Preface

xxv

I Information Processing and Recovery

(32)

The Process of Econometric Information Recovery

(10)

Introduction

(1)

The Nature of Economic Data

(1)

The Probability Approach to Economics

(1)

The Process of Searching for Quantitative Economic Knowledge

(3)

Econometric Model Components

(2)

Econometric Analysis

(1)

The Inverse Problem

(1)

A Comment

(1)

Notation

(2)

Idea Checklist - Knowledge Guides

(1)

Probability-Econometric Models

(20)

Parametric, Semiparametric, and Nonparametric Models

(3)

Parametric Models

(1)

Nonparametric and Semiparametric Models

(2)

The Classical Linear Regression Model

(9)

Establishing a Linkage between Dependent and Explanatory Variables

(3)

The Distribution of Y around the Systematic Component

(1)

Inverse Problems: Estimation, Inference, and Interpretation

(1)

Some Variants of the Linear Regression Model

(4)

A Class of Probability Models

(2)

Class of Inverse Problems and Solutions

(1)

Concluding Comments

(1)

Exercises

(1)

Idea Checklist - Knowledge Guides

(1)

Problems

(1)

References

(2)

II Regression Model - Estimation and Inference

(98)

The Multivariate Normal Linear Regression Model: ML Estimation

(26)

The Linear Regression Model

(4)

The Linearity Assumption and the Inverse Problem

(1)

Linearity and Beyond: Sampling Implication of Model Assumptions

(2)

The Parametric Model

(1)

Maximum Likelihood Estimation of β and σ2

(4)

The Normal Linear Regression Model

(1)

The Maximum Likelihood (ML) Criterion

(1)

Maximum Likelihood Estimators for β and σ2

(1)

Distribution, Moments, and Bias Properties of the ML Estimator

(1)

Efficiency of the Bias-Adjusted ML Estimators of β and σ2

(1)

Consistency, Asymptotic Normality, and Asymptotic Efficiency of ML Estimators of β and σ2

(4)

Consistency

(2)

Asymptotic Normality

(1)

Asymptotic Efficiency

(1)

Summary of the Finite Sample and Asymptotic Sampling Properties of the ML Estimator

(1)

Estimating E and cov (β)

(2)

An Estimator for E

(1)

An Estimator for cov (β)

(1)

Concluding Remarks

(2)

Exercises

(1)

Idea Checklist - Knowledge Guides

(1)

Problems

(1)

Computer Problems

(1)

Appendix: Admissibility of ML Estimator - Introduction to Biased Estimation

(4)

Is the ML Estimator Inadmissible?

(2)

Risk Comparisons for Restricted and Unrestricted ML Estimator

(1)

Appendix: Proofs

(2)

References

(1)

The Multivariate Normal Linear Regression Model: Inference

(25)

Introduction

(1)

Some Basic Sampling Distributions of Functions of β and S2

(2)

Hypothesis Testing

(12)

Test Statistics

(1)

Generalized Likelihood Ratio (GLR) Test

(1)

Properties of the GLR Test

(1)

Testing Hypotheses Relating to Linear Restrictions on β

(5)

Testing Linear Inequality Hypotheses

(1)

Bonferroni Joint Tests of Inequality and Equality Hypotheses about β

(1)

Testing Hypotheses about σ2

(2)

Confidence Interval and Region Estimation

(4)

Meaning of ``Confidence'' Interval or Region

(1)

Rationale for the Use of Confidence Regions

(1)

Confidence Intervals, Regions, and Bounds for β

(2)

Confidence Bounds on σ2

(1)

Pretest Estimators Based on Hypothesis Tests: Introduction

(2)

The Pretest Estimator

(1)

The Pretest Estimator Risk Function

(1)

Concluding Remarks

(2)

Exercises

(1)

Idea Checklist - Knowledge Guides

(1)

Problems

(1)

Computer Exercises

(1)

References

(1)

The Linear Semiparametric Regression Model: Least-Squares Estimation

(19)

The Semiparametric Linear Regression Model

(2)

The Problem of Estimating β

(3)

The Squared-Error Metric and the Least-Squares Principle

(1)

The Least-Squares Estimator

(1)

Statistical Properties of the LS Estimator

(6)

