Prof. Frederico Finan
Econ 103
Fall 2007
Midterm Examination #1
(1 hour and 15 minutes, 35 percent of final grade)
Answer all four parts
Part I. Define or explain in one or two sentences any 4 of the following 5 concepts. If you use a
graph, make sure that you explain what it shows. If you use a formula makes sure you define the
variables. Also please distinguish between estimates and population parameters. Do not answer more
than 4 (5 points each, total of 20 points).
1. Type I error
A type I error occurs when the null hypothesis is rejected when in fact is true.
2. The power of a test
The power of a test is the probability that the test correctly rejects the null hypothesis when the
alternative is true.
3. Heteroskedasticity
The error term
u
i
is heteroskedastic if the variance of the conditional distribution of
u
i
given
X
i
depends on
X
i
.
4. The 95 percent confidence interval for a slope parameter
Is an interval (or set) that contains the true value of the slope population parameter with a 95%
probability when computed over repeated samples.
5. Causal effect
The expected effect of a given intervention or treatment as measured in an ideal randomized
controlled experiment.
Part II. True or false, and very briefly explain why. Select any 4 of the following 5 statements
and do not answer more than 4 (5 points each, for a total of 20 points).
6. Consider the following model:
y
u
u
1
U
u
2
x
1
U
u
3
x
2
U ±
. If
X
1
and
X
2
are highly collinear, then
our estimate of
u
2
will be biased.
FALSE. Multicollinearity does not violate any of the CLRM assumptions so OLS will be BLUE.
However, estimates of
u
2
and
u
3
are likely to be unstable with high standard errors.
1
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View Full Document7. Imagine you regressed earnings of individuals on a constant, a binary variable (“Male”) which
takes on the value 1 for males and is 0 otherwise, and another binary variable (“Female”) which
takes on the value 1 for females and is 0 otherwise. Because females typically earn less than
males, you would expect the coefficient for Male to have a positive sign, and for Female a
negative sign.
FALSE. None of the OLS estimators exist because there is perfect multicollinearity.
8. In a single regressor model, the slope estimator has a smaller standard error, other things equal,
if there is more variation in the exploratory variable, X.
TRUE. Under the GaussMarkov conditions
u
1
, is conditionally unbiased, and the variance of
the conditional distribution of
u
1
, given X is
( )
( )
∑
=

=
n
i
i
u
n
x
x
x
x
1
2
2
1
1
,
,

ˆ
var
σ
β
K
The sample variance of X is given by
( )
( )
∑
=


=
n
i
i
x
x
n
X
1
2
1
1
var
Therefore, as the variance of X increases the slope estimator will have a smaller standard error.
9. Consider the following regression line: TestScore
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 Spring '07
 SandraBlack
 Statistics, Normal Distribution, Regression Analysis, Variance, Prof. Frederico Finan

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