ESSAYS ON MACROECONOMIC DYNAMICS by Daeyup Lee B.A., Korea University, 1994 M.A., Korea University, 2000 Submitted to the Graduate Faculty of the Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2010 UNIVERSITY OF PITTSBURGH ARTS AND SCIENCES This dissertation was presented by Daeyup Lee It was defended on August 4 2010 and approved by Marla Ripoll, PhD, Associate Professor, Dept. of Economics James Feigenbaum, PhD, Assistant Professor, Dept. of Economics and Finance John Duffy, PhD, Professor, Dept. of Economics Jonathan Rubin, PhD, Associate Professor, Dept. of Mathematics Dissertation Advisors: Marla Ripoll, PhD, Associate Professor, Dept. of Economics, James Feigenbaum, PhD, Assistant Professor, Dept. of Economics and Finance ii ABSTRACT ESSAYS ON MACROECONOMIC DYNAMICS Daeyup Lee, PhD University of Pittsburgh, 2010 This thesis deals with macroeconomic dynamics. In chapter 1, I study a one-sector growth model with endogenous discount rate of the sort proposed by Meng[2006]. I extend the model into a heterogeneous agents model with respect to initial wealth, and investigate whether the wealth distribution may converge to a degenerate distribution. I find that if an agent's decision only depends on his or her reference group and if consumption is more important in discounting than income around the steady state, then convergence to a degenerate distribution is a unique solution. Furthermore, if an agent's decision depends on average variables of overall society, I find that there exists a continuum of steady states. In chapter 2, I introduce three mechanisms into otherwise standard Aiyagari[1994] model to generate a realistic wealth distribution. The three mechanisms include: i) a wealth- dependent shock: labor income shock is wealth-dependent; ii) misspecification: people do not take into account the dependence of the labor income process on wealth when they make consumption decisions; iii) status-seeking from some threshold: there is a direct utility gain from being wealthy. The main findings are as follows: i) Wealth-dependent labor income shock with misspecification helps to explain wealth concentration but cannot fully explain the share of the top 1% in wealth distribution. ii) In the full model with status-seeking, the share of top 1% becomes closer to the data. In chapter 3, I build a simple model (two-dimensional discrete dynamical system) to study the interactive dynamics of short-term nominal interest rates of the U.S. and interna- tional risk appetite. Main implications from the research are the followings: First, strong iii interaction between short-term nominal interest rates of the U.S. and international risk ap- petite can induce bifurcations of the dynamical system: stable fixed point to limit cycle and then to chaos. Second, a numerical experiment suggests two possible explanations for rising variance ratios: the reduction of random shock and the bifurcation of a dynamical system. This finding hints the potential of complexity measures (such as Lyapunov exponent and permutation entropy) as early warning signals. iv TABLE OF CONTENTS PREFACE ......................................... xiii 1.0 A CLOSER LOOK AT WEALTH DYNAMICS OF A ONE-SECTOR GROWTH MODEL WITH ENDOGENOUS DISCOUNT RATE ...1 1.1 Introduction...................................1 1.2 Heterogeneous agents with endogenous discounting.............3 1.2.1 General set-up..............................4 1.2.2 Case 1; different discounting......................5 1.2.2.1 Basic results...........................6 1.2.2.2 Partial equilibrium analysis................... 16 1.2.2.3 Discussion: Comparison with earlier literature........ 21 1.2.3 Case 2; same discounting........................ 23 1.2.3.1 Basic results........................... 23 1.2.3.2 Several special cases....................... 28 1.2.3.3 Transition dynamics to a continuum of steady states..... 29 1.2.3.4 Discussion............................ 31 1.3 Conclusion.................................... 32 2.0 WEALTH DISTRIBUTION WITH WEALTH-DEPENDENT LABOR INCOME SHOCK, MISSPECIFICATION, AND STATUS-SEEKING 33 2.1 Introduction................................... 33 2.2 Empirical investigation............................. 38 2.2.1 Review of mechanisms for the feedback from wealth to labor income 38 v 2.2.2 Review of distributions of labor income and wealth from the Panel Study of Income Dynamics (PSID)................... 40 2.2.2.1 Labor income.......................... 41 2.2.2.2 Wealth.............................. 41 2.2.2.3 The relation between labor income and wealth........ 43 2.3 Model...................................... 46 2.3.1 Household's problem........................... 46 2.3.2 Wealth-dependent labor income shock: finite approximation of Q and Q~ ..................................... 