Mean, Covariance, and Unbiasedness

(1)

GAUSS Markov Theorem: β Is Blue, Not Necessarily MVUE

(1)

β Is a Minimax Estimator of β under Quadratic Risk

(1)

Consistency

(1)

Asymptotic Normality

(1)

Estimating E, σ2, and cov (β)

(3)

An Estimator for ε

(1)

An Estimator for σ2 and cov (β)

(1)

Critique

100

(1)

Exercises

101

(2)

Idea Checklist - Knowledge Guides

101

(1)

Problems

101

(1)

Computer Exercises

102

(1)

References

103

(1)

Appendix: Proofs

103

(2)

The Linear Semiparametric Regression Model: Inference

105

(26)

Asymptotics: Why, What Kind, and How Useful?

107

(2)

Why?

107

(1)

What Kind?

108

(1)

How Useful?

108

(1)

Hypothesis Testing: Linear Equality Restrictions on β

109

(11)

Wald (W) Tests

110

(4)

Lagrange Multiplier (LM) Tests

114

(4)

The W and LM Tests under Normality

118

(2)

W and LM Tests: Interrelationship and Extensions

120

(1)

Confidence Region Estimation

120

(3)

Wald-Based Confidence Regions

121

(1)

LM-Based Confidence Regions

122

(1)

Testing Linear Inequality Hypotheses and Generating Confidence Bounds on β

123

(3)

Linear Inequality Hypotheses

124

(1)

Confidence Bounds for cβ

125

(1)

Critique

126

(1)

Comprehensive Computer Application

127

(1)

Exercises

128

(1)

Idea Checklist - Knowledge Guides

128

(1)

Problems

128

(1)

Computer Exercises

129

(1)

References

129

(2)

III Extremum Estimators and Nonlinear and Nonnoramal Regression Models

131

(92)

Extremum Estimation and Inference

133

(24)

Introduction

133

(3)

ML and LS Estimators Expressed in Extremum Estimator Form

136

(1)

Asymptotic Properties of Extremum Estimators

136

(3)

Consistency of Extremum Estimators

136

(2)

Asymptotic Normality of Extremum Estimators

138

(1)

Asymptotic Properties of Maximum Likelihood Estimators in an Extremum Estimator Context

139

(3)

Consistency of the ML-Extremum Estimator

140

(1)

Asymptotic Normality of the ML-Extremum Estimator

141

(1)

Asymptotic Properties of the Least-Squares Estimator in an Extremum Estimator Context

142

(2)

Consistency of the LS-Extremum Estimator

142

(1)

Asymptotic Normality of the LS-Extremum Estimator

143

(1)

Inference Based on Extremum Estimation

144

(9)

Lagrange Multiplier Tests and Confidence Regions

144

(4)

Wald Tests and Confidence Regions

148

(1)

Pseudo-Likelihood Ratio Tests and Confidence Regions

149

(3)

Testing Linear Inequalities and Confidence Bounds

152

(1)

Critique

153

(1)

Exercises

154

(1)

Idea Checklist - Knowledge Guides

154

(1)

Problems

154

(1)

Computer Problems

155

(1)

References

155

(2)

The Nonlinear Semiparametric Regression Model: Estimation and Inference

157

(47)

The Nonlinear Regression Model

157

(5)

Assumed Probability Model Characteristics: Discussion

159

(2)

The Inverse Problem

161

(1)

The Problem of Estimating β

162

(5)

The Nonlinear Least-Squares Estimator

162

(1)

Parameter Identification Relative to a Probability Model

163

(2)

Parameter Identification Relative to the Least-Squares Criterion and Given Data

165

(2)

Sampling Properties of the NLS Estimator

167

(2)

The Problem of Estimating E, σ2, and cov(β)

169

(2)

An Estimator for E

169

(1)

An Estimator for σ2 and cov(β)

170

(1)

Wald Statistics: Tests and Confidence Regions

171

(5)

Hypotheses Relating to Differentiable Functions of β

171

(1)

Wald (W) Tests

172

(1)

Wald Statistic Distribution under Ha

173

(1)

Test Application

174

(1)

Confidence Region Estimation

175

(1)

LM Statistics: Tests and Confidence Regions

176

(4)

