Introductory economettrics: a modern approach

INTERNATIONAL STUDENT EDITION

I n t r o d u c t o r y

E c o n o m e t r ic s

A M o d e r n A p p r o a c h

Third Edition

THIRD EDITION

INTRODUCTORY

ECONOMETRICS

A MODERN APPROACH

JEFFREY M. WOOLDRIDGE

Michigan State University

THOMSON

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Brief Contents

Chapter I The Nature of Econometrics and Economic Data 1

PART 1: Regression Analysis with Cross-Sectional Data 23

Chapter 2 The Simple Regression Model 24

Chapter 3 Multiple Regression Analysis: Estimation 73

Chapter 4 Multiple Regression Analysis: Inference 123

Chapter 5 Multiple Regression Analysis: OLS Asymptotics 176

Chapter 6 Multiple Regression Analysis: Further Issues 192

Chapter 7 Multiple Regression Analysis with Qualitative Information:

Binary (or Dummy) Variables 230

Chapter 8 Heteroskedasticity 271

Chapter 9 More on Specification and Data Problems 304

PART 2: Regression Analysis with Time Series Data 341

Chapter 10 Basic Regression Analysis with Time Series Data 342

Chapter 11 Further Issues in Using OLS with Time Series Data 380

Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regressions 412

PART 3: Advanced Topics 447

Chapter 13 Pooling Cross Sections Across Time: Simple Panel Data Methods 448

Chapter 14 Advanced Panel Data Methods 485

Chapter 15 Instrumental Variables Estimation and Two Stage Least Squares 510

Chapter 16 Simultaneous Equations Models 552

Chapter 17 Limited Dependent Variable Models and Sample Selection Corrections 582

