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
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
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 231: Econometrics
Feb 9, 2012
ANSWERS TO ASSIGNMENT 2
Part I. (Bivariate discrete random variables)
Given the joint p.f. f(x, y):
x=1
0.1
0.2
y=0
y=1
x=2
0.20
0.20
x=3
0.2
0.1
1. The marginal p.f. of X: fX(x) =
P(X=Xj): P(X=1) =.1+.2 = .
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
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
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 ) +
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 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 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 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
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
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
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 ) =
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
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
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
Midterm 2 - Preparation
ECO 231 - Undergraduate Econometrics
Prof. Carolina Caetano
INSTRUCTIONS
The instructions below are the same that will be given to you in the exam.
1. You have received three booklets. Booklet 1 contains the exam instructions and
t
Notes 2: Observational studies, confounding
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
1
Experiments, continuation from last class
1.1
Review
We were talking about the two scientific questions:
How much will attending one extra class im
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
Notes 3: Confounders
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
1
Causal Effects
Why do we care that the treatment and control are comparable? For that matter,
why do we care to find the causal effect?
If we just compare observations th
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
Homework 1
Eco 231 - Undergraduate Econometrics
Prof. Carolina Caetano
1. It is reported that average U.S. person nowadays has spent more on medical and health-related
products/services, compared with the previous decades. Suppose a researcher is interest
Notes 20: Research
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
This class wraps up everything that we learned so far. It will give you a good idea of
how far weve come. It provides a guide of how to go about pursuing a research project.
F
Notes 18: Measurement error
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
In the next two classes we will be talking about failures of the data (as opposed to
failures of the model). Remember assumption 2:
Assumption 2: The data cfw_(yi , x
Notes 19: Multicollinearity and other data failures
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
In the last class, we considered the ways in which assumption 2 could fail.
1. Random sampling
2. No perfect multicollinearity
3. We observe a
Notes 16: Omitted, superfluous, and proxy
variables.
ECO 231W - Undergraduate Econometrics
Prof. Carolina Caetano
1
Review of omitted variables
This is perhaps the most important type of model failure. In fact, many failures of other
assumptions can be un