Problem Set 3
ECON 231W Fall 2014
Due in class Monday October 6th
1. Using the following denitions (which we have seen many times now):
X
=
XY
=
Prove that
XY =
1
n
1
n
1
n
n
Xi
i=1
n
Xi X
Yi Y
i=1
n
Xi X Yi =
i=1
1
n
n
Yi Y Xi
i=1
2. You are interested i
Kuzey YILMAZ
Econ 231W: Econometrics
Jan 30, 2012
Due Feb. 9th
ASSIGNMENT 2
Part I. (Bivariate discrete random variables) To be graded.
Consider the bivariate joint distribution given below.
Y
X
0
1
1
0.1
0.2
2
0.20
0.20
3
0.2
0.1
1. Find the marginal pro
Problem Set 5
ECON 231W Fall 2014
Due Monday November 3rd
1. According to a particular economist, the production of a certain commodity y only needs
two inputs, labor L and capital K. however, the productivity of each factor also depends upon some
unobser
Problem Set 7
ECON 231W Fall 2014
Due Monday November 24th
1. You are using data collected from 545 men who worked every year between 1980 and 1987.
The included variables are as follows
variable
description
id
person identier
year
1980 to 1987
lwage
log(
Kuzey YILMAZ
Econ 231W: Econometrics
Jan 23, 2012
Due Feb. 2nd
ASSIGNMENT 1
Unless stated otherwise, graded part of assignments should be handed in at the end of
the lecture on the due date.
Abbreviation: SW = Stock and Watson (textbook).
Part I. To be gr
Problem Set 6
ECON 231W Fall 2014
Due Monday, November 10th
1. (S&W 11.8) Consider the linear probability model Yi = 0 +1 Xi +ui , where P (Yi = 1 | Xi ) =
0 + 1 Xi .
(a) Show that E (ui | Xi ) = 0
(b) Show that V ar (ui | Xi ) = (0 + 1 Xi ) [1 (0 + 1 Xi
Problem Set 3
ECON 231W Fall 2014
Suggested Solutions
1. From the denition of covariance:
This is identical to:
i=1
(Xi X)Yi (Xi X)Y
(1)
(Yi Y )Xi (Yi Y )X
(2)
i=1
and
XY =
(Xi X)(Yi Y )
n
1
n
XY =
n
1
n
XY =
1
n
n
i=1
Equation (1) can be rewritten as
Econ 231W
Section 2
Exercise 1.
A supermarket has two express lines. Let Xand Y denote the number of customers in the rst
and in the second, respectively, at any given time. During nonrush hours, the joint pdf of X and Y is
summarized by the following tab
Problem Set 8
ECON 231W Fall 2014
Suggested Solutions
1.
a. Yes, reading the newsletter improves the performance by 1.5, which is 15% of the mean,
and seems to be economically signicant. This improvement is also statistically signicant: t-stat
1.5
= 0.15
Econ 231W
Section 1
Properties of Sums
n
i=1
xi stands for the sum x1 + x2 + . . . + xn1 + xn .
Some useful properties of sums are:
N
a = Na
i=1
n
n
axi = a
xi
i=1
i=1
n
n
n
(xi + yi ) =
i=1
i=1
m
n
xi +
n
xi yj =
i=1 j=1
n
xi
yj
j=1
n
m
n
(xij + yij ) =
Econ 231W
Section 2
Exercise 1.
A supermarket has two express lines. Let Xand Y denote the number of customers in the rst
and in the second, respectively, at any given time. During nonrush hours, the joint pdf of X and Y is
summarized by the following tab
Problem Set 1 Due July 16th
ECON 139/239
2010 Summer Term II
Properties of Sums
n
xi stands for the sum x1 + x2 + . . . + xn1 + xn .
i=1
Some useful properties of sums are:
N
a = Na
i=1
n
n
axi = a
i=1
xi
i=1
n
n
n
(xi + yi ) =
i=1
n
xi +
i=1
m
n
xi yj =
ECO 231W
Supplementary Exercises 1
Properties of Sums
Pn
i=1 xi stands for the sum x1 + x2 + . . . + xn1 + xn .
Some useful properties of sums are:
N
X
a = Na
i=1
n
X
n
X
axi = a
i=1
xi
i=1
n
n
n
X
X
X
(xi + yi ) =
xi +
yi
i=1
i=1
m
n X
X
xi yj =
i=1 j=1
Course Outline
ECON 4750
University of Georgia
Prof. Josh Kinsler
Spring 2016
Note: The due dates for problem sets are tentative and are subject to change. Refer to the
problem set handouts for the nal due dates.
Tuesday, January 12
Introduction, course d
Problem Set 7
ECON 231W Fall 2014
Suggested Solutions
1.
a. If we were to include all dummies from 1980 to 1987 and the constant, we run into the perfect
multicollinearity problem.
b.
