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CHAPTER1 The Nature of Econometrics and Economic Data 1

1-1 What Is Econometrics？ 1

1-2 Steps in Empirical Economic Analysis 2

1-3 The Structure of Economic Data 5

1-3a Cross-Sectional Data 5

1-3b Time Series Data 7

1-3c Pooled Cross Sections 8

1-3d Panel or Longitudinal Data 9

1-3e A Comment on Data Structures 10

1-4 Causality，Ceteris Paribus，and Counterfactual Reasoning 10

Summary 14

Key Terms 15

Problems 15

Computer Exercises 15

PART1 Regression Analysis with Cross-Sectional Data 19

CHAPTER 2 The Simple Regression Model 20

2-1 Definition of the Simple Regression Model 20

2-2 Deriving the Ordinary Least Squares Estimates 24

2-2a A Note on Terminology 31

2-3 Properties of OLS on Any Sample of Data 32

2-3a Fitted Values and Residuals 32

2-3b Algebraic Properties of OLS Statistics 32

2-3c Goodness-of-Fit 35

2-4 Units of Measurement and Functional Form 36

2-4a The Effects of Changing Units of Measurement on OLS Statistics 36

2-4b Incorporating Nonlinearities in Simple Regression 37

2-4c The Meaning of “Linear” Regression 40

2-5 Expected Values and Variances of the OLS Estimators 40

2-5a Unbiasedness of OLS 40

2-5b Variances of the OLS Estimators 45

2-5c Estimating the Error Variance 48

2-6 Regression through the Origin and Regression on a Constant 50

2-7 Regression on a Binary Explanatory Variable 51

2-7a Counterfactual Outcomes，Causality，and Policy Analysis 53

Summary 56

Key Terms 57

Problems 58

Computer Exercises 62

CHAPTER 3 Multiple Regression Analysis：Estimation 66

3-1 Motivation for Multiple Regression 67

3-1a The Model with Two Independent Variables 67

3-1 b The Model with k Independent Variables 69

3-2 Mechanics and Interpretation of Ordinary Least Squares 70

3-2a Obtaining the OLS Estimates 70

3-2b Interpreting the OLS Regression Equation 71

3-2c On the Meaning of “Holding Other Factors Fixed”in Multiple Regression 73

3-2d Changing More Than One Independent Variable Simultaneously 74

3-2e OLS Fitted Values and Residuals 74

3-2f A “Partialling Out” Interpretation of Multiple Regression 75

3-2g Comparison of Simple and Multiple Regression Estimates 75

3-2h Goodness-of-Fit 76

3-2i Regression through the Origin 79

3-3 The Expected Value of the OLS Estimators 79

3-3a Including Irrelevant Variables in a Regression Model 83

3-3b Omitted Variable Bias：The Simple Case 84

3-3c Omitted Variable Bias：More General Cases 87

3-4 The Variance of the OLS Estimators 87

3-4a The Components of the OLS Variances：Multicollinearity 89

3-4b Variances in Misspecified Models 92

3-4c Estimating σ2：Standard Errors of the OLS Estimators 93

3-5 Efficiency of OLS：The Gauss-Markov Theorem 95

3-6 Some Comments on the Language of Multiple Regression Analysis 96

3-7 Several Scenarios for Applying Multiple Regression 97

3-7a Prediction 98

3-7b Efficient Markets 98