Lagrange Multiplier Distribution

176

(2)

Classical Form of LM Test

178

(1)

Score Form of LM Test

178

(1)

LM Statistic Distribution under Ha

179

(1)

Test Application

179

(1)

Confidence Region Estimation

180

(1)

Pseudo-Likelihood Ratio Statistic: Tests and Confidence Regions

180

(3)

The Pseudo-Likelihood Ratio Statistic

180

(1)

Distribution of PLR under H0

181

(1)

Test and Confidence Region Application and Properties

182

(1)

Nonlinear Inequality Hypotheses and Confidence Bounds

183

(3)

Testing Nonlinear Inequalities: Z-Statistics

183

(2)

Confidence Bounds

185

(1)

Asymptotic Properties of the NLS-Extremum Estimator

186

(6)

Consistency

186

(1)

Asymptotic Normality

187

(3)

Asymptotic Linearity

190

(1)

Best Asymptotically Linear Consistent Estimator

191

(1)

Concluding Comments

192

(1)

Exercises

192

(2)

Idea Checklist - Knowledge Guides

192

(1)

Problems

193

(1)

Computer Exercises

193

(1)

References

194

(1)

Appendixes

195

(9)

Appendix A: Computation of NLS Estimates (With Ronald Schoenberg)

195

(1)

Newton-Raphson Method

195

(2)

Gauss-Newton Method

197

(1)

Quasi-Newton Methods

198

(1)

Computational Issues

199

(3)

Appendix B: Proofs

202

(2)

Nonlinear and Nonnormal Parametric Regression Models

204

(19)

The Normal Nonlinear Regression Model

204

(5)

Maximum Likelihood-Extremum Estimation

205

(2)

Maximum Likelihood-Extremum Inference

207

(2)

Nonnormality

209

(6)

A Nonnormal Dependent Variable, Normal Noise Component Case: The Box-Cox Transformation

209

(3)

A Nonnormal Noise Component Case

212

(3)

General Considerations in Applying the ML-Extremum Criterion

215

(5)

Point Estimation

216

(1)

Testing and Confidence-Region Estimation

217

(3)

A Final Remark

220

(1)

Exercises

220

(1)

Idea Checklist - Knowledge Guides

220

(1)

Problems

220

(1)

Computer Exercises

221

(1)

References

221

(2)

IV Avoiding the Parametric Likelihood

223

(114)

Stochastic Regressors and Moment-Based Estimation

225

(20)

Introduction

225

(2)

Linear Model Assumptions, Estimation, and Inference Revisited

227

(2)

LS and ML Estimator Properties

229

(4)

LS Estimator Properties: Finite Samples

229

(1)

LS Estimator Properties: Asymptotics

230

(2)

ML Estimation of β and σ2 under Conditional Normality

232

(1)

Hypothesis Testing and Confidence-Region Estimation

233

(2)

Semiparametric Case

233

(1)

Parametric Case

233

(2)

Summary: Statistical Implications of Stochastic X

235

(1)

Method of Moments Concept

235

(6)

Asymptotic Properties

236

(2)

A Linear Model Formulation

238

(1)

Extensions to Nonlinear Models

239

(2)

Concluding Comments

241

(1)

Exercises

242

(1)

Idea Checklist - Knowledge Guides

242

(1)

Problems

242

(1)

Computer Exercises

242

(1)

References

243

(1)

Appendix: Proofs

244

(1)

Quasi-Maximum Likelihood and Estimating Equations

245

(36)

Quasi-Maximum Likelihood Estimation and Inference

247

(1)

QML-E Estimation and Inference

248

(8)

Consistency and Asymptotic Normality

248

(1)

True PDF Approximation Property and Asymptotic Normality of Inconsistent QML-E Estimators

249

(2)

Consistent Estimation of the Asymptotic Covariance Matrix

251

(1)

Necessary and Sufficient Conditions for Consistency and Asymptotic Normality

251

(3)

QML Inference

254

(1)

QML Generalizations

255

(1)

QML Summary Comments

256

(1)

Estimating Equations: LS, ML, QML-E, and Extremum Estimators

256

(14)

Linear and Nonlinear Estimating Functions

259

(2)

