Unformatted text preview: Economics 140A Fall 2011
Sketched Out Midterm Answers Note that not all the details are shown here. The sketches here are just to point you in the right
direction. A good exam answer would have more details.
a. A 1% increase in the number of hours worked per week increases wages
b. Substituting the correct values for each variable yields a prediction of
c. The point estimate for the sum of union and female is
. The correct standard error is
√ of ( . This yields a t-statistic ) which means that we fail to reject the null hypothesis since this is far below any reasonable critical value.
a. (2 pts.) The marginal effect of engine displacement on mpg is
b. (2 pts.) The critical engine displacement is ( ) . c. (3 pts.) There is linear relationship if the sign on the quadratic term is
statistically indistinguishable from 0; therefore, if we can reject the null
we can assume that the relationship isn’t linear. The tstatistic is 16.156, therefore we reject the null of a linear relationship
between engine displacement and mpgs.
d. (2 pts.) The coefficients on the constant and displacement terms are
essentially unchanged. The r-squared increased by 0.025
e. (3 pts.) A 99% confidence interval for the effect of four-wheel drive on fuel
). Which is (
( f. (3 pts.) The required F-Test is ) ⁄( ) which )
compared the critical value for (
which means we reject the
null that the additional variables are jointly zero.
a. A sketch of the proof is:
[ ̂] [ ∑( )] page 2 [∑ ∑] ∑ ∑ b. A sketch of the proof is
[ ̂] [∑
[ ( ∑]
) ( [ )] ( ( ( )
) ) 4. We will give the answers for the general case
a. First rewrite this estimator:
( ̃ ) and then take the expectation:
[̃] [ [̃]
b. Using the previous result:
[̃] [ [ [ ( ) (
c. To show that the variance is greater than the OLS estimator note that ̃
is unbiased (shown in (a)) and that it is linear in , with weights
Since OLS is the BLUE, ̃ must have a larger variance.
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