Rent 9780321278876 | Introduction to Econometrics | Stock, James H.; Watson, Mark W. @knetbooks.com

Summary Table of Contents

Designed for a first course in introductory econometrics, "Introduction to Econometrics, " reflects modern theory and practice, with interesting applications that motivate and match up with the theory to ensure students grasp the relevance of econometrics. Authors James H. Stock and Mark W. Watson integrate real-world questions and data into the development of the theory, with serious treatment of the substantive findings of the resulting empirical analysis.

Introduction to Econometrics, Second Edition, continues i... MORE

Preface

xxvii

PART ONE Introduction and Review

(108)

Economic Questions and Data

(14)

... MORE

Economic Questions We Examine

(4)

Question #1: Does Reducing Class Size Improve Elementary School Education?

(1)

Question #2: Is There Racial Discrimination in the Market for Home Loans?

(1)

Question #3: How Much Do Cigarette Taxes Reduce Smoking?

(1)

Question #4: What Will the Rate of Inflation Be Next Year?

(1)

Quantitative Questions, Quantitative Answers

(1)

Causal Effects and Idealized Experiments

(2)

Estimation of Causal Effects

(1)

Forecasting and Causality

(1)

Data: Sources and Types

(7)

Experimental versus Observational Data

(1)

Cross-Sectional Data

(1)

Time Series Data

(2)

Panel Data

(4)

Review of Probability

(48)

Random Variables and Probability Distributions

(5)

Probabilities, the Sample Space, and Random Variables

(1)

Probability Distribution of a Discrete Random Variable

(2)

Probability Distribution of a Continuous Random Variable

(2)

Expected Values, Mean, and Variance

(6)

The Expected Value of a Random Variable

(1)

The Standard Deviation and Variance

(1)

Mean and Variance of a Linear Function of a Random Variable

(1)

Other Measures of the Shape of a Distribution

(3)

Two Random Variables

(10)

Joint and Marginal Distributions

(1)

Conditional Distributions

(4)

Independence

(1)

Covariance and Correlation

(1)

The Mean and Variance of Sums of Random Variables

(4)

The Normal, Chi-Squared, Student t, and F Distributions

(6)

The Normal Distribution

(4)

The Chi-Squared Distribution

(1)

The Student t Distribution

(1)

The F Distribution

(1)

Random Sampling and the Distribution of the Sample Average

(3)

Random Sampling

(1)

The Sampling Distribution of the Sample Average

(2)

Large-Sample Approximations to Sampling Distributions

(17)

The Law of Large Numbers and Consistency

(3)

The Central Limit Theorem

(11)

Appendix 2.1 Derivation of Results in Key Concept 2.3

(2)

Review of Statistics

(44)

Estimation of the Population Mean

(5)

Estimators and Their Properties

(1)

Properties of Y

(2)

The Importance of Random Sampling

(1)

Hypothesis Tests Concerning the Population Mean

(10)

Null and Alternative Hypotheses

(1)

The p-Value

(2)

Calculating the p-Value When σy Is Known

(1)

The Sample Variance, Sample Standard Deviation, and Standard Error

(1)

Calculating the p-Value When σy Is Unknown

(1)

The t-Statistic

(1)

Hypothesis Testing with a Prespecified Significance Level

(2)

One-Sided Alternatives

(1)

Confidence Intervals for the Population Mean

(2)

Comparing Means from Different Populations

(2)

Hypothesis Tests for the Difference Between Two Means

(1)

Confidence Intervals for the Difference Between Two Population Means

(1)

Differences-of-Means Estimation of Causal Effects Using Experimental Data

(3)

The Causal Effect as a Difference of Conditional Expectations

(2)

Estimation of the Causal Effect Using Differences of Means

(1)

Using the t-Statistic When the Sample Size Is Small

(4)

The t-Statistic and the Student t Distribution

(4)

Use of the Student t Distribution in Practice

(1)

Scatterplot, the Sample Covariance, and the Sample Correlation

(17)

Scatterplots

(1)

Sample Covariance and Correlation

(11)

Appendix 3.1 The U.S. Current Population Survey

105

(1)

Appendix 3.2 Two Proofs That Y Is the Least Squares Estimator of μy

106

(1)

Appendix 3.3 A Proof That the Sample Variance Is Consistent

107

(2)

PART TWO Fundamentals of Regression Analysis

109

(238)

Linear Regression with One Regressor

111

(37)

The Linear Regression Model

112

(4)

Estimating the Coefficients of the Linear Regression Model

116

(7)

The Ordinary Least Squares Estimator

118

(2)

OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio

120

(1)

Why Use the OLS Estimator?

