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Basic Econometrics

by: GUJARATI

Basic Econometrics

by: GUJARATI

ISBN 13:
9780070252141
ISBN 10:
0070252149
Edition: 3rd
Format: Hardcover
Copyright: 01/01/1995
Publisher: MCGRAW HILL BOOK COMPANY
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Summary

Gujarati's Basic Econometrics provides an elementary but comprehensive introduction to econometrics without resorting to matrix algebra, calculus, or statistics beyond the elementary level. Because of the way the book is organized, it may be used at a variety of levels of rigor. For example, if matrix algebra is used, theoretical exercises may be omitted. A CD of data sets is provided with the text.

Preface

xxi

Introduction

(14)

Part 1 Single-Equation Regression Models

(304)

1 The Nature of Regression Analysis

(17)

1.1 Historical Origin of the Term "Regression"

(1)

1.2 The Modern Interpretation of Regression

(3)

Examples

(3)

1.3 Statistical vs. Deterministic Relationships

(1)

1.4 Regression vs. Causation

(1)

1.5 Regression vs. Correlation

(1)

1.6 Terminology and Notation

(1)

1.7 The Nature and Sources of Data for Econometric Analysis

(4)

Types of Data

(1)

The Sources of Data

(2)

The Accuracy of Data

(1)

1.8 Summary and Conclusions

(1)

Exercises

(1)

Appendix 1A

(3)

1A.1 Sources of Economic Data

(2)

1A.2 Sources of Financial Data

(1)

2 Two-Variable Regression Analysis: Some Basic Ideas

(20)

2.1 A Hypothetical Example

(4)

2.2 The Concept of Population Regression Function (PRF)

(1)

2.3 The Meaning of the Term "Linear"

(2)

Linearity in the Variables

(1)

Linearity in the Parameters

(1)

2.4 Stochastic Specification of PRF

(1)

2.5 The Significance of the Stochastic Disturbance Term

(2)

2.6 The Sample Regression Function (SRF)

(4)

2.7 Summary and Conclusions

(1)

Exercises

(7)

3 Two-Variable Regression Model: The Problem of Estimation

(49)

3.1 The Method of Ordinary Least Squares

(7)

3.2 The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares

(10)

How Realistic Are These Assumptions?

(1)

3.3 Precision or Standard Errors of Least-Squares Estimates

(3)

3.4 Properties of Least-Squares Estimators: The Gauss-Markov Theorem

(2)

3.5 The Coefficient of Determination r^2: A Measure of "Goodness of Fit"

(6)

3.6 A Numerical Example

(3)

3.7 Illustrative Examples

(2)

Coffee Consumption in the United States, 1970-1980

(1)

Keynesian Consumption Function for the United States, 1980-1991

(1)

3.8 Computer Output for the Coffee Demand Function

(1)

3.9 A Note on Monte Carlo Experiments

(1)

3.10 Summary and Conclusions

(1)

Exercises

(7)

Questions

(2)

Problems

(5)

Appendix 3A

(7)

3A.1 Derivation of Least-Squares Estimates

(1)

3A.2 Linearity and Unbiasedness Properties of Least-Squares Estimators

(1)

3A.3 Variances and Standard Errors of Least-Squares Estimators

(1)

3A.4 Covariance between Beta(1) and Beta(2)

(1)

3A.5 The Least-Squares Estimator of Sigma^2

(1)

3A.6 Minimum-Variance Property of Least-Squares Estimators

(2)

3A.7 SAS Output of the Coffee Demand Function (3.7.1)

(2)

4 The Normality Assumption: Classical Normal Linear Regression Model (CNLRM)

101

(14)

4.1 The Probability Distribution of Disturbances u(i)

101

(1)

4.2 The Normality Assumption

102

(2)

4.3 Properties of OLS Estimators under the Normality Assumption

104

(3)

4.4 The Method of Maximum Likelihood (ML)

107

(1)

4.5 Probability Distributions Related to the Normal Distribution: The t, Chi-square (x^2), and F Distributions

107

(2)