Cov(it , is )
=
Cov(i + uit , i + uis )
=
Cov(i , i ) + Cov(i , uit ) +
Problem Set 8
ECON 231W Fall 2014
Due Wednesday December 10th
1. You have data on the performance of n mutual fund managers. Their performance is measured by a
variable Y , whose mean, in the sample, is equal to 10. You also have data on whether the manag
Statistics Review
ECO 231W Handout 3
Department of Economics
University of Rochester
Fall 2016
Eco 231W Handout 3 (Rochester)
Statistics Review
Fall 2016
1/1
Population and Sample
Population Parameter
X
X2
N
mean
variance
size
Sample Parameter
X
sX2
n
For
Econ 231W
Section 2
Exercise 1.
A supermarket has two express lines. Let Xand Y denote the number of customers in the first
and in the second, respectively, at any given time. During nonrush hours, the joint pdf of X and Y is
summarized by the following t
Problem Set 2
ECO 231W Fall 2016
Due in class Monday September 26th
1. A quality control plan for an assembly line involves sampling n = 10 finished items per
day and counting Y, the number of defective items. Therefore, if p denotes the probability
of ob
Confidence Intervals and Hypothesis Testing
Eco 231W Handout 4
Department of Economics
University of Rochester
Fall 2016
Eco 231W Handout 4 (Rochester)
Hypothesis Testing
Fall 2016
1/1
Confidence Intervals and Hypothesis Testing (Chapter 3)
So far weve on
Problem Set 6
ECON 231W Fall 2014
Suggested Solutions
1.
a. Since Yi is a binary variable, we know
E(Yi |Xi ) = 1 P r(Yi = 1|Xi ) + 0 P r(Yi = 0|Xi ) = P r(Yi = 1|Xi ) = 0 + 1 Xi .
Thus:
E(ui |Xi ) = E[Yi (0 + 1 Xi )|Xi ] = E(Yi |Xi ) (0 + 1 Xi ) = 0
b. U
Notes 2: Observational studies, confounding
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
1
Course Setup
The course website (http:/www.carolinacaetano.net/teaching/eco231w) is now ready. There
may be a few tweaks to do here and there, but t
Problem Set 1
ECON 231W Fall 2014
Due in class Monday, September 15th
1. A few years ago the news magazine The Economist listed some of the stranger explanations used in the past to predict presidential election outcomes. These included
whether or not the
Problem Set 2
ECON 231W Fall 2014
Due in class Monday September 29th
1. A quality control plan for an assembly line involves sampling n = 10 nished items per
day and counting Y, the number of defective items. Therefore, if p denotes the probability
of obs
Problem Set 4
ECON 231W Fall 2014
Due Monday October 27th
1. The cost of attending your university has gone up once again. Although you have been told
that education is investment in human capital and carries a return of roughly 10% a year,
you (and your
Problem Set 4
ECON 231W Fall 2014
Suggested Solutions
1.
a) An increase in reputation of one unit increases the cost by roughly $3,985. The larger the size
of the university, the lower the cost. An increase of 10,000 students results in a $2,000 lower cos
Problem Set 5
ECON 231W Fall 2014
Suggested Solutions
1.
a)You cannot use OLS, because the equation under consideration is not of the form X1 +X2 +,
where enters additively and the coecients, which we estimate (in power 1), are multiplying the
explanatory
Sun 1
Tiantian Sun
ECO 231W
Term Paper
04/30/2013
Substance Abuse and High School Outcomes
Abstract
Substance abuse among high school students is a serious problem on students performance.
In this paper, the effects of substance abuse are estimated using
Midterm 1
ECO 231 - Undergraduate Econometrics
Prof. Carolina Caetano
INSTRUCTIONS
Reading and understanding the instructions is your responsibility. Failure to comply
may result in loss of points, and there will be no leniency on that respect.
1. You hav
ECON 4750
Supplementary Exercises 3
Exercise 1. You want to estimate a parameter 0 (so 0 is the true value of the parameter you are
estimating) and you use an estimator . We dened the Mean Squared Error of the estimator as
M SE = E
Prove that M SE = V ar
Instrumental Variables
Econ 231W Handout 13
Department of Economics
University of Rochester
Fall 2016
Econ 231W Handout 13 (Rochester)
Instrumental Variables
Fall 2016
1 / 68
Threats to Internal Validity
Recall our definition of internal validity:
A stati
Regression with Panel Data
Econ 231W Handout 12
Department of Economics
University of Rochester
Fall 2014
Econ 231W Handout 12 (Rochester)
Regression with Panel Data
Fall 2014
1 / 52
Threats to Validity (Chapter 9)
Now that we have introduced several empi
ECON 231W
Supplementary Exercises 6
Getting Started with Stata
The point of this discussion section is to get you started using the statistical software package Stata.
After some initial exercises, you will work through an empirical exercise using the Dis
Econ 231W
Section 8
Exercise 1
Using a sample of 1105 i.i.d. observations from the 1978 CPS (Current Population Survey), you have
estimated that the relation between (log of) earnings Ei and years of schooling Si is described by the
following relation
lnE
Econ 231W
Section 9
Exercise
You are undertaking a study of child nutrition in India. You have data for a sample of about 27,000
children (who are under 3 years of age), collected in 1998-99 from the Indian National Family and
Health Survey. The dependent