Sketched_out_answers_Final_Econ140A_2011Spr - Economics...

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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 F-test ( ) 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 Gauss-Markov assumptions hold for ̃, so ̃ is BLUE. page 2 3 a. The estimated gender-caused 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 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 , 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 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 8. 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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