Economic Modeling and Inference

Preface xiii Chapter 1: Introduction 1 1.1 Expected Utility Theory 1 1.2 Uncertainty Aversion, Ellsberg and Allais 4 1.3 Structural Versus Reduced-Form Methods 6 1.4 Exercises 7 1.5 References 8 Chapter 2: Components of a Dynamic Programming Model 9 2.1 Examples 9 2.2 Data Configurations 13 2.3 The Objective Function 16 2.4 The State Variables 17 2.5 The Control Variables 18 2.6 The Transition Distribution 19 2.7 The Curse of Dimensionality 21 2.8 The Curse of Degeneracy 22 2.9 Exercises 24 2.10 References 25 Chapter 3: Discrete States and Controls 26 3.1 Solving DP Problems: Finite Horizon 26 3.2 Solving DP Problems: Infinite Horizon 30 3.2.1 The Method of Successive Approximation 32 3.2.2 The Method of Policy Iteration 34 3.3 Identification: A Preview 35 3.4 Exercises 37 3.5 References 37 Chapter 4: Likelihood Functions for Discrete State/Control Models 38 4.1 Likelihood with Complete Observability 38 4.2 Measurement Error 45 4.3 Imperfect Control 51 4.4 Conclusions 54 4.5 Exercises 55 4.6 References 55 Chapter 5: Random Utility Models 57 5.1 Introduction 57 5.2 The Value Function 59 5.3 A Binary Utility Shock 60 5.4 A Continuously Distributed Utility Shock 62 5.5 Choice Probabilities 65 5.6 Dynamic Continuous Random Utility 66 5.7 Exercises 69 5.8 References 70 Chapter 6: Continuous States, Discrete Controls 71 6.1 Introduction 71 6.2 Transition Distributions and Utility 73 6.3 The Value Function and Backward Recursion 74 6.4 Example: Exercising an American Option 76 6.5 Infinite Horizon: Contraction and Forward Recursion 79 6.6 Example: Optimal Stopping in Discrete Time 83 6.7 Exercises 85 6.8 References 85 Chapter 7: Econometric Framework for the Search Model 87 7.1 The Search Model 87 7.2 Likelihood: General Considerations 89 7.3 Likelihood: Specifics for Wage Data 94 7.3.1 Wage Data Alone--One Parameter 96 7.3.2 Wage Data--Two Parameters 97 7.3.3 Wage Data Alone--Offer Arrival Probability 99 7.4 Likelihood: Wage and Duration Data 100 7.4.1 Wage and Duration Data--Two Parameters 100 7.4.2 Wage and Duration Data--Three Parameters 102 7.4.3 Wage and Duration Data--Gamma Distribution 104 7.5 Exercises 107 7.6 References 108 Chapter 8: Exact Distribution Theory for the Job Search Model 109 8.1 Introduction 109 8.2 The Prototypal Search Model 110 8.3 Alternative Economic Parametrizations 115 8.4 Models for Joint Wage and Duration Data 122 8.5 Conclusion 127 8.6 Exercises 128 8.7 References 128 Chapter 9: Measurement Error in the Prototypal Job Search Model 129 9.1 Introduction 129 9.2 The Prototypal Search Model 130 9.3 The Prototypal Model with Measurement Errors 132 9.4 Characterizing the Distribution of Measurement Errors 134 9.5 Estimation in the Prototypal Model with Measurement Errors 136 9.6 Application to the SIPP Data Set 139 9.7 Conclusions 146 9.8 Exercises 146 9.9 References 147 Chapter 10: Asset Markets 148 10.1 Introduction 148 10.2 General Asset Pricing 148 10.3 The Term Structure of Interest Rates 150 10.4 Forward Contracts 154 10.5 Futures Contracts 156 10.6 Introduction to Options 160 10.7 The Binomial Method 162 10.8 Empirical Applications 166 10.8.1 Time Series Properties 167 10.8.2 Portfolio Models 174 10.8.3 Time-Varying Volatility 181 10.8.4 Term Structure Analysis 184 10.9 Exercises 191 10.10 References 191 Chapter 11: Financial Options 192 11.1 Introduction 192 11.2 Financial Option Exercise and Job Search 192 11.3 Multiple Finite-Horizon Options 194 11.4 Markov Stock Prices 196 11.5 Value Functions for American Options 199 11.6 Option Price Data 205 11.7 Testing Option Market Efficiency 208 11.8 Exercises 212 11.9 References 212 Chapter 12: Retirement 213 12.1 Introduction 213 12.2 A Simple Retirement Model 213 12.3 The Likelihood Function 216 12.4 Longitudinal Data 221 12.5 Regularizing the Likelihood 