THE ECONOMETRICS OF PANEL DATA

Advanced Studies In Theoretical and Applied Econometrics Volume 33

Managing Editors: A.J. Hughes Hallet, University of Strathclyde, Glasgow, United Kingdom J. Marquez, The Federal Reserve System, Washington, D.C., US.A.

Editorial Board: F.G. Adams, University of Pennsylvania, Philadelphia, US.A. P. Balestra, University of Geneva, Switzerland M.G. Dagenais, University of Montreal, Canada D. Kendrick, University of Texas, Austin, US.A. J.H.P. Paelinck, Netherlands Economic Institute, Rotterdam, The Netherlands R.S. Pindyck, Sloane School of Management, M.I. T., US.A. H. Theil, University of Florida, Gainesville, US.A. W. Welfe, University of Lodz, Poland

The titles published in this series are listed at the end of this volume.

The Econometrics of Panel Data A Handbook of the Theory with Applications Second Revised Edition

edited by

Laszl6 Matyas Monash University, Melboume and Budapest University of Economics

and

Patrick Sevestre ERUDITE, Universitli de Paris-Vakie-Mame

KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON

Library of Congress Cataloging-in-Publication Data

The Econometrics of panel data: handbook of the theory with applications / edited by Liszl6· Mityis and Patrick Sevestre. 2nd rev. ed.

p. cm. -- (Advanced studies in theoretfcal and applied econometrics: v. 33)

Includes bib 1 iographical references and index. ISBN -13 :978-94-01 0-6548-1 e-ISBN-13: 978-94-009-0137-7 DOl: 10.1007/978-94-009-0137-7

1. Econometrics. 2. Panel analysis. II. Sevestre, Patrick. III. Series. HB139.E319 1995 330' .01·5195--dc20

ISBN-13 :978-94-01 0-6548-1

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

Kluwer Academic Publishers incorporates the publishing programmes of

1. Mityis, Lisz 16.

D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.

Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A.

In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.

Printed on acid-free paper

All Rights Reserved © 1996 Kluwer Academic Publishers Softcover reprint of the hardcover 2rd edition 1996

95-25633

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

Contents

Preface 1

1. Formulation and Estimation of Econometric Models for Panel Data . . . . . . . . . . . . . . 3 (Marc Nerlove and Pietro Balestra)

1.1. History and Dynamics: How Should We View the Disturbances? ................... 5

1.2. Methodological Developments .......... 7 1.2.1. Maximum Likelihood Estimation of the Dynamic

Model ....................... 10 1.2.2. Other Methodological Issues ..... 15

1.3. Applications of Panel Data Econometrics 17 1.4. Conclusions 19 References . . . . . . . . . . . . . . . . . . . . 21

Part I. Linear Models . . . . . . . . . . . . . . . . . 23

2. Introduction to Linear Models for Panel Data 25 (Pietro Balestra)

2.1. The Nature of Panel Data 26 2.2. The Single Equation Model 27

2.2.1. General Specification . 27 2.2.2. Different Sets of Assumptions: An Overview of the

Different Models . . . . . . . . . . . . . . . . . . 28 2.2.2.1. Specification I: Ordinary Regression Model. 28 2.2.2.2. Specification II: Individual Regression Model 29 2.2.2.3. Specification III: SUR Model ..... 29 2.2.2.4. Specification IV: The Covariance Model 30 2.2.2.5. Specification V: The Error Components

Model .................. 30 2.2.2.6. Specification VI: The Random Coefficients

Model ................... 31 2.3. Extensions 32 References . . . . . 33

3. Fixed Effect Models and Fixed Coefficient Models 34 (Pietro Balestra)

3.1. The Covariance Model: Individual Effects Only . . . 34

vi Contents

3.1.1. Specification 34 3.1.2. Estimation . 36 3.1.3. Inference . . 37

3.2. The Covariance Model: Individual and Time Effects 38 3.2.1. Time Effects Only ..... 38 3.2.2. Time and Individual Effects 39 3.2.3. Inference . . 42 3.2.4. Consistency ......... 42

3.3. Extensions . . . . . . . . . . . . 43 3.3.1. Constant Variables in One Dimension 43 3.3.2. Variable Slope Coefficients . 45 3.3.3. Non-spherical Disturbances 47

References . . . . . . . . . . . . 49

4. Error Components Models 50 (Laszlo Matyas)

4.1. The Model . . . . . . . 51 4.2. Estimation Methods . . 53

4.2.1. The OLS Estimator 53 4.2.1.1. Individual Effects 53 4.2.1.2. Individual and Time Effects 54

4.2.2. The GLS Estimator . . . . . . . 55 4.2.2.1. Properties of the GLS Estimator for the Model

with Only Individual Effects ......... 57 4.2.2.2. The Properties of the GLS estimator for the

Model with Both Individual and Time Effects 58 4.2.3. The Within Estimator 58

4.3. The Estimation of the Variance Components and the FGLS . . . . . . . . . . . . . . . . . . . . . .. 60

4.3.1. Estimators for the Variance Components 60 4.3.1.1. Individual Effects . . . . . . 60 4.3.1.2. Individual and Time Effects .. 61

