common factors or lack of factorability for the dataset (see https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_factor_s ect022.htm) 236

(below 0.5). Thus, the factorability problems posed by this dataset are pervasive and factor analysis should not be used in this case.

Table 41 Communality CFSI 1.05 ABSS 0.86 BBS 0.77 CMBSS 0.96 CPTBS 0.92 CRES 0.81 CBS 0.82 CIS 0.69 FB 0.49 ICB 0.49 ILS 0.99 LS 0.95 RMBSS 0.54 RRES 0.91 SMC 0.73 TYCS 0.93 WDC 0.38

Table 42 KMO and Bartlett’s Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .233 Approx. Chi-Square 126262.359 Bartlett's Test of Sphericity df 136 Sig. .000

Table 43 Anti-Image Correlation Matrix CFSI ABSS CMBSS RMBSS CRES RRES BBS FB ILS ICB CIS LS CPTBS TYCS CBS SMC WDC MSA CFSI 0.225 (0.842) (0.238) (0.995) (0.908) (0.903) (0.652) (0.853) (0.478) (0.778) (0.913) (0.661) (0.654) (0.759) (0.791) (0.998) (0.993) 0.225 ABSS (0.842) 0.259 (0.124) 0.835 0.742 0.825 0.453 0.641 0.480 0.591 0.775 0.533 0.457 0.480 0.708 0.835 0.831 0.259 CMBSS (0.238) (0.124) 0.800 0.237 0.341 0.031 0.131 0.216 (0.092) 0.324 0.345 (0.165) 0.241 0.377 0.139 0.235 0.215 0.800 RMBSS (0.995) 0.835 0.237 0.166 0.896 0.912 0.647 0.863 0.458 0.757 0.898 0.624 0.675 0.725 0.782 0.994 0.991 0.166 CRES (0.908) 0.742 0.341 0.896 0.121 0.695 0.688 0.725 0.506 0.702 0.844 0.563 0.566 0.688 0.612 0.902 0.891 0.121 RRES (0.903) 0.825 0.031 0.912 0.695 0.111 0.587 0.805 0.402 0.665 0.805 0.633 0.585 0.645 0.691 0.908 0.915 0.111 BBS (0.652) 0.453 0.131 0.647 0.688 0.587 0.392 0.606 0.257 0.568 0.608 0.461 0.415 0.611 0.248 0.646 0.647 0.392 FB (0.853) 0.641 0.216 0.863 0.725 0.805 0.606 0.088 0.293 0.617 0.684 0.527 0.669 0.625 0.681 0.863 0.854 0.088 ILS (0.478) 0.480 (0.092) 0.458 0.506 0.402 0.257 0.293 0.517 0.171 0.471 0.465 (0.224) 0.219 0.260 0.471 0.492 0.517 ICB (0.778) 0.591 0.324 0.757 0.702 0.665 0.568 0.617 0.171 0.183 0.761 0.522 0.504 0.842 0.715 0.768 0.780 0.183 CIS (0.913) 0.775 0.345 0.898 0.844 0.805 0.608 0.684 0.471 0.761 0.110 0.614 0.485 0.814 0.680 0.908 0.898 0.110 LS (0.661) 0.533 (0.165) 0.624 0.563 0.633 0.461 0.527 0.465 0.522 0.614 0.439 0.411 0.697 0.454 0.669 0.653 0.439 CPTBS (0.654) 0.457 0.241 0.675 0.566 0.585 0.415 0.669 (0.224) 0.504 0.485 0.411 0.375 0.493 0.601 0.662 0.635 0.375 TYCS (0.759) 0.480 0.377 0.725 0.688 0.645 0.611 0.625 0.219 0.842 0.814 0.697 0.493 0.192 0.609 0.756 0.755 0.192 CBS (0.791) 0.708 0.139 0.782 0.612 0.691 0.248 0.681 0.260 0.715 0.680 0.454 0.601 0.609 0.317 0.781 0.791 0.317 SMC (0.998) 0.835 0.235 0.994 0.902 0.908 0.646 0.863 0.471 0.768 0.908 0.669 0.662 0.756 0.781 0.109 0.991 0.109 WDC (0.993) 0.831 0.215 0.991 0.891 0.915 0.647 0.854 0.492 0.780 0.898 0.653 0.635 0.755 0.791 0.991 0.118 0.118

237

Appendix 7: Chapter 4 Dynamic Factor Analysis

Motivated by the need to obtain and apply a dynamic perspective to the measurement of financial system stress, where latent factors and observations may be interrelated across time, we consider the dynamic factor analysis literature as it relates to our research question.

