University of California
D. Steigerwald
Department of Economics
Economics 140A
Problem Set X
1.
Suppose that you have data
(Y
t
, X
t
)
,
t = 1,...,n
that satisfy
Y
t
=
β
0
+
β
1
X
t
+ U
t
, where
U
t
satisfies all of the standard assumptions.
In examining the
X
t
observations you notice that
the sample variance of the difference
X
t
X
t1
seems to be higher than that of
X
t
due to
extreme variation from observation to observation, so you decide to estimate
β
1
from a
regression of
Y
t
Y
t1
on
X
t
X
t1
.
Is this a good idea?
Why or why not?
2.
In the linear probability model we know that the errors are heteroskedastic.
In fact, their
variance is given by
)
EY
(
EY
)
U
(
E
t
t
t
−
=
1
2
Can we use the residuals to estimate the error variance directly?
If not, what alternative
measure would you propose?
3.
On occasion, municipal governments find that tax receipts fall short of the interest
payments on their bonds.
When this occurs, the municipalities default on their bonds.
In
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 Fall '08
 Staff
 Economics, Econometrics, Linear Regression, Regression Analysis, Variance, Estimation theory, Errors and residuals in statistics

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