4.3.2. The Feasible GLS Estimator ... . 62 4.3.3. The Maximum Likelihood Estimator 64

4.3.3.1. Individual Effects . . . . . . 65 4.3.3.2. Individual and Time Effects 65

4.4. Hypothesis Testing 65 4.5. Extensions of the Model 69

4.5.1. Autocorrelation . 69 4.5.2. Heteroscedasticity 72

References . . . . . . . . . 74

Contents vii

5. Random Coefficients Models 77 ( Cheng Hsiao)

5.1. The Models 78 5.2. Sampling Approach 81 5.3. Bayesian Approach 85 5.4. A Random Coefficient Simultaneous Equation System 90 5.5. Random or Fixed Effects (Parameters) 93 References . . . . . . . . . . . . . . . . . . . . . 98

6. Linear Models With Random Regressors 100 (Patrick Sevestre and Alain Trognon)

6.1. IV and GMM Estimators: The General Setup 101 6.2. The Correlated Specific Effects Model . . . . 106

6.2.1. Properties of the Usual Estimators of a Static Model With Correlated Specific Effects 107

6.2.2. Instrumental Variables Estimation of a Static Model With Correlated Specific Effects. '" 109

6.2.3. Testing For Correlation Between the Regressors and the Specific Effects in Static Models . . . . 111

6.2.4. Dynamic Models ................. 113 6.3. Models With Measurement Errors and Simultaneous

Equations .......... 114 6.3.1. Measurement Errors 115 6.3.2. Simultaneous Equations 116

6.4. Conclusion 117 References . . . . . . . . . . 118

7. Dynamic Linear Models . . . . . . . . . . . . .. 120 (Patrick Sevestre and Alain Trognon)

7.1. Estimation of an Autoregressive Fixed Effects Model 122 7.1.1. Specification of the Model ............ 123 7.1.2. The Inconsistency of the LSDV (Within)

Estimator When T is Finite ........ 123 7.1.3. Instrumental Variables Estimation Methods 125

7.2. The Dynamic Error Components Model 130 7.2.1. The Model . . . . . . . . . . . . . . . . . . 130 7.2.2. The ,x-class Estimators . . . . . . . . . . . 131 7.2.3. Instrumental Variables and Generalized Method of

Moments Estimators ............... 133 7.2.4. Maximum Likelihood Estimators 136 7.2.5. The Chamberlain's 11' Matrix 138

7.3. Conclusion 141 References . . . . . . . . . . . . . . . 143

viii

8. Dynamic Linear Models for Heterogenous Panels (Hashem Pesaran, Ron Smith and Kyung So 1m)

8.1. The Model ...... . 8.2. Alternati,:,~ Estimators

8.2.1. Pooled Estimators 8.2.2. Mean Group Estimator 8.2.3. The Cross Section Estimator

8.3. Testing for Heterogeneity. . ... 8.3.1. Pooled Versus the Mean Group Estimators 8.3.2. Pooled Versus the Cross Section Estimators 8.3.3. Testing the Homogeneity Hypothesis by Means of

Instrument Admissibility Tests ... . . . . . . . 8.4. Monte-Carlo Results for Dynamic Heterogenous

Panels ...... . 8.5. Concluding Remarks Appendix References . . . . . . . .

9. Simultaneous Equations . . . . . . . . . . . . (J ayalakshmi Krishnakumar)

9.1. The Simultaneous Equation Model with Error Components Structure

9.1.1. The Structural Form' ..... . 9.1.1.1. Notation 9.1.1.2. The Stochastic Assumptions

9.1.2. The Reduced Form 9.1.2.1. Derivation ......... . 9.1.2.2. Interpretation ....... .

9.1.3. A Note on the Identification Problem 9.2. Estimation of the Reduced Form ..

9.2.1. Generalised Least Squares 9.2.2. Maximum Likelihood Estimation

9.3. Structural Form Estimation 9.3.1. Single Equation Instrumental Variables Method

9.3.1.1. Generalised Two Stage Least Squares . . . 9.3.1.2. Error Components Two Stage Least Squares

9.3.2. System Instrumental Variables Methods .... . 9.3.2.1. Generalised Three Stage Least Squares .. . 9.3.2.2. Error Components Three Stage Least Squares

9.3.3. Full Information Maximum Likelihood 9.3.4. A Brief Note on the Limited Information

Maximum Likelihood

Contents

145

147 148 148 155 157 159 160 162

163

164 168 170 195

196

197 197 197 198 200 200 201 202 203 203 205 207 207 207 210 211 211 213 214

219

Contents

9.4. Asymptotic Comparisons of the Various Structural Estimators . . . . . . . .

9.5. Small Sample Properties 9.6. Extensions . . . . . . . .

9.6.1. Simultaneous Equation Models with Correlated Specific Effects . . . . . . . . . . . . .

9.6.2. Simultaneous Equations with Random Coefficients . . . . . . . . . . . . . . .

9.6.3. Dynamic Simultaneous Error Component Model 9.6.3.1. The Model ............... . 9.6.3.2. Estimation Method . . . . . . . . . . . . . .

