Economic Modeling and Inference

by Bent Jesper Christensen, Nicholas M. Kiefer

Overview

Economic Modeling and Inference takes econometrics to a new level by demonstrating how to combine modern economic theory with the latest statistical inference methods to get the most out of economic data. This graduate-level textbook draws applications from both microeconomics and macroeconomics, paying special attention to financial and labor economics, with an emphasis throughout on what observations can tell us about stochastic dynamic models of rational optimizing behavior and equilibrium. Bent Jesper Christensen and Nicholas Kiefer show how parameters often thought estimable in applications are not identified even in simple dynamic programming models, and they investigate the roles of extensions, including measurement error, imperfect control, and random utility shocks for inference. When all implications of optimization and equilibrium are imposed in the empirical procedures, the resulting estimation problems are often nonstandard, with the estimators exhibiting nonregular asymptotic behavior such as short-ranked covariance, superconsistency, and non-Gaussianity. Christensen and Kiefer explore these properties in detail, covering areas including job search models of the labor market, asset pricing, option pricing, marketing, and retirement planning. Ideal for researchers and practitioners as well as students, Economic Modeling and Inference uses real-world data to illustrate how to derive the best results using a combination of theory and cutting-edge econometric techniques.

• Covers identification and estimation of dynamic programming models
• Treats sources of error--measurement error, random utility, and imperfect control
• Features financial applications including asset pricing, option pricing, and optimal hedging
• Describes labor applications including job search, equilibrium search, and retirement
• Illustrates the wide applicability of the approach using micro, macro, and marketing examples

Product Details

ISBN-13:	9781400833108
Publisher:	Princeton University Press
Publication date:	07/13/2021
Sold by:	Barnes & Noble
Format:	eBook
Pages:	488
File size:	4 MB

About the Author

Bent Jesper Christensen is professor of economics and management at the University of Aarhus in Denmark. Nicholas M. Kiefer is the Ta-Chung Liu Professor in Economics and Statistical Science at Cornell University.

Table of Contents

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

What People are Saying About This

Dale Mortensen

The authors do a splendid job of showing how to use stochastic dynamic optimization techniques to generate the implied distributions of observables needed for estimation. There are many interesting and useful examples included in the book, ranging from applications of the theory of job search to those of asset pricing theory. This book should be a reference for anyone interested in using dynamic economic models to make inferences about the world we observe.
— Dale Mortensen, Aarhus University, Denmark, and Northwestern University

Campbell

Dynamic programming is an organizing framework that has enabled economists to integrate economic theory with empirical analysis. Few textbooks reflect the integrated nature of contemporary research, but Christensen and Kiefer reveal the power of the dynamic programming approach in a wide variety of applications from job search to portfolio choice. Their new book will be invaluable to students who wish to participate in this exciting enterprise.
— John Y. Campbell, Harvard University

An

Economic Modeling and Inference blends economic theory and statistical inference in a seamless fashion. Every dynamic decision model is discussed with an eye for it to be fit with economic data. Every econometric inference tool is developed for the purpose of testing economic decision models. This book is long overdue. It will influence and benefit young economists for generations to come.
— Mark Y. An, Fannie Mae

Tim Bollerslev

An extremely ambitious and thought-provoking book, one that combines state-of-the-art economic theory with sophisticated econometric techniques. The dynamic programming framework brings together important results and recent developments in a unique, unified way. The book is sure to inspire many PhD students and empirically oriented researchers for years to come.
— Tim Bollerslev, Duke University

Tom Sargent

Christensen and Kiefer's excellent book shows how careful dynamic theory and econometrics go hand in hand, opening up new vistas in the areas of search theory, finance, and macroeconomics.
— Tom Sargent, New York University and the Hoover Institution

Yaw Nyarko

I have been looking for a book like this for quite a while. Economic Modeling and Inference is written for those who want to do applied work and actually apply this to real-life data or run simulations. This much-needed book fills a void. It is certainly a significant contribution to the field.
— Yaw Nyarko, New York University

