ECON425 PROBLEMSET 2 SOLUTIONS
question 1.
part a.
P (A1 (A2 An )
P (A2 An An ) =
P (A1 )
P (A1 A2 ) (A1 An )
=
P (A1 )
Pn
P (A1 Ai )
= i=2
P (A1 )
n
X
P (A1 Ai )
=
P (A1 )
i=2
=
n
X
since (A1 Ai ) (A
ECON 425 PROBLEMSET 10 SOLUTIONS
question 1.
part i.
AT T = E Yi1 Yi0 Di = 1
= E E Yi1 Yi0 Xi , Di = 1 Di = 1
= E E Yi1 Yi0 Xi Di = 1
= E E Yi1 Xi E Yi0 Xi Di = 1
= E E Yi Xi , Di = 1 E
Econ 425: Midterm
February 26, 2015, Thursday
Time Limit : 60 minutes. Total 100 Points
Instructions :
(A) You will be given first 10 minutes as a reading time that is not included in the
one-hour exa
Econ 425: Final Exam
April 13, 2016, Wednesday
Time Limit : 150 minutes. Total 120 Points
Instructions :
(A) You will be given first 10 minutes as a reading time that is not included in the two and a
Econ 425: Midterm
February 26, 2016, Thursday
Time Limit : 60 minutes. Total 100 Points
Instructions :
(A) You will be given first 10 minutes as a reading time that is not included in the
one-hour exa
ECON 425 PS 7 SOLUTIONS
question 1.
part i.
Euit Xit
= E E uit Xit Xi1 , . . . XiT
= E Xit E uit Xi1 , . . . XiT
"
"
#
1X
= E Xit E uit
ui Xi1 , . . . XiT
T
=0
Remark. Note that you must conditi
MIDTERM EXAM SOLUTIONS
Part A.
part i.
AP E = E
E [Yi |Xi = x]
x
= 1 + 22 EXi + 3 EWi
where 1 , 2 , 3 solve the system
Cov(Yi , Xi ) = 1 V ar(Xi ) + 2 Cov(Xi , Xi2 ) + 3 Cov(Xi , Xi Wi )
Cov(Yi , Xi2
ECON 425 PROBLEMSET 3 SOLUTIONS
question 1.
part a.
Cov(Y, h(X) = E [Y h(X)] E[Y ]E[h(X)]
= E E Y h(X)X E[E[Y |X]E[h(X)]
by LIE
= E [h(X)E [Y |X] E[E[Y |X]E [h(X)]
= E [h(X)c] cE [h(X)]
using E [Y
Econ 425 - Problem Set 7
Due March 17 (Thursday) in Class
Instructions. These questions cover the panel regression models. Do your best to make your
arguments rigorous. You may discuss this problem se
Econ 425 - Problem Set 5
Due February 9 (Thursday) in Class
Instructions. These questions cover the regression models. Do your best to make your arguments
rigorous. You may discuss this problem set wi
Econ 425 - Problem Set 6
Due February 16 (Thursday) in Class
Instructions. These questions cover the regression models. Do your best to make your arguments
rigorous. You may discuss this problem set w
ECON425 PROBLEMSET 9 SOLUTION
question 1.
part i. The APE is given by E
x E [Yi |Xi
= x, Di = d] , where
E [Yi |Xi , Di ] = E 1 cfw_0 + 1 Xi + 2 Di + 3 Xi Di ui Xi
= P cfw_0 + 1 Xi + 2 Di + 3 Xi Di
ECON425 PROBLEMSET 4 SOLUTIONS
question 1.
part a. The APE 0 is given by
E Yi Xi1 = x1 , Xi2 = x2
x1
E g(Xi1 , Xi2 ) + ui Xi1 = x1 , Xi2 = x2
=E
x1
E g(Xi1 , Xi2 )Xi1 = x1 , Xi2 = x2 + E ui Xi1 =
Econ 425: Midterm
February 28, 2017, Tuesday
Time Limit : 60 minutes. Total 100 Points
Instructions :
(A) You will be given first 10 minutes as a reading time that is not included in the one-hour
exam
ECON425 PS6 SOLUTION
question 1.
part a. Three
part b. Choose two instruments cfw_Z1i , Z2i , then using Cov(Z1i , vi ) = Cov(Z2i , vi ) =
0,
Cov(Yi , Z1i ) = 1 Cov(Xi , Z1i ) + 2 Cov(Wi , Z1i )
Cov(Y
ECON425 PROBLEMSET 8 SOLUTIONS
question 1.
part i. Suppose we use the FD estimator
PN PT
t=1 Yit1 Yit
= Pi=1
N PT
2
i=1
t=1 (Yit1 )
in the general case,
PN PT
t=1 Yit1 uit
= Pi=1
N PT
2
i=1
t=1 (Yit
Econ 425 - Problem Set 8
Due March 24 (Thursday) in Class
Instructions. These questions cover the panel regression model and binary choice models. Do
your best to make your arguments rigorous. You may
Econ 425 - Problem Set 10
Due April 12 (Wednesday) in Class
Instructions. These questions cover the binary choice model and binary choice models. Do your
best to make your arguments rigorous. You may
Econ 425 - Problem Set 8
Due March 30 (Thursday) in Class
Instructions. These questions cover the binary choice model and binary choice models. Do your
best to make your arguments rigorous. You may di
Econ 425 - Problem Set 2
Due January 19 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You ma
Econ 425 - Problem Set 4
Due February 2 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You ma
ECON 425 PROBLEMSET 1 SOLUTION
problem 1. Suppose A B. Then,
P (B) = P
B AC A
= P (B AC ) + P (A)
P (A)
For this to be a proof it remains to show that B AC F. First, B AC =
C
B C A by De Morgans law,
Econ 425 - Problem Set 3
Due January 27 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You ma
Econ 425 - Problem Set 1
Due January 12 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You ma
Regression with a Single Regressor:
Hypothesis Tests and Confidence Intervals
(SW Chapter 5)
Overview
Now that we have the sampling distribution of OLS
estimator, we are ready to perform hypothesis t
Linear Regression with One Regressor
(SW Chapter 4)
Linear regression allows us to estimate, and make
inferences about, population slope coefficients. Ultimately
our aim is to estimate the causal effe
Introduction to Multiple Regression
(SW Chapter 6)
Outline
1. Omitted variable bias
2. Causality and regression analysis
3. Multiple regression and OLS
4. Measures of fit
5. Sampling distribution of t