9.6.4. Simultaneous Error Component Models with Censored Endogenous Variables ........ .

9.6.4.1. The Model 9.6.4.2. Estimation

9.7. Conclusions References . . . . . . . .

10. Panel Data with Measurement Errors (Erik Bi!Z\rn)

10.1. Basic Model and Notation ...... . 10.1.1. The Basic Regression Model with Measurement

Error ............. . 10.1.2. Some Useful Probability Limits

10.2. Estimators for the Basic Model 10.2.1. Base Estimators ... 10.2.2. Aggregate Estimators ... 10.2.3. Difference Estimators

10.3. Model with Measurement Errors with an Error Components Structure .............. .

10.3.1. The Model ............... . 10.3.2. Bias of Base, Aggregate, and Difference

Estimators . . . . . . . . . . . . . . . . 10.3.3. Consistent Estimation ......... .

10.4. Model with Measurement Errors and Heterogeneity 10.4.1. The Model ................ . 10.4.2. Bias of Base and Aggregate Estimators 10.4.3. Estimation of >. and /-t. The GLS Method 10.4.4. Consistent Estimation .......... .

10.5. Models with Autocorrelated Measurement Errors 10.5.1. One Component Specification. The Model 10.5.2. One Component Specification. Bias of

Estimators . . . . . . . . . . . . . . . . .

ix

220 221 222

222

225 227 227 228

230 230 230 232 234

236

237

237 238 240 240 241 249

253 253

254 258 260 260 261 264 266 268 268

269

x Contents

10.5.3. One Component Specification. Consistent Estimation . . . . . . . . . . . . . . . . . 271

10.5.4. Three Components Specification. The Model 272 10.5.5. Three Components Specification. Bias of

Estimators ... . . . . . . . . . . . . . . . 272 10.5.6. Three Components Specification. Consistent

Estimation . . . 276 10.6. Concluding Remarks 278 References . . . . . . . . 279

11. Pseudo Panel Data ............. 280 (Marno Verbeek)

11.1. Estimation of a Linear Fixed Effects Model 281 11.2. An Instrumental Variables Interpretation 286 11.3. Estimation of Linear Dynamic Models 288 11.4. Concluding Remarks 290 References . . . . . . . . 292

12. Specification Issues ................. 293 (Badi H. Baltagi)

12.1. Misspecifying the Order of the Error Components Model ....................... 293

12.2. Error Components Versus a Kmenta- Type Error Structure . . . . . . . . . . . . . . . . . . . . . . 295

12.3. Hausman's Specification Test ............ 298 12.4. Other Diagnostics for the Error Components Model 303 References . . . . . . . . . . . . . . . . . . . . . . . . .. 305

13. The Pooling Problem . . . . . . . . . 307 (G.S. Maddala and Wan hong Hu)

13.1. The Pretest and Stein-Rule Methods 308 13.2. The Random Coefficient Approach to Pooling 309

13.2.1. The Classical Approach . . . . . . . . . . 310 13.2.2. The Bayesian Approach . . . . . . . . . . 311 13.2.3. Some Comments on the Predictive Approach 313

13.3. Empirical Bayes Approach and Comparison With the Bayesian Approach ............... 314

13.3.1. Estimation of the Heterogeneity Parameter 315 13.3.2. The Issue of Bayes vs. Empirical Bayes 316

13.4. Subset Pooling ................. 316 13.5. Pooling With Time Varying Parameters 318 13.6. Bayesian Model Selection Approach to Pooling 320 References . . . . . . . . . . . . . . . . . . . . . . . 321

Contents

14. The Chamberlain Approach . . . . . . . (Bruno Crepon and Jacques Mairesse)

14.1. The Chamberlain II Matrix Framework . 14.1.1. The II Matrix ........... . 14.1.2. Relations Between II and the Parameters of

Interest ....... . 14.1.3. Four Important Cases .

14.1.3.1. Correlated Effects . 14.1.3.2. Errors in Variables 14.1.3.3. Weak Simultaneity 14.1.3.4. Lagged Dependent Variables

14.1.4. Restrictions on the Covariance Matrix of the Disturbances . . . . . . . . . . . . . .

14.1.5. An Extended View of the Chamberlain Methodology . . . . . . . . . . . . .

14.1.5.1. General Formulation ..... . 14.1.5.2. Simultaneous Equations Models 14.1.5.3. VAR Models .......... . 14.1.5.4. Endogenous Attrition ... . . .

14.1.6. The Vector Representation of Equations Between Moments and Parameters . . .

14.1.7. The Estimation of II .............. . 14.1.7.1. Estimation of the II Matrix ........ . 14.1.7.2. Joint Estimation of the II Matrix and Other

Moments ......... . 14.2. Asymptotic Least Squares

14.2.1. ALS Estimation ....... . 14.2.1.1. Basic Result ....... . 14.2.1.2. Application to the Chamberlain Approach

14.2.2. The Optimal ALS Estimator ........ . 14.2.2.1. Implementation of the Optimal ALS

Estimation . . . . . . . . . . . . . . . . . . 14.2.2.2. Finite Sample Properties of the Optimal ALS

Estimator ................ . 14.2.3. Specification Testing in the ALS Framework . .

