Econometrics Exam 1
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October 24, 2007
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This exam consists of
ten
short questions
(
worth four points apiece
)
and
three
long
questions
(
worth twelve points each
)
, for a total of 76 points.
You have 50 minutes
to answer all completely and clearly in the space provided.
1.
What is “classical measurement error”, and how does it affect the OLS estimator?
The defining characteristic of “classical” measurement error is that it is uncorrelated with any of
the
variables
in
the
model.
CME
causes
OLS
to
be
biased:
E
[
ˆ
!
OLS
]
=
"
var(
x
) /
var(
x
)
+
var(
m
)
( )
.
2.
You estimate the effect of a percentage change in the price of widgets on the
percentage
decrease
in
demand
for
widgets,
using
the
equation
ln
DEMAND
i
=
1
+
2
ln
PRICE
i
+
e
i
(
where
2
is
interpreted
as
the
own

price
elasticity
)
.
You estimate that
ˆ
2
=
"
0.78
, with a standard deviation of
0.21
.
How
would you test the hypothesis that demand is unit elastic
(
H
0
:
2
=
"
1
)
against the
alternative that it is not
(
H
A
:
2
" #
1
)
, without any help from Stata?
You would calculate a t

statistic and compare this to critical values of the t

distribution.
In this
case,
t
=
(
!
0.78
!
(
!
1)) / 0.21
.
If the absolute value of t is greater than the critical value at
your confidence level in a sample with these degrees of freedom
(
greater than 1.96, for the 95
%
confidence level in a large sample
)
, you would reject the null hypothesis.
3.
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 Spring '08
 Staff
 Econometrics, Regression Analysis, Variance, OLS, Econometrics Midterm

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