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Intertemporal Choices with Temporal Preferences

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Intertemporal Choices with Temporal Preferences INTERTEMPORAL CHOICES WITH TEMPORAL PREFERENCES by Hyeon Sook Park B.A./M.A. in Economics, Seoul National University, 1992 M.A. in Economics, The University of Chicago, 1997 M.S. in Mathematics & C.S., Chicago State University, 2001 M.S. in Financial Mathematics, The University of Chicago, 2004 Submitted to the Graduate Faculty of the Kenneth P. Dietrich Arts and Sciences in partial ful…llment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2012 UNIVERSITY OF PITTSBURGH DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Hyeon Sook Park It was defended on May 24, 2012 and approved by John Du¤y, Professor of Economics, University of Pittsburgh James Feigenbaum, Associate Professor of Economics,Utah State University Marla Ripoll, Associate Professor of Economics, University of Pittsburgh David DeJong, Professor of Economics, University of Pittsburgh Dissertation Director: John Du¤y, Professor of Economics, University of Pittsburgh ii INTERTEMPORAL CHOICES WITH TEMPORAL PREFERENCES Hyeon Sook Park, PhD University of Pittsburgh, 2012 This dissertation explores the general equilibrium implications of inter-temporal decision- making from a behavioral perspective. The decision makers in my essays have psychology- driven, non-traditional preferences and they either have short term planning horizons, due to bounded rationality (Essay 1), or have present biased preferences (Essay 2) or their utilities depend not only on the periodic consumption but are also dependent upon their expectations about present and future optimal consumption (Essay 3). Finally, they get utilities from the act of caring for others through giving and volunteering (Essay 4). The decision makers who are de…ned by these preferences are re-optimizing over time if they realize that their past decisions for today are no longer optimal and this is the key mechanism that helps replicate the mean lifecycle consumption data which is known to be hump-shaped over the lifecycle. In the …rst essay, I prove that there is an income structure that leads to a consumption hump for each time preference. Searching via simulation, I …nd the best planning horizon that is compatible with matching data for the US economy. In the second essay, I …nd that the consumption hump is obtained even without the credit constraint if the agent is naive and keeps re-optimizing over time. In a third essay, I demonstrate that reference-dependent preferences can also generate a hump-shaped consumption pro…le when the agent has age- dependent loss aversion. In the fourth and the …nal essay, I show how the inclusion of time endowment generates full-blown lifecycle pattern of not only consumption, but also giving, leisure, and volunteer time, which closely follow the data. iii TABLE OF CONTENTS 1.0 INTRODUCTION ................................. 1 2.0 BOUNDED RATIONALITY AND LIFECYCLE CONSUMPTION .. 5 2.1 Introduction ................................... 5 2.1.1 Main Findings ............................... 9 2.1.2 Related Literature ............................. 11 2.1.3 Chapter Organization ........................... 13 2.2 A Simple Model ................................. 14 2.3 A Lifecycle Model with Short Term Planning ................. 21 2.3.1 Consumer ................................. 22 2.3.1.1 Environment ........................... 22 2.3.1.2 Consumer Optimization ..................... 23 2.3.1.3 Planned and Realized Consumption ............... 24 2.3.2 Technology and General Equilibrium ................... 26 2.4 Quantitative Analysis .............................. 28 2.4.1 Targets in US Data ............................ 28 2.4.2 Calibration ................................. 30 2.4.3 Results ................................... 32 2.4.3.1 Simulation ............................. 32 2.4.3.2 Beta and Gamma ......................... 36 2.4.3.3 The Best Planning Horizon ................... 37 2.4.3.4 Robustness ............................ 38 2.5 Modi…cations ................................... 39 iv 2.5.1 Learning .................................. 40 2.5.2 Cost and Infrequent Planning ................... 41 2.6 Conclusion .................................... 42 3.0 PRESENT BIASED PREFERENCE AND CONSTRAINED CON- SUMER ....................................... 53 3.1 Introduction ................................... 53 3.1.1 Main Findings ............................... 58 3.1.2 Literature Review ............................. 60 3.1.3 Chapter Organization ........................... 61 3.2 Analytic Solution to A Simple Model ...................... 62 3.3 Self Awareness .................................. 72 3.4 A Lifecycle Model with Present Biased Preferences .............. 