Assumptions
A1 Population: true population relationship is linear:
y = 0 + 1 x1 + . + k xk + u
A2 Data are random and independent
A3 No linear dependent/constant variables of x
no perfect collinearity, re-scaled variables
A4 Mean of error doesnt depend on
1 =
PN
i=1 (xi x)(yi y )
PN
2
i=1 (xi x)
=
SSxy
SSxx
SS
XY (X)(Y )
= xy
2
(X 2 ) (X)2
x
P
P 2
(Xi X)2
Ui
= N 2
N 1
=
xy = N xy
2 = SSxx =
P 11 x N 1
1 =
W
P i ( 0 + 1 Xi + U i ) 1
P
Wi1 = 0
W i Xi = 1
E[ 1 |X] = 1 (unbiased)
(assuming E[u|x] = 0)
1 |X
73-363 Econometrics
Fall 2013
Midterm 1 practice questions ANSWERS
Here is a list of questions that will help you prepare the midterm. There are many more questions
here than there will be on the midterm, since the goal to provide several questions for ea
73-363 Econometrics
Fall 2015
Homework 9: Time Series
SOLUTION
We will explore Phillips curve, the (alleged) relationship between inflation and unemployment.
You can find discussion of the model, in Example 11.5 (Section 11.2)
You will need the PHILLIPS d
73-363 Econometrics
Fall 2015
Homework 10: Binary models and Panel data
SOLUTION 20 points
1. (10 points) You will need the EZUNEM dataset. Background information is in Example 13.8
(Section 13.5)
1.a (6 points) Exercise C14.4 in Wooldridge, parts (i) and
73-363 Econometrics
Fall 2015
Homework 3: Inference single equation
SOLUTION 20 points
1. (8 points) You have estimated the Cobb-Douglass production function:
,
ln Y 0 1 ln K 2 ln L
where 0 = ln A. Unfortunately, you computer was damaged, and the only sur
1
73-363 Econometrics
Fall 2015
Homework 7: Endogeneity
Solution
1. (7 points) You have data on worker training and productivity, and are trying to prove that training
increases productivity.
1.a [2 pts] Which regression will you run? How will you use its
73-363 Econometrics
Fall 2015
Homework 8: Heteroskedasticity
Due Wednesday November 11
1. (6 points) Consider the following model:
consumption = 0 + 1income + 2age +3age2 + u
where E(u| income, age) = 0 and V(u| income, age) = 2income2.
Transform the equa
73-363 Econometrics
Fall 2015
Homework 5: Applications
1.(5 points) Consider the following function:
y(x) = 0 + 1 log x
1.a Derive approximate and exact change in y (y) resulting from x decreasing (not increasing) by
x. Your answers should be a function o
73-363 Econometrics
Fall 2015
Homework 6: Assumptions and multicollineariy
SOLUTION 20 points
1. (8 points) In this task, you will checking the OLS assumptions 4-6 using WAGE1 dataset from
previous homeworks. Regress wage on constant, educ, exper, expersq
73-363 Econometrics
Fall 2015
HOMEWORK 1: Simple two-variable regression
SOLUTION - 20 points
1 This exercise will continue using the WAGE1 dataset, derived from the 1976 Current Population
Survey, but we will explore relationship of wage with experience
73-363 Econometrics
Fall 2015
HOMEWORK 2: Multivariate regression
SOLUTION 20 point
We continue to use the WAGE1 dataset from HW1.
1 [4 points] Consider the following regression output:
Dependent variable: wage
coefficient
const
3.39054
educ
0.644272
expe
73-363 Econometrics
Fall 2015
Homework 4: F-test and Prediction
SOLUTION - 20 points
1 (10 points) Let's revisit question 3 from Homework 2. It used the WAGE1 dataset, and tried to
explain wage using educ, exper, as well as two groups of additional variab
73363 ECONOMETRICS
SOLUTIONS TO HW 1
1. (a) The number of variables and observations can be seen by the Stata command describe.
There are 24 variables and 526 observations.
(b) The fraction of female observations with 16 or more years of education (12 yea
73363 Econometrics Homework #1
Out: September 1st In: September 8th
Problem Set #1: Questions 1 and 2 are 25 points each. Question 3 is worth 50 points. Report the
command line of Stata that you use for obtaining your answers.
1. Download the dataset WAGE
73363 - Econometrics Homework #2
Out: Spetember 8th In: September 15th
Questions are equally weighted.
1) A researcher hypothesizes that years of schooling, EDUC, may be related to the number of
siblings (brothers and sisters), SIBLINGS, according to the
73363 ECONOMETRICS
SOLUTIONS TO HW 4
1. (a) We write one parameter in terms of the rest in the given restriction. In this case, = 1
yi = a + li + ki + ui
yi = a + (1 )li + ki + ui
(yi li ) = a + (ki li ) + ui
Therefore, we dene new variables yi = yi li a
73363 ECONOMETRICS
SOLUTIONS TO HW 3
1. (a)
Regression Output: The following Stata output represents regression of S, highest
grade completed, on ASVABC, the ability score, SM, highest grade completed by mother
and SF, highest grade completed by father.
73363 ECONOMETRICS
SOLUTIONS TO HOMEWORK 2
b2
b2
1. (a) The test statistic is t = SE(b22) = SE(b2 ) , since 2 = 0, with degrees of freedom
= 60 2 = 58. Given signicance level , for all the two-tailed tests here, we have
H0 : 2 = 0 versus H1 : 2 = 0. We r
73-240 FALL 20 1 4 SCHOOL OF ausmsss
Short Problems
The nal answer must be written in the space provided.
Problem 1:
Consider the search model of unemployment. Show the effect of an increase in the unem-
ployment benefit (b in the slides) on 1) labor tigh
\
SCHOOL OF BUSlNESS
73-240 FALL 2014
Short Questions
Before you begin, check that you have all the pages and write your name! Good luck!
Question 1:
Consider the steady state of the Solow model with population growth n, labor-augmenting
technology growth
73-200 Spring 2012
73-200 Problem set 2
SOLUTIONS
From the syllabus:
1. Homework must be turned in on the day it is due in the undergraduate program oce
in Tepper 139 by 5:00 pm or to your TA. Late homework will NOT be accepted unless
you are sick and hav
73200 - Problem Set 3
Answer Key
March 27, 2012
Problem 1 (15 points): Solow growth model
1. As the savings rate increases, capital per capita at the steady state increases. To see why, note that
we can rearrange the equation that determines the steady st
73200 - Problem Set 5
Answer Key
May 4, 2012
Problem 1 (15 points): Phillips Curve
Figure 1 shows the relationship between ination and unemployment in the US from 1956 to 1969. Figure
2 shows the same relationship but for the period 1956-2011. We also add
73-200 Spring 2012
Tepper School of Business
73-200 Problem set 4
SOLUTIONS
From the syllabus:
1. Turning in Homework: Homework must be turned in on the day it is due. You may
turn it in during class or in your TAs mailboxes in the PhD lounge, second oor
Course 73-150
Fall 2011
Prof. Christoph Mueller
Problem Set 6
Due: Mon, Dec 5, 2011, beginning of class.
For early submission, please contact: Billie Davis, billie@cmu.edu.
Please print this problem set and answer in the spaces provided. Print single side
Course 73-150
Fall 2011
Prof. Christoph Mueller
Problem Set 5
Due: Fri, Nov 18, 2011, beginning of class.
For early submission, please contact: Billie Davis, billie@cmu.edu.
Please print this problem set and answer in the spaces provided. Print single sid