Chapter 18 Advanced Time Series Topics 632

Chapter 19 Carrying out an Empirical Project 678

A P PEN D IC ES_______________________________________________________________________________

Appendix A Basic Mathematical Tools 707

Appendix B Fundamentals of Probability 728

Appendix C Fundamentals of Mathematical Statistics 763

Appendix D Summary of Matrix Algebra 808

Appendix E The Linear Regression Model in Matrix Form 819

Appendix F Answers to Chapter Questions 834

Appendix G Statistical Tables 847

References 854

Glossary 859

Index 873

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Contents

C H A PT ER 1

The Nat h rc' ot Econometrics

and Economic Data 1

1.1 What Is Econom etricsI

1.2 Steps in Empirical Economic Analysis 2

1.3 The Structure ot’ Economic Data 5

Cross-Sectional Data 6

Time Series Data 8

Pooled Cross Sections 10

Panel or Longitudinal Data 10

,4 Comment on Data Structures I *

1.4 Causality and the Notion ot Ceteris Paribus

in Econometric Analysis 13

Summary 18

Key Terms 19

Problems 19

Computer Exercises 20

Regression Analysis with

Cross-Sectional Data 23

C H A PTER 2

The Simple Regression Model 24

2.1 Definition of the Simple Regression Model 24

2.2 Deriving the Ordinary Least Squares

Estimates 29

.4 Note on Terminology 38

2.3 Properties of OLS on Any Sample of Data 38

Fitted Values and Residuals 39

Algebraic Properties of OLS Statistics 40

Goodness-of-Fit 42

2.4 Units of Measurement and Functional Form 44

The Effects of Changing Units of Measurement

on OLS Statistics 44

Incorporating Xonlinearitics in SimpU

Regrcssiim 46

The Meaning oJ "Linear" Regression 4w

2.5 Expected Values and Variances of the OLS

Estimators 50

L'nbiasedness of OLS 50

Miriam es of the OI.S Estimators 56

Estimating the Error Variance 60

2.6 Regression through the Origin 63

Summary 64

Key Terms 65

Problems 66

Computer Exercises 69

Appendix 2A 71

C H A PTER 3

Multiple Regression Analysis: Estimation ” 3

3.1 Motivation for Multiple Regression 73

The Model with Two Independent Variables 73

The Model with k Independent Variables 76

3.2 Mechanics and Interpretation of Ordinary Least

Squares 78

Obtaining the OLS Estimates 7H

Interpreting the OLS Regression Equation 80

On the Meaning of "Holding Other Factors

Fixed" in Multiple Regression 82

Changing More than One Independent Variable

Simultaneously 82

OLS Fitted Values and Residuals 83

.4 “Partialling Out " Interpretation of Multiple

Regression 83

Comparison of Simple and Multiple Regression

Estimates 84

Goodness-of-Fit 85

Regression through the Origin 88

3.3 The Expected Value of the OLS Estimators 89

Including Irrelevant Variables in a Regression

Model 9 4

Omitted Variable Bias: The Simple Case 95

PART 1

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Contents v

Omitted Variable Bias: More General

Cases 98

3.4 The Variance of the OLS Estimators 99

The Components of the OLS Variances:

Multicollinearity 1 01

Variances in Misspecified Models 105

Estimating a 2: Standard Errors of the OLS

Estimators 106

3.5 Efficiency of OLS: The Gauss-Markov

Theorem 108

Summary 109

Key Terms 111

Problems 111

Computer Exercises 116

Appendix 3A 119

C H A PT ER 4

M ultiple Regression Analysis: Inference 123

4.1 Sampling Distributions

of the OLS Estimators 123

4.2 Testing Hypotheses about a Single

Population Parameter: The t Test 126

Testing against One-Sided Alternatives 129

Two-Sided Alternatives 134

Testing Other Hypotheses about (3j 136

Computing p-Values for t Tests 139

A Reminder on the Language of Classical

Hypothesis Testing 142

Economic, or Practical, versus Statistical

Significance 142

4.3 Confidence Intervals 145

4.4 Testing Hypotheses about a Single Linear

Combination of the Parameters 147

4.5 Testing Multiple Linear Restrictions:

The F Test 150

Testing Exclusion Restrictions 150

Relationship between F and t Statistics 157

The R-Squared Form of the F Statistic 158

Computing p-Values for F Tests 159

The F Statistic fo r Overall Significance

of a Regression 160

Testing General Linear Restrictions 161

4.6 Reporting Regression Results 163

Summary 165

Key Terms 167

Problems 168

Computer Exercises 173

C H A PTER 5

Multiple Regression Analysis:

O LS Asymptotics 1 76

5.1 Consistency 176

Deriving the Inconsistency in OLS 179

5.2 Asymptotic Normality and Large

Sample Inference 181

Other Large Sample Tests: The Lagrange

Multiplier Statistic 185

5.3 Asymptotic Efficiency of OLS 187

Summary 189

Key Terms 189

Problems 190

Computer Exercises 190

Appendix 5A 191

C H A PT ER 6

M ultiple Regression Analysis:

Further Issues 192

6.1 Effects of Data Scaling on OLS Statistics 192

Beta Coefficients 195

6.2 More on Functional Form 197

More on Using Logarithmic Functional

Forms 197

Models with Quadratics 200

Models with Interaction Terms 204

6.3 More on Goodness-of-Fit

and Selection of Regressors 206

Adjusted R -Squared 208

Using Adjusted R -Squared to Choose

between Nonnested Models 209

Controlling for Too Many Factors

in Regression Analysis 211

Adding Regressors to Reduce the Error

Variance 213

6.4 Prediction and Residual Analysis 214

Confidence Intervals for Predictions 214

Residual Analysis 217

Predicting y When log(y) Is the Dependent

Variable 218

Summary 221

Key Terms 222

Problems 222

Computer Exercises 224

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VI Contents

C H A PTER 7

Multiple* Regression Analysis

with Qualitative Information:

Binary (or Dum my) Variables 230

7.1 Describing Qualitative Information 230

7.2 A Single Dummy Independent Variable 232

Interpreting Coefficients on Dummy Explanatory

Variables When the Dependent Variable

Islog(y) 237

7.3 Using Dummy Variables

for Multiple Categories 239

Incorporating Ordinal Information

by Using Dummy Variables 240

7.4 Interactions Involving Dummy Variables 244

Interactions among Dummy Variables 244

Allowing for Different Slopes 245

Testing for Diff erences in Regre s sion Functions

across Groups 249

7.5 A Binary Dependent Variable:

The Linear Probability Model 252

7.6 More on Policy Analysis

and Program Evaluation 258

Summary 260

Key Terms 261

Problems 261

Computer Exercises 265

C H A PTER 8

Heteroskedasticity 271

8.1 Consequences of Heteroskedasticity

for OLS 271

8.2 Heteroskedasticity-Robust Inference

after OLS Estimation 272

Computing Heteroskedasticity-Robust

LM Tests 276

8.3 Testing for Heteroskedasticity 278

The White Test for Heteroskedasticity 282

8.4 Weighted Least Squares Estimation 284

The Heteroskedasticity Is Known

up to a Multiplicative Constant 284

The Heteroskedasticity Function Must

Be Estimated: Feasible GLS 290

8.5 The Linear Probability Model Revisited 295

Summary 297

Key Terms 298

Problems 298

Computer Exercises 300

C H A PTER 9

More on Specification

and Data Problems 304

9.1 Functional Form Misspecification 3(U

RESET as a General Test for Flint tional

Form Misspecification 308

Tests against Nonnested Altematix es 3m

9.2 Using Proxy Variables for Unobserved

Explanatory Variables 310

Using Lagged Dependent Variables

as Proxy Variables 315

A Different Slant on Multiple Regression 31'