Optimal Unbiased Estimating Functions: Finite Sample Optimality of ML

261

(4)

Consistency of the EE Estimator

265

(2)

Asymptotic Normality and Efficiency of EE Estimators

267

(1)

Inference in the Context of EE Estimation

268

(2)

Unifying-Linking OptEF and QML: QML-EE Estimation and Inference

270

(5)

The Best Linear-Unbiased QML-EE

272

(2)

General QML-EE Estimation and Inference

274

(1)

Final Remarks

275

(1)

Exercises

275

(2)

Idea Checklist - Knowledge Guides

275

(1)

Problems

276

(1)

Computer Problems

277

(1)

References

277

(2)

Appendix: Proofs

279

(2)

Empirical Likelihood Estimation and Inference

281

(32)

Empirical Likelihood: iid Case

282

(10)

The EL Concept

283

(1)

Nonparametric Maximum Likelihood Estimate of a Population Distribution

284

(2)

Empirical Likelihood Function for θ

286

(6)

Maximum Empirical Likelihood Estimation: iid Case

292

(6)

Maximum Empirical Likelihood Estimator

292

(1)

MEL Efficiency Property

293

(1)

MEL Estimation of a Population Mean

294

(3)

MEL Estimation Based on Two Moments

297

(1)

Hypothesis Tests and Confidence Regions: iid Case

298

(6)

Empirical Likelihood Ratio Tests and Confidence Regions for c(θ)

299

(1)

Wald Tests and Confidence Regions for c(θ)

300

(1)

Lagrange Multiplier Tests and Confidence Regions for c(θ)

300

(1)

Z-Tests of Inequality Hypotheses for the Value of c(θ)

301

(1)

Testing the Validity of Moment Equations

301

(1)

MEL Testing and Confidence Intervals for Population Mean

302

(1)

Illustrative MEL Confidence Interval Example

303

(1)

MEL in the Linear Regression Model with Stochastic X

304

(3)

MEL Regression Estimation for Stochastic X

304

(2)

EL-Based Testing and Confidence Regions When X Is Stochastic

306

(1)

Extensions to the Nonlinear Regression Model for Stochastic X

307

(1)

MEL in the Linear Regression Model with Nonstochastic X: Extensions to the Non-iid Case

307

(2)

Concluding Comments

309

(1)

Exercises

310

(2)

Idea Checklist - Knowledge Guides

310

(1)

Problems

311

(1)

Computer Exercises

311

(1)

References

312

(1)

Information Theoretic-Entropy Approaches to Estimation and Inference

313

(24)

Solutions to Systems of Estimating Equations and Kullback-Leibler Information

313

(8)

Kullback-Leibler Information Criterion (KLIC)

316

(1)

Relationship Between the MEL Objective and KL Information

317

(2)

Relationship Between the Maximum Entropy (ME) Objective and KL Information

319

(2)

The General MEEL Alternative Empirical Likelihood Formulation

321

(5)

The MEEL Estimator and Likelihood

321

(1)

MEEL Asymptotics

322

(1)

MEEL Inference

323

(3)

Contrasting the Use of Estimating Functions in EE and MEEL Contexts

326

(1)

A Cross-Entropy Formalism and Solution

326

(2)

α-Entropy: Unifying the MEL, MEEL, and CEEL Estimation Objectives

328

(1)

Application of the Maximum Entropy Principle to the Regression Model

329

(3)

Stochastic X in the Linear Model

329

(2)

Fixed x in the Linear Model

331

(1)

Extensions to Nonlinear Regression Models

331

(1)

Inference in Regression Models

331

(1)

Concluding Remarks - Which Criterion?