3-7c Measuring the Tradeoff between Two Variables 99

3-7d Testing for Ceteris Paribus Group Differences 99

3-7e Potential Outcomes，Treatment Effects，and Policy Analysis 100

Summary 102

Key Terms 104

Problems 104

Computer Exercises 109

CHAPTER 4 Multiple Regression Analysis：Inference 117

4-1 Sampling Distributions of the OLS Estimators 117

4-2 Testing Hypotheses about a Single Population Parameter：The tTest 120

4-2a Testing against One-Sided Alternatives 122

4-2b Two-Sided Alternatives 126

4-2c Testing Other Hypotheses about β j 128

4-2d Computing p-Values fort Tests 130

4-2e A Reminder on the Language of Classical Hypothesis Testing 132

4-2f Economic，or Practical，versus Statistical Significance 132

4-3 Confidence Intervals 134

4-4 Testing Hypotheses about a Single Linear Combination of the Parameters 136

4-5 Testing Multiple Linear Restrictions：The F Test 139

4-5a Testing Exclusion Restrictions 139

4-5b Relationship between F and t Statistics 144

4-5c The R-Squared Form of the F Statistic 145

4-5d Computing p- Values for F Tests 146

4-5e The F Statistic for Overall Significance of a Regression 147

4-5f Testing General Linear Restrictions 148

4-6 Reporting Regression Results 149

4-7 Revisiting Causal Effects and Policy Analysis 151

Summary 152

Key Terms 154

Problems 154

Computer Exercises 159

CHAPTER 5 Multiple Regression Analysis：OLS Asymptotics 163

5-1 Consistency 164

5-1a Deriving the Inconsistency in OLS 167

5-2 Asymptotic Normality and Large Sample Inference 168

5-2a Other Large Sample Tests：The Lagrange Multiplier Statistic 172

5-3 Asymptotic Efficiency of OLS 175

Summary 176

Key Terms 176

Problems 176

Computer Exercises 178

CHAPTER 6 Multiple Regression Analysis：Further Issues 181

6-1 Effects of Data Scaling on OLS Statistics 181

6-1a Beta Coefficients 184

6-2 More on Functional Form 186

6-2a More on Using Logarithmic Functional Forms 186

6-2b Models with Quadratics 188

6-2c Models with Interaction Terms 192

6-2d Computing Average Partial Effects 194

6-3 More on Goodness-of-Fit and Selection of Regressors 195

6-3a Adjusted R-Squared 196

6-3b Using Adjusted R-Squared to Choose between Nonnested Models 197

6-3c Controlling for Too Many Factors in Regression Analysis 199

6-3d Adding Regressors to Reduce the Error Variance 200

6-4 Prediction and Residual Analysis 201

6.4a Confidence Intervals for Predictions 201

6-4b Residual Analysis 205

6-4c Predicting y When log（y） Is the Dependent Variable 205

6-4d Predicting y When the Dependent Variable Is log（y） 207

Summary 209

Key Terms 211

Problems 211

Computer Exercises 214

CHAPTER 7 Multiple Regression Analysis with Qualitative Information 220

7-1 Describing Qualitative Information 221

7-2 A Single Dummy Independent Variable 222

7-2a Interpreting Coeffcients on Dummy Explanatory Variables When the Dependent Variable Is log（y） 226

