1
Econ 220B Final Exam
Winter 2009
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam.
Answer all questions on
1.) (60 points total) The least-squares regression model y = X + makes a lot of
assumpt
Answer key for the 2003 nal exam (econ 220b).
1. (a) Since we assume that Ci = Yi , we can substitute for C and Y
to get
Ci aci = (Yi ayi )
and then Ci = Yi + (aci ayi ). So
i
= aci ayi .
(b) The plim of an estimator bT is the constant b (if it exists) s
Answer key for the 2005 final exam (econ 220b).
rt, yt ,
x t x t 1 x t p t and z t
1. a. Let x t
consistently from the formula
x t , r t . Then we can estimate c
ztzt 1
ztqt.
d
b. We need to assume that S xx T 1 X X and S xz T 1 X Z have full rank and
2
E
Answer key for the 2006 nal exam (econ 220b).
1. See the textbook.
2. (a) b = (X 0 X )1 X 0 Y . The OLS estimator is unbiased because the errors
are strictly exogenous, and it is consistent because both the bias and
variance decrease to zero in the limit.
1
Econ 220B
Answers to 220B Winter 2007 Final Exam
1a.)
or
=
0
T
zt
0
zt zt zt
1
yt
zt y t
h
i
0 1
[(zt z)(yt y )]
= (zt z)(zt z)
1b.) m = q
k =q+1
SSRR from regression of yt on 1
SSRU from regression described in 1a
1c.) no further assumptions needed
1
Econ 220B
Answers to 220B Winter 2008 Final Exam
1a.) (X0 X)1 X0 y
h
i
0 1
b.) (Rb)0 Rs2 (X0 X)1 R
(Rb)
R = 1 2
F (1, T 2)
c.)
Rb
p
t(T k )
Rs2 (X0 X)1 R0
d.) Replace s2 (X0 X)1 with
(X0 X)1
T
X
0
e2 xt xt (X0 X)1
t
t=1
e.) Let g ( ) = log b1 2 log b2
Answer key for the nal in 2009
1.)
a.)
b.)
c.)
d.)
e.)
f.)
v
v-vi
v-vi
vii
none
none
2.)
a.) =
T
t=1
1
T
t=1
xt xt
xt yt for xt = (1, xt ) .
b.) = Sxy /Sxx
c.)
T
T
[(yt y ) (xt x)]2
e2 =
t
t=1
t=1
T
T
t=1
T
T
e2
t
t=1
2
(yt y ) +
=
1
T
2
2
(xt x) 2
t=1
(
1
Econ 220B, Winter 2010
Answers to nal exam
1.) a.) plim(b) = 1 xy
xx
0
b.) (1) if for the we are interested in it is the case that E (yt xt )xt = 0, then
OLS is allowing us to estimate this . (2) If our goal is to minimize the mean squared error
0
of a
Answer key for the final exam in 2011
1a.)
T
a
b
exp
yt
x t /2
1
xtxt
exp
x t /2 y t
x t y t is unbiased
X V 1X
alternative form:
c.)
is unbiased
xtyt
x t /2
x t exp
yt
x2
t
xt
b.) Let x t
1
xt
1
X V 1y
a
has smaller variance than
and hypothesis tests hav
1
Econ 220B
James Hamilton
Final Exam
Winter 2004
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam
Answer all questions on
1.) (25 points total) State (but do not prove) the Gauss-Markov Theorem.
1
Econ 220B
James Hamilton
Final Exam
Winter 2005
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam
Answer all questions on
1.) (80 points total) An economist is interested in estimating the price
1
Econ 220B
Final Exam
Winter 2006
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam
Answer all questions on
1.) (25 points) State (but do not prove) the Gauss-Markov Theorem.
2.) (80 points total)
1
Econ 220B
Final Exam
Winter 2007
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam
Answer all questions on
1.) (115 points total) Consider the following regression model,
yt = + 0 zt + t
for zt a
1
Econ 220B
James Hamilton
Final Exam
Winter 2008
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam
Answer all questions on
1.) (80 points total) This question concerns the following regression mod
1
Econ 220B, Winter 2013
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.) (150 points total) This question refers to a regression of yt on a constant and
Answer key for the midterm in 2014
1a.) OLS regression coefficient, square of standard error of regression, and uncentered
coefficient of determination.
p
b.) b
T 1 xtxt 1 T 1 xtyt
Q 1
c.) s 2
T k 1
y 2t 2y t x t b b x t x t b
p
2
E yt
2E y t x t Q 1
Q 1E
1
Econ 220B, Winter 2014
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.) (60 points total) Consider a regression of a scalar yt on a (k 1) vector xt . Co
Answer key for the midterm in 2012
yt 1, zt, zt
1a.) x t
,
1
1
T
T
xtxt
xtyt
t1
t1
T
2
T
1
3
yt
2
xt
t1
b.) Let R
0, 1, 1 and use
s2R
1
xtxt
.
R
Treat as Student t with T 3 degrees of freedom. This is only an approximation since x t includes the
lagged va
1
Econ 220B, Winter 2012
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.) (60 points total) Let yt and zt be stationary and ergodic scalars which are rela
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 Final Exam
Winter 2010
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam.
Answer all questions on
1.) (20 points total) A regression of a scalar yt on a vector xt produces an OLS regres
1
Econ 220B Final Exam
Winter 2011
DIRECTIONS: No books or notes of any kind are allowed.
separate paper. 250 points are possible on this exam.
Answer all questions on
1.) (85 points total) Consider the following regression model:
yt = + xt + t
V=
|X N (0
1
Econ 220B, Winter 2012
James Hamilton
Problem Set 1
Due Thursday, Jan 19
1.) Let X be a (T k ) matrix whose columns are linearly independent, and let M = IT
X(X0 X)1 X0 . Show that M is symmetric and idempotent. Calculate the eigenvalues and
rank of M,
Problem Set 2
Due at 9:20 a.m. on Thursday Jan 26
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:/fhayas
1
Econ 220B, Winter 2012
Problem Set 3
Due Thursday, Feb 2 at 9:20 a.m.
Let cfw_yt T=1 be an i.i.d. N (0, 2 ) sequence. Consider ST , the average squared value of
tP
2
y : ST = T 1 T=1 yt .
t
L
1.) Show that T (ST 2 ) N (0, 2 4 ). State the particular for
Problem Set 4
Due Tuesday, Feb 21
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:/fhayashi.fc2w
1
Econ 220B, Winter 2012
Problem Set 5
Due Tuesday, March 6
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 E
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
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 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