4.6 Summary and Conclusions

109

(1)

Appendix 4A

110

(5)

Maximum Likelihood Estimation of Two-Variable Regression Model

110

(3)

Maximum Likelihood Estimation of the Consumption-Income Example

113

(1)

Appendix 4A Exercises

113

(2)

5 Two-Variable Regression: Interval Estimation and Hypothesis Testing

115

(40)

5.1 Statistical Prerequisites

115

(1)

5.2 Interval Estimation: Some Basic Ideas

116

(1)

5.3 Confidence Intervals for Regression Coefficients Beta(1) and Beta(2)

117

(3)

Confidence Interval for Beta(2)

117

(2)

Confidence Interval for Beta(1)

119

(1)

Confidence Interval for Beta(1) and Beta(2) Simultaneously

120

(1)

5.4 Confidence Interval for Sigma^2

120

(1)

5.5 Hypothesis Testing: General Comments

121

(1)

5.6 Hypothesis Testing: The Confidence-Interval Approach

122

(2)

Two-Sided or Two-Tail Test

122

(2)

One-Sided or One-Tail Test

124

(1)

5.7 Hypothesis Testing: The Test-of-Significance Approach

124

(5)

Testing the Significance of Regression Coefficients: The t-Test

124

(4)

Testing the Significance of Sigma^2: The x^2 Test

128

(1)

5.8 Hypothesis Testing: Some Practical Aspects

129

(5)

The Meaning of "Accepting" or "Rejecting" a Hypothesis

129

(1)

The "Zero" Null Hypothesis and the "2-t" Rule of Thumb

129

(1)

Forming the Null and Alternative Hypotheses

130

(1)

Choosing Alpha, the Level of Significance

131

(1)

The Exact Level of Significance: The p Value

132

(1)

Statistical Significance versus Practical Significance

133

(1)

The Choice between Confidence-Interval and Test-of-Significance Approaches to Hypothesis Testing

134

(1)

5.9 Regression Analysis and Analysis of Variance

134

(3)

5.10 Application of Regression Analysis: The Problem of Prediction

137

(3)

Mean Prediction

137

(1)

Individual Prediction

138

(2)

5.11 Reporting the Results of Regression Analysis

140

(1)

5.12 Evaluating the Results of Regression Analysis

140

(4)

Normality Test

141

(3)

Other Tests of Model Adequacy

144

(1)

5.13 Summary and Conclusions

144

(1)

Exercises

145

(7)

Questions

145

(2)

Problems

147

(5)

Appendix 5A

152

(3)

5A.1 Derivation of Equation (5.3.2)

152

(1)

5A.2 Derivation of Equation (5.9.1)

152

(1)

5A.3 Derivations of Equations (5.10.2) and (5.10.6)

153

(1)

Variance of Mean Prediction

153

(1)

Variance of Individual Prediction

153

(2)

6 Extensions of the Two-Variable Linear Regression Model

155

(36)

6.1 Regression through the Origin

155

(6)

r^2 for Regression-through-Origin Model

159

(1)

An Illustrative Example: The Characteristics Line of Portfolio Theory

159

(2)

6.2 Scaling and Units of Measurement

161

(4)

A Numerical Example: The Relationship between GPDI and GNP, United States, 1974-1983

163

(1)

A Word about Interpretation

164

(1)

6.3 Functional Forms of Regression Models

165

(1)

6.4 How to Measure Elasticity: The Log-Linear Model

165

(4)

An Illustrative Example: The Coffee Demand Function Revisited

167

(2)

6.5 Semilog Models: Log-Lin and Lin-Log Models

169

(4)

How to Measure the Growth Rate: The Log-Lin Model

169

(3)

The Lin-Log Model

172

(1)

6.6 Reciprocal Models

173

(3)

An Illustrative Example: The Phillips Curve for the United Kingdom, 1950-1966

176

(1)

6.7 Summary of Functional Forms

176

(2)

6.8 A Note on the Nature of the Stochastic Error Term: Additive versus Multiplicative Stochastic Error Term

178

(1)