9.3 Properties of OLS under Measurement

Error 318

Measurement Error in the Dependent

Variable 3/8

Measurement Error in tin Explanatory

Variable 321

9.4 Missing Data. Nonrandom Samples,

and Outlying Observations 325

Missing Data 325

Nonrandom Samples 326

Outliers and Influential Observ ations 328

Summary 333

Key Terms 334

Problems 334

Computer Exercises 336

m PART 2

Regression Analysis with

Time Series Data 341

C H A PT ER 10

Basic Regression Analysis

with Time Series Data 342

10.1 The Nature of Time Series Data 342

10.2 Examples of Time Series Regression

Models 344

Static Models 344

Finite Distributed Lag Models 344

A Convention about the Time Index 34

10.3 Finite Sample Properties of OLS

under Classical Assumptions 347

Unbiasedness of OLS 34 7

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Contents

The Variances of the OLS Estimators

and the Gauss-Markov Theorem 351

Inference under the Classical Linear Model

Assumptions 353

10.4 Functional Form. Dummy Variables,

and Index Numbers 355

10.5 Trends and Seasonality 363

Characterizing Trending Time Series 363

Using Trending Variables in Regression

Analysis 3 66

A Detrending Interpretation of Regre ssions

with a Time Trend 368

Computing R-Squared When the Dependent

Variable Is Trending 369

Seasonality 371

Summary 373

Key Terms 375

Problems 375

Computer Exercises 377

C H A PT ER 11

Further Issues in Using O LS

with Time Series Data 380

11.1 Stationary and Weakly Dependent Time

Series 380

Stationary and Nonstationary Time Series 381

Weakly Dependent Time Series 382

11.2 Asymptotic Properties of OLS 385

11.3 Using Highly Persistent Time Series

in Regression Analysis 392

Highly Persistent Time Series 392

Transformations on Highly Persistent Time

Series 397

Deciding Whether a Time Series Is l( I ) 398

11.4 Dynamically Complete Models

and the Absence of Serial Correlation 400

11.5 The Homoskedasticity Assumption

for Time Series Models 403

Summary 403

Key Terms 405

Problems 405

Computer Exercises 408

C H A PT ER 12

Serial Correlation and Heteroskedasticity

in Time Series Regressions 412

12.1 Properties of OLS with Serially Correlated

Errors 412

I nbiasedness and Consistency 412

Efficiency and Inference 413

Goodness-of-Fit 414

Serial Correlation in the Presence

nf Lagged Dependent Variables 415

12.2 Testing for Serial Correlation 416

A t Test for ARl /) Serial Correlation

with Strictly Exogenous Regressors 416

The Durbin-Watson Test under Classical

Assumptions 419

Testing for AR( 1) Serial Correlation

without Strictly Exogenous Regressors 420

Testing for Higher Order Serial

Correlation 422

12.3 Correcting for Serial Correlation

with Strictly Exogenous Regressors 424

Obtaining the Best Linear Unbiased Estimator

in the AR( I ) Model 424

Feasible GLS Estimation with AR( I )

Errors 425

Comparing OLS and FG LS 428

Correcting for Higher Order Serial

Correlation 430

12.4 Differencing and Serial Correlation 431

12.5 Serial Correlation-Robust

Inference after OLS 432

12.6 Heteroskedasticity in Time Series

Regressions 436

Heteroskedasticity -Robust Statistics 436

Testing for Heteroskedasticity 436

Autoregressive Conditional

He te roskedas tici ty 438

Heteroskedasticity and Serial Correlation

in Regression Models 440

Summary 441

Key Terms 442

Problems 442

Computer Exercises 443

PART 3

Advanced Topics 447

C H A PT ER 13

Pooling Cross Sections across Time:

Simple Panel Data Methods 448

13,1 Pooling Independent Cross Sections

across Time 449

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VIII Contents

The Chow Test for Structural Change

across Time 454

13.2 Policy Analysis with Pooled Cross

Sections 454

13.3 Two-Period Panel Data Analysis 460

Organizing Panel Data 467

13.4 Policy Analysis with Two-Period Panel

Data 467

13.5 Differencing with More Than

Two Time Periods 470

Potential Pitfalls in First-Differencing Panel

Data 475

Summary 476

Key Terms 476

Problems 476

Computer Exercises 478

Appendix 13A 483

C H A PTER 14

Advanced Panel Data Methods 485

14.1 Fixed Effects Estimation 485

The Dummy Variable Regression 489

Fixed Effects or First Differencing ? 491

Fixed Effects with Unbalanced Panels 492

14.2 Random Effects Models 493

Random Effects or Fixed Effects? 497

14.3 Applying Panel Data Methods

to Other Data Structures 498

Summary 500

Key Terms 501

Problems 501

Computer Exercises 503

Appendix 14A 507

C H A PT ER 15

Instrumental Variables Estimation

and Two Stage Least Squares 510

15.1 Motivation: Omitted Variables in a Simple

Regression Model 511

Statistical Inference with the IV Estimator 514

Properties of IV with a Poor Instrumental

Variable 519

Computing R -Squared after IV Estimation 520

15.2 IV Estimation of the Multiple Regression

Model 521

15.3 Two Stage Least Squares 525

A Single Endogenous Explanatory

Variable 525

Multicollinearity and 2SLS 528

Multiple Endogenous Explanatory

Variables 528

Testing Multiple Hypotheses after 2SLS

Estimation 529

15.4 IV Solutions to Errors-in-Variables

Problems 530

15.5 Testing for Endogeneity and Testing

0\eridentify ing Restrictions 532

Testing for Endogeneity 532

Testing Overidentification Restrictions 533

15.6 2SLS w ith Heteroskedasticity 535

15.7 Apply ing 2SLS to Time Series Equations 536

15.8 Apply ing 2SLS to Pooled Cross Sections

and Panel Data 538

Summary 540

Key Terms 541

Problems 541

Computer Exercises 544

Appendix 15A 549

C H A PT ER 16

Simultaneous Equations Models 552

16.1 The Nature of Simultaneous

Equations Models 552

16.2 Simultaneity Bias in OLS 557

16.3 Identifying and Estimating

a Structural Equation 559

Identification in a Two-Equation System 559

Estimation by 2SLS 564

16.4 Sy stems with More Than Two Equations 565

Identification in Systems with Three

or More Equations 566

Estimation 567

16.5 Simultaneous Equations Models

w ith Time Series 567

16.6 Simultaneous Equations Models

w ith Panel Data 571

Summary 573

Key Terms 574

Problems 574

Computer Exercises 577

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Contents

C H A PT ER 17

Limited Dependent Variable Models

and Sample Selection Corrections 582

17.1 Logit and Prohit Models for Binary

Response 583

Specifying Logit and Prohit Models 583

Maximum Likelihood Estimation of Logit and

Prohit Models 586

Testing Multiple Hypotheses 587

Interpreting the Logit and Prohit

Estimates 588

17.2 The Tobit Model

for Corner Solution Responses 595

Interpreting the Tobit Estimates 597

Specification Issues in Tobit Models 602

17.3 The Poisson Regression Model 604

17.4 Censored and Truncated Regression

Models 609

Censored Regression Models 610

Truncated Regression Models 613

17.5 Sample Selection Corrections 616

When Is OLS on the Selected Sample

Consistent? 616

Incidental Truncation 618

Summary 622

Key Terms 623

Problems 624

Computer Exercises 625

Appendix 17A 630

C H A PT ER 18

Advanced Time Series Topics 632

18.1 Infinite Distributed Lag Models 633

The Geometric (or Koyck) Distributed Lag

635

Rational Distributed Lag Models 637

18.2 Testing for Unit Roots 639

18.3 Spurious Regression 645

18.4 Cointegration and Error Correction Models 647

Cointegration 6 47

Error Correction Models 652

18.5 Forecasting 654

Types of Regression Models Used

for Forecasting 656

One-Step-Ahead Forecasting 657

Comparing One-Step-Ahead Forecasts 661

Multiple-Step-Ahead Forecasts 662

Forecasting Trending. Seasonal, and Integrated

Processes 665

Summary 670

Key Terms 671

Problems 671

Computer Exercises 674

C H A PT ER 19

Carrying Out an Empirical Project 678

19.1 Posing a Question 678

19.2 Literature Review 680

19.3 Data Collection 681

Deciding on the Appropriate Data Set 681

Entering and Storing Your Data 682

Inspecting. Cleaning, and Summarizing Your

Data 684

19.4 Econometric Analysis 685

19.5 Writing an Empirical Paper 689

Introduction 689

Conceptual (or Theoretical) Framework 689

Econometric Models and Estimation

Methods 690

The Data 692

Results 693

Conclusions 694

Sty le Hints 694

Summary 697

Key Terms 697

Sample Empirical Projects 698

List of Journals 703

Data Sources 704

APPENDICES

A PPE N D IX A

Basic Mathem atical Tools 707

A. I The Summation Operator

and Descriptive Statistics 707

A.2 Properties of Linear Functions 710

A.3 Proportions and Percentages 713

A.4 Some Special Functions and Their

Properties 714

Quadratic Functions 715

The Natural Logarithm 717

The Exponential Function 721

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X C ontenfs

A.5 Differential Calculus 722

Summary 725

Key Terms 725

Problems 725

A P P F \ D I\ K

Fundamentals ot Probabilitv “ JH

B. I Random Variables and Their Probability

Distributions 728

Discrete Random Variables 729

Continuous Random Variables 73!

