This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Economics 140A Spring 2011
Professor Startz
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.
1.
a. The second regression coefficient is
()
̂
̂.
( ) b. There are a couple of ways to do this. The easy one is to use the theorem ( ̂) ()
( ̂ ).
c. The formula for the reported variance is
We know that ( )
. What about ? The residuals for the first regression
̂ . For the second regression,
are
( ̂ )( ). So they’re identical. Since
, the reported
√ √ is unchanged. Thus the reported standard error is . Prove that the reported standard error of ̂ equals the reported standard error of
̂ . (Remember that the reported standard error depends on rather than .)
d. Since the coefficient and standard error both fall in half and the tstat is the ratio, the
two are identical.
2.
a. The second sample mean is
̂ ̂
̂ b. Uh, they’re the same numbers. They have the same expected value, the same
variance, and probably the same horoscope.
c. Write
. We can write the estimator as
(
̂ ) ( )
( The variance is ) page 2
(( ̂ )) ( ) ( ) (
)
()
Taking the expectation we get a lot of zeros and
times. The latter is
because each error term appears twice, so when we square things we get
twice and also the cross product between the first and second appearance of
twice. So we get
(̂) ( ) 3.
a. tstatistic (1.0560)/0.017 = 61.01115
61.01115 > 2.57 > 1.96 Can reject null at 5% and 1% level
(
b. The confidence interval is ). 4. For men, the variable
. So comparing men only Blacks earn 18.4 percent less
than Whites and Asians earn 3.8 percent less. The coefficient on FE indicates that all
women start off with a 30.5% gap. However, the last two coefficients change this by
giving Black women a “deduction” of 18.4% plus an addition of 14.3%. So the difference
between Black and White Women is just over 4 percent. (Asian women earn about 11%
more than White women.) So, for example, controlling for education Black women earn
34.6% (
) less than White men. Comparing Asian women to the
omitted reference group, White men, the gap is
.
5.
a. The point estimate of the difference is .305+.1464. The variance of this estimate
is
. So the tstat is


√
So do not reject
b. We need an Ftest. We can write this as
(
)⁄
⁄(
)
Since the critical value is 2.61, this is way rejected. ( ) ...
View
Full
Document
This note was uploaded on 12/26/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff
 Economics

Click to edit the document details