7-3 Using Dummy Variables for Multiple Categories 228

7-3a Incorporating Ordinal Information by Using Dummy Variables 230

7-4 Interactions Involving Dummy Variables 232

7-4a Interactions among Dummy Variables 232

7-4b Allowing for Different Slopes 233

7-4c Testing for Differences in Regression Functions across Groups 237

7-5 A Binary Dependent Variable：The Linear Probability Model 239

7-6 More on Policy Analysis and Program Evaluation 244

7-6a Program Evaluation and Unrestricted Regression Adjustment 245

7-7 Interpreting Regression Results with Discrete Dependent Variables 249

Summary 250

Key Terms 251

Problems 251

Computer Exercises 256

CHAPTER 8 Heteroskedasticity 262

8-1 Consequences of Heteroskedasticity for OLS 262

8-2 Heteroskedasticity-Robust Inference after OLS Estimation 263

8-2a Computing Heteroskedasticity-Robust LM Tests 267

8-3 Testing for Heteroskedasticity 269

8-3a The White Test for Heteroskedasticity 271

8-4 Weighted Least Squares Estimation 273

8-4a The Heteroskedasticity Is Known up to a Multiplicative Constant 273

8-4b The Heteroskedasticity Function Must Be Estimated：Feasible GLS 278

8-4c What If the Assumed Heteroskedasticity Function Is Wrong？ 281

8-4d Prediction and Prediction Intervals with Heteroskedasticity 283

8-5 The Linear Probability Model Revisited 284

Summary 286

Key Terms 287

Problems 287

Computer Exercises 290

CHAPTER 9 More on Specification and Data Issues 294

9-1 Functional Form Misspecification 295

9-1a RESET as a General Test for Functional Form Misspecification 297

9-1b Tests against Nonnested Alternatives 298

9-2 Using Proxy Variables for Unobserved Explanatory Variables 299

9-2a Using Lagged Dependent Variables as Proxy Variables 303

9-2b A Different Slant on Multiple Regression 304

9-2c Potential Outcomes and Proxy Variables 305

9-3 Models with Random Slopes 306

9-4 Properties of OLS under Measurement Error 308

9-4a Measurement Error in the Dependent Variable 308

9-4b Measurement Error in an Explanatory Variable 310

9-5 Missing Data，Nonrandom Samples，and Outlying Observations 313

9-5a Missing Data 313

9-5b Nonrandom Samples 315

9-5c Outliers and Influential Observations 317

9-6 Least Absolute Deviations Estimation 321

Summary 323

Key Terms 324

Problems 324

Computer Exercises 328

PART2 Regression Analysis with Time Series Data 333

CHAPTER 10 Basic Regression Analysis with Time Series Data 334

10-1 The Nature of Time Series Data 334

10-2 Examples of Time Series Regression Models 335

10-2a Static Models 336

10-2b Finite Distributed Lag Models 336

10-2c A Convention about the Time Index 338

10-3 Finite Sample Properties of OLS under Classical Assumptions 339

10-3a Unbiasedness of OLS 339

10-3b The Variances of the OLS Estimators and the Gauss-Markov Theorem 342

10-3c Inference under the Classical Linear Model Assumptions 344

10-4 Functional Form，Dummy Variables，and Index Numbers 345

10-5 Trends and Seasonality 351

10-5a Characterizing Trending Time Series 351

10-5b Using Trending Variables in Regression Analysis 354

10-5c A Detrending Interpretation of Regressions with a Time Trend 356

10-5d Computing R-Squared When the Dependent Variable Is Trending 357

10-5e Seasonality 358

Summary 360

Key Terms 361

Problems 361

Computer Exercises 363

CHAPTER 11 Further Issues in Using OLS with Time Series Data 366

11-1 Stationary and Weakly Dependent Time Series 367

11-1a Stationary and Nonstationary Time Series 367

11-1b Weakly Dependent Time Series 368

11-2 Asymptotic Properties of OLS 370

11-3 Using Highly Persistent Time Series in Regression Analysis 376

11-3a Highly Persistent Time Series 376

11-3b Transformations on Highly Persistent Time Series 380

11-3c Deciding Whether a Time Series Is Ⅰ（1） 381

11-4 Dynamically Complete Models and the Absence of Serial Correlation 382

11-5 The Homoskedasticity Assumption for Time Series Models 385

Summary 386

Key Terms 387

Problems 387

Computer Exercises 390

CHAPTER 12 Serial Correlation and Heteroskedasticity in Time Series Regressions 394

12-1 Properties of OLS with Serially Correlated Errors 395

12-1a Unbiasedness and Consistency 395

12-1b Efficiency and Inference 395

12-1c Goodness-of-Fit 396

12-1d Serial Correlation in the Presence of Lagged Dependent Variables 396

12-2 Serial Correlation-Robust Inference after OLS 398

12-3 Testing for Serial Correlation 401

12-3a A t Test forAR（1） Serial Correlation with Strictly Exogenous Regressors 402

12-3b The Durbin-Watson Test under Classical Assumptions 403

12-3c Testing for AR（1） Serial Correlation without Strictly Exogenous Regressors 404

