SOLUTION MANUAL
, CONTENTS
PREFACE iii
SUGGESTED COURSE OUTLINES iv
Chapter 1 The Nature of Econometrics and Economic Data 1
Chapter 2 The Simple Regression Model 5
Chapter 3 Multiple Regression Analysis: Estimation 15
Chapter 4 Multiple Regression Analysis: Inference 28
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 41
Chapter 6 Multiple Regression Analysis: Further Issues 46
Chapter 7 Multiple Regression Analysis with Qualitative 62
Information: Binary (or Dummy) Variables
Chapter 8 Heteroskedasticity 79
Chapter 9 More on Specification and Data Problems 91
Chapter 10 Basic Regression Analysis with Time Series Data 102
Chapter 11 Further Issues in Using OLS with Time Series Data 114
Chapter 12 Serial Correlation and Heteroskedasticity in 127
Time Series Regressions
Chapter 13 Pooling Cross Sections Across Time. Simple 139
Panel Data Methods
Chapter 14 Advanced Panel Data Methods 154
Chapter 15 Instrumental Variables Estimation and Two Stage 167
Least Squares
Chapter 16 Simultaneous Equations Models 183
Chapter 17 Limited Dependent Variable Models and Sample 196
Selection Corrections
i
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, Chapter 18 Advanced Time Series Topics 217
Chapter 19 Carrying Out an Empirical Project 233
Appendix A Basic Mathematical Tools 234
Appendix B Fundamentals of Probability 236
Appendix C Fundamentals of Mathematical Statistics 238
Appendix D Summary of Matrix Algebra 242
Appendix E The Linear Regression Model in Matrix Form 244
ii
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, 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, 4e.
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 offensive). 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.
I solved the computer exercises using various versions of Stata, starting with version 4.0 and
running through version 9.0. 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 keep a list of any substantive
errors on the Web site for the book, www.international.cengage.com. 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 .
I hope you find this instructor’s manual useful, and I look forward to hearing your reactions to
the second edition.
Jeffrey M. Wooldridge
Department of Economics
Michigan State University
110 Marhall-Adams Hall
East Lansing, MI 48824-1038
iii
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, 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.) 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 terms of multiple regression
than in tests of a population mean, 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 masters level, could begin with some of
the material in Chapter 9, particularly with the issues of proxy variables and measurement error.
The advanced chapters, starting with Chapter 13, are useful for students who have an interest in
policy analysis. The pooled cross section and panel data chapters (Chapters 13 and 14)
emphasize how these data sets 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 error. I have intentionally separated out
the conceptually more difficult topic of simultaneous equations models in Chapter 16.
iv
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, CONTENTS
PREFACE iii
SUGGESTED COURSE OUTLINES iv
Chapter 1 The Nature of Econometrics and Economic Data 1
Chapter 2 The Simple Regression Model 5
Chapter 3 Multiple Regression Analysis: Estimation 15
Chapter 4 Multiple Regression Analysis: Inference 28
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 41
Chapter 6 Multiple Regression Analysis: Further Issues 46
Chapter 7 Multiple Regression Analysis with Qualitative 62
Information: Binary (or Dummy) Variables
Chapter 8 Heteroskedasticity 79
Chapter 9 More on Specification and Data Problems 91
Chapter 10 Basic Regression Analysis with Time Series Data 102
Chapter 11 Further Issues in Using OLS with Time Series Data 114
Chapter 12 Serial Correlation and Heteroskedasticity in 127
Time Series Regressions
Chapter 13 Pooling Cross Sections Across Time. Simple 139
Panel Data Methods
Chapter 14 Advanced Panel Data Methods 154
Chapter 15 Instrumental Variables Estimation and Two Stage 167
Least Squares
Chapter 16 Simultaneous Equations Models 183
Chapter 17 Limited Dependent Variable Models and Sample 196
Selection Corrections
i
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, Chapter 18 Advanced Time Series Topics 217
Chapter 19 Carrying Out an Empirical Project 233
Appendix A Basic Mathematical Tools 234
Appendix B Fundamentals of Probability 236
Appendix C Fundamentals of Mathematical Statistics 238
Appendix D Summary of Matrix Algebra 242
Appendix E The Linear Regression Model in Matrix Form 244
ii
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, 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, 4e.
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 offensive). 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.
I solved the computer exercises using various versions of Stata, starting with version 4.0 and
running through version 9.0. 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 keep a list of any substantive
errors on the Web site for the book, www.international.cengage.com. 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 .
I hope you find this instructor’s manual useful, and I look forward to hearing your reactions to
the second edition.
Jeffrey M. Wooldridge
Department of Economics
Michigan State University
110 Marhall-Adams Hall
East Lansing, MI 48824-1038
iii
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
, 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.) 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 terms of multiple regression
than in tests of a population mean, 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 masters level, could begin with some of
the material in Chapter 9, particularly with the issues of proxy variables and measurement error.
The advanced chapters, starting with Chapter 13, are useful for students who have an interest in
policy analysis. The pooled cross section and panel data chapters (Chapters 13 and 14)
emphasize how these data sets 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 error. I have intentionally separated out
the conceptually more difficult topic of simultaneous equations models in Chapter 16.
iv
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