6.9 Summary and Conclusions

179

(1)

Exercises

180

(6)

Questions

180

(3)

Problems

183

(3)

Appendix 6A

186

(5)

6A.1 Derivation of Least-Squares Estimators for Regression through the Origin

186

(3)

6A.2 SAS Output of the Characteristic Line (6.1.12)

189

(1)

6A.3 SAS Output of the United Kingdom Phillips Curve Regression (6.6.2)

190

(1)

7 Multiple Regression Analysis: The Problem of Estimation

191

(47)

7.1 The Three-Variable Model: Notation and Assumptions

192

(2)

7.2 Interpretation of Multiple Regression Equation

194

(1)

7.3 The Meaning of Partial Regression Coefficients

195

(2)

7.4 OLS and ML Estimation of the Partial Regression Coefficients

197

(4)

OLS Estimators

197

(1)

Variances and Standard Errors of OLS Estimators

198

(1)

Properties of OLS Estimators

199

(2)

Maximum Likelihood Estimators

201

(1)

7.5 The Multiple Coefficient of Determination R^2 and the Multiple Coefficient of Correlation R

201

(2)

7.6 Example 7.1: The Expectations-Augmented Phillips Curve for the United States, 1970-1982

203

(1)

7.7 Simple Regression in the Context of Multiple Regression: Introduction to Specification Bias

204

(3)

7.8 R^2 and the Adjusted R^2

207

(4)

Comparing Two R^2 Values

209

(1)

Example 7.2: Coffee Demand Function Revisited

210

(1)

The "Game" of Maximizing R^2

211

(1)

7.9 Partial Correlation Coefficients

211

(3)

Explanation of Simple and Partial Correlation Coefficients

211

(2)

Interpretation of Simple and Partial Correlation Coefficients

213

(1)

7.10 Example 7.3: The Cobb-Douglas Production Function: More on Functional Form

214

(3)

7.11 Polynomial Regression Models

217

(4)

Example 7.4: Estimating the Total Cost Function

218

(2)

Empirical Results

220

(1)

7.12 Summary and Conclusions

221

(1)

Exercises

221

(10)

Questions

221

(3)

Problems

224

(7)

Appendix 7A

231

(7)

7A.1 Derivation of OLS Estimators Given in Equations (7.4.3) and (7.4.5)

231

(1)

7A.2 Equality between a(1) of (7.3.5) and Beta(2) of (7.4.7)

232

(1)

7A.3 Derivation of Equation (7.4.19)

232

(1)

7A.4 Maximum Likelihood Estimation of the Multiple Regression Model

233

(1)

7A.5 The Proof that E(b(12)) = Beta(2) + Beta(3)b(32) (Equation 7.7.4)

234

(2)

7A.6 SAS Output of the Expectations-Augmented Phillips Curve (7.6.2)

236

(1)

7A.7 SAS Output of the Cobb-Douglas Production Function (7.10.4)

237

(1)

8 Multiple Regression Analysis: The Problem of Inference

238

(44)

8.1 The Normality Assumption Once Again

238

(1)

8.2 Example 8.1: U.S. Personal Consumption and Personal Disposal Income Relation, 1956-1970

239

(3)

8.3 Hypothesis Testing in Multiple Regression: General Comments

242

(1)

8.4 Hypothesis Testing about Individual Partial Regression Coefficients

242

(2)

8.5 Testing the Overall Significance of the Sample Regression

244

(10)

The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test

245

(3)

An Important Relationship between R^2 and F

248

(2)

The "Incremental," or "Marginal," Contribution of an Explanatory Variable

250

(4)

8.6 Testing the Equality of Two Regression Coefficients

254

(2)

Example 8.2: The Cubic Cost Function Revisited

255

(1)

8.7 Restricted Least Squares: Testing Linear Equality Restrictions

256

(6)

The t Test Approach

256

(1)

The F Test Approach: Restricted Least Squares

257

(2)

Example 8.3: The Cobb-Douglas Production Function for Taiwanese Agricultural Sector, 1958-1972

259

(1)

General F Testing

260

(2)