12-3d Testingfor Higher-Order Serial Correlation 406

12-4 Correcting for Serial Correlation with Strictly Exogenous Regressors 407

12-4a Obtaining the Best Linear Unbiased Estimator in the AR（1） Model 408

12-4b Feasible GLS Estimation with AR（1）Errors 409

12-4c Comparing OLS and FGLS 411

12-4d Correcting for Higher-Order Serial Correlation 413

12-4e What if the Serial Correlation Model Is Wrong？ 413

12-5 Differencing and Serial Correlation 414

12-6 Heteroskedasticity in Time Series Regressions 415

12-6a Heteroskedasticity-Robust Statistics 416

12-6b Testing for Heteroskedasticity 416

12-6c Autoregressive Conditional Heteroskedasticity 417

12-6d Heteroskedasticity and Serial Correlation in Regression Models 418

Summary 419

Key Terms 420

Problems 420

Computer Exercises 421

PART3 Advanced Topics 425

CHAPTER 13 Pooling Cross Sections across Time：Simple Panel Data Methods 426

13-1 Pooling Independent Cross Sections across Time 427

13-1 a The Chow Test for Structural Change across Time 431

13-2 Policy Analysis with Pooled Cross Sections 431

13-2a Adding an Additional Control Group 436

13-2b A General FrameworkforPolicy Analysis with Pooled Cross Sections 437

13-3 Two-Period Panel Data Analysis 439

13-3a Organizing Panel Data 444

13-4 Policy Analysis with Two-Period Panel Data 444

13-5 Differencing with More Than Two Time Periods 447

13-5a Potential Pitfalls in First Differencing Panel Data 451

Summary 451

Key Terms 452

Problems 452

Computer Exercises 453

CHAPTER 14 Advanced Panel Data Methods 462

14-1 Fixed Effects Estimation 463

14-1a The Dummy Variable Regression 466

14-1b Fixed Effects or First Differencing？ 467

14-1c Fixed Effects with Unbalanced Panels 468

14-2 Random Effects Models 469

14-2a Random Effects or Pooled OLS？ 473

14-2b Random Effects or Fixed Effects？ 473

14-3 The Correlated Random Effects Approach 474

14-3a Unbalanced Panels 476

14-4 General Policy Analysis with Panel Data 477

14-4a Advanced Considerations with Policy Analysis 478

14-5 Applying Panel Data Methods to Other Data Structures 480

Summary 483

Key Terms 484

Problems 484

Computer Exercises 486

CHAPTER 15 Instrumental Variables Estimation and Two-Stage Least Squares 495

15-1 Motivation：Omitted Variables in a Simple Regression Model 496

15-1 a Statistical Inference with the Ⅳ Estimator 500

15-1 b Properties of Ⅳ with a Poor Instrumental Variable 503

15-1 c Computing R -Squared after Ⅳ Estimation 505

15-2 Ⅳ Estimation of the Multiple Regression Model 505

15-3 Two-Stage Least Squares 509

15-3a A Single Endogenous Explanatory Variable 509

15-3b Multicollinearity and 2SLS 511

15-3c Detecting Weak Instruments 512

15-3d Multiple Endogenous Explanatory Variables 513

15-3e Testing Multiple Hypotheses after 2SLS Estimation 513

15-4 Ⅳ Solutions to Errors-in-Variables Problems 514

15-5 Testing for Endogeneity and Testing Overidentifying Restrictions 515

15-5a Testing for Endogeneity 515

15-5b Testing Overidentification Restrictions 516

15-6 2SLS with Heteroskedasticity 518

15-7 Applying 2SLS to Time Series Equations 519

15-8 Applying 2SLS to Pooled Cross Sections and Panel Data 521

Summary 522

Key Terms 523

Problems 523

Computer Exercises 526

CHAPTER 16 Simultaneous Equations Models 534

16-1 The Nature of Simultaneous Equations Models 535

16-2 Simultaneity Bias in OLS 538

16-3 Identifying and Estimating a Structural Equation 539

16-3a Identification in a Two-Equation System 540

16-3b Estimation by 2SLS 543

16-4 Systems with More Than Two Equations 545

16-4a Identification in Systems with Three or More Equations 545

16-4b Estimation 546

16-5 Simultaneous Equations Models with Time Series 546

16-6 Simultaneous Equations Models with Panel Data 549

Summary 551

Key Terms 552

Problems 552

Computer Exercises 555

CHAPTER 17 Limited Dependent Variable Models and Sample Selection Corrections 559

