Bayesian Estimation of Monetary DSGE Models and Testing for Indeterminacy Qazi Haque Thesis submitted to The University of Adelaide in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics School of Economics March 2018 Table of Contents List of Tables v List of Figures vi List of Publications vii Abstract viii Declaration ix Acknowledgements x I Introduction 1 II Monetary Policy and Indeterminacy after the 2001 Slump 6 1 Introduction 6 2 Baseline model 11 3 Estimation and baseline results 12 3.1 Dataandpriors.............................. 12 3.2 Testing for indeterminacy . 13 3.3 How important are sunspots and what drives the results? . 15 4 Sensitivity analysis 17 4.1 Rollingwindows.............................. 17 4.2 Alternative measures of output . 18 4.3 Real-timedata .............................. 19 4.4 Further tests of robustness . 20 5 Which measure of inflation to choose? 20 6 An economy that distinguishes between core and headline inflation 22 6.1 Model ................................... 24 6.2 Econometric strategy and results . 26 7 Concluding remarks 30 Appendix A 32 A.1 Framework of the structural analysis . 32 A.2 Sensitivity analysis . 42 A.3 A micro-founded distinction between core and headline inflation . 50 ii References 59 III Monetary Policy, Inflation Target and the Great Moderation: An Empirical Investigation 64 1 Introduction 64 2 Model 70 2.1 The log-linearized model . 71 2.2 Rational expectations solutions under indeterminacy . 73 2.3 Equilibrium determinacy and trend inflation . 74 3 Econometric strategy 75 3.1 Bayesian estimation with Sequential Monte Carlo (SMC) algorithm . 75 3.2 Data.................................... 77 3.3 Calibrated parameters . 77 3.4 Prior distributions . 78 4 Estimation Results 78 4.1 Modelcomparison............................. 80 4.2 Parameter estimates . 81 4.3 Forecast error variance decomposition . 83 5 What explains the switch from indeterminacy to determinacy in the pre-Volcker period? 87 6 Federal Reserve’sinflation target 88 7 What explains the Great Moderation in the U.S.? 91 7.1 Counterfactuals . 93 8 Further investigation 95 8.1 Firm-specificlabor ............................ 96 8.2 Estimation over the entire parameter space . 97 9 Conclusion 99 Appendix A 101 A.1Model....................................101 References 110 iii IV Do we really know that U.S. monetary policy was destabilizing in the 1970s? 118 1 Introduction 118 2 Model 122 2.1 Households ................................ 122 2.2 Firms ...................................124 2.3 Monetarypolicy.............................. 128 3 Solution under indeterminacy 129 4 Econometric strategy 130 4.1 Bayesian estimation with Sequential Monte Carlo (SMC) algorithm . 130 4.2 Data....................................132 4.3 Calibrated parameters . 133 4.4 Prior distributions . 133 5 Estimation results 135 5.1 Modelcomparison............................. 135 5.2 Parameter estimates . 139 5.3 Implications of the model for macroeconomic volatility . 143 6 Trade-off between inflation and output gap stabilization 144 7 Propagation of commodity price shock 146 8 Sensitivity analysis 148 8.1 Indexation................................. 148 8.2 Alternative Taylor rule . 150 8.3 Boundary ................................. 150 8.4 Flexible-price output gap . 151 8.5 Estimation over the entire parameter space . 152 8.6 Oil as an observable . 152 9 Conclusion 153 Appendix A 155 A.1Framework ................................. 155 A.2 Derivation of the Output Gap . 159 References 164 V Conclusion 168 iv List of Tables 1 Priors and posteriors of DSGE parameters . 14 2 Determinacy versus Indeterminacy . 15 3 Determinacy versus Indeterminacy (Robustness) . 19 4 Determinacy versus Indeterminacy (DSGE-Factor) . 22 5 Parameter Estimation Results (DSGE-Factor) . 23 6 Priors and posteriors for DSGE parameters . 28 7 Determinacy versus Indeterminacy . 29 8 Variance Decomposition . 40 9 Benchmark Model versus Determinate Model with Habit . 41 10 Parameter Estimation Results . 42 11 Determinacy versus Indeterminacy (Robustness) . 44 12 Priors and posteriors for DSGE parameters (Trend Inflation) . 47 13 Posteriors for DSGE parameters estimated using PCE (Trend Inflation) 48 14 Determinacy versus Indeterminacy (Core CPI) . 50 15 Determinacy versus Indeterminacy . 56 16 Priors and posteriors for DSGE parameters. 57 1 Prior distributions for parameters . 79 2 Determinacy versus Indeterminacy . 80 3 Posterior estimates for DSGE parameters under time-varying target . 82 4 Forecast Error Variance Decompositions: Pre-1979 Sub-sample . 84 5 Forecast Error Variance Decompositions: Post-1984 Sub-sample . 85 6 Implications of the model for volatility and predictability . 