SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
SOLUTION MANUAL FOR
INTRODUCTORY ECONOMETRICS A
MODERN APPROACH 7TH BY
WOOLDRIDGE
3
,SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
CHAPTER 1
TEACHING NOTES
You Have Substantial Latitude About What To Emphasize In Chapter 1. I Find It
Useful To Talk About The Economics Of Crime Example (Example 1.1) And The
Wage Example (Example 1.2) So That Students See, At The Outset, That
Econometrics Is Linked To Economic Reasoning, If Not Economic Theory.
I Like To Familiarize Students With The Important Data Structures That
Empirical Economists Use, Focusing Primarily On Cross-Sectional And Time
Series Data Sets, As These Are What I Cover In A First-Semester Course. It Is
Probably A Good Idea To Mention The Growing Importance Of Data Sets That
Have Both A Cross-Sectional And Time Dimension.
I Spend Almost An Entire Lecture Talking About The Problems Inherent In
Drawing Causal Inferences In The Social Sciences. I Do This Mostly Through The
Agricultural Yield, Return To Education, And Crime Examples. These Examples
Also Contrast Experimental And Nonexperimental Data. Students Studying
Business And Finance Tend To Find The Term Structure Of Interest Rates Example
More Relevant, Although The Issue There Is Testing The Implication Of A Simple
Theory, As Opposed To Inferring Causality. I Have Found That Spending Time
Talking About These Examples, In Place Of A Formal Review Of Probability And
Statistics, Is More Successful (And More Enjoyable For The Students And Me).
CHAPTER 1
SOLUTIONS TO PROBLEMS1.1
(i) Ideally, We Could Randomly Assign Students To Classes Of Different Sizes. That Is,
Eachstudent Is Assigned A Different Class Size Without Regard To Any Student
Characteristics Such Asability And Family Background. For Reasons We Will See In Chapter
2, We Would Like Substantialvariation 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 Withsmaller 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 Parentstend To Be More Involved In Their
Children’s Education.(Iii) Given The Potential For Confounding Factors – Some Of Which Are
Listed In (Ii) – Finding Anegative 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 Thesubject Of Multiple Regression Analysis.
1.3
It Does Not Make Sense To Pose The Question In Terms Of Causality. Economists Would
Assumethat Students Choose A Mix Of Studying And Working (And Other Activities, Such As
4
,SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
Attending Class,Leisure, And Sleeping) Based On Rational Behavior, Such As Maximizing
Utility Subject To Theconstraint That There Are Only 168 Hours In A Week. We Can Then Use
Statistical Methods Tomeasure The Association Between Studying And Wo rking, Including
Regression Analysis That Wecover 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 EXERCISESC1.1
(i) The Average
Of Educ
Is About 12.6 Years. There Are Two People Reporting Zero Years Ofeducation, 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
, TeDent
, The CPI Was 56.9 In1976 And 184.0 In 2003.(Iv) To Convert 1976 Dollars Into 2003 Dollars,
We Use The Ratio Of The Cpis, Which Is. Therefore, The Average Hourly Wage In 2003 Dollars
Is Roughly, Which Is A Reasonable Figure.184/56.93.23
≈
3.23($5.90
)
≈
$19.06 1
2 (V) The Sample Contains 252 Women (The Number Of Observations With
Female
= 1) And 274men.
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 Leastin 2001, The Reading Test Was Harder To Pass.(V) The Sample
Correlation Between
Math
4
And
Read
4
Is About .843, Which Is A Very Highdegree Of (Linear) Association. Not Surprisingly, Schools
That Have High Pass Rates On One Testhave 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, Whichshows Rather Wide Variation
In Spending Per Pupil. [The Minimum Is $1,206.88 And Themaximum Is $11,957.64.
5
, SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
CHAPTER 2
TEACHING NOTES
This Is The Chapter Where I Expect Students To Follow Most, If Not All, Of The
Algebraic Derivations. In Class I Like To Derive At Least The Unbiasedness Of The
OLS Slope Coefficient, And Usually I Derive The Variance. At A Minimum, I Talk
About The Factors Affecting The Variance. To Simplify The Notation, After I
Emphasize The Assumptions In The Population Model, And Assume Random
Sampling, I Just Condition On The Values Of The Explanatory Variables In The
Sample. Technically, This Is Justified By Random Sampling Because, For
Example, E(Ui|X1,X2,…,Xn) = E(Ui|Xi) By Independent Sampling. I Find That
Students Are Able To Focus On The Key Assumption SLR.3 And Subsequently
Take My Word About How Conditioning On The Independent Variables In The
Sample Is Harmless. (If You Prefer, The Appendix To Chapter 3 Does The
Conditioning Argument Carefully.) Because Statistical Inference Is No More
Difficult In Multiple Regression Than In Simple Regression, I Postpone Inference
Until Chapter 4. (This Reduces Redundancy And Allows You To Focus On The
Interpretive Differences Between Simple And Multiple Regression.)
You Might Notice How, Compared With Most Other Texts, I Use Relatively Few
Assumptions To Derive The Unbiasedness Of The OLS Slope Estimator, Followed
By The Formula For Its Variance. This Is Because I Do Not Introduce Redundant
Or Unnecessary Assumptions. For Example, Once SLR.3 Is Assumed, Nothing
Further About The Relationship Between U And X Is Needed To Obtain The
Unbiasedness Of OLS Under Random Sampling.
