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Unformatted text preview: Economics 140A Spring 2011
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 F-test ( ) or Since the 5% critical value is 3.00, we can reject the hypothesis.
2 . a.
̃ ( ) ( ̃) ( () ()
( ̃) (( ̃ )) (( ∑ ) ) () ((∑ ) ) ()∑
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 Gauss-Markov assumptions hold for ̃, so ̃ is BLUE. page 2
The estimated gender-caused difference in earnings between Black men and Black
. 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
. The square
. 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
. Combining this with the gender effect in the previous
section, Black women earn 12 percent less than Black men.
4. ̂ ( . So ).
5. ) doesn’t matter.)
If we write the equation as then the immediate impact is and the long-run 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
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 quasi-differences. Note that the RHS variable is all ones, so
the quasi-difference there is just
The variance is just the usual formula, applied to the quasi-differenced 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
If we think of this as errors-in-variables we can use
either or as an instrument. Taking a quick-and-dirty 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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