332

(2)

Exercises

334

(1)

Idea Checklist - Knowledge Guides

334

(1)

Problems

334

(1)

Computer Problems

334

(1)

References

335

(1)

Supplemental References

335

(2)

V Generalized Regression Models

337

(66)

Regression Models with a Known General Noise Covariance Matrix

339

(31)

Applying LS-ML to the Linear Model and Untransformed Data: Ignoring that &PSgr; I

340

(4)

Point Estimation

341

(1)

Testing and Confidence-Region Estimation

342

(2)

GLS-ML-Extremum Analysis of the Linear Model: Incorporating a Known &PSgr;

344

(6)

ML-Extremum Estimators for β and σ2

344

(1)

LS-Extremum Estimators for β and σ2: Transformed Linear Model

345

(2)

Asymptotic Properties

347

(2)

Hypothesis Testing and Confidence Regions

349

(1)

GLS-ML-Extremum Analysis of the Nonlinear Model: Incorporating a Known &PSgr;

350

(3)

Estimator Properties

350

(1)

Hypothesis Testing and Confidence Regions

351

(1)

Applying NLS to Untransformed Data

352

(1)

Parametric Specifications of Noise Covariance Matrices

353

(3)

Estimation and Inference with AR(1) Noise

354

(1)

Heteroscedasticity - Structural Specification Known, Parameters Unknown

355

(1)

General Considerations

356

(1)

Sets of Regression Equations

356

(5)

Sets of Linear Equations

357

(2)

Sets of Nonlinear Equations

359

(2)

The Estimating Equations - Quasi-Maximum Likelihood View: A Unified Approach

361

(6)

EE Estimation of β and σ2 in the Linear Model When &PSgr; Is Known

361

(2)

EE Estimation of β and σ2 in the Nonlinear Model When &PSgr; Is Known

363

(1)

EE Estimation of β and σ2 in the Linear or Nonlinear Normal Parametric Regression Model When &PSgr; Is Known

364

(1)

QML-EE Estimation of β and σ2 in the Linear or Nonlinear Regression Model

365

(1)

EE Estimation of β and σ2 in Systems of Regression Equations

366

(1)

Some Comments

367

(1)

Exercises

368

(1)

Idea Checklist - Knowledge Guides

368

(1)

Problems

368

(1)

Computer Exercises

369

(1)

References

369

(1)

Regression Models with an Unknown General Noise Covariance Matrix

370

(33)

Linear Regression Models with Unknown Noise Covariance

371

(7)

Single-Equation Semiparametric Linear Regression Model

372

(5)

Single-Equation Parametric Linear Regression Model - The ML Approach

377

(1)

System of Linear Regression Equations

378

(5)

Estimation: Semiparametric Case

379

(1)

Testing and Confidence Regions: Semiparametric Case

380

(1)

ML Approach: Parametric Case

381

(2)

Nonlinear Regression Models with Unknown Noise Covariance

383

(4)

Single-Equation Semiparametric Nonlinear Regression Model

383

(1)

Estimation

383

(1)

Testing and Confidence Regions

384

(1)

Single-Equation Parametric Nonlinear Regression Model - ML Approach

385

(1)

Sets of Nonlinear Regression Equations

386

(1)

Robust Solution Methods: OLS and Robust Covariance Matrix Estimation

387

(6)

Heteroscedasticity

389

(2)

Heteroscedasticity and Autocorrelation

391

(2)

The Estimating Equations - Quasi-Maximum Likelihood View: A Unified Approach

393

(5)

A Unified EE Characterization of Inverse Problem Solutions

393

(2)

QML-EE Estimation

395

(1)

EE Extensions

396

(1)

MEL and MEEL Applications of EE

397

(1)

Some Comments

398

(2)

Exercises

400

(1)

idea Checklist - Knowledge Guides

400

(1)

Problems

400

(1)

Computer Exercises

400

(1)

References

401

(2)

VI Simultaneous Equation Probability Models and General Moment-Based Estimation and Inference

403

(92)

Generalized Moment-Based Estimation and Inference

405

(41)

Parameter Estimation in Just-determined and Overdetermined Models with iid Observations: Back to the Future

406

(6)

OptEF Approach

409

(1)

Empirical Likelihood Approaches

410

(1)

Summary and Foreword

411

(1)

GMM Solutions for Unbiased Estimating Equations in the Overdetermined Case

412

(11)

GMM Concept

412

(1)

GMM Linear Model Estimation

413

(7)

GMM Estimators - General Properties

420

(3)

IV Solutions in the Just-determined Case When E[X'E] ≠ 0

423

(6)

Traditional Instrumental Variable Estimator in the Linear Model

424

(2)

GLS as an IV Estimator

426

(1)

Extensions: Nonlinear IV Formulations and Non-iid Sampling

427

(1)