14.2.3.1. Andrews' Problem ............. . 14.2.4. Manipulation of Equations and Parameters in the

ALS Framework . . . . . . . . . . . . . . . . . 14.2.4.1. 'Ifansformation of the Estimating Equations 14.2.4.2. Eliminating Parameters of Secondary

Interest ................... . 14.2.4.3. Recovering Parameters of Secondary Interest

Once Eliminated . . . . . . . . . . . . . . . 14.2.4.4. Elimination of Auxiliary Parameters . . . .

xi

323

324 324

326 329 329 329 330 331

331

333 333 334 335 336

337 338 339

339 340 340 341 341 342

343

344 345 345

347 347

348

349 352

xii Contents

14.3. The Equivalence of the GMM and the Chamberlain Methods ....................... 353

14.3.1. A Reminder on the GMM . . . . . . . . . . .. 354 14.3.2. Equivalence of the GMM and the Chamberlain

Methods ........... 355 14.3.3. Equivalence in Specific Cases 356

14.3.3.1. Correlated Effects . 357 14.3.3.2. Errors in Variables 357 14.3.3.3. Weak Simultaneity 358 14.3.3.4. Restriction on the Variance Matrix of the

Disturbances ..... 14.4. Monte-Carlo Simulations

14.4.1. Design of the Simulations 14.4.2. Consistency and Bias 14.4.3. Efficiency and Robustness 14.4.4. Standard Errors . 14.4.5. Specification Tests

Appendix References . . . . . . . . . .

Appendix: Matrix Algebra for Linear Models

Part II. Nonlinear Models . . . . . . .

359 360 360 362 364 365 367 379 390

392

397

15. Introduction to Nonlinear Models 399 (Christian Gourieroux)

15.1. Examples of Nonlinear Models 399 15.2. The Heterogeneity Bias 402 15.3. Integrating Out the Heterogeneity Factor 404 15.4. Testing for Neglected Heterogeneity 405 15.5. Prediction of Individual Effects 407 15.6. Outline of Part II 408

16. Logit and Probit Models 410 (Cheng Hsiao)

16.1. Probit and Logit Models 411 16.2. Estimation of the Fixed Effects Model 414

16.2.1. Maximum Likelihood Estimator 414 16.2.2. Conditional Maximum Likelihood Estimator 416 16.2.3. Semi-Parametric Estimator . . . . 419

16.3. Estimation of Random Effects Models 420 16.4. Test for Heterogeneity ......... 423

Contents xiii

References 427

17. Nonlinear Latent Variable Models (Cheng Hsiao)

429

17.1. The Model ............ . 17.2. Models that are Nonlinear in Parameters But Linear

in Variables 17.3. Models Nonlinear-in-Variables ........ .

17.3.1. Inconsistency of the Instrumental Variables Estimator ................. .

17.3.2. Maximum Likelihood and Minimum Distance

430

431 433

433

Estimators . . . . . . . . . . . . . 434 17.3.3. A Two-Step Estimation Procedure 435 17.3.4. Approximate MLE . . . . 436 17.3.5. Bias Adjusted Estimator 437

17.4. Binary Choice Models 440 17.4.1. The Model . 440 17.4.2. Identification 441 17.4.3. Estimation 443

17.5. Conclusions 445 References . . . . . . 446

18. Incomplete Panels and Selection Bias 449 (Marno Verbeek and Theo Nijman)

18.1. Nonresponse in Panel Data 450 18.1.1. Classification of Nonresponse .. 451 18.1.2. Conclusion .. . . . . . . . . . . 453

18.2. Ignorable and Non-ignorable Selection Rules 453 18.2.1. Definitions of Ignorability . . . . . . . . 454 18.2.2. Examples of Ignorable and Non-Ignorable

Nonresponse . . . . . . . . . . . . . . . . 455 18.2.3. Further Refinements of Ignorability 457 18.2.4. Example: a Simple Model of Nonresponse in

Panel Data . . . . . . . . . . . . . . . . 459 18.3. Estimation with an Ignorable Selection Rule 460

18.3.1. Maximum Likelihood .......... 460 18.3.2. The EM Algorithm .......... 464

18.4. Identification with a Non-Ignorable Selection Rule 466 18.5. Panel Data Regression Models with Non-Ignorable

Nonresponse .. . . . . . . . . . . . . . . . . . . . 470 18.5.1. Sufficient Conditions for Consistency of the

Standard Fixed and Random Effects Estimators 470 18.5.2. A Consistent Two-step Estimator for the

Random Effects Regression Model ....... 472

xiv Contents

18.5.3. ML Estimation of a Random Effects Model with Selection Bias .................. 474

18.5.4. Consistent Estimation of a Fixed Effects Model with Selection Bias ..... 475

18.6. Testing for Non-Ignorability . . . 477 18.6.1. The Lagrange Multiplier Test 477 18.6.2. Quasi-Hausman Tests . . . . 479 18.6.3. Variable Addition Tests . . . 480

18.7. Some Examples of Selection Problems in Panel Data 481 18.7.1. Attrition in Experimental Data . . . 482 18.7.2. Real Wages Over the Business Cycle 483

18.8. Concluding Remarks 485 References . . . . . . . 487

19. Duration Models 491 (Jean-Pierre Florens, Denis Fougere and Michel Mouchart)

19.1. Marginal Models .. , . . . . . . . . . . . 493 19.1.1. Distribution and Survivor Functions . 493

19.1.1.1. General Definitions and Properties 493 19.1.1.2. (Absolutely) Continuous Case 494 19.1.1.3. Discrete Case ........... 495 19.1.1.4. Remarks .......... . . . . 496

