Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2004 Threshold cointegration test of the Fisher effect Biyong Xu Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Finance Commons, and the Finance and Financial Management Commons Recommended Citation Xu, Biyong, "Threshold cointegration test of the Fisher effect " (2004). Retrospective Theses and Dissertations. 1207. https://lib.dr.iastate.edu/rtd/1207 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Threshold cointegration test of the Fisher effect by Biyong Xu A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Economics Program of Study Committee: Barry Falk, Major Professor Helle Bunzel Wayne Fuller Peter Orazem John Schroeter Iowa State University Ames, Iowa 2004 Copyright © Biyong Xu, 2004. All rights reserved. UMI Number: 3158382 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3158382 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 11 Graduate College Iowa State University This is to certify that the doctoral dissertation of Biyong Xu has met the dissertation requirements of Iowa State University Signature was redacted for privacy. ijor Professor Signature was redacted for privacy. For the Major Program iii To my mother and to the memory of my father iv TABLE OF CONTENTS INTRODUCTION 1 CHAPTER ONE: LITERATURE REVIEW ON THE FISHER EFFECT 5 1.1 The Fisher Hypothesis 5 1.2 Literature Review 9 1.3 Threshold Cointegration Test of the Fisher Effect 17 1.4 Description of Data 34 CHAPTER TWO: UNIT ROOT TESTS 37 2.1 Linear Unit Root Tests 37 2.2 Unit Root Test under the Threshold Alternative 42 2.3 End-of-chapter Summary 45 CHAPTER THREE: COINTEGRATION TESTS 46 3.1 Linear Cointegration Tests 46 3.2 Nonlinearity Tests 53 3.3 End-of-chapter Summary 56 CHAPTER FOUR: THRESHOLD ERROR CORRECTION MODEL 57 4.1 Hansen and Seo's (2002) Two-Regime TVECM 57 4.2 The Estimated Threshold Error Correction Model 62 4.3 Test of Equal Forecast Efficiency 67 4.4 End-of-Chapter Summary 73 CHAPTER FIVE: CONCLUSIONS AND FINAL REMARKS 74 APPENDIX A: TECHNICAL BACKGROUND 77 APPENDIX B: TABLES 80 APPENDIX C: FIGURES 86 REFERENCES 88 ACKNOWLEDGEMENTS 92 1 INTRODUCTION Interest rate and inflation are two fundamental variables in the economy. For decades, economists have been trying to disclose the relationship between them. One of the most well-known hypotheses is the Fisher hypothesis, which was first proposed by the famous economist Irving Fisher in Fisher (1930). According to the hypothesis, the nominal interest rate on bonds moves one-to-one with the rate of inflation anticipated by the public, and the expected real rate of return is constant over time. The hypothesis implies that in the long run there is a one-to-one correspondence between changes of the nominal interest rate and the changes of inflation, which is often referred to as the Fisher effect in the literature. The Fisher hypothesis, however, is controversial in both macroeconomic theories and empirical studies. Different macroeconomic and financial models give conflicting explanations of the relationship between the nominal interest rate and the inflation rate. For example, we have the hypothesis of supemeutrality of money, which claims that the inflation does not affect real variables, but at the same time we also have proposition of Tobin effect, which describes a possible negative relationship between the real interest rate and the inflation that depresses the Fisher effect1. The empirical studies do not help much to reduce the controversy in the theoretical literature. Fama (1975) argues that the nominal interest rate is the best possible predictor of 1 See Section 1.2.1 for more details on the theoretical literature. 2 the inflation rate and claims that the Fisher effect holds in the United States. With ADF and Philips-Perron tests, Ross (1988) claims that US ex post real interest rate is nonstationary, which can be a contradiction to the assumption of constant expected real interest rate inherent in the Fisher hypothesis. By applying Engle and Granger (1987) cointegration procedure, Mishkin (1992) asserts that the nominal interest rate and the inflation rate are cointegrated and that the Fisher effect exists in the long run. With the inflation rate modeled by a Markov regime switching process, Evans and Lewis (1995) argue that the rational anticipation of infrequent shifts in the inflation process could have led to a significant downward bias in the estimate of the long-run Fisher