121

(2)

Measures of Fit

123

(3)

The R2

123

(1)

The Standard Error of the Regression

124

(1)

Application to the Test Score Data

125

(1)

The Least Squares Assumptions

126

(5)

Assumption #1: The Conditional Distribution of ui Given Xi Has a Mean of Zero

126

(2)

Assumption #2: (Xi, Yi), i = I, . . . , n Are Independently and Identically Distributed

128

(1)

Assumption #3: Large Outliers Are Unlikely

129

(1)

Use of the Least Squares Assumptions

130

(1)

The Sampling Distribution of the OLS Estimators

131

(4)

The Sampling Distribution of the OLS Estimators

132

(3)

Conclusion

135

(13)

Appendix 4.1 The California Test Score Data Set

143

(1)

Appendix 4.2 Derivation of the OLS Estimators

143

(1)

Appendix 4.3 Sampling Distribution of the OLS Estimator

144

(4)

Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals

148

(38)

Testing Hypotheses About One of the Regression Coefficients

149

(6)

Two-Sided Hypotheses Concerning β1

149

(4)

One-Sided Hypotheses Concerning β1

153

(2)

Testing Hypotheses About the Intercept β0

155

(1)

Confidence Intervals for a Regression Coefficient

155

(3)

Regression When X Is a Binary Variable

158

(2)

Interpretation of the Regression Coefficients

158

(2)

Heteroskedasticity and Homoskedasticity

160

(6)

What Are Heteroskedasticity and Homoskedasticity?

160

(3)

Mathematical Implications of Homoskedasticity

163

(1)

What Does This Mean in Practice?

164

(2)

The Theoretical Foundations of Ordinary Least Squares

166

(3)

Linear Conditionally Unbiased Estimators and the Gauss-Markov Theorem

167

(1)

Regression Estimators Other Than OLS

168

(1)

Using the t-Statistic in Regression When the Sample Size Is Small

169

(2)

The t-Statistic and the Student t Distribution

170

(1)

Use of the Student t Distribution in Practice

170

(1)

Conclusion

171

(15)

Appendix 5.1 Formulas for OLS Standard Errors

180

(2)

Appendix 5.2 The Gauss-Markov Conditions and a Proof of the Gauss-Markov Theorem

182

(4)

Linear Regression with Multiple Regressors

186

(34)

Omitted Variable Bias

186

(7)

Definition of Omitted Variable Bias

187

(2)

A Formula for Omitted Variable Bias

189

(2)

Addressing Omitted Variable Bias by Dividing the Data into Groups

191

(2)

The Multiple Regression Model

193

(3)

The Population Regression Line

193

(1)

The Population Multiple Regression Model

194

(2)

The OLS Estimator in Multiple Regression

196

(4)

The OLS Estimator

197

(1)

Application to Test Scores and the Student-Teacher Ratio

198

(2)

Measures of Fit in Multiple Regression

200

(2)

The Standard Error of the Regression (SER)

200

(1)

The R2

200

(1)

The ``Adjusted R2''

201

(1)

Application to Test Scores

202

(1)

The Least Squares Assumptions in Multiple Regression

202

(3)

Assumption #1: The Conditional Distribution of ui Given X1i, X2i, . . . , Xki Has a Mean of Zero

203

(1)

Assumption #2: (X1i, X2i, . . . , Xki, Yi) i = 1, . . . , n Are i.i.d.

203

(1)

Assumption #3: Large Outliers Are Unlikely

203

(1)

Assumption #4: No Perfect Multicollinearity

203

(2)

The Distribution of the OLS Estimators in Multiple Regression

205

(1)

Multicollinearity

206

(4)

Examples of Perfect Multicollinearity

206

(3)

Imperfect Multicollinearity

209

(1)

Conclusion

210

(10)

Appendix 6.1 Derivation of Equation (6.1)

218

(1)

Appendix 6.2 Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors

218

(2)

Hypothesis Tests and Confidence Intervals in Multiple Regression

220

(34)

Hypothesis Tests and Confidence Intervals for a Single Coefficient

221

(4)

Standard Errors for the OLS Estimators

221

(1)