19.1.2. Truncated Distributions and Hazard Functions 496 19.1.2.1. Motivations ......... 496 19.1.2.2. Hazard Functions ............. 497 19.1.2.3. Truncated Survivor Function . . . . . . . 499 19.1.2.4. Truncated Expected Duration (Expected

Residual Life) ................ 500 19.1.3. Some Useful Distributions for Duration Data 501

19.1.3.1. Exponential Distribution 502 19.1.3.2. Gamma Distribution 503 19.1.3.3. The Weibull Distribution 504 19.1.3.4. The log-normal Distribution 505 19.1.3.5. The Log-logistic Distribution 505 19.1.3.6. Other Distributions 507

19.1.4. Derived Distributions ...... 507 19.1.4.1. Basic Ideas . . . . . . . . . . 507 19.1.4.2. Homethetic Transformation of the Hazard

Function ................... 508 19.1.4.3. Transformation of Time . . . . 508

19.2. Conditional Models .......... 510 19.2.1. Proportional Hazard or Cox Model 512

Contents xv

19.2.1.1. Definition ......... 512 19.2.1.2. Identification ....... 513 19.2.1.3. Semi-parametric Modelling 513 19.2.1.4. A Particular Case 514

19.2.2. Accelerated Life ........ 515 19.2.2.1. The Basic Idea ...... 515 19.2.2.2. Empirical Test for the Accelerated Time

Model .................... 515 19.2.2.3. Regression Representation of the Accelerated

Time Model ................. 515 19.2.3. Aggregation and Heterogeneity . . . . . . . .. 516

19.3. Competing Risks and Multivariate Duration Models 518 19.3.1. Multivariate Durations .......... 519 19.3.2. Competing Risks Models: Definitions . . . 522 19.3.3. Identifiability of Competing Risks Models 526 19.3.4. Right-censoring .............. 527 19.3.5. Dependent Bivariate Duration Distributions 529

19.3.5.1. Marshall-Olkin Class of Distributions 529 19.3.5.2. Gamma Mixture Models 531 19.3.5.3. Positive Stable Mixture Models 533

19.4. Conclusions 534 References . . . . . . 535

20. Point Processes ............... 537 (Jean-Pierre Florens and Denis Fougere)

20.1. Probability Tools . . . . . . . . . . . . . . 538 20.1.1. Point Processes and Counting Processes 538 20.1.2. Distribution of Point and Counting Processes 540 20.1.3. Stochastic Intensity and Compensator .... 542 20.1.4. The Likelihood Function of a Counting Process 543 20.1.5. Two Examples: Poisson and Bivariate Duration

Models .. . . . . . . . . . . . 544 20.2. Markov Processes ......... 547

20.2.1. Definitions and Basic Concepts 547 20.2.2. Distributions Related to a Time-Homogeneous

Standard Markov Process . . . . . . . . . . 549 20.2.3. Statistical Inference for Time-Homogeneous

Markov Models ............... 553 20.2.4. Marginalization of Markov Processes: State

Aggregation and Heterogeneity . . . . . . . 556 20.2.4.1. State Aggregation . . . . . . . . . . . . 556 20.2.4.2. Mixing Distributions on Markov Processes 560

20.2.5. Semi-Markov Processes ............ 562

xvi

20.3. A General Semi-Parametric Approach to Point Processes .................... .

20.3.1. Description of the Model ......... . 20.3.2. The Cox Likelihood ............. . 20.3.3. The Martingale Estimation of the Integrated

Baseline Intensity 20.4. Conclusions References . . . . . . . . . .

21. Improved Estimation Procedures (Offer Lieberman and Laszlo Matyas)

21.1. Integrating Out the Individual Effects 21.1.1. Small-sigma Asymptotics 21.1.2. Laplace Approximation 21.1.3. Discussion

21.2. Applications 21.2.1. Count Data 21.2.2. Duration Models 21.2.3. The Pro bit and Logit Models

21.3. Conclusion References . . . . . . . . . . . . . . . .

22. Some GMM Estimation Methods and

Contents

565 565 567

568 570 571

573

574 574 576 577 577 577 579 580 581 582

Specification Tests for Nonlinear Models 583 (Michael Lechner and Jorg Breitung)

22.1. GMM Estimation With Conditional Moment Restrictions .................. 584

22.1.1. Basic Notations and Assumptions of the Model 584 22.1.2. Estimation .. . . . . . . . . . . 586 22.1.3. Inference and Specification Tests 588

22.1.3.1. Introduction . . . . . . . . 588 22.1.3.2. Classical Tests . . . . . . . 589 22.1.3.3. Conditional Moment Tests 590

22.~. Applications to Panel Data 591 22.2.1. The Choice of Conditional Moments 592

22.2.1.1. Limited Dependent Variable Models 592 22.2.2. The Poisson Model 596 22.2.3. Fixed Effects . . . . . . . . . . . . . . . 596 22.2.4. Unbalanced Panels . . . . . . . . . . . . 598 22.2.5. Some Special GMM Estimators and the Choice of