B.2 Joint Distributions, Conditional Distributions,

and Independence 733

Joint Distributions and Independent e '34

Conditional Distributions 736

B.3 Features of Probability Distributions 737

A Measure of Central Tendency:

The Expected Value 737

Properties of Expected Values 739

Another Measure of Central Tendency:

The Median 740

Measures of Variability: Variance

and Standard Deviation 741

Variance 742

Standard Deviation 743

Standardizing a Random Variable 744

B.4 Features of Joint and Conditional

Distributions 744

Measures of Association:

Covariance and Correlation 744

Covariance 745

Correlation Coefficient 746

Variance of Sums of Random Variables 74 7

Conditional Expectation 748

Properties of Conditional Expectation 750

Conditional Variance 753

B.5 The Normal and Related Distributions 753

The Normal Distribution 753

The Standard Normal Distribution 754

Additional Properties of the Normal

Distribution 757

The Chi-Square Distribution 757

The t Distribution 758

The F Distribution 759

Summary 760

Key Terms 761

Problems 761

A PPEN D IX C

Fundamentals of Mathematic al Statistic *

C. I Populations. Parameters, and Random

Sampling 763

Sampling 764

C.2 Finite Sample Properties of Estimators

Estimators and Estimates 765

I nbiascdncss 766

The Sam/fling Variance of Estimators '<'>>

Efficiency 77/

C.3 Asymptotic or Larger Sample Properties

of Estimators 772

Consistency 772

Asymptotic Normality 775

C.4 General Approaches to Parameter

Estimation 111

Method of Moments 777

Maximum Likelihood 778

Least Squares 779

C.5 Interval Estimation and Confidence

Intervals 780

The Nature of Interval Estimation 7Hi)

Confidence Intervals for the Mean from a

Normally Distributed Population 782

A Simple Rule of Thumb for a 95c/r Con fidence

Interval 786

Asymptotic Confidence Intervals for Nonnormal

Populations 787

C.6 Hy pothesis Testing 788

F undamentals of Hypothesis Testing 7H8

Testing Hypotheses about the Mean in a Normal

Population 790

Asymptotic Tests for Nonnormal

Populations 794

Computing and Using p-Values 794

The Relationship between Confidence Intervals

and Hypothesis Testing 798

Practical versus Statistical Significance ~W

C.7 Remarks on Notation 800

Summary 801

Key Terms 801

Problems 802

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Contents XI

A PPEN D IX D

Summary of Matrix Algebra 808

D. I Basic Definitions 808

D.2 Matrix Operations 809

Matrix Addition 809

Scalar Multiplication 810

Matrix Multiplication 810

Transpose 811

Partitioned Matrix Multiplication 812

Trace 812

Inverse 813

D.3 Linear Independence and Rank

of a Matrix 813

D.4 Quadratic Forms and Positive Definite

Matrices 814

D.5 Idempotent Matrices 814

D.6 Differentiation of Linear and Quadratic

Forms 815

D.7 Moments and Distributions of Random

Vectors 815

Expected Value 816

Variance-Covariance Matrix 816

Multivariate Normal Distribution 816

Chi-Square Distribution 817

t Distribution 817

¥ Distribution 817

Summary 817

Key Terms 818

Problems 818

A PPEN D IX E

The Linear Regression Model

in Matrix Form 819

E.l The Model and Ordinary Least Squares

Estimation 819

E.2 Finite Sample Properties of OLS 822

E.3 Statistical Inference 826

E.4. Some Asymptotic Analysis 827

Wald Statistics for Testing Multiple

Hypotheses 830

Summary 831

Key Terms 831

Problems 832

A PPEN D IX F

Answers to Chapter Questions 834

A PPEN D IX G

Statistical Tables 847

References 854

Glossary 859

Index 873

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Preface

M y motivation for writing the first edition of Introductory Econom etrics: \ Modem

Approach was that I saw a fairly wide gap between how econometrics is taught to under￾graduates and how empirical researchers think about and apply econometric methods. I

became convinced that teaching introductory econometrics from the perspective of pro￾fessional users of econometrics would actually simplify the presentation, in addition to

making the subject much more interesting.