92 7 Counterfactual standard deviations . 94 8 Counterfactual predictability . 95 9 Determinacy versus Indeterminacy (firm-specific labor) . 96 10 Posteriors distribution (Estimation over entire parameter space) . 98 11 Fixed target and Homogenous labor . 107 12 Firm-specificlabor ............................ 108 13 Firm-specific labor - estimation over entire parameter space . 109 1 Prior distributions for parameters . 134 2 Determinacy versus Indeterminacy . 136 3 Determinacy versus Indeterminacy (1966:I - 1979:II) . 137 4 Parameter Estimates (1966:I-1979:II) . 141 5 Parameter Estimates (1984:I-2008:II) . 142 6 The Great Moderation . 144 7 Determinacy versus Indeterminacy (Robustness) . 149 8 Parameter Estimates, Robustness (1966:I-1979:II) . 162 9 Parameter Estimates, Robustness (1984:I-2008:II) . 163 v List of Figures 1 Probability of determinacy using rolling window estimation. The fig- ure plots the probability at the first quarter of a window. 18 2 Inflationmeasures............................. 35 3 Correlation pattern of various inflation measures . 35 4 Impulse responses under determinacy from the model estimated over the period 2002:I - 2007:III using Core PCE inflation. 38 5 Impulse responses under indeterminacy from the model estimated over the period 2002:I - 2007:III using CPI inflation. 39 6 Determinacy region for the Blanchard and Gali (2009) model . 58 1 Determinacy region and trend inflation . 75 2 Federal Reserve’sInflation Target . 89 3 A comparison of inflation target estimates . 90 1 IRF to commodity price shock under alternative degree of real wage rigidity................................... 145 2 Estimated IRF to commodity price shock . 146 3 Counterfactual IRFs to commodity price shock . 147 vi List of Publications Doko Tchatoka, F., Groshenny, N., Haque, Q. and Weder, M., 2017. Monetary Policy and Indeterminacy after the 2001 Slump. Journal of Economic Dynamics and Control, 82, pp. 83-95. vii Abstract This thesis consists of three self-contained papers on U.S. monetary policy. The first paper examines monetary policy in the early 2000s, a prolonged period of low interest rates for which the effi cacy of policy is intensely debated. Through the lens of an estimated simple New Keynesian (NK) model, the paper finds that when measuring inflation using headline CPI, the Federal Reserve’s response to inflation turns out to be passive, therefore implying indeterminacy. Only when measuring inflation using core PCE does monetary policy appear to have been suffi ciently active to rule out indeterminacy. Faced with this dilemma, the paper finally estimates an extended model that distinguishes between core and headline inflation. Estimation results from this model decisively rule out indeterminacy and suggest that indeed the Fed has put more weight on core PCE. The second paper contrasts interest rate rules featuring fixed versus time-varying inflation target. It finds that the rule embedding time variation in inflation target empirically fits better and that the Fed has been responding strongly to the inflation gap not only in the Great Moderation period but also in the Great Inflation era. Therefore, this finding rules out self-fulfilling inflation expectations as an explanation of the high inflation episode in the 1970s. The paper also documents that changes in monetary policy have dampened most of the fluctuations in the inflation gap and contributed to the decline in its persistence and predictability. The third paper investigates the impact of commodity price fluctuations on mon- etary policy and estimates a NK model with an explicit role for commodity price fluctuations. It finds that the pre-Volcker period is characterized by a determinate version of the model featuring high degree of real wage rigidity In this environment, the commodity price shocks of the 1970s created a severe trade-off between inflation and output gap stabilization. Faced with this puzzle, the central bank chose to react aggressively to both inflation and output growth, but not to the output gap, thereby ruling out indeterminacy. The paper further documents that oil price shocks are no longer as inflationary as they used to be due to a decline in real wage rigidity, thereby explaining the resilience of the economy to sustained oil price hikes in the 2000s. viii Declaration I, Qazi Haque, certify that this work contains no material which has been accepted for the award of any other degree or diploma in my name, in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. In addition, I certify that no part of this work will, in the future, be used in a submission in my name, for any other degree or diploma in any university or other tertiary institution