University of California
D. Steigerwald
Department of Economics
Economics 140A
Exercise 5
1.
(A difficult question.
Answer for extra credit.)
We will investigate the following claim
(which appears in nearly this form in Studenmund's undergraduate econometrics text)
If an equation that contains a lagged dependent variable as a regressor has a serially
correlated error term, then OLS estimates of the coefficients will be inconsistent.
To investigate, we define a regression model in a slightly different way.
Let
t
Y
be a
strictly stationary and ergodic random variable that is observed into the infinite past.
Assume that
0
t
EY
and
2
t
EY
.
Define
t
t
t
Y
Var
Y
Y
Cov
,
1
and
1
t
t
t
Y
Y
U
so that we can write
t
t
t
U
Y
Y
1
for
t=1,…,n
.
a.
Show that
0
t
EU
and
0
,
1
t
t
U
Y
Cov
.
b.
Show that the OLS estimator
B
from a regression of
t
Y
on
1
t
Y
, for
t=1,…,n
, is
consistent for
β
.
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 Fall '08
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 Economics, Yt, Qt, ln Qt, ln PMt

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