Hypothesis Testing and Confidence Regions

428

(1)

Summary: IV Approach to Estimation and Inference

429

(1)

Solutions in the Overdetermined Case When E[X'ε] ≠ 0

429

(12)

Unbiased Estimating Equations Basis for Inverse Problem Solutions When E[X'ε] ≠ 0

430

(1)

GMM Approach

431

(1)

MEL and MEEL Approaches

432

(4)

OptEF-Quasi-ML Approach: Asymptotic Unification of Inverse Solution Methods

436

(1)

Asymptotic Sampling Properties and Inference

437

(1)

Testing Moment Equation Validity

438

(1)

Relationship Between Estimator Efficiency and the Number and Type of Estimating Equations

439

(2)

Concluding Comments

441

(2)

Exercises

443

(1)

Idea Checklist - Knowledge Guides

443

(1)

Problems

443

(1)

Computer Exercises

444

(1)

References

444

(2)

Simultaneous Equations Econometric Models: Estimation and Inference

446

(49)

Linear Simultaneous Equations Models

447

(11)

An Equivalent Vectorized System of Equations

450

(1)

The Reduced-Form Regression Model

451

(2)

Estimating the Reduced-Form Coefficients

453

(2)

The Identification Problem

455

(3)

Least-Squares and GMM Estimation: The Semiparametric Case

458

(7)

Estimators of Parameters for a Just-Identified Structural Equation

459

(1)

GMM Estimator of Parameters for an Overidentified Structural Equation

460

(2)

Estimation of a Complete System of Equations

462

(3)

Maximum Likelihood Estimation in the Linear Model: The Parametric Case

465

(3)

Full-Information Maximum Likelihood (FIML)

465

(2)

Limited Information Maximum Likelihood (LIML)

467

(1)

Nonlinear Simultaneous Equations

468

(7)

Single-Equation Estimation: Semiparametric Case

469

(3)

Complete System Estimation: Semiparametric Case

472

(1)

Nonlinear Maximum Likelihood Estimation: Parametric Case

473

(1)

Identification in Nonlinear Systems of Equations

474

(1)

Information Theoretic Procedures

475

(11)

Minimum KLIC Approach: MEEL and MEL

476

(3)

MEEL Estimation and Inference

479

(5)

MEL Estimation

484

(1)

The KLIC-MEEL-MEL Procedures: Critique

485

(1)

OptEF Estimation and Inference

486

(2)

The OptEF Estimator in Simultaneous Equations Models

486

(1)

OptEF Asymptotic Unification of Inverse Problem Solutions

487

(1)

Concluding Comments

488

(1)

Exercises

489

(2)

Idea Checklist - Knowledge Guides

489

(1)

Problems

489

(1)

Computer Problems

490

(1)

References

491

(1)

Appendix: Historical Perspective

492

(3)

VII Model Discovery

495

(66)

Model Discovery: The Problem of Variable Selection and Conditioning

497

(31)

Introduction

497

(3)

Experiments in Nonexperimental Model Building

498

(1)

The Chapter Format

499

(1)

Variable Selection Problem in a Loss or MSE Context

500

(7)

Bias-Variance Trade-Off in Incorrect Variable Selection

501

(2)

Statistical Implications under an MSE Matrix Measure

503

(2)

Statistical Implications under a Quadratic Risk Function Measure

505

(1)

Extensions to Nonlinear Models, General Covariance Structures, and Systems of Equations

506

(1)

Fisherian Testing and Model Choice: Critique

507

(2)

Estimated Risk Criteria and Model Choice: Mallows Cp Criterion

509

(2)

An Information Theoretic Model Selection Criterion: Akaike Information

511

(3)

Basic Rationale for the AIC and Variants

511

(2)

A Comment

513

(1)

Shrinkage as a Basis for Dealing with Variable Uncertainty

514

(3)

Stein-Like Shrinkage Estimators

514

(1)

Multiple Shrinkage Estimator

515

(2)

The Problem of an Ill-Conditioned Explanatory Variable Matrix

517

(4)

Penalized Estimation

518

(2)

Finite Sample Performance

520

(1)

Final Comments and Critique

521

(3)

Exercises

524

(1)

Idea Checklist - Knowledge Guides

524

(1)

