73-261 Econometrics
Fall 2011
Homework 2: Multivariate regression
SOLUTION - 20 points
1 [3 points] Consider the following regression, which was generated using WAGE2 dataset with wage
being the dependent variable, and is aimed at studying the effects of
73-261 Econometrics
November 16, 2011
Midterm #2
SOLUTION - 50 points.
Draft: score allocations will be added later
1. [20 points] In US, government pensions (Social Security) are relatively small, and many people
use private pension plans which fall into
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 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 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 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 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
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 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
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 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 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
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
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
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
73-261 Econometrics
October 12, 2011
Midterm #1
SOLUTION 50 points
1. Tepper School of Business conducted a survey of the MBA class that graduated in 2010, and
found a linear relationship between wage and years of experience (prior to starting the MBA):
w
73-261 Econometrics
Fall 2011
Homework 9: Simultaneous Equations
SOLUTION
1. (4 points) Exercise 16.2 (pp. 567-568 in Wooldridge 4th edition).
Determine whether each equation is identified, and explain how would you estimate them by using
only OLS regress
73-261 Econometrics
Fall 2011
Homework 8: Time Series & Discrete Choice
SOLUTION
1. (3 points) Consider the following AR(1) process:
yt = c + yt-1 + et,
where et is i.i.d. r.v. with zero mean and | < 1.
Prove that E[yt] = c / (1 ). Show your work.
Take ex
73-261 Econometrics
Fall 2011
Homework 7: Heteroskedasticity
SOLUTION 20 points
1. (6 points) Exercise 8.2 in Wooldridge (p.294 in the 4th edition), with a different expression for
the conditional variance of the residual: V(u|) = 2inc3.
As V(u|) = 2inc3,
73-261 Econometrics
Fall 2011
Homework 6: Endogeneity
SOLUTION 20 point
1. (5 points) Exercise 3.10 (p.108 in Wooldridge 4th ed.), parts (i) and (ii)
~
Hint: use the E1 1 1 2 formula that we derived in class,
and determine how large (or small) 1 and 2 are
73-261 Econometrics
PROBLEM SET 5: Assumptions and Multicollinearity
SOLUTION 20 points
Fall 2011
1. (10 points) In this task, you will checking the OLS assumptions 4-6 using WAGE1 dataset.
and regress log(wage) on constant, educ, exper and female. Make s
73-261 Econometrics
Fall 2011
Homework 4: Multiple hypotheses and prediction
Solution 20 points
1 (12 points) Let's revisit question 3 from Homework 2, dealing with possible controls for ability in
a regression of wage on educ and other controls. It will
73-261 Econometrics
Fall 2011
Homework 3: Inference: single equation
Solution 20 points
1 [18 points] Consider the regression from Q1 of HW2. You will also need the variance-covariance
matrix that you generated in Q2.c; make sure it matches the one in the
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
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 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 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