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University of California
D. Steigerwald
Department of Economics
Economics 245B
Problem Set VIII
1.
Consider the regression model
y
t
=
β
0
+
β
1
y
t1
+
ε
t
where {
ε
t
}
t=1,.
..,T
is a mean zero white noise process.
a.
For
β
1
< 1, find what the OLS estimator of
β
1
converges to in probability.
Is
$
β
1
unbiased?
b.
Suppose
β
1
< 1 and
ε
t
=
ρε
t1
+ u
t
, where
ρ
< 1 and {u
t
}
t=1,.
..,T
is a sequence of
independent identically distributed random variables.
Find what
$
β
1
converges to in
probability.
How does your answer change if
ε
t
=
ρε
t1
+ u
t
?
If your answer differs
from those given in parts a. or b., explain intuitively why it differs.
c.
Suppose
β
1
= 1, and
ε
t
is a white noise process.
Find what
$
β
1
converges to in
probability.
How does your answer change if
ε
t
=
ρε
t1
+ u
t
?
If your answer differs
from those given in parts a. or b., explain intuitively why it differs.
d.
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This note was uploaded on 12/26/2011 for the course ECON 245b taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff
 Economics

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