8.8 Comparing Two Regressions: Testing for Structural Stability of Regression Models

262

(3)

8.9 Testing the Functional Form of Regression: Choosing between Linear and Log-Linear Regression Models

265

(2)

Example 8.5: The Demand for Roses

266

(1)

8.10 Prediction with Multiple Regression

267

(1)

8.11 The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Tests

268

(1)

8.12 Summary and Conclusions

269

(1)

The Road Ahead

269

(1)

Exercises

270

(10)

Questions

270

(3)

Problems

273

(7)

Appendix 8A

280

(2)

Likelihood Ratio (LR) Test

280

(2)

9 The Matrix Approach to Linear Regression Model

282

(37)

9.1 The k-Variable Linear Regression Model

282

(2)

9.2 Assumptions of the Classical Linear Regression Model in Matrix Notation

284

(3)

9.3 OLS Estimation

287

(5)

An Illustration

289

(1)

Variance-Covariance Matrix of Beta

290

(1)

Properties of OLS Vector Beta

291

(1)

9.4 The Coefficient of Determination R^2 in Matrix Notation

292

(1)

9.5 The Correlation Matrix

292

(1)

9.6 Hypothesis Testing about Individual Regression Coefficients in Matrix Notation

293

(1)

9.7 Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notation

294

(1)

9.8 Testing Linear Restrictions: General F Testing Using Matrix Notation

295

(1)

9.9 Prediction Using Multiple Regression: Matrix Formulation

296

(2)

Mean Prediction

296

(1)

Individual Prediction

296

(1)

Variance of Mean Prediction

297

(1)

Variance of Individual Prediction

298

(1)

9.10 Summary of the Matrix Approach: An Illustrative Example

298

(5)

9.11 Summary and Conclusions

303

(1)

Exercises

304

(5)

Appendix 9A

309

(10)

9A.1 Derivation of k Normal or Simultaneous Equations

309

(1)

9A.2 Matrix Derivation of Normal Equations

310

(1)

9A.3 Variance-Covariance Matrix of Beta

310

(1)

9A.4 Blue Property of OLS Estimators

311

(8)

Part 2 Relaxing the Assumptions of the Classical Model

319

(180)

10 Multicollinearity and Micronumerosity

319

(36)

10.1 The Nature of Multicollinearity

320

(3)

10.2 Estimation in the Presence of Perfect Multicollinearity

323

(2)

10.3 Estimation in the Presence of "High" but "Imperfect" Multicollinearity

325

(1)

10.4 Multicollinearity: Much Ado about Nothing? Theoretical Consequences of Multicollinearity

325

(2)

10.5 Practical Consequences of Multicollinearity

327

(5)

Large Variances and Covariances of OLS Estimators

328

(1)

Wider Confidence Intervals

329

(1)

"Insignificant" t Ratios

330

(1)

A High R^2 but Few Significant t Ratios

330

(1)

Sensitivity of OLS Estimators and Their Standard Errors to Small Changes in Data

331

(1)

Consequences of Micronumerosity

332

(1)

10.6 An Illustrative Example: Consumption Expenditure in Relation to Income and Wealth

332

(3)

10.7 Detection of Multicollinearity

335

(4)

10.8 Remedial Measures

339

(5)

10.9 Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Only

344

(1)

10.10 Summary and Conclusions

345

(1)

Exercises

346

(9)

Questions

346

(5)

Problems

351

(4)

11 Heteroscedasticity

355

(45)

11.1 The Nature of Heteroscedasticity

355

(4)

11.2 OLS Estimation in the Presence of Heteroscedasticity

359

(3)

11.3 The Method of Generalized Least Squares (GLS)

362

(3)

Difference between OLS and GLS

364

(1)

11.4 Consequences of Using OLS in the Presence of Heteroscedasticity

365

(2)

OLS Estimation Allowing for Heteroscedasticity

365

(1)

OLS Estimation Disregarding Heteroscedasticity

366

(1)

11.5 Detection of Heteroscedasticity

367

(14)

Informal Methods

368

(1)