effect. Crowder and Hoffman (1996) consider the tax-adjusted Fisher equation in Johansen (1988) cointegration framework and claim that the estimated Fisher effect is consistent with the theoretically predicted value.1 Most of the previous empirical studies are using linear models in time series, which was predicated on the assumption that the path of adjustment towards long-run equilibrium is necessarily symmetric. The assumption of symmetric adjustment, however, may not be warranted. It is frequently argued that that some fundamental economic variables, including the real GNP and the unemployment rate, display asymmetric adjustment paths, which cannot be properly modeled by linear models2. Since the real interest rate is closely related to these variables, it may also follow an asymmetric adjustment path. 1 See Section 1.2.2 for more details on the empirical literature. 2 See Neftci (1984) and Hamilton (1989) for examples. 3 In this dissertation, we are going to study the Fisher relationship within a fresh nonlinear framework. The dissertation is filling several blanks in the empirical literature. 1. Testing the stationarity of the nominal interest rate and the inflation rate under a nonlinear threshold autoregressive model (TAR). If the nominal interest rate and/or the inflation rate follow a TAR process, linear unit root tests1 are misspecified under the alternative and therefore their power will suffer. To address the possible power distortion, Enders and Granger (1998) test, which allows an asymmetric path of adjustment, will be preformed to check the order of integration. 2. Testing threshold cointegration between the nominal interest rate and the inflation rate. To test for possible nonlinearity in the Fisher relationship, threshold cointegration analysis described in Balke and Fomby (1997) is to be implemented. 3. Modeling the Fisher relationship in a TVECMframework. A two-regime threshold vector error correction model (TVECM) described in Hansen and Seo (2002) will be applied to capture the nonlinearity in the Fisher relationship. Further more, the encompassing tests described in Clark and McCracken (2001) will be carried out to compare the performance of the linear cointegration analysis and the TVECM. 1 Here the linear unit root tests refer to the class of unit root tests that are linear under both the null and the alternative. For example, the ADF test and Phillips-Perron unit root test. 4 Correspondingly, there are five chapters in this dissertation. In Chapter One, we will extensively review the literature on the Fisher effect, the threshold cointegration and the TVECM. The results of unit root tests, including one nonlinear unit root test (Enders and Granger (1998)) and two linear unit root tests (ADF and ADFGLS), will be presented in Chapter Two. In Chapter Three, we are going to test for the presence of nonlinearity in the relationship between the nominal interest rate and the inflation rate, following the two-step procedure of the Balke and Fomby (1997). Linear cointegration analyses, including the Johansen (1988) and Phillips-Ouliaris (1990), will be performed in the first step and nonlinearity tests will be applied to the cointegration residuals in the second step. In Chapter Four, we will model the nonlinearity in the Fisher relationship with a two-regime TVECM in Hansen and Seo (2002) and compare its out-of-sample forecast efficiency with the linear cointegraiton analysis. Chapter Five is the conclusions and directions for future research. 5 CHAPTER ONE: LITERATURE REVIEW ON THE FISHER EFFECT 1.1 The Fisher Hypothesis An interesting topic in macroeconomics and financial economics is the relationship between the nominal interest rate and inflation. A well-known hypothesis about this relationship was proposed by Fisher (1930). The original proposition is that the nominal interest rate on bonds is the sum of the expected real interest, which is the expected rate of returns associated with holding real assets, and the rate of inflation anticipated by the public. 1.1.1 The Basic Fisher Equation The Fisher hypothesis can be summarized in the following mathematical terms it=Et7rt+ Etrt (1.1) where it =nominal interest rate at time t for one-period bonds maturing at time t+1 ; Et rt = real expected rate of return in period t (the period between time t and H-l)1, which is the expected rate of returns associated with holding real assets; Etnt =expected inflation rate between time t and t+l.