224 12.6 Generalizations 232 12.7 Alternative Models 236 12.8 Application: The Joint Retirement of Married Couples 240 12.9 Exercises 242 12.10 References 243 Chapter 13: Continuous States and Controls 244 13.1 Introduction 244 13.2 The Linear-Quadratic Model: Finite Horizon 245 13.2.1 An Application: Macroeconomic Control 247 13.2.2 Rational Expectations 248 13.3 The Linear-Quadratic Model: Infinite Horizon 249 13.3.1 Application: Macro Policy with Rational Expectations 250 13.4 Estimation of Linear-Quadratic Models 251 13.4.1 The Curse of Degeneracy 251 13.4.2 Sources of Noise 251 13.4.3 Measurement Error 253 13.4.4 Imperfect Control 253 13.4.5 Random Utility 254 13.5 The General (Non-LQ) Case 256 13.6 Smoothness: Euler Equations 260 13.7 Discussion and Examples 261 13.8 Random Utility in the General Case 264 13.9 Exercises 264 13.10 References 265 Chapter 14: Continuous-Time Models 266 14.1 Introduction 266 14.2 Optimal Stopping in Continuous Time 269 14.3 A Jump Process Application: Allocation of Time over Time 270 14.4 Dynamic Consumption and Portfolio Choice 274 14.5 Application: Changing Investment Opportunities 278 14.6 Derivatives, Hedging, and Arbitrage Pricing 281 14.7 Stochastic Volatility and Jumps 289 14.8 The Term Structure of Interest Rates in Continuous Time 298 14.9 Exercises 310 14.10 References 310 Chapter 15: Microeconomic Applications 312 15.1 Introduction 312 15.2 Bus Engine Replacement 313 15.3 Aircraft Engine Maintenance 314 15.4 Medical Treatment and Absenteeism 316 15.5 Nuclear Power Plant Operation 317 15.6 Fertility and Child Mortality 319 15.7 Costs of Price Adjustment 320 15.8 Schooling, Work, and Occupational Choice 322 15.9 Renewal of Patents 323 15.10 Marketing--Direct Mailing of Catalogs 324 15.11 Scrapping Subsidies and Automobile Purchases 326 15.12 On-the-Job Search and the Wage Distribution 327 15.13 Exercises 329 15.14 References 330 Chapter 16: Macroeconomic Applications 331 16.1 Consumption as a Random Walk 331 16.2 Consumption and Asset Returns 333 16.3 Dynamic Labor Demand 334 16.4 Time Inconsistency of Optimal Plans 336 16.5 Time to Build 338 16.6 Nonseparable Utility 339 16.7 Preferences of Monetary Authorities 341 16.8 Dynamic Labor Supply 342 16.9 Effects of U.S. Farm Subsidies 345 16.10 Exercises 346 16.11 References 346 Chapter 17: Finance Application: Futures Hedging 347 17.1 Hedging Strategies 347 17.2 Self-Financing Trading Strategies 350 17.3 Estimation 353 17.4 Exercises 359 17.5 References 359 Chapter 18: Intertemporal Asset Pricing 360 18.1 Introduction 360 18.2 Prices and Returns 361 18.3 Capital Asset Pricing Model 362 18.4 Estimation 363 18.5 A Structural Model 365 18.6 Asset Pricing Puzzles 369 18.7 Exercises 376 18.8 References 376 Chapter 19: Dynamic Equilibrium: The Search Model 377 19.1 Introduction 377 19.2 Homogeneous Equilibrium Search 378 19.3 Data Distribution and Likelihood 383 19.4 Panels with Partially Missing Observations 389 19.4.1 The Contribution of Unemployment Duration 390 19.4.2 The Contribution of Wages 390 19.4.3 The Contribution of Employment Duration 392 19.4.4 A Numerical Example 394 19.5 Geometric Information Decomposition 395 19.5.1 Destination State Information 400 19.6 Data and Summary Statistics 403 19.7 Empirical Results 406 19.8 Conclusion 414 19.9 Exercises 415 19.10 References 415 Chapter 20: Dynamic Equilibrium: Search Equilibrium Extensions 416 20.1 Introduction 416 20.2 Measurement Error in Wages 416 20.3 Heterogeneity in Productivity: The Discrete Case 420 20.4 Heterogeneity in Productivity: The Continuous Case 424 20.5 Conclusion 429 20.6 Exercises 429 20.7 References 429 Appendix: Brief Review of Statistical Theory 431 A.1 Introduction 431 A.2 Exponential Families 432 A.3 Maximum Likelihood 434 A.4 Classical Theory of Testing 437 References 441 Index 469