Problems

524

(1)

Computer Problems

524

(1)

References

525

(3)

Model Discovery: The Problem of Noise Covariance Matrix Specification

528

(33)

Introduction

528

(2)

Specific Parametric Specifications of the Noise Covariance Matrix: Estimation and Inference

530

(5)

AR(1) Noise

530

(3)

Heteroscedastic Noise: σi2 = (zi.α)2

533

(2)

Tests for Heteroscedasticity: Rationale and Application

535

(8)

Types of Heteroscedasticity Tests

536

(1)

Motivation for Tests Based on ε2

536

(4)

Motivation for the Test Based on ln(E2t)

540

(1)

Motivation for Test Based on εt

541

(1)

More Tests

542

(1)

Tests for Autocorrelation: Rationale and Application

543

(8)

Autocorrelation Processes

543

(3)

Estimation

546

(1)

Autocorrelation Tests

547

(4)

Pretest Estimators Defined by Heteroscedasticity or Autocorrelation Testing

551

(5)

Two-Equation Linear System with Potential Heteroscedasticity

552

(1)

A Heteroscedasticity Pretest Estimator

553

(2)

An Autocorrelation Pretest Estimator

555

(1)

Concluding Comments

556

(1)

Exercises

557

(1)

Idea Checklist - Knowledge Guides

557

(1)

Problems

557

(1)

Computer Problems

557

(1)

References

558

(3)

VIII Special Econometric Topics

561

(82)

Qualitative-Censored Response Models

563

(36)

Binary-Discrete Choice Response Models

565

(5)

A Linear probability Model

566

(1)

A Reformulated Binary Response Model

567

(3)

Maximum Likelihood Estimation and Inference for the Discrete Choice Model

570

(5)

Logit Model

571

(2)

Probit Model

573

(2)

Probit or Logit?

575

(1)

Multinomial Discrete Choice

575

(10)

Multinomial Logit

576

(5)

Information Theoretic Estimation of the Multinomial Decision Model

581

(3)

Ordered Multinomial Choice

584

(1)

Censored Response Data

585

(7)

Censoring Versus Truncation

585

(2)

Tobit Model

587

(4)

Extensions of the Tobit Formulation

591

(1)

Concluding Remarks

592

(2)

Exercises

594

(1)

Idea Checklist - Knowledge Guides

594

(1)

Problems

594

(1)

Computer Problems

595

(1)

References

595

(2)

Appendix

597

(2)

Introduction to Nonparametric Density and Regression Analysis

599

(44)

Density Estimation via Kernels

601

(10)

Kernels

602

(2)

IMSE, AIMSE, and Kernel Choice

604

(2)

Bandwidth Choice

606

(2)

Other Properties and Issues

608

(1)

Multivariate Extensions

609

(2)

Kernel Regression Estimators

611

(11)

Nonparametric Regression Model Specification

612

(1)

Nadarya-Watson Kernel Regression: Alias Zero-Order Local polynomial Regression

613

(9)

Local Polynomial Regression

622

(2)

Prequel of Fundamental Concepts: Local Weighted Averages, Local Linear Regressions, and Histograms

624

(12)

Nonparametric Regression under Repeated Sampling: Simple Sample Means

625

(1)

Local Sample Means: Using Data Neighborhoods

626

(2)

Local Weighted Averages within Data Neighborhoods: Local Least-Squares Regressions

628

(1)

Local Polynomial Regressions

629

(1)

Histograms: Precursor to Kernel Density Estimation

630

(6)

Concluding Comments

636

(1)

Exercises

637

(1)

Idea Checklist - Knowledge Guides

637

(1)

Problems

637

(1)

Computer Problems

638

(1)

References

638

(2)

Appendix: Derivation of Equation (21.4.31)

640

(3)

IX Bayesian Estimation and Inference

643

(68)

Bayesian Estimation: General Principles with a Regression Focus

645

(30)

Introduction

645

(4)

Bayes Theorem

646

(1)

A Format for Bayesian Reasoning

647

(2)

Bayesian Probability Models and Posterior Distributions

649

(3)

Prior Distributions

650

(1)

Posterior Probability Distributions

651

(1)

The Bayesian Linear-Regression-Based Probability Model

652

(6)

