Introductory Econometrics A Modern
Approach 7th Edition
3
,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).
4
, 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.
5
, 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.3 Fails.
2.2 In The Equation Y = 0 + 1x + U, Add And Subtract 0 From The Right Hand Side To Get Y =
(0 +
0) + 1x + (U − 0). Call The New Error E = U − 0, So That E(E) = 0. The New Intercept Is 0
+ 0, But The Slope Is Still 1.
N
2.3 (I) Let Yi = Gpai, Xi = Acti, And N = 8. Then X = 25.875, Y = 3.2125, (Xi – X )(Yi – Y ) =
I=1
5.8125,
And N (X – X )2 = 56.875. From Equation (2.9), We Obtain The
Slope As ˆ =
I 1
I=1
5.8125/56.875 .1022, Rounded To Four Places After The Decimal. From ˆ0 = Y –
(2.17),
ˆ1 x 3.2125 – (.1022)25.875 .5681. So We Can Write
□ A = .5681 + .1022 ACT
GP
N = 8.
The Intercept Does Not Have A Useful Interpretation Because ACT Is Not Close To Zero For
□ A Increases By .1022(5) = .511.
The Population Of Interest. If ACT Is 5 Points Higher, G P
(ii) The Fitted Values And Residuals — Rounded To Four Decimal Places — Are Given
Along With The Observation Number I And GPA In The Following Table:
I GPA GP□A Uˆ
1 2.8 2.7143 .0857
2 3.4 3.0209 .3791
3 3.0 3.2253 –.2253
4 3.5 3.3275 .1725
5 3.6 3.5319 .0681
6 3.0 3.1231 –.1231
7 2.7 3.1231 –.4231
8 3.7 3.6341 .0659
6
Approach 7th Edition
3
,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).
4
, 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.
5
, 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.3 Fails.
2.2 In The Equation Y = 0 + 1x + U, Add And Subtract 0 From The Right Hand Side To Get Y =
(0 +
0) + 1x + (U − 0). Call The New Error E = U − 0, So That E(E) = 0. The New Intercept Is 0
+ 0, But The Slope Is Still 1.
N
2.3 (I) Let Yi = Gpai, Xi = Acti, And N = 8. Then X = 25.875, Y = 3.2125, (Xi – X )(Yi – Y ) =
I=1
5.8125,
And N (X – X )2 = 56.875. From Equation (2.9), We Obtain The
Slope As ˆ =
I 1
I=1
5.8125/56.875 .1022, Rounded To Four Places After The Decimal. From ˆ0 = Y –
(2.17),
ˆ1 x 3.2125 – (.1022)25.875 .5681. So We Can Write
□ A = .5681 + .1022 ACT
GP
N = 8.
The Intercept Does Not Have A Useful Interpretation Because ACT Is Not Close To Zero For
□ A Increases By .1022(5) = .511.
The Population Of Interest. If ACT Is 5 Points Higher, G P
(ii) The Fitted Values And Residuals — Rounded To Four Decimal Places — Are Given
Along With The Observation Number I And GPA In The Following Table:
I GPA GP□A Uˆ
1 2.8 2.7143 .0857
2 3.4 3.0209 .3791
3 3.0 3.2253 –.2253
4 3.5 3.3275 .1725
5 3.6 3.5319 .0681
6 3.0 3.1231 –.1231
7 2.7 3.1231 –.4231
8 3.7 3.6341 .0659
6