Formal Methods

369

(12)

11.6 Remedial Measures

381

(6)

When Sigma^2(i) Is Known: The Method of Weighted Least Squares

381

(1)

When Sigma^2 Is Not Known

382

(5)

11.7 A Concluding Example

387

(2)

11.8 Summary and Conclusions

389

(1)

Exercises

390

(8)

Questions

390

(2)

Problems

392

(6)

Appendix 11A

398

(2)

11A.1 Proof of Equation (11.2.2)

398

(1)

11A.2 The Method of Weighted Least Squares

399

(1)

12 Autocorrelation

400

(52)

12.1 The Nature of the Problem

400

(6)

12.2 OLS Estimation in the Presence of Autocorrelation

406

(3)

12.3 The BLUE Estimator in the Presence of Autocorrelation

409

(1)

12.4 Consequences of Using OLS in the Presence of Autocorrelation

410

(5)

OLS Estimation Allowing for Autocorrelation

410

(1)

OLS Estimation Disregarding Autocorrelation

411

(4)

12.5 Detecting Autocorrelation

415

(11)

Graphical Method

415

(4)

The Runs Test

419

(1)

Durbin-Watson d Test

420

(5)

Additional Tests of Autocorrelation

425

(1)

12.6 Remedial Measures

426

(7)

When the Structure of Autocorrelation Is Known

427

(1)

When p Is Not Known

428

(5)

12.7 An Illustrative Example: The Relationship between Help-Wanted Index and the Unemployment Rate, United States: Comparison of the Methods

433

(3)

12.8 Autoregressive Conditional Heteroscedasticity (ARCH) Model

436

(3)

What to Do If ARCH Is Present?

438

(1)

A Word on the Durbin-Watson d Statistic and the ARCH Effect

438

(1)

12.9 Summary and Conclusions

439

(1)

Exercises

440

(9)

Questions

440

(6)

Problems

446

(3)

Appendix 12A

449

(3)

12A.1 TSP Output of United States Wages (Y)-Productivity (X) Regression, 1960-1991

449

(3)

13 Econometric Modeling I: Traditional Econometric Methodology

452

(28)

13.1 The Traditional View of Econometric Modeling: Average Economic Regression (AER)

452

(3)

13.2 Types of Specification Errors

455

(1)

13.3 Consequences of Specification Errors

456

(3)

Omitting a Relevant Variable (Underfitting a Model)

456

(2)

Inclusion of an Irrelevant Variable (Overfitting a Model)

458

(1)

13.4 Tests of Specification Errors

459

(8)

Detecting the Presence of Unnecessary Variables

460

(1)

Tests for Omitted Variables and Incorrect Functional Form

461

(6)

13.5 Errors of Measurement

467

(5)

Errors of Measurement in the Dependent Variable Y

468

(1)

Errors of Measurement in the Explanatory Variable X

469

(1)

An Example

470

(1)

Measurement Errors in the Dependent Variable Y Only

471

(1)

Errors of Measurement in X

472

(1)

13.6 Summary and Conclusions

472

(1)

Exercises

473

(4)

Questions

473

(3)

Problems

476

(1)

Appendix 13A

477

(3)

13A.1 The Consequences of Including an Irrelevant Variable: The Unbiasedness Property

477

(1)

13A.2 Proof of (13.5.10)

478

(2)

14 Econometric Modeling II: Alternative Econometric Methodologies

480

(19)

14.1 Leamer's Approach to Model Selection

481

(4)

14.2 Hendry's Approach to Model Selection

485

(1)

14.3 Selected Diagnostic Tests: General Comments

486

(1)

14.4 Tests of Nonnested Hypothesis

487

(7)

The Discrimination Approach

487

(1)

The Discerning Approach

488

(6)

14.5 Summary and Conclusions

494

(1)

Exercises

494

(5)

Questions

494

(1)

Problems

495

(4)

Part 3 Topics in Econometrics

499

(136)

15 Regression on Dummy Variables

499

(41)

15.1 The Nature of Dummy Variables

499

(3)

Example 15.1: Professor's Salary by Sex

500

(2)

15.2 Regression on One Quantitative Variable and One Qualitative Variable with Two Classes, or Categories

502

(3)

Example 15.2: Are Inventories Sensitive to Interest Rates?