A7.1. Motivations for dynamic factor analysis

We begin the review by reflecting on an early article by Anderson (1963) that discusses factor analysis of time series data and analyzes the research motivations that condition the choices of static vs. dynamic factor analytic perspectives. Anderson (1963) points out that the econometric traditions of time series analysis can be considered a form of dynamic factor methods. Predominant among the econometric approaches to dynamic models are the stochastic difference equations with i.i.d. random pairs

(, ). Anderson discusses that latent factor identification can be considered to consist

in the weighted loadings of the component data. Anderson asks what are the compelling

reasons to do factor analysis to begin with and what research questions can be answered

with this method. Anderson gives three possible motivations.

Measurement of underlying traits or states. As a first motivation (measurement),

factor analysis has been developed to shed light on the underlying “traits”—hidden

distinguishing characteristics of a particular entity. These characteristics are latent, that is

cannot be measured directly, except through other observable variables which they affect.

The latent factor at a particular point in time is then a linear function of observable data at

that point in time. The problem of analyzing traits can be posed longitudinally, e.g. for

one entity across time, cross-sectionally, e.g. for multiple entities at one point in time. In

238

these two cases the factors that are highlighted by such analysis might be different.

Cattell (1952) considers the cross-sectional factors as traits and longitudinal factors as states. In the longitudinal analysis states are temporary, that is they generally vary at each point in time.

Exploration of underlying data patterns. As a second motivation (exploration), factor analysis is developed to enable investigation of a large set of variables to select a smaller set of variables that may shed light on an underlying pattern of data. Typically, exploration of this kind is useful when it is important to understand a possible data- generation mechanism and little is known about it. This exploration is typically only a starting point in the inquiry. The fundamental problem of factor analysis is that the relationships between variables are still studied without regard to time. Important aspects of the relationships between variables that develop over time are not specifically considered (considered invariant). Once the important factors are revealed by exploration, researcher will need to ask additional question, for example, the critical question about why the factors are formed in the way suggested by the exploration of statistical properties of the observable variables. Thus, from the exploratory perspective, the addition of dynamic processes between manifest and latent variables would serve to improve the measurement model to the extent that the dynamic processes are evidenced.

Analysis of change mechanism for traits or states. As a third motivation

(analysis of the data), we need to understand how one state leads to another state or how one trait affects another trait. Specifically, in describing the mechanism of the relationships between the factors we are interested in understanding the mechanism of factor relationships. For example, are they simply additive at each point in time, implying

239

independence? Are they interacting in a particular way? Are they consistently related where an external shock tends to affect them in a regular sequence? Are they consistently related where an internal shock in one of them tends to result in consistent response pattern in the other factors? When considering these questions that grapple with our understanding of the mechanism, in each case, we are interested in distinguishing irregular or random effects from regular or systematic pattern. Our combined longitudinal measure of the variations in temporal states of the factors then seeks to build a reliable model for the mechanism by which the systematic pattern of the relationships between factor states builds over time. Anderson further details the extent to which factor analysis can help the understanding of the mechanism of state and trait factors and the insidious problems that arise in the analysis of factors.

A7.2. Insidious problems and remedies for longitudinal analysis

Anderson (1963) discusses four particular problems: 1) independence of errors, 2) symmetrical treatment of variables, 3) interpretation of factors, and 4) time sequence effect.

In the factor analysis model, given by the equations (91) and (92) below, the first of these insidious problems is that the errors in observations of data series are assumed to be idiosyncratic, that is uncorrelated to systematic variation in these series.

However, in longitudinal data, particularly in the economic and financial data, it is quite common for the sequential observations to be related, so that a current observation of is in fact partially explained through some accumulation of past “irregularities” of over time. This insidious problem needs to be confronted by recognizing it the analytic model.

240

(91),

and ∑ (92).

The second insidious problem is that research needs to be careful about differentiating related variables that may otherwise be treated “symmetrically”: for instance, the exogenous vs. endogenous variables, or the variables measured with error vs. those measured without error, or the variables measured in different units.