Hypothesis Tests for a Single Coefficient

221

(2)

Confidence Intervals for a Single Coefficient

223

(1)

Application to Test Scores and the Student-Teacher Ratio

223

(2)

Tests of Joint Hypotheses

225

(7)

Testing Hypotheses on Two or More Coefficients

225

(2)

The F-Statistic

227

(2)

Application to Test Scores and the Student-Teacher Ratio

229

(1)

The Homoskedasticity-Only F-Statistic

230

(2)

Testing Single Restrictions Involving Multiple Coefficients

232

(2)

Confidence Sets for Multiple Coefficients

234

(1)

Model Specification for Multiple Regression

235

(4)

Omitted Variable Bias in Multiple Regression

236

(1)

Model Specification in Theory and in Practice

236

(1)

Interpreting the R2 and the Adjusted R2 in Practice

237

(2)

Analysis of the Test Score Data Set

239

(5)

Conclusion

244

(10)

Appendix 7.1 The Bonferroni Test of a Joint Hypotheses

251

(3)

Nonlinear Regression Functions

254

(58)

A General Strategy for Modeling Nonlinear Regression Functions

256

(8)

Test Scores and District Income

256

(4)

The Effect on Y of a Change in X in Nonlinear Specifications

260

(4)

A General Approach to Modeling Nonlinearities Using Multiple Regression

264

(1)

Nonlinear Functions of a Single Independent Variable

264

(13)

Polynomials

265

(2)

Logarithms

267

(8)

Polynomial and Logarithmic Models of Test Scores and District Income

275

(2)

Interactions Between Independent Variables

277

(13)

Interactions Between Two Binary Variables

277

(3)

Interactions Between a Continuous and a Binary Variable

280

(6)

Interactions Between Two Continuous Variables

286

(4)

Nonlinear Effects on Test Scores of the Student-Teacher Ratio

290

(6)

Discussion of Regression Results

291

(4)

Summary of Findings

295

(1)

Conclusion

296

(16)

Appendix 8.1 Regression Functions That Are Nonlinear in the Parameters

307

(5)

Assessing Studies Based on Multiple Regression

312

(35)

Internal and External Validity

313

(3)

Threats to Internal Validity

313

(1)

Threats to External Validity

314

(2)

Threats to Internal Validity of Multiple Regression Analysis

316

(11)

Omitted Variable Bias

316

(3)

Misspecification of the Functional Form of the Regression Function

319

(1)

Errors-in-Variables

319

(3)

Sample Selection

322

(2)

Simultaneous Causality

324

(1)

Sources of Inconsistency of OLS Standard Errors

325

(2)

Internal and External Validity When the Regression Is Used for Forecasting

327

(2)

Using Regression Models for Forecasting

327

(1)

Assessing the Validity of Regression Models for Forecasting

328

(1)

Example: Test Scores and Class Size

329

(9)

External Validity

329

(7)

Internal Validity

336

(1)

Discussion and Implications

337

(1)

Conclusion

338

(9)

Appendix 9.1 The Massachusetts Elementary School Testing Data

344

(3)

PART THREE Further Topics in Regression Analysis

347

(176)

Regression with Panel Data

349

(34)

Panel Data

350

(3)

Example: Traffic Deaths and Alcohol Taxes

351

(2)

Panel Data with Two Time Periods: ``Before and After'' Comparisons

353

(3)

Fixed Effects Regression

356

(5)

The Fixed Effects Regression Model

356

(3)

Estimation and Inference

359

(1)

Application to Traffic Deaths

360

(1)

Regression with Time Fixed Effects

361

(3)

Time Effects Only

361

(1)

Both Entity and Time Fixed Effects

362

(2)

The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression

364

(3)

The Fixed Effects Regression Assumptions

364

(2)

Standard Errors for Fixed Effects Regression

366

(1)

Drunk Driving Laws and Traffic Deaths

367

(4)

Conclusion

371

(12)

Appendix 10.1 The State Traffic Fatality Data Set

378

(1)

Appendix 10.2 Standard Errors for Fixed Effects Regression with Serially Correlated Errors

379

(4)

Regression with a Binary Dependent Variable

383

(38)

Binary Dependent Variables and the Linear Probability Model

384

(5)

Binary Dependent Variables

385

(2)

The Linear Probability Model

387

(2)

Probit and Logit Regression

389

(7)