48 2.3.3 Stationary Competitive Market Equilibrium.............. 49 2.3.3.1 Definition of Stationary Competitive Market Equilibrium.. 49 2.3.3.2 Computation of an equilibrium................. 50 2.4 Results...................................... 53 2.4.1 The effect of wealth-dependent shock................. 53 2.4.1.1 Calibration............................ 53 2.4.1.2 The effect of wealth-dependent shock............. 54 2.4.2 Wealth-dependent shock and status seeking.............. 55 2.5 Conclusion.................................... 62 3.0 FROM THE \GREAT MODERATION" TO THE FINANCIAL CRI- SIS OF 2007-9: ON THE INTERACTIVE DYNAMICS OF SHORT- TERM NOMINAL INTEREST RATES OF THE U.S. AND INTER- NATIONAL RISK APPETITE WITH BIFURCATION ANALYSIS . 64 3.1 Introduction................................... 64 3.2 Interaction between interest rates of the U.S. and international risk appetite 71 3.2.1 The U.S. as a key currency country................... 71 3.2.2 International risk appetite........................ 72 3.2.3 The interaction between interest rates of the U.S. and international risk appetite............................... 73 3.3 Empirical investigation on short-term interest rates and interest spreads during the \Great Moderation"........................ 76 vi 3.3.1 Interest rates and spreads in the U.S.................. 77 3.3.2 International comparison........................ 78 3.4 A model..................................... 82 3.4.1 The overview of the model....................... 82 3.4.1.1 Two sources of nonlinearity of the model........... 82 3.4.1.2 Bifurcation analysis....................... 83 3.4.2 Model................................... 86 3.4.2.1 A simple model for interactive dynamics of the U.S. interest rates and international risk appetite............. 87 3.4.2.2 The stronger influence of international risk appetite on the U.S. interest rates (iws ") and its effect on dynamics of the model............................... 91 3.4.2.3 The stronger influence of the U.S. interest rates on interna- tional risk appetite (si ") and its effect on dynamics of the model............................... 93 3.4.2.4 The simultaneous effect of two parameters, iws and si .... 97 3.4.2.5 Random shock and variance ratios............... 98 3.5 Conclusion.................................... 100 APPENDIX A. PROOFS ............................... 103 A.1 Proof of Proposition 1.2.2........................... 103 A.2 Proof of proposition 1.2.8........................... 104 APPENDIX B. SIMULATED PATHS ....................... 107 APPENDIX C. AN UNSTABLE LIMIT CYCLE AND THE NOTION OF \CORRIDOR STABILITY" ........................... 114 C.1 A model..................................... 115 C.2 Numerical Analysis............................... 118 C.3 Discussion.................................... 121 APPENDIX D. PSID .................................. 122 D.1 Data I: Head Wage............................... 122 D.2 Data II: Total Head labor income....................... 124 vii D.3 Data III: Wealth................................ 125 APPENDIX E. GENERAL FRAMEWORK ................... 126 APPENDIX F. RESULTS ............................... 130 APPENDIX G. WEALTH IN UTILITY: THE SPIRIT OF CAPITALISM 135 APPENDIX H. DHM TEST STATISTICS .................... 138 APPENDIX I. DATA .................................. 140 I.1 Interest rates of the U.S............................. 140 I.2 Short-term nominal interest rates of 10 countries............... 140 APPENDIX J. SCATTER PLOTS ......................... 143 APPENDIX K. VARIANCE RATIO TESTS ................... 145 APPENDIX L. AN EXAMPLE OF THE \BUTTERFLY EFFECT" ... 147 APPENDIX M. PATHS OF COMPONENTS OF THE MODEL ...... 148 APPENDIX N. BIFURCATION DIAGRAMS .................. 149 BIBLIOGRAPHY .................................... 150 viii LIST OF TABLES 1 OLS of 2.6 ...................................... 45 2 OLS of 2.7 ...................................... 46 3 Parameter values.................................. 53 4 Benchmark model and endogenous shock.................... 55 5 Wealth-dependent shock and the strongest status-seeking........... 58 6 The strongest status seeking without endogenous shock............ 61 7 Models on wealth distribution.......................... 61 8 Daily correlations between domestic interest spreads and TB(3m,U.S.).... 77 9 Random walk tests of quarterly nominal interest rates and quarterly interest spreads in U.S. (time lag = 65 days)....................... 79 10 Daily correlation between international interest spreads and TB(3m, U.S.) ..... 80 11 Random walk tests: Quarterly nominal interest rates (time lag = 65 days) ..... 81 12 Main actions of a model.............................