Instruments ............... 599 22.2.6. Tests for the GMM Panel Probit .... 604

22.2.6.1. Tests Based on Explicit Alternatives 604

Contents

22.2.6.2. Tests Not Based on Explicit Alternatives 22.3. Conclusion References . . . . . . . . . .

23. Simulation Techniques ...... . (J ean-Franc;ois Richard)

23.1. Pseudorandom Number Generation 23.1.1. Univariate Distributions ..

23.1.1.1. Inversion . . . . . . . . 23.1.1.2. Rejection (Acceptance) 23.1.1.3. Decomposition .....

23.1.2. Multivariate Distributions . 23.1.2.1. Sequential Factorizations 23.1.2.2. Gibbs Sampling ..... 23.1.2.3. Conditional Independence

23.1.3. Additional Comments .... 23.2. Monte-Carlo Numerical Integration

23.2.1. Introduction ......... . 23.2.2. Randomized Monte-Carlo Procedures 23.2.3. Common Random Numbers

23.3. Efficient Monte-Carlo Sampling 23.3.1. Acceleration ..... .

23.3.1.1. Antithetic Variables .. 23.3.1.2. Control Variates .... 23.3.1.3. Conditional Expectations 23.3.1.4. Comment ....... .

23.3.2. Efficient Sampling . . . . . . 23.4. Simulation Based Inference Procedures

23.4.1. Integration In Panel Data Models 23.4.2. Simulated Likelihood ..... 23.4.3. Simulated Method of Moments . 23.4.4. Bayesian Posterior Moments

23.5. Numerical Properties of Simulated Estimators 23.6. Conclusion References . . . . . . . . . . . . . . . . . . . . . .

24. Inference in Panel Data Models via Gibbs Sampling ................... . (Siddhartha Chib)

24.1. The Gibbs Sampler ........... . 24.2. The Basic Panel Model ......... . 24.3. The Gaussian Model With Random Effects 24.4. Panel Probit Model With Random Effects

xvii

606 607 611

613

614 614 615 615 617 617 618 618 619 619 620 620 622 '625 626 627 627 627 627 628 628 630 630 631 632 633 634 636 637

639

639 641 644 646

xviii Contents

24.5. Extensions ...... 648 24.5.1. Missing Data . . . 648 24.5.2. Residual Analysis 648

24.6. Conclusion 649 References . . . . . . . . . . 650

Part III. Selected Applications 653

Introduction to the Applications 655 (Zvi Griliches)

References . . . . . . . . . . . . 659

25. Dynamic Labour Demand Models 660 (Georges Bresson, Francis Kramarz and Patrick Sevestre)

25.1. The General Framework . . . . . . . . . 662 25.2. Continuous Adjustment Costs Functions 665

25.2.1. Quadratric Costs .......... 665 25.2.2. Taking Into Account the Relative Variations of

Employment .. . . . . . . . . . . . . . 669 25.2.3. Taking Into Account the Asymmetry of

Adjustment Costs ........... 669 25.3. Discontinuous Adjustment Costs Functions 671

25.3.1. Fixed Costs Models .......... 671 25.3.2. Quadratic and Linear Asymmetric Costs 673

25.4. Labour Demand Models With Heterogeneous Workers ....................... 674

25.4.1. The Case When Only the Total Employment is Observable . . . . . . . . . . . . . . . . 674

25.4.2. The Case When Disaggregated Data on Employment is Available 677

25.5. Conclusion 679 References . . . . . . . . . . . . . . 682

26. Econometric Models of Company Investment 685 (Richard Blundell, Stephen Bond and Costas Meghir)

26.1. Economic Models of Investment . . . . 687 26.1.1. Adjustment Costs and Investment 688 26.1.2. The Q Model. . . . . . . . . . 690 26.1.3. The Abel and Blanchard model 694 26.1.4. The Euler Equation Approach 695

26.2. Sources of Data .......... 696

Contents

26.3. Econometric Methods 26.4. Selected Applications 26.5. Current Areas of Research 26.6. Conclusion References . . . . . . . . . . . .

27. Consumption Dynamics and Panel Data: A Survey ................... . (Jean-Marc Robin)

27.1. The Basic Life-cycle Consumption Model 27.2. Liquidity Constraints ......... . 27.3. Allowing for Durability ........ . 27.4. Allowing for Intra-temporal Substitution 27.5. Concluding Remarks References . . . . . . . . . . . . . . . . . . . .

28. Estimation of Labour Supply Functions Using Panel Data: A Survey ............ . (Franc;ois Laisney, Winfried Pohlmeier and Matthias Staat)

28.1. The Basic Model of Life Cycle Labour Supply 28.2. Relaxing the Assumptions of the Basic Model 28.3. Alternative Parameterization and Implications 28.4. Relaxing the Assumption of Intertemporal

Separa.bility in Preferences ............ . 28.5. Data Issues . . . . . . . . . . . . . . . . . . . . . 28.6. Overview of Qualitative and Quantitative Results 28.7. Concluding Comments References . . . . . . . . . . . . . . . . . . . .