The third insidious problem is a problem of interpretation. It is important to consider the meaning of the factors beyond the output of statistical procedures. Anderson suggests that the factors may be broadly considered in three groups: (i) factors relating only to individual (endogenous) characteristics, (ii) factors relating only to environmental

(exogenous) characteristics, and (iii) factors relating to combination of endogenous and exogenous characteristics. Factors that are pairwise uncorrelated are orthogonal, whereas the factors that are pairwise correlated are oblique. Rotation is an important technique for simplifying the structure of the relationships between oblique factors that is intended to highlight the meaning of the factors and improve their interpretation. Mathematically, rotation can be considered to transform a set of estimated observations (factor loadings

∗ ∗ ∗,∗ ∗,∗ and factor scores ) to a simplified set (of factor loadings , and factor scores , ) in the following two-step process:

∗,∗ ∑ , (93),

∗ ∗,∗ and ∑ , (94).

241

In the first step (equation 93), the matrix is chosen to make the matrix of

∗ loadings . more meaningful. At the same time, in the second step (equation 94) the

∗ inverse matrix is used to also improve the interpretation of the factor scores .

The fourth insidious problem is the time sequence effect that is particularly difficult to address in the initial factor analysis and requires further careful study. This problem stems from the fact that in conventional (static) factor analysis, the estimation of loadings is done from covariances or correlations of variables (e.g. and ) at the

same time, but the problem of the mechanism of the variable variation may in fact be a

function of time (e.g. where clear relationships may exist between and ,). This typically occurs when the observable variables exhibit inherent cyclicality or temporal dependence.111

Anderson (1963) discusses two principal remedies to the above problems. First,

he proposes that the factor model needs to be adjusted to take into account factors (like

time-related observations, time trends, cyclical components) that are observed without

error.112 Second, he proposes extending the static (point-in-time) factor analysis in the

time dimension by considering variable lags as additional observational variables in the

factor-analytic model. In contrast to some proposals to keep the dimensions of the

original static covariance matrix by substituting pairwise maximum covariances across

111 For example, the extent of all transactions in the real estate market last quarter becomes known to the securitization market participants this quarter. This extent then has an additional incremental effect on prices in the securitization market this quarter. 112 Anderson (1963: 15): “2. These functions may be powers of t (yielding polynomials) and cyclical functions (often expressed as sines and cosines). Such variables have no real errors of measurement, and it is hard to give any meaning to the assignment of a specific factor to such a variable (unless the variable itself is a specific factor; that is, uncorrelated with all the other variables).”

242

lags (Cattell, 1957), Anderson suggests that increasing the size of the covariance matrix by additional lagged terms captures a richer pattern of temporal dependency information between variables that should not be ignored.113 Mathematically, the first of his remedies

is summarized by the following transformations:

∑ (setting error 0) (95),

∑ ) (96),

representing factor of the variable observed with error by a linear combination of the

variable and other factors.

Equation (92) transforms to (97):

∑ (97),

where systematic part for the non-time dependent variables consists of a constant, linear combination of the m-1 factors, and a multiple of the error-free observed variable.

After a rotational transformation, the above model can be simplified. Taking the

final model to be nearly orthogonal allows further simplification, where 0 |

1,..,1, then

(98),

where is orthogonal to the m-1 factors.

Then the systematic part from equation (97) transforms to (99) and has a factor structure with m-1 factors. If the loadings were known, the individual observations could be adjusted to remove the time dependency over m-1 factors: (100)

113 As we shall see later, this is a seminal idea in dynamic factor analysis, that is implemented is subsequent research through the Toeplitz matrix. 243

. When the loadings are unknown, they can be estimated by regressing

on .

The second method of remedying problems extends the factor analysis

dynamically by including additional lagged covariances (101) ∑ ̅ ,

114 ̅ | 1, 2, …

A7.3. Two perspectives of dynamic processes

There is a certain amount of confusion in dynamic factor research literature, in

that two related but distinct classes of models have been pursued to explain dynamic

effects: the process model (PFA) and the shock model (SFA) (Browne and Nesselroade,

2005). The conceptual distinctions between the two alternative models naturally

condition their distinct mathematical forms. In the process perspective (Engle and

Watson, 1981), current latent factors are explained through past latent factors via their

autoregressive properties. In the shock model perspective (Geweke, 1977; Geweke and

Singleton, 1981), current observations are explained through current and lingering latent

factor effects. The “shock” aspect comes from the assumption that the idiosyncratic noise

in manifest observations is due to potentially random shocks.

