Index 275

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Contents
1 Overview 1
I Theory
2 Theory of Dynamic Programming 7
2.1 Overview 7
2.2 Indirect Utility 7
2.2.1 Consumers 7
2.2.2 Firms 8
2.3 Dynamic Optimization: A Cake-Eating Example 9
2.3.1 Direct Attack 10
2.3.2 Dynamic Programming Approach 12
2.4 Some Extensions of the Cake-Eating Problem 16
2.4.1 Infinite Horizon 16
2.4.2 Taste Shocks 20
2.4.3 Discrete Choice 22
2.5 General Formulation 24
2.5.1 Nonstochastic Case 24
2.5.2 Stochastic Dynamic Programming 29
2.6 Conclusion 31
3 Numerical Analysis 33
3.1 Overview 33
3.2 Stochastic Cake-Eating Problem 34
3.2.1 Value Function Iterations 34
3.2.2 Policy Function Iterations 40
3.2.3 Projection Methods 41
3.3 Stochastic Discrete Cake-Eating Problem 46
3.3.1 Value Function Iterations 47
3.4 Extensions and Conclusion 50
3.4.1 Larger State Spaces 50
3.5 Appendix: Additional Numerical Tools 52
3.5.1 Interpolation Methods 52
3.5.2 Numerical Integration 55
3.5.3 How to Simulate the Model 59
4 Econometrics 61
4.1 Overview 61
4.2 Some Illustrative Examples 61
4.2.1 Coin Flipping 61
4.2.2 Supply and Demand Revisited 74
4.3 Estimation Methods and Asymptotic Properties 79
4.3.1 Generalized Method of Moments 80
4.3.2 Maximum Likelihood 83
4.3.3 Simulation-Based Methods 85
4.4 Conclusion 97
II Applications
5 Stochastic Growth 103
5.1 Overview 103
5.2 Nonstochastic Growth Model 103
5.2.1 An Example 105
5.2.2 Numerical Analysis 107
5.3 Stochastic Growth Model 111
5.3.1 Environment 112
5.3.2 Bellman’s Equation 113
5.3.3 Solution Methods 115
5.3.4 Decentralization 120
5.4 A Stochastic Growth Model with Endogenous Labor
Supply 122
5.4.1 Planner’s Dynamic Programming Problem 122
5.4.2 Numerical Analysis 124
5.5 Confronting the Data 125
5.5.1 Moments 126
5.5.2 GMM 128
5.5.3 Indirect Inference 130
5.5.4 Maximum Likelihood Estimation 131
viii Contents
5.6 Some Extensions 132
5.6.1 Technological Complementarities 133
5.6.2 Multiple Sectors 134
5.6.3 Taste Shocks 136
5.6.4 Taxes 136
5.7 Conclusion 138
6 Consumption 139
6.1 Overview and Motivation 139
6.2 Two-Period Problem 139
6.2.1 Basic Problem 140
6.2.2 Stochastic Income 143
6.2.3 Portfolio Choice 145
6.2.4 Borrowing Restrictions 146
6.3 Infinite Horizon Formulation: Theory and Empirical
Evidence 147
6.3.1 Bellman’s Equation for the Infinite Horizon
Problem 147
6.3.2 Stochastic Income 148
6.3.3 Stochastic Returns: Portfolio Choice 150
6.3.4 Endogenous Labor Supply 153
6.3.5 Borrowing Constraints 156
6.3.6 Consumption over the Life Cycle 160
6.4 Conclusion 164
7 Durable Consumption 165
7.1 Motivation 165
7.2 Permanent Income Hypothesis Model of Durable
Expenditures 166
7.2.1 Theory 166
7.2.2 Estimation of a Quadratic Utility Specification 168
7.2.3 Quadratic Adjustment Costs 169
7.3 Nonconvex Adjustment Costs 171
7.3.1 General Setting 172
7.3.2 Irreversibility and Durable Purchases 173
7.3.3 A Dynamic Discrete Choice Model 175
8 Investment 187
8.1 Overview and Motivation 187
8.2 General Problem 188
Contents ix
8.3 No Adjustment Costs 189
8.4 Convex Adjustment Costs 191
8.4.1 Q Theory: Models 192
8.4.2 Q Theory: Evidence 193
8.4.3 Euler Equation Estimation 198
8.4.4 Borrowing Restrictions 201
8.5 Nonconvex Adjustment: Theory 202
8.5.1 Nonconvex Adjustment Costs 203
8.5.2 Irreversibility 208
8.6 Estimation of a Rich Model of Adjustment Costs 209
8.6.1 General Model 209
8.6.2 Maximum Likelihood Estimation 212
8.7 Conclusion 213
9 Dynamics of Employment Adjustment 215
9.1 Motivation 215
9.2 General Model of Dynamic Labor Demand 216
9.3 Quadratic Adjustment Costs 217
9.4 Richer Models of Adjustment 224
9.4.1 Piecewise Linear Adjustment Costs 224
9.4.2 Nonconvex Adjustment Costs 226
9.4.3 Asymmetries 228
9.5 The Gap Approach 229
9.5.1 Partial Adjustment Model 230
9.5.2 Measuring the Target and the Gap 231
9.6 Estimation of a Rich Model of Adjustment Costs 235
9.7 Conclusion 238
10 Future Developments 241
10.1 Overview and Motivation 241
10.2 Price Setting 241
10.2.1 Optimization Problem 242
10.2.2 Evidence on Magazine Prices 244
10.2.3 Aggregate Implications 245
10.3 Optimal Inventory Policy 248
10.3.1 Inventories and the Production-Smoothing
Model 248
10.3.2 Prices and Inventory Adjustment 252
10.4 Capital and Labor 254
x Contents
10.5 Technological Complementarities: Equilibrium
Analysis 255
10.6 Search Models 257
10.6.1 A Simple Labor Search Model 257
10.6.2 Estimation of the Labor Search Model 259
10.6.3 Extensions 260
10.7 Conclusion 263
Bibliography 265