–1–
Econ 220B
James Hamilton
Final Exam
Winter 2005
DIRECTIONS: No books or notes of any kind are allowed.
Answer all questions on
separate paper. 250 points are possible on this exam
1.) (80 points total) An economist is interested in estimating the price elasticity of
petroleum supply in the United States. She reasons that the log of demand (
q
d
t
)
depends
on the log of the relative price of petroleum
(
p
t
)
and the log of U.S. real GDP
(
y
t
)
,
whereas
supply
(
q
s
t
)
depends on price and the log of proved petroleum reserves
(
r
t
)
:
q
d
t
=
ap
t
+
by
t
+
u
t
q
s
t
=
cp
t
+
dr
t
+
v
t
.
We assume that the market is in equilibrium so that
q
d
t
=
q
s
t
=
q
t
.
Suppose that the
vector
(
q
t
,p
t
,y
t
,r
t
)
0
is stationary and ergodic and that the vector
(
u
t
,v
t
)
0
is a martingale dif-
ference sequence with respect to
u
t
−
1
,u
t
−
2
, ..., u
1
,v
t
−
1
,v
t
−
2
, ..., v
1
,r
t
,r
t
−
1
, ..., r
1
,y
t
,y
t
−
1
, ..., y
1
with
E
(
u
2
t
)=
σ
2
u
,E
(
v
2
t
)=
σ
2
v
,E
(
u
t
v
t
=0)
,
and
E
½·
u
t
v
t
¸¯
¯
¯
¯
y
t
,r
t
¾
=
·
0
0
¸
.
a.) (30 points) Write down a formula for a consistent estimate of