Based on the positive reactions to the first two editions, it appears that m> hunch was

correct. A growing number of instructors, with a variety of backgrounds and interests, and

teaching students with different levels of preparation, have embraced the modem approach

to econometrics espoused in this text. Consequently, the structure of the third edition is

much like the second, although I describe some notable changes below. The emphasis is

still on applying econometrics to real-world problems. Each econometric method is moti￾vated by a particular issue facing researchers analyzing nonexperimental data. The focus

in the main text is on understanding and interpreting the assumptions in light of actual

empirical applications: the mathematics required is no more than college algebra and basic

probability and statistics.

Organized for Today's Econometrics Instructor

The third edition preserves the overall organization of the second edition. The most notice￾able feature that distinguishes this text from most others is the separation of topics by the

kind of data being analyzed. This is a clear departure from the traditional approach, w hich

presents a linear model, lists all assumptions that may be needed at some future point in

the analysis, and then proves or asserts results without clearly connecting them to the

assumptions. M y approach is to first treat, in Part One, multiple regression analysis with

cross-sectional data, under the assumption of random sampling. This setting is natural to

students because they are familiar with random sampling from a population from their

introductory statistics courses. Importantly, it allows us to distinguish between assump￾tions made about the underlying population regression model— assumptions that can be

given economic or behavioral content— from assumptions about how the data were sam￾pled. Discussions about the consequences of nonrandom sampling can be treated in an

intuitive fashion after the students have a good grasp of the multiple regression model esti￾mated using random samples.

An important feature of a modem approach is that the explanatory variables— along

with the dependent v ariable— are treated as outcomes of random variables. For the social

sciences, allowing random explanatory variables is much more realistic than the traditional

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Preface XIII

assumption of nonrandom explanatory variables. As a nontrivial benefit, the population

model/random sampling approach reduces the number of assumptions that students must

absorb and understand. Ironically, the classical approach to regression analysis, which

treats the explanatory variables as fixed in repeated samples and is pervasive in introduc￾tory texts, literally applies to data collected in an experimental setting. In addition, the

contortions required to state and explain assumptions can be confusing to students.

M y focus on the population model emphasizes that the fundamental assumptions under￾lying regression analysis, such as the zero mean assumption on the unobservables, are prop￾erly stated conditional on the explanatory variables. This leads to a clear understanding of

the kinds of problems, such as heteroskedasticity (nonconstant variance), that can invali￾date standard inference procedures. Plus, I am able to dispel several misconceptions that

arise in econometrics texts at all levels. For example, I explain why the usual /^-squared is

still valid as a goodness-of-fit measure in the presence of heteroskedasticity (Chapter 8) or

serially correlated errors (Chapter 12); I demonstrate that tests for functional form should

not be viewed as general tests of omitted variables (Chapter 9); and I explain why one

should always include in a regression model extra control variables that are uncorrelated

with the explanatory variable of interest, such as a policy variable (Chapter 6).

Because the assumptions for cross-sectional analysis are relatively straightforward yet

realistic, students can get involved early with serious cross-sectional applications without

having to worry about the thorny issues of trends, seasonality, serial correlation, high per￾sistence, and spurious regression that are ubiquitous in time series regression models. Ini￾tially, I figured that my treatment of regression with cross-sectional data followed by

regression with time series data would find favor with instructors whose own research

interests are in applied microeconomics, and that appears to be the case. It has been grat￾ifying that adopters of the text with an applied time series bent have been equally enthu￾siastic about the structure of the text. By postponing the econometric analysis of time

series data, I am able to put proper focus on the potential pitfalls in analyzing time series

data that do not arise with cross-sectional data. In effect, time series econometrics finally

gets the serious treatment it deserves in an introductory text.

