Topics in dynamic macroeconomic theory [Elektronische Ressource] : on the causes and consequences of income growth and uncertainty / vorgelegt von Christian Bauer
309 Pages
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Topics in dynamic macroeconomic theory [Elektronische Ressource] : on the causes and consequences of income growth and uncertainty / vorgelegt von Christian Bauer

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Topics in Dynamic Macroeconomic Theory: On the Causes andConsequences of Income Growth and UncertaintyDissertationzur Erlangung des Grades eines Doktors der Wirtschaftswissenschafteingereicht an derWirtschaftswissenschaftlichen Fakult¨atder Universit¨at Regensburgvorgelegt vonChristian BauerBerichterstatter:Prof. Dr. Lutz Arnold (Universit¨at Regensburg)Prof. Dr. Alfred Maußner (Universit¨at Augsburg)Tag der Disputation: 30.10.2008OverviewI Trade with Imperfect Competition and Heterogeneous Firms 11 An “Almost Static” Model with Fixed Export Costs 32 Melitz (2003) with Pareto-Distributed Productivities 433 A Dynamic Model of Growth and Trade 57II On the Growth and Welfare Effects of Monopolistic Competition 1194 Monopolistic Competition and Endogenous Growth 1215 Monopolistic Distortions and Growth Reconsidered 151III Idiosyncratic Income Risk and the Labor Market 1716 Labor Market Matching with Savings 1737 Optimal Unemployment Policy 2098 Job Search with Borrowing Constraint under CARA 2279 Changing Prudence and Risk Aversion 271Bibliography 281iiiContentsI Trade with Imperfect Competition and Heterogeneous Firms 11 An “Almost Static” Model with Fixed Export Costs 31.1 The Melitz (2003) Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Autarky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Topics in Dynamic Macroeconomic Theory: On the Causes and
Consequences of Income Growth and Uncertainty
Dissertation
zur Erlangung des Grades eines Doktors der Wirtschaftswissenschaft
eingereicht an der
Wirtschaftswissenschaftlichen Fakult¨at
der Universit¨at Regensburg
vorgelegt von
Christian Bauer
Berichterstatter:
Prof. Dr. Lutz Arnold (Universit¨at Regensburg)
Prof. Dr. Alfred Maußner (Universit¨at Augsburg)
Tag der Disputation: 30.10.2008Overview
I Trade with Imperfect Competition and Heterogeneous Firms 1
1 An “Almost Static” Model with Fixed Export Costs 3
2 Melitz (2003) with Pareto-Distributed Productivities 43
3 A Dynamic Model of Growth and Trade 57
II On the Growth and Welfare Effects of Monopolistic Competition 119
4 Monopolistic Competition and Endogenous Growth 121
5 Monopolistic Distortions and Growth Reconsidered 151
III Idiosyncratic Income Risk and the Labor Market 171
6 Labor Market Matching with Savings 173
7 Optimal Unemployment Policy 209
8 Job Search with Borrowing Constraint under CARA 227
9 Changing Prudence and Risk Aversion 271
Bibliography 281
iiiContents
I Trade with Imperfect Competition and Heterogeneous Firms 1
1 An “Almost Static” Model with Fixed Export Costs 3
1.1 The Melitz (2003) Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Autarky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 The Autarky Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.3 Who Pays for Entry?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3 Open Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.1 Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3.3 The Impact of Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.4 Measured Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.4 A Remark on the ZCP Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Appendix 1.A Substituting for Firms with Productivity Levels . . . . . . . . . . . . . . . . 39
Appendix 1.B Existence and Uniqueness of the Equilibrium . . . . . . . . . . . . . . . . . 40
1.B.1 Existence and Uniqueness of the Autarky Equilibrium . . . . . . . . . . . . . . 40
1.B.2 Existence and Uniqueness of the Equilibrium with International Trade . . . . . 41
2 Melitz (2003) with Pareto-Distributed Productivities 43
2.1 Autarky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1.1 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1.2 The Autarky Equilibrium under the Pareto Distribution . . . . . . . . . . . . . 45
2.1.3 On the Impact of Fixed Production and Entry Costs on the Cutoff . . . . . . . 46
2.2 Open Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
iii2.2.1 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 Equilibrium with International Trade . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.3 Who Wins from Trade Liberalization? . . . . . . . . . . . . . . . . . . . . . . . 53
Appendix 2.A The Distribution of Input Coefficients . . . . . . . . . . . . . . . . . . . . . 56
3 A Dynamic Model of Growth and Trade 57
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Heterogeneous Firms, Trade, and the Jones (1995) Model . . . . . . . . . . . . 61
3.3.3 Autarky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.4 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.5 Aggregation for a Given Cutoff . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3.6 The Equilibrium Cutoff Productivity . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.7 Properties of the Autarky Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.8 Balanced Growth Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4 Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.1 Open Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.4.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.5 Trade Liberalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.5.1 Cutoffs and Industry Reallocation . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.5.2 Labor Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.5.3 Trade Liberalization and the Incentives to Innovate. . . . . . . . . . . . . . . . 113
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
∗ ∗ ∗ ∗Appendix 3.A Derivation of ν , z , l , and γ . . . . . . . . . . . . . . . . . . . . . . . . . 116
II On the Growth and Welfare Effects of Monopolistic Competition 119
4 Monopolistic Competition and Endogenous Growth 121