Probit Regression

389

(5)

Logit Regression

394

(2)

Comparing the Linear Probability, Probit, and Logit Models

396

(1)

Estimation and Inference in the Logit and Probit Models

396

(4)

Nonlinear Least Squares Estimation

397

(1)

Maximum Likelihood Estimation

398

(1)

Measures of Fit

399

(1)

Application to the Boston HMDA Data

400

(7)

Summary

407

(14)

Appendix 11.1 The Boston HMDA Data Set

415

(1)

Appendix 11.2 Maximum Likelihood Estimation

415

(3)

Appendix 11.3 Other Limited Dependent Variable Models

418

(3)

Instrumental Variables Regression

421

(47)

The IV Estimator with a Single Regressor and a Single Instrument

422

(10)

The IV Model and Assumptions

422

(1)

The Two Stage Least Squares Estimator

423

(1)

Why Does IV Regression Work?

424

(4)

The Sampling Distribution of the TSLS Estimator

428

(2)

Application to the Demand for Cigarettes

430

(2)

The General IV Regression Model

432

(7)

TSLS in the General IV Model

433

(1)

Instrument Relevance and Exogeneity in the General IV Model

434

(1)

The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator

434

(3)

Inference Using the TSLS Estimator

437

(1)

Application to the Demand for Cigarettes

437

(2)

Checking Instrument Validity

439

(6)

Assumption #1: Instrument Relevance

439

(4)

Assumption #2: Instrument Exogeneity

443

(2)

Application to the Demand for Cigarettes

445

(5)

Where Do Valid Instruments Come From?

450

(5)

Three Examples

451

(4)

Conclusion

455

(13)

Appendix 12.1 The Cigarette Consumption Panel Data Set

462

(1)

Appendix 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4)

462

(1)

Appendix 12.3 Large-Sample Distribution of the TSLS Estimator

463

(1)

Appendix 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid

464

(2)

Appendix 12.5 Instrumental Variables Analysis with Weak Instruments

466

(2)

Experiments and Quasi-Experiments

468

(55)

Idealized Experiments and Causal Effects

470

(2)

Ideal Randomized Controlled Experiments

470

(1)

The Differences Estimator

471

(1)

Potential Problems with Experiments in Practice

472

(5)

Threats to Internal Validity

472

(3)

Threats to External Validity

475

(2)

Regression Estimators of Causal Effects Using Experimental Data

477

(9)

The Differences Estimator with Additional Regressors

477

(3)

The Differences-in-Differences Estimator

480

(4)

Estimation of Causal Effects for Different Groups

484

(1)

Estimation When There Is Partial Compliance

484

(1)

Testing for Randomization

485

(1)

Experimental Estimates of the Effect of Class Size Reductions

486

(8)

Experimental Design

486

(1)

Analysis of the STAR Data

487

(5)

Comparison of the Observational and Experimental Estimates of Class Size Effects

492

(2)

Quasi-Experiments

494

(6)

Examples

495

(2)

Econometric Methods for Analyzing Quasi-Experiments

497

(3)

Potential Problems with Quasi-Experiments

500

(2)

Threats to Internal Validity

500

(2)

Threats to External Validity

502

(1)

Experimental and Quasi-Experimental Estimates in Heterogeneous Populations

502

(5)

Population Heterogeneity: Whose Causal Effect?

502

(1)

OLS with Heterogeneous Causal Effects

503

(1)

IV Regression with Heterogeneous Causal Effects

504

(3)

Conclusion

507

(16)

Appendix 13.1 The Project STAR Data Set

516

(1)

Appendix 13.2 Extension of the Differences-in-Differences Estimator to Multiple Time Periods

517

(1)

Appendix 13.3 Conditional Mean Independence

518

(2)

Appendix 13.4 IV Estimation When the Causal Effect Varies Across Individuals

520

(3)

PART FOUR Regression Analysis of Economic Time Series Data

523

(152)

Introduction to Time Series Regression and Forecasting

525

(66)

Using Regression Models for Forecasting

527

(1)

Introduction to Time Series Data and Serial Correlation

528

(7)

The Rates of Inflation and Unemployment in the United States

528

(1)

Lags, First Differences, Logarithms, and Growth Rates

528

(4)

Autocorrelation

532

(1)

Other Examples of Economic Time Series

533

(2)

Autoregressions

535

(6)

The First Order Autoregressive Model

535

(3)

The pth Order Autoregressive Model

538

(3)

Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model

541

(8)

Forecasting Changes in the Inflation Rate Using Past Unemployment Rates

541

(3)

Stationarity

544

(1)

Time Series Regression with Multiple Predictors

545

(3)

Forecast Uncertainty and Forecast Intervals

548

(1)

Lag Length Selection Using Information Criteria

549

(5)

Determining the Order of an Autoregression

551

(2)

Lag Length Selection in Time Series Regression with Multiple Predictors

553

(1)

Nonstationarity I: Trends

554

(11)

What Is a Trend?

