Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 6
Reference :Wooldridge (2012). Introductory Econometrics, 5th Edition.
Exercises from Chapter 7 and 8.
Chapter 7
7.2
\ = .0044(10) = .044, which means a

PS6 Solutions
4.10 (i) We need to compute the F statistic for the overall significance of the regression with
n = 142 and k = 4: F = [.0395/(1 .0395)](137/4) = 1.41. The 5% critical value with 4
numerator df and using 120 for the numerator df, is 2.45, wh

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;

Solutions to PS8
7.2 (i) If cigs = 10 then log(bwght) = .0044(10) = .044, which means about a 4.4% lower
birth weight.
(ii) A white child is estimated to weigh about 5.5% more, other factors in the first equation
fixed. Further, twhite 4.23, which is well

Problem Set 2 Solutions
2.6 (i) A one-percent increase in distance from the incinerator is associated with a 0.3-percent
increase in the price. This is the sign we expect. If living closer to an incinerator depresses
housing prices, then being farther awa

Problem Set 7 Solutions
6.3 (i) The turnaround point is given by 1 /(2|2 |), or 0.0003/0.000000014 21,428.57;
remember, this is sales in millions of dollars.
(ii) Probably. Its t statistic is about 1.89, which is significant against the one-sided
alternat

PS8 Solutions
ECON 452
December 17, 2016
Question 2
With Var(u | inc, price, educ, f emale) = 2 inc2 , h(X) = inc2p
, where h(X) is the heteroskedasticity function defined in equation (8.21). Therefore, h(X) = inc, and so the
transformed equation is obtai

Problem Set 3 Solutions
3.4 (i) A larger rank for a law school means that the school has less prestige; this lowers
starting salaries. For example, a rank of 100 means there are 99 schools thought to be better.
(ii) 1 > 0, 2 > 0. Both LSAT and GPA are mea

SOLUTIONS TO PROBLEMS
4.1 (i) and (iii) generally cause the t statistics not to have a t distribution under H0.
Homoskedasticity is one of the CLM assumptions. An important omitted variable violates
Assumption MLR.4. The CLM assumptions contain no mention

The Simple Regression Model - Chapter 2
September 28, 2016
1
Definition of the Simple Regression Model
Assume that y and X are two (scalar) random variables and we are interested in explaining y in terms of X. Examples: y is soybean crop and X
is amount

Thermodynamics 1
Fall 2016
Instructor: Don Siegel
What is thermodynamics?
The science that deals with heat and work
and the properties of substances in relation to heat
and work
Alternatively, its the science of energy and entropy
Topics to be Covered
In

Question 3.10
(i) This solution extends the lecture notes (A Partialling Out Interpretation of Multiple
Regression) to the case of three regressors. Denote the model and two estimated
equations as
y = 0 + 1 X1 + 2 X2 + 3 X3 + u
yi = 0 + 1 Xi1
yi = 0 + 1 X

Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 1
(1)
\
We want to show that: Cov(
yi , u
i ) = 0. We will make use of two important results that
P
P
come from the OLS First order conditions, namely: (

Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 4
Reference :Wooldridge (2012). Introductory Econometrics, 5th Edition.
Exercises from Chapter 4.
Chapter 4
4.7
(i) While the standard error on hrsemphas

Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 5
Reference :Wooldridge (2012). Introductory Econometrics, 5th Edition.
Exercises from Chapter 6.
Chapter 6
6.3
(i) From taking the derivative of the fit

Problem Set 3 - Due Date 2/22/2017
February 12, 2017
Chapter 3:
Problems: 9, 10, 11 and 12
Computer Exercises: C8, C9 and C10
Chapter 4:
Problems: 1, 2 and 3
1

P.S. 2
February 2, 2017
This problem set will not be graded. But I strongly recommend that you do
it.
From Chapter 3, solve:
Problems - 2, 4, 5 and 7
Computer Exercises: C2, C3, C4 and C6.
1

PS 1 - Due Date: 1/27/2017
January 18, 2017
1) Prove that the sample covariance between yi (OLS fitted values) and u
i
(OLS residuals) is zero.
2) From Wooldridges Chapter 2 (Introductory Econometrics, 5th edition)
solve problems 1, 4, 5 and 6. OBS: Item

Problem Set 4
March 6, 2017
This problem set will not be graded but I strongly recommend that you try
to solve it.
From Chapter 4, solve Problems 7, 9, 10, 11 and 12.
1

Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 3
Reference :Wooldridge (2012). Introductory Econometrics, 5th Edition.
Exercises from Chapter 3 and 4.
Chapter 3
3.9
(i) 1 < 0, since more pollution can

Introduction to Econometrics
University of Michigan - Winter 2017
Suggested solutions for Problem Set 2
Reference :Wooldridge (2012). Introductory Econometrics, 5th Edition.
Exercises from Chapter 3.
3.2
(i) The estimated coefficient is negative, which is

Economics 452 Fall 2015
Professor Jeffrey Smith
Lecture: Fundamentals of mathematical statistics (Appendix C)
Version of September 7, 2015
Populations, Parameters and Random Sampling
We now turn to consideration of statistical inference.
This means obtain

Economics 452 Fall 2015
Professor Jeffrey Smith
Lecture: Simple Panel Data Methods
Version of November 29, 2015
This version of the lecture covers only Sections 13.1 to 13.3 in the Wooldridge book.
Introduction
This chapter considers the basics of what yo

Econ 452 Section 4 - STATA
Connor Cole
October 1, 2015
Basic Statistical Tools, Continued
Chi-Squared Tests and Frequency Tables
Again, the document available on Canvas should describe how chi-squared tests work. Chi-squared
tests with tables assess wheth

Econ 452 Section 5 - STATA
Connor Cole
October 8, 2015
Using STATA as a Calculator
If you would like to use STATA as a calculator for scalars, you can use the display command.
Just prex some calculation you would like to run using the display command:
dis

Econ 452 Section 2 - STATA
Connor Cole
September 18, 2015
Basic Data Management
Dropping Observations
In our problem sets, we will often drop observations if they are missing values for variables of
interest (note that some researchers, instead of droppin

Econ 452 Section 8 - STATA
Connor Cole
November 5, 2015
Monte Carlo Simulations in STATA
NOTE: This material on Monte Carlo simulations is meant to elaborate on what was
discussed in class and is completely optional.
Last week we saw a few examples of wha

Econ 452 Section 11 - STATA
Connor Cole
November 20, 2015
2
Adjusted R2 (Or R )
As we discussed in class, R2 is:
R2 =
=1
n
y
2
i=1 (i y )
n
2
i=1 (yi y )
n
(i yi )2
y
i=1
n
2
i=1 (yi y )
Or:
SSM
SST
SSE
=1
SST
R2 =
2
Adjusted R2 , or R can be computed as