i
CONTENTS
PREFACE iii
SUGGESTED COURSE OUTLINES iv
Chapter 1 The Nature of Econometrics and Economic Data 1
Chapter 2 The Simple Regression Model 6
Chapter 3 Multiple Regression Analysis: Estimation 19
Chapter 4 Multiple Regression Analysis: Inference 34
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 48
Chapter 6 Multiple Regression Analysis: Further Issues 54
Chapter 7 Multiple Regression Analysis with Qualitative 71
Information: Binary (or Dummy) Variables
Chapter 8 Heteroskedasticity 89
Chapter 9 More on Specification and Data Problems 103
Chapter 10 Basic Regression Analysis with Time Series Data 117
Chapter 11 Further Issues in Using OLS with Time Series Data 129
Chapter 12 Serial Correlation and Heteroskedasticity in 143
Time Series Regressions
Chapter 13 Pooling Cross Sections Across Time. Simple 156
Panel Data Methods
Chapter 14 Advanced Panel Data Methods 172
Chapter 15 Instrumental Variables Estimation and Two Stage 187
Least Squares
Chapter 16 Simultaneous Equations Models 205
Chapter 17 Limited Dependent Variable Models and Sample 219
Selection Corrections

iii
PREFACE
This manual contains suggested course outlines, teaching notes, and detailed solutions to all of
the problems and computer exercises in Introductory Econometrics: A Modern Approach, 5e.
For several problems, I have added additional notes about interesting asides or suggestions for
how to modify or extend the problem.
Some of the answers given here are subjective, and you may want to supplement or replace them
with your own answers. I wrote all solutions as if I were preparing them for the students, so you
may find some solutions a bit tedious (if not bordering on an insult to your intelligence). This
way, if you prefer, you can distribute my answers to some of the even-numbered problems
directly to the students. (The student study guide contains answers to all odd-numbered
problems.) Many of the equations in the Word files were created using MathType, and the
equations will not look quite right without MathType. Some equations I have created using the
equation editor in Word 2007.
I solved the computer exercises using various versions of Stata, starting with version 4.0 and
running through version 12.0. Nevertheless, almost all of the estimation methods covered in the
text have been standardized, and different econometrics or statistical packages should give the
same answers. There can be differences when applying more advanced techniques, as
conventions sometimes differ on how to choose or estimate auxiliary parameters. (Examples
include heteroskedasticity-robust standard errors, estimates of a random effects model, and
corrections for sample selection bias.)
While I have endeavored to make the solutions mistake-free, some errors may have crept in. I
would appreciate hearing from you if you find mistakes. I will update the manual occasionally
and correct any mistakes that have been found. I heard from many of you regarding the earlier
editions of the text, and I incorporated many of your suggestions. I welcome any comments that
will help me make improvements to future editions. I can be reached via e-mail at
wooldri1@.msu.edu.
The fifth edition of the text drops the chapter numbers preceding the problems and computer
exercises. I have kept the chapter numbers in the solutions manual so that it is easy to keep track
of where one is. For example, the solution to problem 4 in chapter 3 is labeled 3.4 and computer
exercise 6 in chapter 8 is labeled C8.6.
I hope you find this instructor’s manual useful, and I look forward to hearing your reactions to
the fifth edition.
Jeffrey M. Wooldridge
Department of Economics
Michigan State University
486 W. Circle Drive
110 Marshall-Adams Hall
East Lansing, MI 48824-1038

iv
SUGGESTED COURSE OUTLINES
For an introductory, one-semester course, I like to cover most of the material in Chapters 1
through 8 and Chapters 10 through 12, as well as parts of Chapter 9 (but mostly through
examples). I do not typically cover all sections or subsections within each chapter. Under the
chapter headings listed below, I provide some comments on the material I find most relevant for
a first-semester course.
An alternative course ignores time series applications altogether, while delving into some of the
more advanced methods that are particularly useful for policy analysis. This would consist of
Chapters 1 through 8, much of Chapter 9, and the first four sections of Chapter 13. Chapter 9
discusses the practically important topics of proxy variables, measurement error, outlying
observations, and stratified sampling. In addition, I have written a more careful description of
the method of least absolute deviations, including a discussion of its strengths and weaknesses.
Chapter 13 covers, in a straightforward fashion, methods for pooled cross sections (including the
so-called “natural experiment” approach) and two-period panel data analysis. The basic cross-
sectional treatment of instrumental variables in Chapter 15 is a natural topic for cross-sectional,
policy-oriented courses. For an accelerated course, the nonlinear methods used for cross-
sectional analysis in Chapter 17 can be covered.
I typically do not begin with a review of basic algebra, probability, and statistics. In my
experience, this takes too long and the payoff is minimal. (Students tend to think that they are
taking another statistics course and start to drift away from the material.) Instead, when I need a
tool (such as the summation or expectations operator), I briefly review the necessary definitions
and key properties. Statistical inference is not more difficult to describe in the context of multiple
regression than in testing about mean a mean from a population, and so I briefly review the
principles of statistical inference during multiple regression analysis. Appendices A, B, and C are
fairly extensive. When I cover asymptotic properties of OLS, I provide a brief discussion of the
main definitions and limit theorems. If students need more than the brief review provided in
class, I point them to the appendices.
For a master’s level course, I include a couple of lectures on the matrix approach to linear
regression. This could be integrated into Chapters 3 and 4 or covered after Chapter 4. Again, I do
not summarize matrix algebra before proceeding. Instead, the material in Appendix D can be
reviewed as it is needed in covering Appendix E.
A second semester course, at either the undergraduate or master’s level, could begin with some
of the material in Chapter 9, particularly with the issues of proxy variables and measurement
error. Least absolute deviations and, more generally, quantile regression are used more and more
in empirical work, and the fifth edition has sections that can be used as an introduction to
quantile regression. The advanced chapters, starting with Chapter 13, are particularly useful for
students with an interest in policy analysis. The pooled cross section and panel data chapters
(Chapters 13 and 14) emphasize how these data structures can be used, in conjunction with
econometric methods, for policy evaluation. Chapter 15, which introduces the method of
instrumental variables, is also important for policy analysis. Most modern IV applications are
used to address the problems of omitted variables (unobserved heterogeneity) or measurement

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Solution Manual for Introductory Econometrics: A Modern Approach, 5th Edition

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