From the Publisher

"Christensen and Kiefer's excellent book shows how careful dynamic theory and econometrics go hand in hand, opening up new vistas in the areas of search theory, finance, and macroeconomics."—Tom Sargent, New York University and the Hoover Institution

"There is no other book that mixes dynamic economic theory, statistical inference, and real quantitative applications like this one. Christensen and Kiefer will challenge the top tier of students and take them to the research frontier."—Robert Lucas, University of Chicago

"Dynamic programming is an organizing framework that has enabled economists to integrate economic theory with empirical analysis. Few textbooks reflect the integrated nature of contemporary research, but Christensen and Kiefer reveal the power of the dynamic programming approach in a wide variety of applications from job search to portfolio choice. Their new book will be invaluable to students who wish to participate in this exciting enterprise."—John Y. Campbell, Harvard University

"The authors do a splendid job of showing how to use stochastic dynamic optimization techniques to generate the implied distributions of observables needed for estimation. There are many interesting and useful examples included in the book, ranging from applications of the theory of job search to those of asset pricing theory. This book should be a reference for anyone interested in using dynamic economic models to make inferences about the world we observe."—Dale Mortensen, Aarhus University, Denmark, and Northwestern University

"An extremely ambitious and thought-provoking book, one that combines state-of-the-art economic theory with sophisticated econometric techniques. The dynamic programming framework brings together important results and recent developments in a unique, unified way. The book is sure to inspire many PhD students and empirically oriented researchers for years to come."—Tim Bollerslev, Duke University

"I have been looking for a book like this for quite a while. Economic Modeling and Inference is written for those who want to do applied work and actually apply this to real-life data or run simulations. This much-needed book fills a void. It is certainly a significant contribution to the field."—Yaw Nyarko, New York University

"Economic Modeling and Inference blends economic theory and statistical inference in a seamless fashion. Every dynamic decision model is discussed with an eye for it to be fit with economic data. Every econometric inference tool is developed for the purpose of testing economic decision models. This book is long overdue. It will influence and benefit young economists for generations to come."—Mark Y. An, Fannie Mae

Robert Lucas

There is no other book that mixes dynamic economic theory, statistical inference, and real quantitative applications like this one. Christensen and Kiefer will challenge the top tier of students and take them to the research frontier.
— Robert Lucas, University of Chicago

Editorial Reviews

"Economic Modeling and Inference offers a technically sophisticated grounding in the structural approach to analyzing data. The book does an excellent job of illustrating the wide range of questions that the empirical dynamic programming approach can tackle by explicitly bridging economic theory and econometrics. . . . Books such as these will undoubtedly help the structural paradigm more successfully compete in the market for applied econometric methodologies."—-Robert M. Sauer, Journal of Economic Literature

"Overall, the book is well structured and will be useful for many different purposes, ranging from a main text for a PhD-level course to practical guidance for researchers who do empirical work based on dynamic programming models."—-Dong-Hyuk Kim, Economic Record

From the Publisher

"Economic Modeling and Inference gives an excellent overview of dynamic modeling techniques in economics and fills an important gap among current textbooks. [It] is an excellent book, especially for graduate students in economics. . . . [I]t is also a must for economists who need a refresher course in dynamic modeling . . . [and] should also be on the bookshelf of practicing researchers interested in expanding the number of models used in their work."

Journal of the American Statistical Association

Economic Modeling and Inference offers a technically sophisticated grounding in the structural approach to analyzing data. The book does an excellent job of illustrating the wide range of questions that the empirical dynamic programming approach can tackle by explicitly bridging economic theory and econometrics. . . . Books such as these will undoubtedly help the structural paradigm more successfully compete in the market for applied econometric methodologies.

Journal of Economic Literature - Robert M. Sauer

Economic Modeling and Inference offers a technically sophisticated grounding in the structural approach to analyzing data. The book does an excellent job of illustrating the wide range of questions that the empirical dynamic programming approach can tackle by explicitly bridging economic theory and econometrics. . . . Books such as these will undoubtedly help the structural paradigm more successfully compete in the market for applied econometric methodologies.
— Robert M. Sauer

Journal of Economic Literature