The starting point for both dynamic factor modeling perspectives is the static factor model estimated using the P-technique (Cattell, 1988).115 Regardless of the data

technique, the common factor model is represented by:

Λ (102),

114 Instead of the division by T, equation (102) can also be divided by the number of terms used. 115 The traditional application of the common factor model fits covariation of multiple variables across a sample of subjects on a single occasion (R-technique). By contrast, a P-technique common factor models fits covariation of multiple variables across time. See Cattell (1988) for detailed discussion. 244

where is a p-variate observed time-series at ∈ 1,2, … , , is a k-variate series of latent factors, is a p-variate times series of individual disturbances, and Λ is a

matrix of factor loadings.

General process factor analysis model. The process factor analysis (PFA) perspective hypothesizes that latent “process factors affect only concurrent manifest variables and time series of process factors are specified as vector autoregressive processes with moving average residuals (VARMA)” (Zhang et al., 2014: 445) according to

Λ (103), where, as before, is a p-variate observed stationary time-series at ∈ 1,2, … , , is a 1 matrix of means of at time , is a 1 matrix of latent common factors at time , is a p-variate times series of individual disturbances, and Λ is a

matrix of factor loadings. To estimate this model, process models make an assumption that follows the VARMA (p, q) form:

Λ Λ ⋯Λ B B ⋯

B (104),

where the random shocks are characterized by a covariance matrix  and expectation of

zero ( 0).

The above VARMA (p,q) dynamic process for the latent factors is typically

expressed as

∑ ∑ (105),

245

where is a matrix of autoregressive weights for the relevant dynamic influences of past

latent process factors on the current factors , while B is a matrix of moving

average weights for the dynamic influences of past random shocks on the current

latent factors. In this model specification, “The random shocks can inter-correlate within

the same time point but not across different time points.” (Zhang et al., 2014: 446).

Nomological configuration of the PFA model naturally varies depending both on

the specific form (autoregressive, moving average) and the length of the time dependency. Following Browne & Nesselroade (2005), Figure 43 diagrams PFA (1, 0)— a simple autoregressive form of the general PFA (p, q). Figure 44 shows PFA (0, 1)—a simple moving average form of the general PFA (p, q). Note that in both configurations, the factors are endogenous, while the shocks are exogenous. The dynamic process factor

model expressed by the set of equations (103) and (105) is not identifiable without

imposition of additional constraints. As shown, typically, the following constraints are

imposed: the endogenous factor loading (autoregressive) matrix is constrained for

invariance across time, the exogenous shock loading (moving average) matrix is constrained for invariance across time; and the variances of exogenous random shocks are constrained to unity ( 1 | i1,2,…,q).

246

Figure 43 Process Factor Analysis Model: PFA (1,0)

Note: After Browne & Nesselroade (2005).

Figure 44 Process Factor Analysis Model: PFA (0,1)

Note: After Browne & Nesselroade (2005).

247

Previous econometric research generally mostly focuses on the special case of

VARMA (p, 0) (Engle & Watson, 1981; Creal et al., 2014)—a model that is also known as direct autoregressive factor score model (DAFS) in psychometric literature

(Nesselroade et al., 2001; Zhang et al., 2008).

Consideration of the process model perspective in terms of representational generality exposes its principal challenges. These generality challenges apply particularly to the assumption that the dynamic mechanism occurs only between latent factors and the subsequent imposition of either static autoregressive ( ) or static moving average

( ) relationships.

General shock factor analysis model. By contrast with the process factor

perspective, the shock perspective allows infinite variability in factor loadings, where the

factors are treated as “white noise” (Wold, 1938; Geweke, 1977; Geweke & Singleton,

1981):

Λ Λ ⋯Λ (106),

where variables follow the definitions for equation (102). Thus, shock factors act

randomly at each time , influencing the manifest variables over the time horizon ∞.

In practice, the influence of economic factors on subsequent observations can be

expected to diminish over time and expire over some number of periods q. Thus, a

simplified SFA() form (Molenaar, 1985; Molenaar, 1994; Wood & Brown, 1994) of the

general SFA(∞) dynamic model can be stated as:

Λ Λ ⋯Λ (107).

The SFA() model responds to the Anderson (1963) critiques of the P-technique

common factor model for longitudinal data. In this model, each of the shock factors is a 248

time-dependent series, and the systematic part of each observation at time is formed by a weighted sum of all the factor series at , 1, …, , . Thus, all of the shock factor series are conceived as temporal causes influencing all current and subsequent observations of data and taking , 1, …, , to exhaust. Molenaar (1985) emphasizes that a consistent estimator for the SFA() form of dynamic model can be established by stating the problem in terms a Markovian state model and estimated via the Kalman filter. Nomological configuration of the SFA() model varies depending on the length of the time dependency. Following Browne & Nesselroade (2005), Figure 45 diagrams SFA (1).

