Problem Set 4
Due Wednesday February 19
This problem set asks you to replicate and extend the analysis by Hayashi
and Fama of the joint hypothesis of ecient markets and constant ex ante
real interest rates. You can download the data set from
http:/fhayash
1
Econ 220B, Winter 2014
Problem Set 6
Due Monday, March 10
This problem set asks you to perform certain calculations with the shortened version of
the Griliches data set available from http:/fhayashi.fc2web.com/datasets.htm and described
on pp. 250-251 i
Answer key for the midterm in 2008
1.) a.)
There is no difference in estimating between Option 1 and Option 2.
Validity of t test:
- Advantage: t test using Option 2 is asymptotically valid in the presence of an unknown form of
heteroskedasticity.
- Disad
1
Econ 220B, Winter 2014
Problem Set 5
Due Monday, March 3
This problem set invites you to choose a published economics article that estimates a
regression with the intention of measuring the eect of x on y. Do not use any of the
articles discussed in Eco
Problem Set 2
Due Wednesday January 22
This problem set asks you to replicate and extend the analysis by Hayashi and Nerlove of cost
functions for electricity generation. Note that data sets for Hayashis text can be downloaded from
http:/fhayashi.fc2web.c
1
Econ 220B, Winter 2014
Problem Set 1
Due Wednesday, Jan 15
1.) Let X be a (T k) matrix whose columns are linearly independent, and let M = IT
X(X X)1 X . Show that M is symmetric and idempotent. Calculate the eigenvalues and
rank of M, and show that it
1
Econ 220B, Winter 2014
Problem Set 3
Due Wednesday January 29
Let cfw_yt T be an i.i.d. N (0, 2 ) sequence. Consider ST , the average squared value of
t=1
2
y : ST = T 1 T yt .
t=1
L
1.) Show that T (ST 2 ) N(0, 2 4 ). State the particular form of the c
1
Econ 220B, Winter 2011
James Hamilton
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 150 points are possible on this exam.
Answer all questions on
1.) (55 points total) An economist is interested in comparing the wag
1
Econ 220B, Winter 2010
Answers to midterm exam
1.) a.) E ( 2 ) = 2 . b.) |X N (0, IT )
2.) Let a() = 1/ and
A() =
Then for T = T 1
(the delta method)
PT
t=1
yt by CLT
a
1
= 2.
L
T ( T ) N (0, 2 ) and from Hayashi Lemma 2.5
L
T [a( T ) a()] N (0, [A()]2
1
Econ 220B, Winter 2009
James Hamilton
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 150 points are possible on this exam.
Answer all questions on
1.) (50 points) Consider the following regression model:
y = X +
|X
1
Econ 220B, Winter 2010
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 150 points are possible on this exam.
Answer all questions on
1.) (20 points) Consider the following equations:
y = X +
b = (X0 X)1 X0 y.
Here y
Answer key for the midterm in 2009
1. a.)
XX
1
Xy
X V 1X
1
X V 1y
OLS
b.)
GLS
c.)
R2
OLS
R2
GLS
because
T
arg min
OLS
t1
yt
2
xt
.
d.) The appropriate test statistic is
1
m
R
s2R X V 1X
r
GLS
1
1
R
R
r,
GLS
where
V 1 y X GLS
Tk
Under the null hypothesis,
Answer key for the midterm in 2011
1a.)
1
b1
nM
0
y t x t1
b2
0
nF
y t x t2
b 1 is exactly equal to the average wage earned by male workers in the sample.
b.) s 2
T 21
y t x t1 b 1 x t2 b 2 2
c.)
b1 b2 2
b1 b2 2
s 2 n M1 n F1
n M1 0
1
2
11s
0 n F1
1
d.) O
1
Econ 220B, Winter 2008
James Hamilton
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 150 points are possible on this exam.
Answer all questions on
1.) (30 points) A colleague of yours is interested in estimating the
Answer key for the midterm in 2007
1.) The sample correlation of e t and x t is always zero in OLS because from the normal equation
T
etxt
0.
t1
2
2.) When E
V X , premultiply the regression model by P 1 where V X
PP . Then
I T where
P 1 . Therefore, the
1
Econ 220B, Winter 2007
James Hamilton
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 150 points are possible on this exam.
Answer all questions on
1.) (15 points) Comment very briey on the following statement. Econom