As in the earlier editions, I have consciously chosen topics that are important for read￾ing journal articles and for conducting basic empirical research. Within each topic, I have

deliberately omitted many tests and estimation procedures that, while traditionally

included in textbooks, have not withstood the empirical test of time. Likewise. I have

emphasized more recent topics that have clearly demonstrated their usefulness, such as

obtaining test statistics that are robust to heteroskedasticity (or serial correlation) of

unknown form, using multiple years of data for policy analysis, or solving the omitted

variable problem by instrumental variables methods. I appear to have made sound choices,

as I have received only a few suggestions for adding or deleting material. Like the second

edition, the third edition contains an introductory treatment of least absolute deviations

estimation (L A D ) in Chapter 9. L A D is becoming more and more popular in empirical

work, especially when the conditional distribution of the dependent variable is asymmet￾ric or has fat tails. Students reading empirical research in labor economics, public eco￾nomics. and other fields are more and more likely to run across linear models estimated

by LA D .

In rewriting segments of the text, I have tried to further improve on the systematic

approach of the second edition. B y systematic, I mean that each topic is presented by Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

XIV Preface

building on the previous material in a logical fashion, and assumptions are introduced only

as they are needed to obtain a conclusion. For example, professional users of economet￾rics understand that not all of the Gauss-Markov assumptions are needed to show that the

ordinary least squares (O L S ) estimators are unbiased. Yet. the vast majority of economet￾rics texts introduce the full set of assumptions (many of which are redundant or. in some

cases, even logically conflicting) before pros ing unbiasedness of O LS. Similarly, the nor￾mality assumption is often included among the assumptions that are needed for the Gauss￾Markov Theorem, even though it is fairly well known that normality plays no role in show￾ing that the O LS estimators are the best linear unbiased estimators.

M y systematic approach carries over to studying large sample properties, where

assumptions for consistency are introduced only as needed. This makes it relatively easy

to cover more advanced topics, such as using pooled cross sections, exploiting panel data

structures, and applying instrumental variables methods. I have worked to provide a uni￾fied view of econometrics, by which I mean that all estimators and test statistics are

obtained using just a few. intuitively reasonable principles of estimation and testing

(which, of course, also have rigorous justification). For example, regression-based tests

for heteroskedasticity and serial correlation are easy for students to grasp because they

already have a solid understanding of regression. This is in contrast to treatments that give

a set of disjointed recipes for outdated econometric procedures.

Throughout the text. I emphasize ceteris paribus relationships, which is why. after one

chapter on the simple regression model. I move to multiple regression analysis. This moti￾vates students to think about serious applications early. I also give much more prominence

to policy analysis with all kinds of data structures. Practical topics, such as using proxy

variables to obtain ceteris paribus effects and obtaining standard errors for partial effects

in models with interaction terms, are covered in a simple fashion.

New to This Edition

I have made changes in the third edition that are meant to make the text more user-fnendly.

First, in the earlier editions, some empirical examples could not be replicated (because 1

did not make the data available) or confirmed by reading a journal article. In the third edi￾tion. all empirical results either can be replicated using the included data sets or can be

found in a published article. Because replication is more helpful to students. I have

changed a few examples so that the numbers can be obtained using a new data set. A

notable example is Example 7.7. which studies the effect of “ beauty" on wages.

Based on several requests, I have added summaries of assumptions at the end of the

relevant chapters (Chapters 3. 4. 10, and 11). Consequently, students now have a quick

reference tor the assumptions, as well as brief descriptions of how each is used.

An important difference from earlier editions, especially for instructors who have writ￾ten lecture notes from the first or second edition, is that I have slightly reordered the

assumptions tor simple and multiple regression (as well as for panel data analysis and

instrumental variables estimation in the more advanced part). In particular. I have reversed

Assumptions S L R .3 and S L R .4 in Chapter 2 and. likewise. Assumptions M L R .3 and

M L R .4 in Chapter 3. as noted below. (Sim ilar changes are made in Chapters 5. 10. and

11.) Pedagogically. the new ordering is more natural, and I give credit to Angelo Mehno

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