Figure 45 Shock Factor Analysis Model: SFA (1)

Note: After Browne & Nesselroade (2005).

Observation of the nomological network for SFA(1) reveals its similarity to

PFA(0,1), where random shock factors influence manifest variables directly without

the need for redundant common process factors by constraining (108)

| 1,2,3,4. Indeed, substituting with 0 from the 1

249

PFA , equation (104)116 into equation (103) yields: (109)

ΛB ΛB ⋯ΛB . Expressed this way, it is easy to see that the

equivalence of PFA(0,1) model to SFA(1) from equation (107) with

ΛΛ (110). Λ ΛB | 1, … ,

In psychometric literature, the shock factor model is also discussed as the white

noise factor score (WNFS) model. Nesselroade et al., (2001: 243-244) highlight that

WNFS models are particularly distinguished by their factor loading patterns which

“differ according to the amount of lag” and express time-dependent manifestations of

factor influences (e.g. decay, latency) “via differences in the magnitude of the factor’s

loadings on the variables as a function of time.”

Comparative discussion. Nesselroade et al. (2001) and Browne & Nesselroade

(2005) compare the process and shock models nomologically and mathematically. As

Nesselroade et al. (2001: 245) emphasize: “The two models differ fundamentally in the

presumed nature of the common factors—especially the nature of the loading patterns at

different lags—and thus represent process in distinctly different ways within the

constraints dictated by the common factor model. Both models allow for a representation

of continuity despite changes over time—a key feature of process—but the mechanisms

by which factors drive variables, however, are notably different in the two model specifications.” In the process perspective, current manifest variables are influenced

only by the current latent factors, which in turn are only influenced either by past

systematic factors or by past shock factors or both simultaneously in an invariant

116 (14*): B B ⋯B. 250

pattern over time. In the shock perspective, current manifest variables are influenced

by the current and past shock factors . Table 44 summarizes the nomological

comparison extending Nesselroade et al. (2001).

Table 44 Summary Nomological Comparison of Process and Shock Dynamic Factor Models Elements Shock model PFA model  Shock factor loadings can be time-variant with  Process factor loadings are time-invariant with Factor loadings amount of lag. amount of lag.  Several random shock factors can act within each  Several process factors can act within each lag. lag.  Number of process shock factors can be time variant. Factor correlations  Number of shock factors can be time variant.  Process factors can be correlated within lags and  Shock factors can be correlated within lags. across lags (through autoregressive connections).  Disturbances can be correlated within variables and  Disturbances can be correlated within variables and Disturbances are uncorrelated across variables. are uncorrelated across variables. Note: Extending Nesselroade et al. (2001, Table 9.1).

Browne & Nesselroade (2005) provide an interesting mathematical comparison

between the process and shock models. Applying Wold’s decomposition (Lütkepohl,

2005), it can be shown that from the general PFA(, ) model (B14) can be expressed

as an infinite vector moving average process VMA (∞) defined by a set of vector

∗ ∗ ∗ matrices ,,…,, such that:

∗ ∗ ∗ ∗ ⋯ | →0, →∞ (111).

Therefore, any PFA(, ) can be expressed as a constrained SFA(∞) shock model, generalizing (B20) with:

ΛΛ ∗ (112). Λ Λ | 1, … , ∞

A7.4. Model estimation

A number of statistical estimation approaches for dynamic factor analysis have been advanced.117 Naturally, these estimation methods have been applied separately for

117 See Brown & Nesselroade (2005) and Zhang et al., (2008) for overviews. 251

both types of dynamic factor models. It is useful to briefly review the typology of the estimation methods to obtain a perspective on their generalizability. To the extent that some estimation methods can be readily applied to both types of dynamic models, they make a practical foundation for exploratory dynamic factor analysis seeking to advance the dynamic theory through empirical evidence.

Process factor model estimation. Four alternative estimation approaches have been applied to process models. First, they have been estimated using Kalman filter estimation for the state-space representation of the model (Harvey, 1989; Forni et al.,

2000; Durbin & Koopman, 2001) and for a special class of process models (PFA , ) with diagonally-constrained factor and shock covariance matrices (Immink, 1986).