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2 The Grossman and Helpman (1991b, Ch. 3) Model . . . . . . . . . . . . . . . . . . . . 122
iv4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.2.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2.3 Producers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.2.4 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.2.5 Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3.1 No Endogenous Growth in the Long-Run . . . . . . . . . . . . . . . . . . . . . 131
4.3.2 Sustainable Growth with Knowledge Spillovers . . . . . . . . . . . . . . . . . . 134
4.4 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.4.1 Static Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.4.2 Dynamic Allocation with Perfectly Appropriable Knowledge . . . . . . . . . . . 140
4.4.3 Dynamic Allocation with Knowledge Externalities . . . . . . . . . . . . . . . . 142
4.5 R&D Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.5.1 R&D Subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.5.2 Inefficacy of Sales Subsidies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.6 Scale Effects in the Grossman-Helpman (1991b, Ch. 3) Model . . . . . . . . . . . . . . 147
Appendix 4.A Rational Expectations and Diverging Trajectories . . . . . . . . . . . . . . . 150
5 Monopolistic Distortions and Growth Reconsidered 151
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Appendix 5.A Imitation Acts Like Additional Discounting . . . . . . . . . . . . . . . . . . 170
III Idiosyncratic Income Risk and the Labor Market 171
6 Labor Market Matching with Savings 173
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.2 A Baseline Model of Matching with Savings . . . . . . . . . . . . . . . . . . . . . . . . 178
v6.2.1 An Individual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.2.2 Optimal Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.3 The Euler Equation in Continuous-Time Matching and Saving Problems . . . . . . . . 185
6.3.1 Deriving the Evolution of the Costate Variable . . . . . . . . . . . . . . . . . . 185
6.3.2 Deriving the General Consumption Euler Equation . . . . . . . . . . . . . . . . 186
6.4 Consumption and Wealth Dynamics under CRRA . . . . . . . . . . . . . . . . . . . . 188
6.4.1 Consumption and Wealth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.4.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Appendix 6.A Derivation of the System of Partial Differential Equations . . . . . . . . . . 197
Appendix 6.B Existence and Uniqueness of the Wealth Thresholds . . . . . . . . . . . . . 197
Appendix 6.C Endogenous Reservation Wages . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.C.1 Derivation of the HJB Equation with Reservation Wage . . . . . . . . . . . . . 198
6.C.2 The Reduced Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Appendix 6.D Technical Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.D.1 On the Boundary Conditions of the General Model . . . . . . . . . . . . . . . . 202
6.D.2 No “Typical” Closed-Form Solution in the Baseline Model . . . . . . . . . . . . 205
6.D.3 Matching with Savings under CARA: A Boundary Condition . . . . . . . . . . 206
7 Optimal Unemployment Policy 209
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
7.2 The Shimer and Werning (2008) Model . . . . . . . . . . . . . . . . . . . . . . . . . . 211
7.3 Optimal Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.3.1 Optimal Behavior under UIP I . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.3.2 Optimal Behavior under UIP II . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
7.4 Characterization of the Equilibrium under UIP I . . . . . . . . . . . . . . . . . . . . . 217
7.4.1 Exploring the Linear Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
7.5 Characterization of the Equilibrium under UIP II . . . . . . . . . . . . . . . . . . . . . 218
Appendix 7.A Derivation of the Expected Insurance Costs . . . . . . . . . . . . . . . . . . 221
Appendix 7.B Derivation of the Evolution of Utility . . . . . . . . . . . . . . . . . . . . . . 222
Appendix 7.C Recursive Formulation of the Participation Constraint . . . . . . . . . . . . 223
Appendix 7.D Derivation of the Insurance Costs under UIP I and CARA . . . . . . . . . . 223
viAppendix 7.E A Useful Property of CARA . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
8 Job Search with Borrowing Constraint under CARA 227
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
8.3 The Case without a Wage Offer Distribution . . . . . . . . . . . . . . . . . . . . . . . 231
8.3.1 A Closed-Form Solution without a Borrowing Constraint . . . . . . . . . . . . 231
8.3.2 The Intertemporal Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . 233
8.3.3 Optimal Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
8.4 Wage Distribution and Reservation Wage . . . . . . . . . . . . . . . . . . . . . . . . . 238
8.4.1 The Closed-Form Solution without a Borrowing Constraint . . . . . . . . . . . 238
8.4.2 The Intertemporal Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . 240
8.4.3 Optimal Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Appendix 8.A Deriving an Intertemporal Budget Constraint . . . . . . . . . . . . . . . . . 252
Appendix 8.B Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
8.B.1 Consumption and Wealth Paths in the Job Search Model . . . . . . . . . . . . 254
8.B.2 Changing the Attitude Towards Risk . . . . . . . . . . . . . . . . . . . . . . . . 265
Appendix 8.C On the Agency’s Problem if Unemployment is Temporary . . . . . . . . . . 267
9 Changing Prudence and Risk Aversion 271
9.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
9.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
9.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
9.4 The Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
9.5 The Interaction of Changes in Prudence and Risk Aversion . . . . . . . . . . . . . . . 275
9.6 An Impossibility Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
9.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Bibliography 281
viiviii