17-1 Logit and Probit Models for Binary Response 560

17-1a Specifying Logit and Probit Models 560

17-1 b Maximum Likelihood Estimation of Logit and Probit Models 563

17-1c Testing Multiple Hypotheses 564

17-1d Interpreting the Logit and Probit Estimates 565

17-2 The Tobit Model for Corner Solution Responses 571

17-2a Interpreting the Tobit Estimates 572

17-2b Specification Issues in Tobit Models 578

17-3 The Poisson Regression Model 578

17-4 Censored and Truncated Regression Models 582

17-4a Censored Regression Models 583

17-4b Truncated Regression Models 586

17-5 Sample Selection Corrections 588

17-5a When Is OLS on the Selected Sample Consistent？ 588

17-5b Incidental Truncation 589

Summary 593

Key Terms 593

Problems 594

Computer Exercises 596

CHAPTER 18 Advanced Time Series Topics 604

18-1 Infinite Distributed Lag Models 605

18-1 a The Geometric （or Koyck） Distributed Lag Model 607

18-1 b Rational Distributed Lag Models 608

18-2 Testing for Unit Roots 610

18-3 Spurious Regression 614

18-4 Cointegration and Error Correction Models 616

18-4a Cointegration 616

18-4b Error Correction Models 620

18-5 Forecasting 622

18-5a Types of Regression Models Used for Forecasting 623

18-5b One-Step-Ahead Forecasting 624

18-5c Comparing One-Step-Ahead Forecasts 627

18-5d Multiple-Step-Ahead Forecasts 628

18-5e Forecasting Trending，Seasonal，and Integrated Processes 631

Summary 635

Key Terms 636

Problems 636

Computer Exercises 638

CHAPTER 19 Carrying Out an Empirical Project 642

19-1 Posing a Question 642

19-2 Literature Review 644

19-3 Data Collection 645

19-3a Deciding on the Appropriate Data Set 645

19-3b Entering and Storing Your Data 646

19-3c Inspecting，Cleaning，and Summarizing Your Data 647

19-4 Econometric Analysis 648

19-5 Writing an Empirical Paper 651

19-5a Introduction 651

19-5b Conceptual （or Theoretical） Framework 652

19-5c Econometric Models and Estimation Methods 652

19-5d The Data 654

19-5e Results 655

19.5f Conclusions 656

19-5g Style Hints 656

Summary 658

Key Terms 658

Sample Empirical Projects 658

List of Journals 664

Data Sources 665

MATH REFRESHER A Basic Mathematical Tools 666

A-1 The Summation Operator and Descriptive Statistics 666

A-2 Properties of Linear Functions 668

A-3 Proportions and Percentages 671

A-4 Some Special Functions and Their Properties 672

A-4a Quadratic Functions 672

A-4b The Natural Logarithm 674

A-4c The Exponential Function 677

A-5 Differential Calculus 678

Summary 680

Key Terms 681

Problems 681

MATH REFRESHER B Fundamentals of Probability 684

B-1 Random Variables and Their Probability Distributions 684

B-1 a Discrete Random Variables 685

B-1b Continuous Random Variables 687

B-2 Joint Distributions，Conditional Distributions，and Independence 688

B-2a Joint Distributions and Independence 688

B-2b Conditional Distributions 690

B-3 Features of Probability Distributions 691

B-3a A Measure of Central Tendency：The Expected Value 691

B-3b Properties of Expected Values 692

B-3c Another Measure ofCentral Tendency：The Median 694

B-3d Measures of Variability：Variance and Standard Deviation 695

B-3e Variance 695

B-3f Standard Deviation 696

B-3g Standardizing a Random Variable 696

