Introductory Econometrics: A Modern Approach

886 Pages·2010·5.96 MB·English

by  Jeffrey Wooldridge

Introductory
Econometrics
A Modern Approach
4e
Jeffrey M. Wooldridge
Michigan State University
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Introductory Econometrics, Fourth Edition © 2009, 2006 South-Western, a part of Cengage Learning
Jeff rey M. Wooldridge
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Brief Contents
Chapter 1 The Nature of Econometrics and Economic Data 1
PART 1: REGRESSION ANALYSIS WITH CROSS-SECTIONAL DATA 21
Chapter 2 The Simple Regression Model 22
Chapter 3 Multiple Regression Analysis: Estimation 68
Chapter 4 Multiple Regression Analysis: Inference 117
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 167
Chapter 6 Multiple Regression Analysis: Further Issues 184
Chapter 7 Multiple Regression Analysis with Qualitative Information:
Binary (or Dummy) Variables 225
Chapter 8 Heteroskedasticity 264
Chapter 9 More on Specifi cation and Data Issues 300
PART 2: REGRESSION ANALYSIS WITH TIME SERIES DATA 339
Chapter 10 Basic Regression Analysis with Time Series Data 340
Chapter 11 Further Issues in Using OLS with Time Series Data 377
Chapter 12 Serial Correlation and Heteroskedasticity in Time
Series Regressions 408
PART 3: ADVANCED TOPICS 443
Chapter 13 Pooling Cross Sections across Time: Simple Panel
Data Methods 444
Chapter 14 Advanced Panel Data Methods 481
Chapter 15 Instrumental Variables Estimation and Two Stage Least Squares 506
Chapter 16 Simultaneous Equations Models 546
Chapter 17 Limited Dependent Variable Models and Sample
Selection Corrections 574
Chapter 18 Advanced Time Series Topics 623
Chapter 19 Carrying Out an Empirical Project 668
APPENDICES
Appendix A Basic Mathematical Tools 695
Appendix B Fundamentals of Probability 714
Appendix C Fundamentals of Mathematical Statistics 747
Appendix D Summary of Matrix Algebra 788
Appendix E The Linear Regression Model in Matrix Form 799
Appendix F Answers to Chapter Questions 813
Appendix G Statistical Tables 823
References 830
Glossary 835
Index 849
iii
Contents
2.5 Expected Values and Variances of the OLS
CHAPTER 1
Estimators 46
The Nature of Econometrics Unbiasedness of OLS 47
and Economic Data 1 Variances of the OLS Estimators 52
Estimating the Error Variance 56
2.6 Regression through the Origin 58
1.1 What Is Econometrics? 1
Summary 59
1.2 Steps in Empirical Economic Analysis 2
Key Terms 60
1.3 The Structure of Economic Data 5
Problems 61
Cross-Sectional Data 5
Computer Exercises 64
Time Series Data 8
Appendix 2A 66
Pooled Cross Sections 9
Panel or Longitudinal Data 10
CHAPTER 3
A Comment on Data Structures 12
1.4 Causality and the Notion of Ceteris Paribus in Multiple Regression Analysis:
Econometric Analysis 12
Estimation 68
Summary 17
Key Terms 17
3.1 Motivation for Multiple Regression 68
Problems 17
The Model with Two Independent
Computer Exercises 18
Variables 68
The Model with k Independent Variables 71
PART 1
3.2 Mechanics and Interpretation of Ordinary Least
Regression Analysis with Squares 73
Cross-Sectional Data 21 Obtaining the OLS Estimates 73
Interpreting the OLS Regression Equation 74
On the Meaning of “Holding Other Factors
CHAPTER 2
Fixed” in Multiple Regression 77
The Simple Regression Model 22 Changing More Than One Independent Variable
S imultaneously 77
2.1 Definition of the Simple Regression OLS Fitted Values and Residuals 77
Model 22 A “Partialling Out” Interpretation of
2.2 Deriving the Ordinary Least Squares Multiple Regression 78
Estimates 27 Comparison of Simple and Multiple Regression
A Note on Terminology 35 Estimates 79
2.3 Properties of OLS on Any Sample of Data 36 Goodness-of-Fit 80
Fitted Values and Residuals 36 Regression through the Origin 83
Algebraic Properties of OLS Statistics 37 3.3 The Expected Value of the OLS
Goodness-of-Fit 40 Estimators 84
2.4 Units of Measurement and Functional Including Irrelevant Variables in a Regression
Form 41 Model 89
The Effects of Changing Units of Measurement Omitted Variable Bias: The Simple Case 89
on OLS Statistics 41 Omitted Variable Bias: More General Cases 93
Incorporating Nonlinearities in Simple 3.4 The Variance of the OLS Estimators 94
Regression 43 The Components of the OLS Variances:
The Meaning of “Linear” Regression 46 Multicollinearity 95
iv
Contents v
Variances in Misspecified Models 99 5.2 Asymptotic Normality and Large Sample
Estimating (cid:1)2: Standard Errors of the Inference 172
OLS Estimators 101 Other Large Sample Tests: The Lagrange
3.5 Efficiency of OLS: The Gauss-Markov Multiplier Statistic 176
Theorem 102 5.3 Asymptotic Efficiency of OLS 179
Summary 104 Summary 180
Key Terms 105 Key Terms 181
Problems 105 Problems 181
Computer Exercises 110 Computer Exercises 181
Appendix 3A 113 Appendix 5A 182
CHAPTER 4 CHAPTER 6
Multiple Regression Analysis: Multiple Regression Analysis:
Inference 117 Further Issues 184
4.1 Sampling Distributions of the OLS 6.1 Effects of Data Scaling on OLS
Estimators 117 Statistics 184
4.2 Testing Hypotheses about a Single Population Beta Coefficients 187
Parameter: The t Test 120 6.2 More on Functional Form 189
Testing against One-Sided Alternatives 123 More on Using Logarithmic Functional
Two-Sided Alternatives 128 Forms 189
Testing Other Hypotheses about (cid:2) 130 Models with Quadratics 192
j
Computing p-Values for t Tests 133 Models with Interaction Terms 197
A Reminder on the Language of Classical 6.3 More on Goodness-of-Fit and Selection
Hypothesis Testing 135 of Regressors 199
Economic, or Practical, versus Statistical Adjusted R-Squared 200
Significance 135 Using Adjusted R-Squared to Choose between
4.3 Confidence Intervals 138 Nonnested Models 201
4.4 Testing Hypotheses about a Single Linear Controlling for Too Many Factors in
Combination of the Parameters 140 Regression Analysis 203
4.5 Testing Multiple Linear Restrictions: Adding Regressors to Reduce the Error
The F Test 143 Variance 205
Testing Exclusion Restrictions 143 6.4 Prediction and Residual Analysis 206
Relationship between F and t Statistics 149 Confidence Intervals for
The R-Squared Form of the F Statistic 150 Predictions 206
Computing p-Values for F Tests 151 Residual Analysis 209
The F Statistic for Overall Significance of a Predicting y When log(y) Is the Dependent
Regression 152 Variable 210
Testing General Linear Restrictions 153 Summary 215
4.6 Reporting Regression Results 154 Key Terms 215
Summary 156 Problems 216
Key Terms 158 Computer Exercises 218
Problems 159 Appendix 6A 223
Computer Exercises 163
CHAPTER 7
CHAPTER 5
Multiple Regression Analysis with
Multiple Regression Analysis:
Qualitative Information: Binary
OLS Asymptotics 167
(or Dummy) Variables 225
5.1 Consistency 167
Deriving the Inconsistency in OLS 170 7.1 Describing Qualitative Information 225
vi Contents
7.2 A Single Dummy Independent Variable 226 RESET as a General Test for Functional Form
Interpreting Coefficients on Dummy Explanatory Misspecification 303
Variables When the Dependent Variable Is Tests against Nonnested Alternatives 305
log(y) 231 9.2 Using Proxy Variables for Unobserved
7.3 Using Dummy Variables for Multiple Explanatory Variables 306
Categories 233 Using Lagged Dependent Variables as Proxy
Incorporating Ordinal Informationby Using Variables 310
Dummy Variables 235 A Different Slant on Multiple
7.4 Interactions Involving Dummy Variables 238 Regression 312
Interactions among Dummy Variables 238 9.3 Models with Random Slopes 313
Allowing for Different Slopes 239 9.4 Properties of OLS under Measurement
Testing for Differences in Regression Functions Error 315
across Groups 243 Measurement Error in the Dependent
7.5 A Binary Dependent Variable: The Linear Variable 316
Probability Model 246 Measurement Error in an Explanatory
7.6 More on Policy Analysis and Program Variable 318
Evaluation 251 9.5 Missing Data, Nonrandom Samples, and
Summary 254 Outlying Observations 322
Key Terms 255 Missing Data 322
Problems 255 Nonrandom Samples 323
Computer Exercises 258 Outliers and Influential Observations 325
9.6 Least Absolute Deviations Estimation 330
CHAPTER 8
Summary 331
Heteroskedasticity 264 Key Terms 332
Problems 332
8.1 Consequences of Heteroskedasticity for OLS 264 Computer Exercises 334
8.2 Heteroskedasticity-Robust Inference after
OLS Estimation 265 PART 2
Computing Heteroskedasticity-Robust
LM Tests 269 Regression Analysis with
8.3 Testing for Heteroskedasticity 271 Time Series Data 339
The White Test for Heteroskedasticity 274
8.4 Weighted Least Squares Estimation 276