505

(1)

15.3 Regression on One Quantitative Variable and One Qualitative Variable with More than Two Classes

505

(2)

15.4 Regression on One Quantitative Variable and Two Qualitative Variables

507

(1)

15.5 Example 15.3: The Economics of "Moonlighting"

508

(1)

15.6 Testing for Structural Stability of Regression Models: Basic Ideas

509

(3)

Example 15.4: Savings and Income, United Kingdom, 1946-1963

509

(3)

15.7 Comparing Two Regressions: The Dummy Variable Approach

512

(2)

15.8 Comparing Two Regressions: Further Illustration

514

(2)

Example 15.5: The Behavior of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971

514

(2)

15.9 Interaction Effects

516

(1)

15.10 The Use of Dummy Variables in Seasonal Analysis

517

(2)

Example 15.6: Profits-Sales Behavior in U.S. Manufacturing

517

(2)

15.11 Piecewise Linear Regression

519

(3)

Example 15.7: Total Cost in Relation to Output

521

(1)

15.12 The Use of Dummy Variables in Combining Time Series and Cross-Sectional Data

522

(3)

Pooled Regression: Pooling Time Series and Cross-Sectional Data

522

(2)

Example 15.8: Investment Functions for General Motors and Westinghouse Companies

524

(1)

15.13 Some Technical Aspects of Dummy Variable Technique

525

(3)

The Interpretation of Dummy Variables in Semilogarithmic Regressions

525

(1)

Example 15.9: Semilogarithmic Regression with Dummy Variable

525

(1)

Another Method of Avoiding the Dummy Variable Trap

526

(1)

Dummy Variables and Heteroscedasticity

527

(1)

Dummy Variables and Autocorrelation

527

(1)

15.14 Topics for Further Study

528

(1)

15.15 Summary and Conclusions

529

(1)

Exercises

530

(8)

Questions

530

(5)

Problems

535

(3)

Appendix 15A

538

(2)

15A.1 Data Matrix for Regression (15.8.2)

538

(1)

15A.2 Data Matrix for Regression (15.10.2)

539

(1)

16 Regression on Dummy Dependent Variable: The LPM, Logit, Probit, and Tobit Models

540

(44)

16.1 Dummy Dependent Variable

540

(1)

16.2 The Linear Probability Model (LPM)

541

(1)

16.3 Problems in Estimation of LPM

542

(4)

Nonnormality of the Disturbances ui

542

(1)

Heteroscedastic Variances of the Disturbances

543

(1)

Nonfulfillment of (XXX)

544

(1)

Questionable Value of R^2 as a Measure of Goodness of Fit

545

(1)

16.4 LPM: A Numerical Example

546

(2)

16.5 Applications of LPM

548

(4)

Example 16.1: Cohen-Rea-Lerman study

548

(3)

Example 16.2: Predicting a Bond Rating

551

(1)

Example 16.3: Predicting Bond Defaults

552

(1)

16.6 Alternatives to LPM

552

(2)

16.7 The Logit Model

554

(2)

16.8 Estimation of the Logit Model

556

(2)

16.9 The Logit Model: A Numerical Example

558

(3)

16.10 The Logit Model: Illustrative Examples

561

(2)

Example 16.4: "An Application of Logit Analysis to Prediction of Merger Targets"

561

(1)

Example 16.5: Predicting a Bond Rating

562

(1)

16.11 The Probit Model

563

(4)

16.12 The Probit Model: A Numerical Example

567

(2)

Logit versus Probit

567

(1)

Comparing Logit and Probit Estimates

568

(1)

The Marginal Effect of a Unit Change in the Value of a Regressor

569

(1)

16.13 The Probit Model: Example 16.5

569

(1)

16.14 The Tobit Model

570

(5)

16.15 Summary and Conclusions

575

(1)

Exercises

576

(8)

