CONTENTS
PREFACE
SUGGESTED COURSE OUTLINES
Chapter 1 The Nature of Econometrics and Economic Data
Chapter 2 The Simple Regression Model iii iv 1
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Chapter 3 Multiple Regression Analysis: Estimation
Chapter 4 Multiple Regression Analysis: Inference
Chapter 5 Multiple Regression Analysis: OLS Asymptotics
Chapter 6 Multiple Regression Analysis: Further Issues
Chapter 7 Multiple Regression Analysis with Qualitative
Chapter 8 Heteroskedasticity
Chapter 9 More on Specification and Data Problems
Chapter 10 Basic Regression Analysis with Time Series Data
Chapter 11 Further Issues in Using OLS with Time Series Data
Chapter 12 Serial Correlation and Heteroskedasticity in
Chapter 13 Pooling Cross Sections Across Time. Simple Panel Data Methods
Chapter 14 Advanced Panel Data Methods
Chapter 15 Instrumental Variables Estimation and Two Stage Least Squares
Chapter 16 Simultaneous Equations Models
Chapter 17 Limited Dependent Variable Models and Sample Selection Corrections
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19 34 48 54 71
89 103 117 129 143 156
172 187
205 219
Information: Binary (or Dummy) Variables Time Series Regressions Chapter 18 Advanced Time Series Topics
Chapter 19 Carrying Out an Empirical Project
Appendix A Basic Mathematical Tools
Appendix B Fundamentals of Probability
Appendix C Fundamentals of Mathematical Statistics 243 259 260 263 265
Appendix D Summary of Matrix Algebra
Appendix E The Linear Regression Model in Matrix Form
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269 271
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
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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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error. I have intentionally separated out the conceptually more difficult topic of simultaneous equations models in Chapter 16.
Chapter 17, in particular the material on probit, logit, Tobit, and Poisson regression models, is a good introduction to nonlinear econometric methods. Specialized courses that emphasize
applications in labor economics can use the material on sample selection corrections. Duration models are also briefly covered as an example of a censored regression model.
Chapter 18 is much different from the other advanced chapters, as it focuses on more advanced or recent developments in time series econometrics. Combined with some of the more advanced topics in Chapter 12, it can serve as the basis for a second semester course in time series topics, including forecasting.
Most second semester courses would include an assignment to write an original empirical paper, and Chapter 19 should be helpful in this regard.
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