CHAPTER 10
The Heteroskedasticity Is Known up to a
Multiplicative Constant 277 Basic Regression Analysis with Time
The Heteroskedasticity Function Must Be Series Data 340
Estimated: Feasible GLS 282
What If the Assumed Heteroskedasticity
10.1 The Nature of Time Series Data 340
Function Is Wrong? 287
10.2 Examples of Time Series Regression
Prediction and Prediction Intervals with
Models 342
Heteroskedasticity 289
Static Models 342
8.5 The Linear Probability Model Revisited 290
Finite Distributed Lag Models 342
Summary 293
A Convention about the Time Index 345
Key Terms 294
10.3 Finite Sample Properties of OLS under Classical
Problems 294
Assumptions 345
Computer Exercises 296
Unbiasedness of OLS 345
The Variances of the OLS Estimators and the
CHAPTER 9
Gauss-Markov Theorem 349
More on Specifi cation and
Inference under the Classical Linear Model
Data Issues 300 Assumptions 351
10.4 Functional Form, Dummy Variables, and
9.1 Functional Form Misspecification 300 Index Numbers 353
Contents vii
10.5 Trends and Seasonality 360 Serial Correlation in the Presence of Lagged
Characterizing Trending Time Series 360 Dependent Variables 411
Using Trending Variables in Regression 12.2 Testing for Serial Correlation 412
Analysis 363 A t Test for AR(1) Serial Correlation with
A Detrending Interpretation of Regressions with Strictly Exogenous Regressors 412
a Time Trend 365 The Durbin-Watson Test under Classical
Computing R-Squared when the Dependent Assumptions 415
Variable Is Trending 366 Testing for AR(1) Serial Correlation without
Seasonality 368 Strictly Exogenous Regressors 416
Summary 370 Testing for Higher Order Serial
Key Terms 371 Correlation 417
Problems 371 12.3 Correcting for Serial Correlation with Strictly
Computer Exercises 373 Exogenous Regressors 419
Obtaining the Best Linear Unbiased Estimator
CHAPTER 11 in the AR(1) Model 419
Feasible GLS Estimation with AR(1)
Further Issues in Using OLS with
Errors 421
Time Series Data 377
Comparing OLS and FGLS 423
Correcting for Higher Order Serial
11.1 Stationary and Weakly Dependent Correlation 425
Time Series 377 12.4 Differencing and Serial Correlation 426
Stationary and Nonstationary Time 12.5 Serial Correlation-Robust Inference
Series 378 after OLS 428
Weakly Dependent Time Series 379 12.6 Heteroskedasticity in Time Series
11.2 Asymptotic Properties of OLS 381 Regressions 432
11.3 Using Highly Persistent Time Series in Heteroskedasticity-Robust Statistics 432
Regression Analysis 388 Testing for Heteroskedasticity 432
Highly Persistent Time Series 388 Autoregressive Conditional
Transformations on Highly Persistent Heteroskedasticity 433
Time Series 393 Heteroskedasticity and Serial Correlation in
Deciding Whether a Time Series Regression Models 435
Is I(1) 394 Summary 437
11.4 Dynamically Complete Models and the Absence Key Terms 437
of Serial Correlation 396 Problems 438
11.5 The Homoskedasticity Assumption for Time Computer Exercises 438
Series Models 399
Summary 400
PART 3
Key Terms 401
Problems 401 Advanced Topics 443
Computer Exercises 404
CHAPTER 13
CHAPTER 12
Pooling Cross Sections across Time:
Serial Correlation and
Simple Panel Data Methods 444
Heteroskedasticity in Time
Series Regressions 408 13.1 Pooling Independent Cross Sections
across Time 445
12.1 Properties of OLS with Serially Correlated The Chow Test for Structural Change
Errors 408 across Time 449
Unbiasedness and Consistency 408 13.2 Policy Analysis with Pooled Cross Sections 450
Efficiency and Inference 409 13.3 Two-Period Panel Data Analysis 455
Goodness-of-Fit 410 Organizing Panel Data 461
viii Contents
13.4 Policy Analysis with Two-Period 15.4 IV Solutions to Errors-in-Variables
Panel Data 462 Problems 525
13.5 Differencing with More Than Two 15.5 Testing for Endogeneity and Testing
Time Periods 465 Overidentifying Restrictions 527
Potential Pitfalls in First Differencing Testing for Endogeneity 527
Panel Data 470 Testing Overidentification Restrictions 529
Summary 471 15.6 2SLS with Heteroskedasticity 531
Key Terms 471 15.7 Applying 2SLS to Time Series Equations 531
Problems 471 15.8 Applying 2SLS to Pooled Cross Sections and
Computer Exercises 473 Panel Data 534
Appendix 13A 478 Summary 536
Key Terms 536
CHAPTER 14 Problems 536
Advanced Panel Data Methods 481 Computer Exercises 539