Questions

576

(2)

Problems

578

(6)

17 Dynamic Econometric Model: Autoregressive and Distributed-Lag Models

584

(51)

17.1 The Role of "Time," or "Lag," in Economics

585

(4)

17.2 The Reasons for Lags

589

(1)

17.3 Estimation of Distributed-Lag Models

590

(2)

Ad Hoc Estimation of Distributed-Lag Models

590

(2)

17.4 The Koyck Approach to Distributed-Lag Models

592

(4)

The Median Lag

595

(1)

The Mean Lag

595

(1)

17.5 Rationalization of the Koyck Model: The Adaptive Expectations Model

596

(3)

17.6 Another Rationalization of the Koyck Model: The Stock Adjustment, or Partial Adjustment, Model

599

(2)

17.7 Combination of Adaptive Expectations and Partial Adjustment Models

601

(1)

17.8 Estimation of Autoregressive Models

602

(2)

17.9 The Method of Instrumental Variables (IV)

604

(1)

17.10 Detecting Autocorrelation in Autoregressive Models: Durbin h Test

605

(2)

17.11 A Numerical Example: The Demand for Money in India

607

(2)

17.12 Illustrative Examples

609

(3)

Example 17.7: The Fed and the Real Rate of Interest

609

(2)

Example 17.8: The Short- and Long-Run Aggregate Consumption Functions for the United States, 1946-1972

611

(1)

17.13 The Almon Approach to Distributed-Lag Models: The Almon or Polynomial Distributed Lag (PDL)

612

(8)

17.14 Causality in Economics: The Granger Test

620

(3)

The Granger Test

620

(2)

Empirical Results

622

(1)

17.15 Summary and Conclusions

623

(1)

Exercises

624

(11)

Questions

624

(6)

Problems

630

(5)

Part 4 Simultaneous-Equation Models

635

(74)

18 Simultaneous-Equation Models

635

(18)

18.1 The Nature of Simultaneous-Equation Models

635

(1)

18.2 Examples of Simultaneous-Equation Models

636

(6)

Example 18.1: Demand-and-Supply Model

636

(2)

Example 18.2: Keynesian Model of Income Determination

638

(1)

Example 18.3: Wage-Price Models

639

(1)

Example 18.4: The IS Model of Macroeconomics

639

(1)

Example 18.5: The LM Model

640

(1)

Example 18.6: Econometric Models

641

(1)

18.3 The Simultaneous-Equation Bias: Inconsistency of OLS Estimators

642

(3)

18.4 The Simultaneous-Equation Bias: A Numerical Example

645

(2)

18.5 Summary and Conclusions

647

(1)

Exercises

648

(5)

Questions

648

(3)

Problems

651

(2)

19 The Identification Problem

653

(25)

19.1 Notations and Definitions

653

(4)

19.2 The Identification Problem

657

(7)

Underidentification

657

(3)

Just, or Exact, Identification

660

(3)

Overidentification

663

(1)

19.3 Rules for Identification

664

(5)

The Order Condition of Identifiability

665

(1)

The Rank Condition of Identifiability

666

(3)

19.4 A Test of Simultaneity

669

(3)

Hausman Specification Test

670

(1)

Example 19.5: Pindyck-Rubinfeld Model of Public Spending

671

(1)

19.5 Tests for Exogeneity

672

(1)

A Note on Causality and Exogeneity

673

(1)

19.6 Summary and Conclusions

673

(1)

Exercises

674

(4)

20 Simultaneous-Equation Methods

678

(31)

20.1 Approaches to Estimation

678

(2)

20.2 Recursive Models and Ordinary Least Squares

680

(2)

20.3 Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS)

682

(4)

An Illustrative Example

683

(3)

Properties of ILS Estimators

686

(1)

20.4 Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS)

686

(4)

20.5 2SLS: A Numerical Example

690

(3)

20.6 Illustrative Examples

693

(6)

Example 20.1: Advertising, Concentration, and Price Margins

693

(1)

Example 20.2: Klein's Model I

694

(1)