Bayesian Regression Analysis under Normality and Uninformative Priors

653

(1)

Uninformative Priors and Proper Marginal Posteriors

654

(1)

Posterior Distribution under an Uninformative Prior

655

(1)

Marginal Posteriors

656

(2)

Bayesian Regression Analysis under Normality and Conjugate Informative Priors

658

(3)

The Joint Posterior Distribution under the Conjugate Prior

660

(1)

The Marginal Posteriors

660

(1)

Bayesian Point Estimates

661

(4)

Minimum Expected Risk

663

(1)

Admissibility

663

(1)

Consistency and Asymptotic Normality

663

(1)

Comments on Bayes Estimator Properties

664

(1)

On the Use of Conjugate Priors and Coincidence of Classical and Bayesian Estimates

665

(1)

Concluding Remarks

666

(1)

Exercises

667

(2)

Idea Checklist - Knowledge Guides

667

(1)

Problems

667

(1)

Computer Problems

668

(1)

References

669

(1)

Appendix: Bayesian Asymptotics

669

(6)

Bayesian Asymptotics: Specific Cases

670

(2)

Bayesian Asymptotics: General Considerations

672

(2)

Appendix References

674

(1)

Alternative Bayes Formulations for the Regression Model

675

(23)

g-Priors

676

(3)

A Family of g-priors and Associated Posteriors

676

(2)

Rationalizing and Specifying g-priors

678

(1)

An Empirical Bayes Estimator

679

(3)

General Bayesian Regression Analysis with Nonconjugate Informative-Uninformative Prior

682

(6)

Normal Noise Component

682

(5)

Nonnormal Noise Component

687

(1)

Summary Comments

688

(1)

Bayesian Method of Moments

688

(5)

Continuous Entropy Formulation

691

(1)

A Posterior Density Function

692

(1)

Concluding Remarks

693

(1)

Exercises

694

(2)

Idea Checklist - Knowledge Guides

694

(1)

Problems

694

(1)

Computer Problems

695

(1)

References

696

(2)

Bayesian Inference

698

(13)

Credible Regions

699

(3)

General Principles

699

(1)

Highest Posterior Density Credible Regions

700

(1)

Credible Regions in the Regression Model

701

(1)

Hypothesis Evaluation and Decision

702

(2)

General Principles

703

(1)

General Hypothesis Testing and Credible Sets in the Regression Model

704

(4)

Evaluating Composite Hypotheses about β and Bayes Factors

704

(2)

Evaluating Simple Hypotheses about β

706

(2)

A Comment

708

(1)

Exercises

708

(1)

Idea Checklist - Knowledge Guides

708

(1)

Problems

708

(1)

Computer Problems

709

(1)

References

709

(2)

X Epilogue

711

(2)

Appendix: Introduction to Computer Simulation and Resampling Methods

713

(26)

A.1 Pseudorandom Number Generation

713

(6)

A.1.1 Generating U(0,1) Pseudorandom Numbers

714

(1)

A.1.2 Generating Continuous Nonuniform Pseudorandom Numbers

715

(2)

A.1.3 Generating Discrete Pseudorandom Numbers

717

(1)

A.1.4 Evaluating the Performance of Pseudorandom Number Generators

718

(1)

A.2 Monte Carlo Simulation

719

(5)

A.2.1 Background and Conceptual Motivation

720

(1)

A.2.2 Key Assumptions

721

(1)

A.2.3 Basic Properties of Monte Carlo Simulation Estimators

722

(2)

A.3 Bootstrap Resampling

724

(6)

A.3.1 Basic Properties of the Bootstrap

725

(3)

A.3.2 Bootstrap Simulation Procedures for Regression Models

728

(2)

A.4 Numerical Tools for Evaluating Posterior Distributions

730

(4)

A.4.1 The Gibbs Sampling Algorithm

731

(2)

A.4.2 The Metropolis-Hastings Algorithm

733

(1)

A.5 Concluding Remarks

734

(1)

A.6 Exercises

735

(1)

A.6.1 Idea Checklist

735

(1)

A.6.2 Problems

735

(1)

A.6.3 Computer Problems

735

(1)

A.7 References

736

(3)

Author Index

739

(4)

Subject Index

743

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