SOLUTIONS MANUAL FOR
th
Introductory Econometrics: A Modern Approach, 4 Edition by Jeffrey M. Wooldridge
Chapter 1-18 With Appendix [A B C D E]
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
CONTENTS
Chapter 1 Introduction 1
Chapter 2 The Simple Regression Model 3
Chapter 3 Multiple Regression Analysis: Estimation 9
Chapter 4 Multiple Regression Analysis: Inference 17
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 24
Chapter 6 Multiple Regression Analysis: Further Issues 27
Chapter 7 Multiple Regression Analysis With Qualitative 34
Information: Binary (or Dummy) Variables
Chapter 8 Heteroskedasticity 42
Chapter 9 More on Specification and Data Problems 47
Chapter 10 Basic Regression Analysis With Time Series Data 52
Chapter 11 Further Issues in Using OLS With Time Series Data 58
Chapter 12 Serial Correlation and Heteroskedasticity in 65
Time Series Regressions
Chapter 13 Pooling Cross Sections Across Time. Simple 71
Panel Data Methods
Chapter 14 Advanced Panel Data Methods 78
Chapter 15 Instrumental Variables Estimation and Two Stage 85
Least Squares
Chapter 16 Simultaneous Equations Models 92
, Chapter 17 Limited Dependent Variable Models and Sample 99
Selection Corrections
Chapter 18 Advanced Time Series Topics 110
Appendix A Basic Mathematical Tools 117
Appendix B Fundamentals of Probability 119
Appendix C Fundamentals of Mathematical Statistics 120
Appendix D Summary of Matrix Algebra 122
Appendix E The Linear Regression Model in Matrix Form 123
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
, CHAPTER 1
SOLUTIONS TO PROBLEMS
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These
disciplines
1.1 (i) Ideally, we could randomly assign students to classes of different sizes. That is, each
student is assigned a different class size without regard to any student characteristics such as
ability and family background. For reasons we will see in Chapter 2, we would like substantial
variation in class sizes (subject, of course, to ethical considerations and resource constraints).
(ii) A negative correlation means that larger class size is associated with lower performance.
We might find a negative correlation because larger class size actually hurts performance.
However, with observational data, there are other reasons we might find a negative relationship.
For example, children from more affluent families might be more likely to attend schools with
smaller class sizes, and affluent children generally score better on standardized tests. Another
possibility is that, within a school, a principal might assign the better students to smaller classes.
Or, some parents might insist their children are in the smaller classes, and these same parents
tend to be more involved in their children’s education.
(iii) Given the potential for confounding factors – some of which are listed in (ii) – finding a
negative correlation would not be strong evidence that smaller class sizes actually lead to better
performance. Some way of controlling for the confounding factors is needed, and this is the
subject of multiple regression analysis.
1.3 It does not make sense to pose the question in terms of causality. Economists would assume
that students choose a mix of studying and working (and other activities, such as attending class,
leisure, and sleeping) based on rational behavior, such as maximizing utility subject to the
constraint that there are only 168 hours in a week. We can then use statistical methods to
measure the association between studying and working, including regression analysis that we
cover starting in Chapter 2. But we would not be claiming that one variable ―causes‖ the other.
They are both choice variables of the student.
SOLUTIONS TO COMPUTER EXERCISES
C1.1 (i) The average of educ is about 12.6 years. There are two people reporting zero years of
education, and 19 people reporting 18 years of education.
(ii) The average of wage is about $5.90, which seems low in the year 2008.
(iii) Using Table B-60 in the 2004 Economic Report of the President, the CPI was 56.9 in
1976 and 184.0 in 2003.
(iv) To convert 1976 dollars into 2003 dollars, we use the ratio of the CPIs, which is
.9 3.23 . Therefore, the average hourly wage in 2003 dollars is roughly
3.23($5.90) $19.06 , which is a reasonable figure.
, (v) The sample contains 252 women (the number of observations with female = 1) and 274
men.
C1.3 (i) The largest is 100, the smallest is 0.
(ii) 38 out of 1,823, or about 2.1 percent of the sample.
(iii) 17
(iv) The average of math4 is about 71.9 and the average of read4 is about 60.1. So, at least
in 2001, the reading test was harder to pass.
(v) The sample correlation between math4 and read4 is about .843, which is a very high
degree of (linear) association. Not surprisingly, schools that have high pass rates on one test
have a strong tendency to have high pass rates on the other test.
(vi) The average of exppp is about $5,194.87. The standard deviation is $1,091.89, which
shows rather wide variation in spending per pupil. [The minimum is $1,206.88 and the
maximum is $11,957.64.]
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
CHAPTER 2
SOLUTIONS TO PROBLEMS
2.1 (i) Income, age, and family background (such as number of siblings) are just a few
possibilities. It seems that each of these could be correlated with years of education. (Income
and education are probably positively correlated; age and education may be negatively correlated
because women in more recent cohorts have, on average, more education; and number of siblings
and education are probably negatively correlated.)