29. Individual Labour Market Transitions (Denis Fougere and Thierry Kamionka)

29.1. Continuous-Time Discrete-State Models with Continuous-Time Observations ....... .

29.1.1. General Framework ............ . 29.1.2. Non-Parametric and Parametric Estimation

29.1.2.1. Non-Parametric Estimation

xix

699 703 705 707 708

711

712 715 721 727 729 731

733

734 738 744

749 755 760 766 767

771

772 773 777 777

29.1.2.2. Parametric Estimation . . . . . . 779 29.1.3. Heterogeneity and Correlation Between Spell~ 782

29.2. Markov Processes Using Discrete-Time Observations 786 29.2.1. The Time-Homogeneous Markovian Model 787

xx Contents

29.2.1.1. Maximum Likelihood Estimator of the Matrix P Using Discrete-Time (Multiwave) Panel Data . . . . . . . . . . . . . . . . .. 788

29.2.1.2. Necessary Conditions for Embeddability .. 789 29.2.1.3. Resolving the Equation P(O,T)= exp (QT) 789 29.2.1.4. The Scoring Procedure 791 29.2.1.5. Bayesian Inference 793 29.2.1.6. Tenure Records 794

29.2.2. The Mover-Stayer Model 796 29.2.2.1. MLE for the Discrete-Time Mover-Stayer

Model .................... 796 29.2.2.2. Bayesian Inference for the Continuous-Time

Mover-Stayer Model . . . . . . . . . . . .. 800 29.3. Concluding Remarks 805 References . . . . . . . . . . . . . . . . . . . . . . . . 806

30. Modelling Companies' Dividend Policy Using Account Panel Data ............... 810 (Jean-Francois MaIecot)

30.1. Theoretical Issues ........... 810 30.2. Behavioural Models of Dividend Policy 813 30.3. A Model of Corporate Dividend Policy 815 30.4. Conclusion 818 References . . . . . . . . . . . . . . . . . . . 821

31. Panel Data, Multinational Enterprises and Direct Investment . . . . . . . . . . . . . . . . . . . . . .. 823 (Claude Mathieu)

31.1. The Analytical Framework of Multinational Firms and Direct Investments ............... 824

31.1.1. Firm Specific Advantages and Market Imperfections .................. 824

31.1.1.1. Tariff-Jumping and 'fransfer of Firm Specific Advantage: The Horst-Buckley-Casson Model ................... 825

31.1.1.2. Direct Investment as an Entry Barrier on Local Markets: The Horstman-Markusen Model ................... 828

31.1.2. Country Differences and Sp~cific Risk of International Operations: Cuhsman's Model .. 830

31.2. From Theory to Measurement: Data Issues . . . .. 834 31.3. Econometric Models: Micro- and Macro-Economic

Determinants .................. 836 31.3.1. Direct Investment and Specific Firm Assets 836

Contents xxi

31.3.2. Direct Investment and Macro-Economic Factors 837 31.3.3. Direct Investment: Firm and Locational Factors 839

31.4. Concluding Remarks 841 References . . . . . . . . . . . . . . . . . . 842

32. Production Frontiers and Efficiency Measurement ..................... 845 (Christopher Cornwell and Peter Schmidt)

32.1. Measurement of Firm Efficiency . . . . . . . . . . 846 32.2. Introduction to the Estimation of Firm Efficiency 849

32.2.1. Deterministic Frontiers 850 32.2.2. Stochastic Frontiers .......... 851

32.2.2.1. The Basic Model ......... 851 32.2.2.2. Firm-Specific Efficiency Estimates 853 32.2.2.3. Duality and Allocative Efficiency . 853

32.3. Panel Data with Time-Invariant Inefficiency 855 32.3.1. Advantages of Panel Data 856 32.3.2. Fixed Effects . . . . . . . . . . . . . . . 857 32.3.3. Random Effects ............. 859 32.3.4. Joint Estimation of Technical and Allocative

Efficiency . . . . . . . . . . . . . . . . 861 32.3.5. Inference About Inefficiencies . . . . . 862

32.4. Panel Data with Time-Varying Efficiency 864 32.4.1. Intercepts Which Depend Linearly on

Observables .............. 865 32.4.2. Parametric Specification of the Temporal Pattern

of Inefficiency ................. 867 32.4.3. Unrestricted Temporal Pattern of Inefficiency 868

32.5. Applications ........... 869 32.5.1. Egyptian Tile Manufacturers 869 32.5.2. Indonesian Rice Farmers 871

32.6. Concluding Remarks 874 References . . . . . . 875

33. Software Review . . . . . . . . . . . 879 (Pierre Blanchard)

33.1. Panel Data Software: An Overview 881 33.1.1. GAUSS (Version 3.2 - 1994) with D.P.D.

Program (Version 9/89) . . . . . . 881 33.1.2. LIMDEP (Version 6.0 - 1992) . 886 33.1.3. PANMARK (Version 2.2 - 1991) 890 33.1.4. RATS (Version 4.10 - 1994) " 892 33.1.5. SAS (Version 6.08 for Windows - 1994) 895

xxii

33.1.6. TSP (Version 4.2B - 1993) . 33.2. Evaluation by Criteria . . . . . . 33.3. Performance Hints and Accuracy. 33.4. Conclusion ..... . Appendix ......... . Package's Editor References References