555

(2)

Problems Caused by Stochastic Trends

557

(3)

Detecting Stochastic Trends: Testing for a Unit AR Root

560

(4)

Avoiding the Problems Caused by Stochastic Trends

564

(1)

Nonstationarity II: Breaks

565

(12)

What Is a Break?

565

(1)

Testing for Breaks

566

(5)

Pseudo Out-of-Sample Forecasting

571

(5)

Avoiding the Problems Caused by Breaks

576

(1)

Conclusion

577

(14)

Appendix 14.1 Time Series Data Used in Chapter 14

586

(1)

Appendix 14.2 Stationarity in the AR(1) Model

586

(2)

Appendix 14.3 Lag Operator Notation

588

(1)

Appendix 14.4 ARMA Models

589

(1)

Appendix 14.5 Consistency of the BIC Lag Length Estimator

589

(2)

Estimation of Dynamic Causal Effects

591

(46)

An Initial Taste of the Orange Juice Data

593

(2)

Dynamic Causal Effects

595

(5)

Causal Effects and Time Series Data

596

(2)

Two Types of Exogeneity

598

(2)

Estimation of Dynamic Causal Effects with Exogenous Regressors

600

(4)

The Distributed Lag Model Assumptions

601

(1)

Autocorrelated ut, Standard Errors, and Inference

601

(1)

Dynamic Multipliers and Cumulative Dynamic Multipliers

602

(2)

Heteroskedasticity- and Autocorrelation-Consistent Standard Errors

604

(4)

Distribution of the OLS Estimator with Autocorrelated Errors

604

(2)

HAC Standard Errors

606

(2)

Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors

608

(10)

The Distributed Lag Model with AR(1) Errors

609

(3)

OLS Estimation of the ADL Model

612

(1)

GLS Estimation

613

(2)

The Distributed Lag Model with Additional Lags and AR(p) Errors

615

(3)

Orange Juice Prices and Cold Weather

618

(6)

Is Exogeneity Plausible? Some Examples

624

(3)

U.S. Income and Australian Exports

625

(1)

Oil Prices and Inflation

626

(1)

Monetary Policy and Inflation

626

(1)

The Phillips Curve

627

(1)

Conclusion

627

(10)

Appendix 15.1 The Orange Juice Data Set

634

(1)

Appendix 15.2 The ADL Model and Generalized Least Squares in Lag Operator Notation

634

(3)

Additional Topics in Time Series Regression

637

(38)

Vector Autoregressions

638

(4)

The VAR Model

638

(3)

A VAR Model of the Rates of Inflation and Unemployment

641

(1)

Multiperiod Forecasts

642

(6)

Iterated Multiperiod Forecasts

643

(2)

Direct Multiperiod Forecasts

645

(2)

Which Method Should You Use?

647

(1)

Orders of Integration and the DF-GLS Unit Root Test

648

(7)

Other Models of Trends and Orders of Integration

648

(2)

The DF-GLS Test for a Unit Root

650

(3)

Why Do Unit Root Tests Have Non-normal Distributions?

653

(2)

Cointegration

655

(9)

Cointegration and Error Correction

655

(3)

How Can You Tell Whether Two Variables Are Cointegrated?