Example 20.3: The Capital Asset Pricing Model Expressed as a Recursive System

694

(3)

Example 20.4: Revised Form of St. Louis Model

697

(2)

20.7 Summary and Conclusions

699

(1)

Exercises

700

(4)

Questions

700

(3)

Problems

703

(1)

Appendix 20A

704

(5)

20A.1 Bias in the Indirect Least-Squares Estimators

704

(1)

20A.2 Estimation of Standard Errors of 2SLS Estimators

705

(4)

Part 5 Time Series Econometrics

709

(46)

21 Time Series Econometrics I: Stationarity, Unit Roots, and Cointegration

709

(25)

21.1 A Look at Selected U.S. Economic Time Series

710

(1)

21.2 Stationary Stochastic Process

710

(4)

21.3 Test of Stationarity Based on Correlogram

714

(4)

21.4 The Unit Root Test of Stationarity

718

(4)

Is the U.S. GDP Time Series Stationary?

720

(1)

Is the First-Differenced GDP Series Stationary?

721

(1)

21.5 Trend-Stationary (TS) and Difference-Stationary (DS) Stochastic Process

722

(2)

21.6 Spurious Regression

724

(1)

21.7 Cointegration

725

(3)

Engle-Granger (EG) or Augmented Engle-Granger (AEG) Test

726

(1)

Cointegrating Regression Durbin-Watson (CRDW) Test

727

(1)

21.8 Cointegration and Error Correction Mechanism (ECM)

728

(1)

21.9 Summary and Conclusions

729

(1)

Exercises

730

(2)

Questions

730

(1)

Problems

731

(1)

Appendix 21A

732

(2)

21A.1 A Random Walk Model

732

(2)

22 Time Series Econometrics II: Forecasting with ARIMA and VAR Models

734

(21)

22.1 Approaches to Economic Forecasting

734

(2)

22.2 AR, MA, and ARIMA Modeling of Time Series Data

736

(2)

An Autoregressive (AR) Process

736

(1)

A Moving Average (MA) Process

737

(1)

An Autoregressive and Moving Average (ARMA) Process

737

(1)

An Autoregressive Integrated Moving Average (ARIMA) Process

737

(1)

22.3 The Box-Jenkins (BJ) Methodology

738

(1)

22.4 Identification

739

(3)

22.5 Estimation of the ARIMA Model

742

(1)

22.6 Diagnostic Checking

743

(1)

22.7 Forecasting

744

(1)

22.8 Further Aspects of the BJ Methodology

745

(1)

22.9 Vector Autoregression (VAR)

746

(6)

Estimation of VAR

746

(1)

Forecasting with VAR

747

(1)

Some Problems with VAR Modeling

747

(3)

An Application of VAR: A VAR Model of the Texas Economy

750

(2)

22.10 Summary and Conclusions

752

(1)

Exercises

753

(2)

Questions

753

(1)

Problems

753

(2)

Appendixes

755

(69)

A A Review of Some Statistical Concepts

755

(36)

B Rudiments of Matrix Algebra

791

(13)

C A List of Statistical Computer Packages

804

(3)

D Statistical Tables

807

(17)

Table D.1 Areas under the Standardized Normal Distribution

808

(1)

Table D.2 Percentage Points of the t Distribution

809

(1)

Table D.3 Upper Percentage Points of the F Distribution

810

(6)

Table D.4 Upper Percentage Points of the x^2 Distribution

816

(2)

Table D.5 Durbin-Watson d Statistic: Significant Points of d(L) and d(U) at 0.05 and 0.01 Levels of Significance

818

(4)

Table D.6 Critical Values of Runs in the Runs Test

822

(2)

Selected Bibliography

824

(3)

Indexes

827

Name Index

827

(4)

Subject Index

831

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Basic Econometrics

Basic Econometrics

9780070252141

0070252149

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Table of Contents

Supplemental Materials

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Amazon no longer offers textbook rentals. We do!

Basic Econometrics

Basic Econometrics

9780070252141

0070252149

Summary

Table of Contents

Supplemental Materials

Write a Review

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