Index

Contents

899 901 908 910 911 912 913

914

Contributors

Pietro Balestra, University of Geneva and University of Bourgogne

Badi H. Baltagi, Texas A& M University

Erik Bif6rn, University of Oslo

Pierre Blanchard, ERUDITE, Universite de Paris-Val de Marne

Richard Blundell, University College London and Institute for Fiscal Studies

Stephen Bond, University of Oxford and Institute for Fiscal Studies

Jorg Breitung, Humboldt University

Georges Bresson, Universite Paris II and ERUDITE

Siddhartha Chib, Washington University

Christopher M. Cornwell, University of Georgia

Bruno Crepon, INSEE, Paris

Jean-Pierre Florens, Universite des Sciences Sociales, Toulouse

Denis Fougere, CREST and CNRS, Paris

Christian Gourieroux, CEPREMAP and CREST, Paris

Zvi Griliches, Harvard University

Cheng Hsiao, University of Southern California

Wanhong Hu, Ohio State University

Thierry Kamionka, Universite des Sciences Sociales, Toulouse

Francis Kramarz, INSEE, Paris

Jayalakshmi Krishnakumar, University of Geneva

Franc,;ois Laisney, Universite Louis Pasteur and ZEW, Mannheim

Michael Lechner, University of Mannheim

Offer Lieberman, Technion, Haifa

G.S. Maddala, Ohio State University

Jacques Mairesse, CREST, Paris

Jean-Franc;ois Malecot, Universite de Paris-Dauphine

Claude Mathieu, ERUDITE, Universite de Paris-Val de Marne

LaszlO Matyas, Monash University and Budapest University of Economics

Costas Meghir, University College London and Institute for Fiscal Studies

Michel Mouchart, Universite Catholique de Louvain

Marc Nerlove, University of Maryland

Theo Nijman, Tilburg University

Hashem Pesaran, University of Cambridge

Winfried Pohlmeier, University of Konstanz

Jean-Franc;ois Richard, University of Pittsburgh

Jean-Marc Robin, CREST, Paris

Patrick Sevestre, ERUDITE, Universite de Paris-Val de Marne

Peter Schmidt, Michigan State University

Ron Smith, Birkbeck College

Matthias Staat, University of Mannheim

Alain Trognon, GENES, INSEE, Paris

Marno Verbeek, Tilburg University

PREFACE

The aim of this volume is to provide a general overview of the econometrics of panel data, both from a theoretical and from an applied viewpoint. Since the pioneering papers by Edwin Kuh (1959), Yair Mundlak (1961), Irving Hoch (1962), and Pietro Balestra and Marc Nerlove (1966), the pooling of cross sections and time series data has become an increasingly popular way of quantifying economic relationships. Each series provides information lacking in the other, so a combination of both leads to more accurate and reliable results than would be achievable by one type of series alone.

Over the last 30 years much work has been done: investigation of the properties of the applied estimators and test statistics, analysis of dynamic models and the effects of eventual measurement errors, etc. These are just some of the problems addressed by this work. In addition, some specific diffi­culties associated with the use of panel data, such as attrition, heterogeneity, selectivity bias, pseudo panels etc., have also been explored.

The first objective of this book, which takes up Parts I and II, is to give as complete and up-to-date a presentation of these theoretical developments as possible. Part I is concerned with classical linear models and their extensions; Part II deals with nonlinear models and related issues: logit and pro bit models, latent variable models, duration and count data models, incomplete panels and selectivity bias, point processes, and simulation techniques.

The second objective is to provide insights into the use of panel data in empirical studies. Since the beginning, interest in panel data has been empirically based, and over time has become increasingly important in applied economic studies. This is demonstrated by growing numbers of conferences and special issues of economic journals devoted to the subject. Part III deals with studies in several major fields of applied economics, such as labour and investment demand, labour supply, consumption, transitions on the labour market, finance, research and development, foreign investment, and produc­tion frontiers.

The double emphasis of this book (theoretical and applied), together with the fact that all the chapters have been written by well-known specialists in the field, encourage us to hope that it will become a standard reference textbook for all those who are concerned with the use of panel data in econometrics, whether they are advanced students, professional economists or researchers.

The editors have tried to standardize the notation, language, depth, etc. in order to present a coherent book. However, each chapter is capable of standing on its own as a reference in its own topic.

2 Preface

Readers may wonder what has motivated a second, bulkier edition so soon, less than three years after the first. One consideration was that some topics, which since turned out to be important, received less attention in the first edition than deserved. The most important reason, however, has been the extraordinary evolution in the techniques and procedures available, especially for nonlinear models. While linear panel data modelling has given a signifi­cant boost to the development of numerous areas in theoretical and applied econometrics, we believe that nonlinear panel data models and methods are going to help to re-think and change the way we do econometrics.

* * *

We must address our thanks to all those who have facilitated the creation of this book: the contributors who, despite onerous instructions and tight deadlines, produced quality work, then took part in an internal refereeing process to ensure a high overall standard for the completed book; Kluwer Academic Publishers, who had the foresight to publish in a subject which, at the time of the first edition, had a limited, but expanding, audience; the University of Paris-Val de Marne in France; the Monash Research Fund and the Australian Research Council in Australia, and the Budapest University of Economics and the Hungarian Research Fund (aTKA) in Hungary, who provided financial support.

The original papers have been polished with the help of Beth Morgan, Karlis Rozenbergs and Sylvana Lau; most of the chapters have been typeset by Erika Mihalik.

The final camera-ready copy was prepared by the editors using 'lEX and the Initbook (Gabor Korosi and Laszlo Matyas) macro package.

LAsZL6 MATyAS and PATRICK SEVESTRE