B-3h Skewness and Kurtosis 697

B-4 Features of Joint and Conditional Distributions 697

B-4a Measures of Association：Covariance and Correlation 697

B-4b Covariance 697

B-4c Correlation Coefficient 698

B-4d Variance of Sums of Random Variables 699

B-4e Conditional Expectation 700

B-4f Properties of Conditional Expectation 702

B-4g Conditional Variance 704

B-5 The Normal and Related Distributions 704

B-5a The Normal Distribution 704

B-5b The Standard Normal Distribution 705

B-5c Additional Properties of the Normal Distribution 707

B-5d The Chi-Square Distribution 708

B-5e The t Distribution 708

B-5f The F Distribution 709

Summary 711

Key Terms 711

Problems 711

MATH REFRESHER C Fundamentals of Mathematical Statistics 714

C-1 Populations，Parameters，and Random Sampling 714

C-1 a Sampling 714

C-2 Finite Sample Properties of Estimators 715

C-2a Estimators and Estimates 715

C-2b Unbiasedness 716

C-2C The Sampling Variance of Estimators 718

C-2d Efficiency 719

C-3 Asymptotic or Large Sample Properties of Estimators 721

C-3a Consistency 721

C-3b Asymptotic Normality 723

C-4 General Approaches to Parameter Estimation 724

C-4a Method of Moments 725

C-4b Maximum Likelihood 725

C-4c Least Squares 726

C-5 Interval Estimation and Confidence Intervals 727

C-5a The Nature of Interval Estimation 727

C-5b Confidence Intervals for the Mean from a Normally Distributed Population 729

C-5c A Simple Rule of Thumbfor a 95onfidence Interval 731

C-5d Asymptotic Confidence Intervals for Nonnormal Populations 732

C-6 Hypothesis Testing 733

C-6a Fundamentals of Hypothesis Testing 733

C-6b Testing Hypotheses about the Mean in a Normal Population 735

C-6c Asymptotic Tests for Nonnormal Populations 738

C-6d Computing and Using p- Values 738

C-6e The Relationship between Confidence Intervals and Hypothesis Testing 741

C-6f Practical versus Statistical Significance 742

C-7 Remarks on Notation 743

Summary 743

Key Terms 744

Problems 744

ADVANCED TREATMENT D Summary of Matrix Algebra 749

D-1 Basic Definitions 749

D-2 Matrix Operations 750

D-2a Matrix Addition 750

D-2b Scalar Multiplication 750

D-2c Matrix Multiplication 751

D-2d Transpose 752

D-2e Partitioned Matrix Multiplication 752

D-2f Trace 753

D-2g Inverse 753

D-3 Linear Independence and Rank of a Matrix 754

D-4 Quadratic Forms and Positive Definite Matrices 754

D-5 Idempotent Matrices 755

D-6 Differentiation of Linear and Quadratic Forms 755

D-7 Moments and Distributions of Random Vectors 756

D-7a Expected Value 756

D-7b Variance-Covariance Matrix 756

D-7c Multivariate Normal Distribution 756

D-7d Chi-Square Distribution 757

D-7e t Distribution 757

D-7f F Distribution 757

Summary 757

Key Terms 757

Problems 758

ADVANCED TREATMENT E The Linear Regression Model in Matrix Form 760

E-1 The Model and Ordinary Least Squares Estimation 760

E-1 a The Frisch-Waugh Theorem 762

E-2 Finite Sample Properties of OLS 763

E-3 Statistical Inference 767

E-4 Some Asymptotic Analysis 769

E-4a Wald Statistics for Testing Multiple Hypotheses 771

Summary 771

Key Terms 771

Problems 772

Answers to Going Further Questions 775

Statistical Tables 784

References 791

Glossary 797

Index 812