(ii) Not if the factors we listed in part (i) are correlated with educ. Because we would like to
hold these factors fixed, they are part of the error term. But if u is correlated with educ then
E(u|educ) 0, and so SLR.4 fails.
n
2.3 (i) Let yi = GPAi, xi = ACTi, and n = 8. Then x = 25.875, y = 3.2125, (xi – x )(yi – y ) =
i1
n
5.8125, and (xi – x )2 = 56.875. From equation (2.9), we obtain the slope as ˆ =
i1
th
Introductory Econometrics: A Modern Approach, 4 Edition by Jeffrey M. Wooldridge
Chapter 1-18 With Appendix [A B C D E]
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
CONTENTS
Chapter 1 Introduction 1
Chapter 2 The Simple Regression Model 3
Chapter 3 Multiple Regression Analysis: Estimation 9
Chapter 4 Multiple Regression Analysis: Inference 17
Chapter 5 Multiple Regression Analysis: OLS Asymptotics 24
Chapter 6 Multiple Regression Analysis: Further Issues 27
Chapter 7 Multiple Regression Analysis With Qualitative 34
Information: Binary (or Dummy) Variables
Chapter 8 Heteroskedasticity 42
Chapter 9 More on Specification and Data Problems 47
Chapter 10 Basic Regression Analysis With Time Series Data 52
Chapter 11 Further Issues in Using OLS With Time Series Data 58
Chapter 12 Serial Correlation and Heteroskedasticity in 65
Time Series Regressions
Chapter 13 Pooling Cross Sections Across Time. Simple 71
Panel Data Methods
Chapter 14 Advanced Panel Data Methods 78
Chapter 15 Instrumental Variables Estimation and Two Stage 85
Least Squares
Chapter 16 Simultaneous Equations Models 92
, Chapter 17 Limited Dependent Variable Models and Sample 99
Selection Corrections
Chapter 18 Advanced Time Series Topics 110
Appendix A Basic Mathematical Tools 117
Appendix B Fundamentals of Probability 119
Appendix C Fundamentals of Mathematical Statistics 120
Appendix D Summary of Matrix Algebra 122
Appendix E The Linear Regression Model in Matrix Form 123
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
, CHAPTER 1
SOLUTIONS TO PROBLEMS
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These
disciplines
1.1 (i) Ideally, we could randomly assign students to classes of different sizes. That is, each
student is assigned a different class size without regard to any student characteristics such as
ability and family background. For reasons we will see in Chapter 2, we would like substantial
variation in class sizes (subject, of course, to ethical considerations and resource constraints).
(ii) A negative correlation means that larger class size is associated with lower performance.
We might find a negative correlation because larger class size actually hurts performance.
However, with observational data, there are other reasons we might find a negative relationship.
For example, children from more affluent families might be more likely to attend schools with
smaller class sizes, and affluent children generally score better on standardized tests. Another
possibility is that, within a school, a principal might assign the better students to smaller classes.
Or, some parents might insist their children are in the smaller classes, and these same parents
tend to be more involved in their children’s education.
(iii) Given the potential for confounding factors – some of which are listed in (ii) – finding a
negative correlation would not be strong evidence that smaller class sizes actually lead to better
performance. Some way of controlling for the confounding factors is needed, and this is the
subject of multiple regression analysis.
1.3 It does not make sense to pose the question in terms of causality. Economists would assume
that students choose a mix of studying and working (and other activities, such as attending class,
leisure, and sleeping) based on rational behavior, such as maximizing utility subject to the
constraint that there are only 168 hours in a week. We can then use statistical methods to
measure the association between studying and working, including regression analysis that we
cover starting in Chapter 2. But we would not be claiming that one variable ―causes‖ the other.
They are both choice variables of the student.
SOLUTIONS TO COMPUTER EXERCISES
C1.1 (i) The average of educ is about 12.6 years. There are two people reporting zero years of
education, and 19 people reporting 18 years of education.
(ii) The average of wage is about $5.90, which seems low in the year 2008.
(iii) Using Table B-60 in the 2004 Economic Report of the President, the CPI was 56.9 in
1976 and 184.0 in 2003.
(iv) To convert 1976 dollars into 2003 dollars, we use the ratio of the CPIs, which is
.9 3.23 . Therefore, the average hourly wage in 2003 dollars is roughly
3.23($5.90) $19.06 , which is a reasonable figure.
, (v) The sample contains 252 women (the number of observations with female = 1) and 274
men.
C1.3 (i) The largest is 100, the smallest is 0.
(ii) 38 out of 1,823, or about 2.1 percent of the sample.
(iii) 17
(iv) The average of math4 is about 71.9 and the average of read4 is about 60.1. So, at least
in 2001, the reading test was harder to pass.
(v) The sample correlation between math4 and read4 is about .843, which is a very high
degree of (linear) association. Not surprisingly, schools that have high pass rates on one test
have a strong tendency to have high pass rates on the other test.
(vi) The average of exppp is about $5,194.87. The standard deviation is $1,091.89, which
shows rather wide variation in spending per pupil. [The minimum is $1,206.88 and the
maximum is $11,957.64.]
IntroductionExams serve as a fundamental tool in evaluating a student's understanding of a subject, particularly in fields as diverse as business, law, and mathematics. These disciplines
CHAPTER 2
SOLUTIONS TO PROBLEMS
2.1 (i) Income, age, and family background (such as number of siblings) are just a few
possibilities. It seems that each of these could be correlated with years of education. (Income
and education are probably positively correlated; age and education may be negatively correlated
because women in more recent cohorts have, on average, more education; and number of siblings
and education are probably negatively correlated.)
(ii) Not if the factors we listed in part (i) are correlated with educ. Because we would like to
hold these factors fixed, they are part of the error term. But if u is correlated with educ then
E(u|educ) 0, and so SLR.4 fails.
n
2.3 (i) Let yi = GPAi, xi = ACTi, and n = 8. Then x = 25.875, y = 3.2125, (xi – x )(yi – y ) =
i1
n
5.8125, and (xi – x )2 = 56.875. From equation (2.9), we obtain the slope as ˆ =
i1
