Essays in Panel Data Econometrics

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ISBN: 9780521022460 | 0521022460
Cover: Paperback
Copyright: 11/10/2005

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This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent new essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role of the substantive context in shaping appropriate methods of inference and the increasing importance of computer-intensive methods.

Preface to the Book

xiii

1 The History of Panel Data Econometrics, 1861-1997

(114)

Preface

(3)

1. Introduction

(3)

2. In the Beginning: Astronomy, Agronomy, and Statistics

(10)

a. Fixed- versus Random-Effects Models

(1)

b. An Example in Which Mostly Fixed Effects Are Appropriate

(1)

c. An Example in Which Mostly Random Effects Are Appropriate; Airy's Problem

(3)

d. Fisher

(1)

e. Daniels and Eisenhart

(1)

f Further Development of the Statistical Literature

(3)

3. Econometric Development, the Early Years: From Chicago to the Paris Conference of 1977

(18)

a. Hildreth

(1)

b. Management Bias and the Estimation of Production Functions: Hoch and Mundlak

(3)

c. Balestra and Nerlove: Error Components and Dynamic Panel Models

(5)

d. Highlights of the Ten Years Preceding the First Paris Conference, 1967-1976

(9)

e. The First Paris Conference, 1977

(1)

4. Econometric Development, the Later Years: From Paris to Paris

(35)

a. Problems of Testing Specification: Fixed versus Random Effects; Serially Correlated Effects

(10)

(1) Hausman Tests

(3)

(2) Serially Correlated Remainder Effects

(2)

(3) Serially Correlated Period Effects

(5)

b. Dynamics: Comparative Properties of Alternative Estimators and the Problem of Initial Conditions

(12)

(1) Inconsistency of the Pooled-Sample OLS Estimates of the Dynamic Error-Components Model

(1)

(2) Inconsistency of the OLS Estimators of the Dummy Variable, or Fixed-Effects; Model

(1)

(3) Generalized Least Squares and Feasible GLS

(2)

(4) Maximum Likelihood and the Problem of Initial Observations

(6)

c. Estimation of Limited Dependent Discrete, and Qualitative Panel Data Models

(12)

(1) Incidental or Nuisance Parameters

(3)

(2) Logit and Probit Models

(5)

(a) Nondynamic Models

(3)

(b) Dynamic Models

(2)

(3) Limited Dependent Variables

(2)

(a) Nondynamic Models

(2)

(b) Dynamic Models

(1)

(4) Hazard and Duration Models

(1)

d. The Second Paris Conference, 1997

(1)

5. Beyond Paris

(13)

Appendices to Chapter 1

Appendix A: Decomposition of the Sum of Squares of a Variable Observed in a Two-Dimensional Panel

(3)

Appendix B: Alternative Formulations of the Concentrated Likelihood Function for the Two-Component Random-Effects Model

(6)

Appendix C: Introduction to The Econometrics of Panel Data, Colloque International du CN RS, INSEE, Paris 22-24 August 1977

(10)

Appendix D: Derivation of the Likelihood Function for the Three-Component Random-Effects Nondynamic Panel Model with Serially Correlated Period Effects

102

(3)

Appendix E: Likelihood for Stationary Panel Data-Generating Processes with Exogenous Variables and Individual-Specific Random Effects

105

(6)

Appendix F: Antemiya's Classification of Limited Dependent Variable or Tobit Models

111

(4)

2 Pooling Cross-Section and Time-Series Data in the Estimation of a Dynamic Model: The Demand for Natural Gas (with Pietro Balestra)

115

(34)

Preface

115

(5)

1. The Dynamic Model of Gas Demand

120

(3)

2. Estimation by Ordinary Least-Squares Methods

123

(4)

3. The Residual Model

127

(6)

4. Estimation Procedures

133

(11)

5. Conclusions 143 Appendix: Derivation of the Maximum-Likelihood Estimates of ρ and &sigma²

144

(5)

3 Experimental Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections

149

(40)

Preface

149

(4)

1. Background

153

(8)

2. Design of the Experiments

161

(8)

a. Generation of the Observations

161

(3)

b. Parameter Values

164

(1)

c. Methods of Estimation

164

(5)

3. The Results

169

(5)

a. Generalized Least Squares

171

(1)

b. Ordinary Least Squares

171

(1)

c. Least Squares with Individual Constant Terms

172

(1)

d. Maximum Likelihood

172

(1)

e. Two Round

173

(1)

f Comparison of Various Methods

173

(1)

4. Conclusions

174

(3)

Appendix: Parameter Values

177

(12)

4 Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections

189

(30)

Preface

189

(4)

1. Introduction

193

(7)

2. Design of the Experiments

200

(10)

a. Generation of the Observations

200

(5)

b. Parameter Values

205

(1)

c. Methods of Estimation

205

(5)

(1) Generalized Least-Squares Estimates Employing the True Value of p Used in the Generation of the Observations

205

(2)

(2) Ordinary Least-Squares Estimates of the Relation (2.1) (i.e., Not Including Individual Constant Terms)

