Unformatted text preview: Economics 140A Spring 2011
Professor Startz
Sketched Out Final Exam 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.
1. This needs an Ftest ( ) or Since the 5% critical value is 3.00, we can reject the hypothesis.
2 . a.
̃ ( ) ( ̃) ( () ()
) b.
( ̃) (( ̃ )) (( ∑ ) ) () ((∑ ) ) ()∑
c. Note that , so is just OLS on this equation. is the same as Note that this is a true equation, the RHS variable (1.0) is fixed, the errors have mean
zero, are uncorrelated, and (( ) ) () () () , so the errors are homoskedastic. All the GaussMarkov assumptions hold for ̃, so ̃ is BLUE. page 2
3 a.
The estimated gendercaused difference in earnings between Black men and Black
women is
. So gender explains a 16 percent wage differential. The
variance of the sum in the two coefficients is the sum of the two variances plus twice the
(
)
covariance
. The square
root is
. Since the gender difference is 10 standard errors, it is off the scale significant.
b. Black women get 0.29 years more education than black men. This increases their relative
earnings by
. Combining this with the gender effect in the previous
section, Black women earn 12 percent less than Black men.
4. ̂ ( . So ).
( (The
5. ) doesn’t matter.)
If we write the equation as then the immediate impact is and the longrun effect is So a two point jump in inflation will cause a 2.4 point jump in the inflation rate in the long run.
The immediate effect is
, which is too small to measure. Even if
, after
10 weeks the effect would be 0.06, which is almost too small to measure. By 100 weeks, were
at half a percentage point or so. Basically, it would take a couple of years for the change in
inflation to have a really noticeable effect.
6. GLS is just the regression on the quasidifferences. Note that the RHS variable is all ones, so
the quasidifference there is just
.
(
)(
)
(
)
̂
(
)
(
)
The variance is just the usual formula, applied to the quasidifferenced variables
(̂ ) ( ) 7. Using Theil’s misspecification theorem we have
(
̂ ( ) ) That last piece is the regression coefficient in the last regression, so we have (When I generated the data, the truth was .) page 3
8.
If we think of this as errorsinvariables we can use
either or as an instrument. Taking a quickanddirty plim goes like
)(
)
((
)(
)
((
For 2SLS we’d use both and in the first stage. as the noisy measure of an use ...
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 Fall '08
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 Economics

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