77 3.4.1 Consumer ................................. 77 3.4.1.1 Environment ........................... 77 3.4.1.2 Constrained Consumer Optimization .............. 78 3.4.1.3 Planned and Realized Consumption in Partial Equilibrium .. 81 3.4.2 Technology and General Equilibrium ................... 82 3.4.3 Extended General Equilibrium Model with Mortality Risk, Bequest and Social Security ............................... 84 3.5 Quantitative Analysis .............................. 86 3.5.1 Targets in US Data ............................ 87 3.5.2 Calibration ................................. 87 3.5.3 Results ................................... 89 3.5.3.1 The Result for the Baseline Model ............... 90 3.5.3.2 Simulation Result for the Extended Model ........... 93 3.5.3.3 Robustness ............................ 97 3.6 Conclusion .................................... 97 4.0 A GE MODEL OF DECISION MAKERS WITH BELIEF DEPEN- DENT PREFERENCES ............................. 100 4.1 Introduction ................................... 100 v 4.1.1 Other Related Literatures ......................... 105 4.1.2 Modeling Reference-Dependent Preference ................ 107 4.2 A Simple Model ................................. 109 4.2.1 Two-Periods ................................ 109 4.2.2 Beyond Two-Periods ........................... 114 4.2.2.1 Three-Periods ........................... 115 4.2.2.2 Utility Comparison ........................ 118 4.2.2.3 Consumption Hump in Simple Model .............. 121 4.2.3 A Simple Lifecycle Model ......................... 123 4.3 Dynamic Reference-Dependent Model ..................... 126 4.3.1 Dynamic Decision Makers ......................... 126 4.3.1.1 Reference Points in the Dynamic Model ............ 127 4.3.1.2 Saver’sDynamic Optimization .................. 134 4.3.2 The Sub-Period Perfect Reference Point ................. 136 4.4 A General Equilibrium with Dynamic Model .................. 138 4.4.1 A Dynamic Lifecycle Model ........................ 138 4.4.1.1 A Simple Dynamic Model .................... 138 4.4.1.2 The Consumption Hump ..................... 141 4.4.2 An Overlapping Generations General Equilibrium ........... 147 4.4.2.1 The RDP Consumer ....................... 147 4.4.2.2 Production and Calibrated General Equilibrium ........ 151 4.4.2.3 General Equilibrium with both Savers and Over-consumers .. 154 4.5 Comparison with Bounded Rationality Model ................. 156 4.5.1 A RDP Model of S-Period Updating ................... 156 4.6 Uncertainty and Precautionary Saving ..................... 162 4.6.1 Stochastic Reference Points ........................ 163 4.6.2 A Two-Period Uncertainty Model .................... 165 4.6.2.1 Market Clearing and General Equilibrium ........... 169 4.6.3 State Dependence ............................. 170 4.7 Conclusion .................................... 173 vi 5.0 A LIFECYCLE MODEL OF CHARITABLE GIVING: A QUANTI- TATIVE ANALYSIS OF SOCIAL PREFERENCES ............ 181 5.1 Introduction ................................... 182 5.1.1 Charitable Giving and Warm Glow ................... 182 5.1.2 US Giving Reports ............................ 186 5.1.3 Literatures ................................. 191 5.1.4 Chapter Organization ........................... 193 5.2 A Model of Warm Glow ............................. 193 5.2.1 Solving Intra-temporal optimization ................... 197 5.2.2 Solving Inter-temporal optimization ................... 206 5.2.3 Endogenous Retirement .......................... 207 5.3 A Lifecycle Model of Charitable Giving .................... 211 5.3.1 Consumer ................................. 211 5.3.1.1 Environment ........................... 211 5.3.1.2 Consumer Optimization Behavior ................ 211 5.3.1.3 Extended Preference with Status or Social Pressure ...... 213 5.3.2 Technology, Government and General Equilibrium ........... 216 5.4 Quantitative Analysis .............................. 219 5.4.1 Targets in US Data ............................ 219 5.4.2 Calibration Method ............................ 220 5.4.2.1 Results ............................... 222 5.4.2.2 Experiments and Sensitivity ................... 226 5.5 Conclusion .................................... 232 6.0 CONCLUSION ................................... 233 APPENDIX A. PROOFS FOR CHAPTER 2 ................... 236 APPENDIX B. PROOFS FOR CHAPTER 4 ................... 238 APPENDIX C. PROOFS FOR CHAPTER 5 ................... 245 BIBLIOGRAPHY .................................... 247 vii LIST OF TABLES 1 Parameters and Targets .............................. 31 2 Optimal Beta Values over Gamma and Planning Horizon ........... 45 3 Optimal Beta Values over Planning Horizon ................... 47 4 The Highest Value of Gamma Less than One .................. 47 5 Sensitivity to Alternative Calibration .....................
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