6
WOOLDRIDGE
SOLUTION MANUAL FOR
INTRODUCTORY ECONOMETRICS A
MODERN APPROACH 7TH BY
WOOLDRIDGE
3
,SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
CHAPTER 1
TEACHING NOTES
You Have Substantial Latitude About What To Emphasize In Chapter 1. I Find It
Useful To Talk About The Economics Of Crime Example (Example 1.1) And The
Wage Example (Example 1.2) So That Students See, At The Outset, That
Econometrics Is Linked To Economic Reasoning, If Not Economic Theory.
I Like To Familiarize Students With The Important Data Structures That
Empirical Economists Use, Focusing Primarily On Cross-Sectional And Time
Series Data Sets, As These Are What I Cover In A First-Semester Course. It Is
Probably A Good Idea To Mention The Growing Importance Of Data Sets That
Have Both A Cross-Sectional And Time Dimension.
I Spend Almost An Entire Lecture Talking About The Problems Inherent In
Drawing Causal Inferences In The Social Sciences. I Do This Mostly Through The
Agricultural Yield, Return To Education, And Crime Examples. These Examples
Also Contrast Experimental And Nonexperimental Data. Students Studying
Business And Finance Tend To Find The Term Structure Of Interest Rates Example
More Relevant, Although The Issue There Is Testing The Implication Of A Simple
Theory, As Opposed To Inferring Causality. I Have Found That Spending Time
Talking About These Examples, In Place Of A Formal Review Of Probability And
Statistics, Is More Successful (And More Enjoyable For The Students And Me).
CHAPTER 1
SOLUTIONS TO PROBLEMS1.1
(i) Ideally, We Could Randomly Assign Students To Classes Of Different Sizes. That Is,
Eachstudent Is Assigned A Different Class Size Without Regard To Any Student
Characteristics Such Asability And Family Background. For Reasons We Will See In Chapter
2, We Would Like Substantialvariation 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 Withsmaller 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 Parentstend To Be More Involved In Their
Children’s Education.(Iii) Given The Potential For Confounding Factors – Some Of Which Are
Listed In (Ii) – Finding Anegative 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 Thesubject Of Multiple Regression Analysis.
1.3
It Does Not Make Sense To Pose The Question In Terms Of Causality. Economists Would
Assumethat Students Choose A Mix Of Studying And Working (And Other Activities, Such As
4
,SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
Attending Class,Leisure, And Sleeping) Based On Rational Behavior, Such As Maximizing
Utility Subject To Theconstraint That There Are Only 168 Hours In A Week. We Can Then Use
Statistical Methods Tomeasure The Association Between Studying And Wo rking, Including
Regression Analysis That Wecover 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 EXERCISESC1.1
(i) The Average
Of Educ
Is About 12.6 Years. There Are Two People Reporting Zero Years Ofeducation, 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
, TeDent
, The CPI Was 56.9 In1976 And 184.0 In 2003.(Iv) To Convert 1976 Dollars Into 2003 Dollars,
We Use The Ratio Of The Cpis, Which Is. Therefore, The Average Hourly Wage In 2003 Dollars
Is Roughly, Which Is A Reasonable Figure.184/56.93.23
≈
3.23($5.90
)
≈
$19.06 1
2 (V) The Sample Contains 252 Women (The Number Of Observations With
Female
= 1) And 274men.
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 Leastin 2001, The Reading Test Was Harder To Pass.(V) The Sample
Correlation Between
Math
4
And
Read
4
Is About .843, Which Is A Very Highdegree Of (Linear) Association. Not Surprisingly, Schools
That Have High Pass Rates On One Testhave 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, Whichshows Rather Wide Variation
In Spending Per Pupil. [The Minimum Is $1,206.88 And Themaximum Is $11,957.64.
5
, SOLUTION MANUAL FOR INTRODUCTORY ECONOMETRICS A MODERN APPROACH 7TH BY
WOOLDRIDGE
CHAPTER 2
TEACHING NOTES
This Is The Chapter Where I Expect Students To Follow Most, If Not All, Of The
Algebraic Derivations. In Class I Like To Derive At Least The Unbiasedness Of The
OLS Slope Coefficient, And Usually I Derive The Variance. At A Minimum, I Talk
About The Factors Affecting The Variance. To Simplify The Notation, After I
Emphasize The Assumptions In The Population Model, And Assume Random
Sampling, I Just Condition On The Values Of The Explanatory Variables In The
Sample. Technically, This Is Justified By Random Sampling Because, For
Example, E(Ui|X1,X2,…,Xn) = E(Ui|Xi) By Independent Sampling. I Find That
Students Are Able To Focus On The Key Assumption SLR.3 And Subsequently
Take My Word About How Conditioning On The Independent Variables In The
Sample Is Harmless. (If You Prefer, The Appendix To Chapter 3 Does The
Conditioning Argument Carefully.) Because Statistical Inference Is No More
Difficult In Multiple Regression Than In Simple Regression, I Postpone Inference
Until Chapter 4. (This Reduces Redundancy And Allows You To Focus On The
Interpretive Differences Between Simple And Multiple Regression.)
You Might Notice How, Compared With Most Other Texts, I Use Relatively Few
Assumptions To Derive The Unbiasedness Of The OLS Slope Estimator, Followed
By The Formula For Its Variance. This Is Because I Do Not Introduce Redundant
Or Unnecessary Assumptions. For Example, Once SLR.3 Is Assumed, Nothing
Further About The Relationship Between U And X Is Needed To Obtain The
Unbiasedness Of OLS Under Random Sampling.
6