Appendix 15A 543
14.1 Fixed Effects Estimation 481
CHAPTER 16
The Dummy Variable Regression 485
Fixed Effects or First Differencing? 487 Simultaneous Equations Models 546
Fixed Effects with Unbalanced Panels 488
14.2 Random Effects Models 489
16.1 The Nature of Simultaneous Equations
Random Effects or Fixed Effects? 493
Models 546
14.3 Applying Panel Data Methods to Other
16.2 Simultaneity Bias in OLS 550
Data Structures 494
16.3 Identifying and Estimating a Structural
Summary 496
Equation 552
Key Terms 496
Identification in a Two-Equation System 552
Problems 497
Estimation by 2SLS 557
Computer Exercises 498
16.4 Systems with More Than Two Equations 559
Appendix 14A 503
Identification in Systems with Three or
More Equations 559
CHAPTER 15
Estimation 560
Instrumental Variables Estimation 16.5 Simultaneous Equations Models with
and Two Stage Least Squares 506 Time Series 560
16.6 Simultaneous Equations Models with
Panel Data 564
15.1 Motivation: Omitted Variables in a Simple
Summary 566
Regression Model 507
Key Terms 567
Statistical Inference with the
Problems 567
IV Estimator 510
Computer Exercises 570
Properties of IV with a Poor Instrumental
Variable 514
CHAPTER 17
Computing R-Squared after
IV Estimation 516 Limited Dependent Variable
15.2 IV Estimation of the Multiple Regression Models and Sample Selection
Model 517
Corrections 574
15.3 Two Stage Least Squares 521
A Single Endogenous Explanatory
Variable 521 17.1 Logit and Probit Models for Binary
Multicollinearity and 2SLS 523 Response 575
Multiple Endogenous Explanatory Specifying Logit and Probit Models 575
Variables 524 Maximum Likelihood Estimation of Logit and
Testing Multiple Hypotheses after Probit Models 578
2SLS Estimation 525 Testing Multiple Hypotheses 579
Contents ix
Interpreting the Logit and Probit 19.2 Literature Review 670
Estimates 580 19.3 Data Collection 671
17.2 The Tobit Model for Corner Solution Deciding on the Appropriate Data Set 671
Responses 587 Entering and Storing Your Data 672
Interpreting the Tobit Estimates 589 Inspecting, Cleaning, and Summarizing
Specification Issues in Tobit Models 594 Your Data 673
17.3 The Poisson Regression Model 595 19.4 Econometric Analysis 675
17.4 Censored and Truncated Regression 19.5 Writing an Empirical Paper 678
Models 600 Introduction 678
Censored Regression Models 601 Conceptual (or Theoretical) Framework 679
Truncated Regression Models 604 Econometric Models and Estimation
17.5 Sample Selection Corrections 606 Methods 679
When Is OLS on the Selected Sample The Data 682
Consistent? 607 Results 682
Incidental Truncation 608 Conclusions 683
Summary 612 Style Hints 684
Key Terms 613 Summary 687
Problems 614 Key Terms 687
Computer Exercises 615 Sample Empirical Projects 687
Appendix 17A 620 List of Journals 692
Appendix 17B 621 Data Sources 693
CHAPTER 18 APPENDIX A
Advanced Time Series Topics 623 Basic Mathematical Tools 695
18.1 Infinite Distributed Lag Models 624 A.1 The Summation Operator and Descriptive
The Geometric (or Koyck) Distributed Lag 626 Statistics 695
Rational Distributed Lag Models 628 A.2 Properties of Linear Functions 697
18.2 Testing for Unit Roots 630 A.3 Proportions and Percentages 699
18.3 Spurious Regression 636 A.4 Some Special Functions and
18.4 Cointegration and Error Correction Models 637 Their Properties 702
Cointegration 637 Quadratic Functions 702
Error Correction Models 643 The Natural Logarithm 704
18.5 Forecasting 645 The Exponential Function 708
Types of Regression Models Used for A.5 Differential Calculus 709
Forecasting 646 Summary 711
One-Step-Ahead Forecasting 647 Key Terms 711
Comparing One-Step-Ahead Forecasts 651 Problems 711
Multiple-Step-Ahead Forecasts 652
Forecasting Trending, Seasonal, and Integrated APPENDIX B
Processes 655
Fundamentals of Probability 714
Summary 660
Key Terms 661
Problems 661 B.1 Random Variables and Their Probability
Computer Exercises 663 Distributions 714
Discrete Random Variables 715
CHAPTER 19 Continuous Random Variables 717
B.2 Joint Distributions, Conditional Distributions,
Carrying Out an Empirical
and Independence 719
Project 668
Joint Distributions and Independence 719
Conditional Distributions 721
19.1 Posing a Question 668 B.3 Features of Probability Distributions 722