Second, they have been estimated using Bayesian framework using Gibbs sampling, state-space form and Markov chain Monte Carlo (MCMC) method (Kim & Nelson, 1999,

2001; Aguilar & West, 2000). Third, they have been estimated using the least squares method applied to the block-Toeplitz matrix of manifest covariances (Browne & Zhang,

2005). Fourth, they have been estimated using maximum likelihood (MLE) methods, such as expectation maximization (Dempster et al., 1977; Watson & Engle, 1983; Zuur et al., 2003). Within MLE method, “no software for dynamic factor analysis by maximum likelihood is readily available” (Browne and Nesselroade, 2005: 448). Therefore, most researchers estimate dynamic factors as structural equation models (SEM) conditioned on block-Toeplitz matrix of manifest covariances and with appropriate adjustments for

252

lagged correlation matrices (Wood & Brown, 1994; Hershberger, 1998; Browne &

Zhang, 2006; Nesselroade et al., 2001).)118

Zhang et al., (2008: 399) conducted simulated comparative analysis of the four

estimation methods for a PFA (1,0) model and found that “four methods yielded

acceptable parameter estimates with comparable accuracy in almost all conditions.”119

Shock factor model estimation. By contrast with process factor model, estimation for the shock factor models has included only two types of approaches: MLE and

Bayesian. First, MLE has been applied to block-Toeplitz matrix of manifest covariance using the structural equation modeling (SEM) framework (Molenaar, 1985; Wood &

Brown, 1994; Nesselroade et al., 2001)).120 Second, parameter estimates have been

obtained by Bayesian estimation using Gibbs sampling (Justiniano, 2004).

MLE on block-Toeplitz data as a starting point for exploratory dynamic factor

analysis. Based on the review of the available estimation approaches, it appears that two

approaches can be generally applied for exploratory dynamic factor analysis when the

model form for a particular dynamic phenomenon (process vs. shock) is has not been

established by prior theory. These approaches are 1) MLE estimation on block-Toeplitz data using SEM framework and 2) Bayesian estimation using Gibbs sampling and

MCMC. Following Occam’s principle, it is reasonable to begin the estimation process with a simple and a clear approach first to obtain useful insights on the properties of the

118 SEM models can presently be estimated using readily available software (e.g. LISREL, Mplus, IBM SPSS Amos, Stata, SAS, and R). 119 Zhang (2006 a, b, c, d) provides the four respective estimation scripts: a) MKFM6 using Kalman filter, b) WinBUGS using Bayesian method, c) DyFA least squares, and d) Mplus using MLE on block- Toeplitz covariance matrices. 120 Wood & Brown (1994) provide a SAS macro program to perform exploratory DFA. Hershberger (1998) and Nesselroade et al., (2001) provide LISREL code to estimate both process factor and shock factor models using the MLE/Toeplitz/SEM approach. 253

data, then to advance to a more complicated perspective, if necessary. The dominant precedent for estimation of dynamic factor models, therefore, pursues the MLE approach, using readily available structural equation modeling software and adjusting the models for lagged correlation matrices.

A7.5. Empirical algorithm

A fundamental empirical means of MLE-SEM estimation consists of exploration of the dimensionality of the dynamic effects and the set-up of the block-Toeplitz matrix of covariances that can be estimated within the structural equation framework. Wood

(2012) clarifies this approach and proposes important additional stages: the use of

Cholesky decomposition to differentiate effect dimensionality among the dynamic factors and the use of parallel factor analysis to determine the number of dynamic factors to retain. In all, Wood’s (2012) suggestions amount to an iterative five-stage empirical algorithm for MLE-SEM based dynamic factor analysis. In the first stage—exploration of dimensionality—researcher confirms the data suitability for dynamic factor analysis and establishes an initial window size for lagged covariance structure of the observed variables. In the second stage—block-diagonal Toeplitz matrix—the researcher constructs the Toeplitz matrix of covariances for the lagged set of observable data that would be estimated by SEM. In the following two stages, the researcher seeks to find a factor solution of the block-diagonal Toeplitz matrix that would be empirically and theoretically sound. Specifically, in the third stage—Cholesky factorization—researcher decomposes the Toeplitz matrix to determine the potential dynamic factors. In the fourth stage—parallel factor analysis—the researcher examines whether the candidate dynamic factors should be retained by comparing them with randomization of observed data. In

254

the fifth stage—adjustment—the researcher seeks to validate the factor solution by reconfirming the time dependency of the retained factors and to adjust the factor solution if necessary. The above exploratory dynamic factor analysis results in a set of candidate dynamic factors with an established lagged dependency structure.

255

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