207

(1)

(3) Least-Squares Estimates of the Parameters

207

(1)

(4) Instrumental-Variable Estimates Using xit-1 as an Instrument for yit-1

207

(1)

(5) "Two-Round" Estimates Equivalent to Generalized Least Squares Using Not the True Value of p but the Estimate rc Obtained in (3), a Least-Squares Regression with Individual Constant Terms

208

(1)

(6) "Two-Round" Estimates Similar to (5) but using an Estimate of p Based on the Calculated Residuals from the Instrumental-Variable Estimate of Equation (2.1) as Given in (2.17)

208

(1)

(7) Maximum-Likelihood Estimates Obtained by Maximizing the Logarithmic Likelihood Function

208

(2)

3. Comparative Properties of Different Estimation Procedures

210

(6)

a. Bias

210

(3)

b. Relative Mean-Square Errors

213

(1)

c. Characteristics of the Maximum-Likelihood Estimates

214

(2)

4. Conclusions

216

(3)

Appendices for Chapter 4 (Available in pdf Format at http://wwwarec.umd.edu/mnerlove/Tables1971.ZIP)

5 A Note on Error-Components Models

219

(18)

Preface

219

(2)

Errata

221

(1)

1. Introduction

222

(4)

2. The Characteristic Roots and Vectors of Ω

226

(2)

3. The Square Root of &Omega

228

(3)

4. The Inverse of Ω and the GLS Estimates of β

231

(2)

5. An Interpretation of β and Its Asymptotic Distribution

233

(4)

6 Growth-Rate Convergence, Fact or Artifact? An Essay on Panel Data Econometrics

237

(36)

Preface

237

(3)

1. Introduction

240

(2)

2. The Neoclassical Theory of Growth Convergence

242

(4)

a. The Solow/Swan Model

243

(1)

b. Growth Convergence in the Neoclassical Model with Exogenous Population Growth and Savings

244

(2)

3. Empirical Investigations of Convergence and the Rate of Convergence

246

(3)

4. Alternative Methods for Estimating Rates of Convergence

249

(11)

a. Inconsistency of the Pooled-Sample OLS Estimates of the Dynamic Error-Components Model

250

(1)

b. Inconsistency of the OLS Estimators of the Dummy Variable or Fixed-Effects Model

251

(1)

c. Country Means Regression and the Estimation of p

252

(1)

d. Generalized Least Squares and Feasible GLS

253

(1)

e. Bounds for the Coefficient of the Lagged Dependent Variable

254

(1)

f Maximum-Likelihood Conditional on the Initial Value of the Lagged Dependent Variable

255

(2)

g. Unconditional Maximum Likelihood

257

(3)

5. Empirical Evidence on Growth-Rate Convergence and the Comparative Performance of Different Panel Data Methods

260

(8)

a. Numerical Results

260

(5)

b. Graphical Results

265

(3)

6. Conclusions

268

(5)

Appendix

270

(3)

7 Properties of Alternative Estimators of Dynamic Panel Models: An Empirical Analysis of Cross-Country Data for the Study of Economic Growth

273

(32)

Preface

273

(1)

1. Introduction

274

(3)

2. Recent Empirical Investigations of Convergence and the Rate of Convergence

277

(4)

3. Alternative Methods for Estimation

281

(12)

a. Inconsistency of the Pooled-Sample OLS Estimates of the Dynamic Error-Components Model

282

(1)

b. Inconsistency of the OLS Estimators of the Dummy Variable or Fixed-Effects Model

283

(2)

c. Generalized Least Squares and Feasible GLS

285

(1)

d. Bounds for the Coefficient of the Lagged Dependent Variable

286

(1)

e. Maximum Likelihood Conditional on the Initial Value of the Lagged Dependent Variable

287

(2)

f Unconditional Likelihood and Unconditional Maximum Likelihood

289

(4)

4. Empirical Evidence on the Comparative Performance of Different Panel Data Methods

293

(6)

5. Conclusions

299

(6)

8 Likelihood Inference for Dynamic Panel Models

305

(44)

Preface

305

(3)

1. Introduction

308

(2)

2. The Likelihood Principle

310

(4)

3. Likelihood Functions for Two Basic Dynamic Panel Models

314

(12)

a. The Model in Levels

316

(7)

(1) Specification of the Joint Distribution of the Observations, Both Conditional and Unconditional on the Initial Observations

316

(5)

(2) The Joint Likelihood Conditional on the Initial Observations and the Exogenous Variables

321

(1)

(3) The Joint Likelihood Unconditional on the Initial Observations

322

(1)

b. The Model in First Differences

323

(3)

4. An Empirical Example: A Study of Cross-Country Economic Growth Using Panel Data

326

(23)

a. Recent Empirical Investigations

327

(4)

b. New Estimates Based on Maximizing the Conditional and Unconditional Likelihood Functions

331

(18)

Index

349

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Essays in Panel Data Econometrics

Summary

Table of Contents

Supplemental Materials