658

(2)

Estimation of Cointegrating Coefficients

660

(1)

Extension to Multiple Cointegrated Variables

661

(1)

Application to Interest Rates

662

(2)

Volatility Clustering and Autoregressive Conditional Heteroskedasticity

664

(5)

Volatility Clustering

665

(1)

Autoregressive Conditional Heteroskedasticity

666

(1)

Application to Stock Price Volatility

667

(2)

Conclusion

669

(6)

Appendix 16.1 U.S. Financial Data Used in Chapter 16

674

(1)

PART FIVE The Econometric Theory of Regression Analysis

675

(80)

The Theory of Linear Regression with One Regressor

677

(27)

The Extended Least Squares Assumptions and the OLS Estimator

678

(2)

The Extended Least Squares Assumptions

678

(2)

The OLS Estimator

680

(1)

Fundamentals of Asymptotic Distribution Theory

680

(6)

Convergence in Probability and the Law of Large Numbers

681

(2)

The Central Limit Theorem and Convergence in Distribution

683

(2)

Slutsky's Theorem and the Continuous Mapping Theorem

685

(1)

Application to the t-Statistic Based on the Sample Mean

685

(1)

Asymptotic Distribution of the OLS Estimator and t-Statistic

686

(2)

Consistency and Asymptotic Normality of the OLS Estimators

686

(1)

Consistency of Heteroskedasticity-Robust Standard Errors

686

(2)

Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic

688

(1)

Exact Sampling Distributions When the Errors Are Normally Distributed

688

(3)

Distribution of β1 with Normal Errors

688

(2)

Distribution of the Homoskedasticity-only t-Statistic

690

(1)

Weighted Least Squares

691

(13)

WLS with Known Heteroskedasticity

691

(1)

WLS with Heteroskedasticity of Known Functional Form

692

(3)

Heteroskedasticity-Robust Standard Errors or WLS?

695

(5)

Appendix 17.1 The Normal and Related Distributions and Moments of Continuous Random Variables

700

(2)

Appendix 17.2 Two Inequalities

702

(2)

The Theory of Multiple Regression

704

(51)

The Linear Multiple Regression Model and OLS Estimator in Matrix Form

706

(4)

The Multiple Regression Model in Matrix Notation

706

(1)

The Extended Least Squares Assumptions

707

(1)

The OLS Estimator

708

(2)

Asymptotic Distribution of the OLS Estimator and t-Statistic

710

(3)

The Multivariate Central Limit Theorem

710

(1)

Asymptotic Normality of β

710

(1)

Heteroskedasticity-Robust Standard Errors

711

(1)

Confidence Intervals for Predicted Effects

712

(1)

Asymptotic Distribution of the t-Statistic

713

(1)

Tests of Joint Hypotheses

713

(2)

Joint Hypotheses in Matrix Notation

713

(1)

Asymptotic Distribution of the F-Statistic

714

(1)

Confidence Sets for Multiple Coefficients

714

(1)

Distribution of Regression Statistics with Normal Errors

715

(4)

Matrix Representations of OLS Regression Statistics

715

(1)

Distribution of β with Normal Errors

716

(1)

Distribution of s2/4

717

(1)

Homoskedasticity-Only Standard Errors

717

(1)

Distribution of the t-Statistic

718

(1)

Distribution of the F-Statistic

718

(1)

Efficiency of the OLS Estimator with Homoskedastic Errors

719

(2)

The Gauss-Markov Conditions for Multiple Regression

719

(1)

Linear Conditionally Unbiased Estimators

719

(1)

The Gauss-Markov Theorem for Multiple Regression

720

(1)

Generalized Least Squares

721

(6)

The GLS Assumptions

722

(2)

GLS When Ω Is Known

724

(1)

GLS When Ω Contains Unknown Parameters

725

(1)

The Zero Conditional Mean Assumption and GLS

725

(2)

Instrumental Variables and Generalized Method of Moments Estimation

727

(28)

The IV Estimator in Matrix Form

728

(1)

Asymptotic Distribution of the TSLS Estimator

729

(1)

Properties of TSLS When the Errors Are Homoskedastic

730

(3)

Generalized Method of Moments Estimation in Linear Models

733

(10)

Appendix 18.1 Summary of Matrix Algebra

743

(4)

Appendix 18.2 Multivariate Distributions

747

(1)

Appendix 18.3 Derivation of the Asymptotic Distribution of β

748

(1)

Appendix 18.4 Derivations of Exact Distributions of OLS Test Statistics with Normal Errors

749

(2)

Appendix 18.5 Proof of the Gauss-Markov Theorem for Multiple Regression

751

(1)

Appendix 18.6 Proof of Selected Results for IV and GMM Estimation

752

(3)

Appendix

755

(8)

References

763

(4)

Answers to ``Review the Concepts'' Questions

767

(8)

Glossary

775

(8)

Index

783

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Introduction to Econometrics

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