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Answer keys for HW3
7.4
(i) The approximate difference is just the coefficient on
utility
times 100, or –28.3%.
The
t
statistic is
.283/.099
2.86, which is very statistically significant.
(ii) 100
[exp(
.283) – 1)
24.7%, and so the estimate is somewhat smaller in magnitude.
(iii) The proportionate difference is .181
.158 = .023, or about 2.3%.
One equation that can
be estimated to obtain the standard error of this difference is
log(
salary
)
=
0
+
1
log(
sales
) +
2
roe
+
1
consprod
+
2
utility
+
3
trans
+
u
,
where
trans
is a dummy variable for the transportation industry.
Now, the base group is
finance
,
and so the coefficient
1
directly measures the difference between the consumer products and
finance industries, and we can use the
t
statistic on
consprod
.
C7.8
(i) If the appropriate factors have been controlled for,
1
> 0 signals discrimination against
minorities:
a white person has a greater chance of having a loan approved, other relevant factors
fixed.
(ii) The simple regression results are
±
approve
=
.708 + .201
white
(.018)
(.020)
n
= 1,989,
R
2
= .049.
The coefficient on
white
means that, in the sample of 1,989 loan applications, an application
submitted by a white application was 20.1% more likely to be approved than that of a nonwhite
applicant.
This is a practically large difference and the
t
statistic is about 10.
(We have a large
sample size, so standard errors are pretty small.)
(iii) When we add the other explanatory variables as controls, we obtain
1
ˆ
.129, se(
1
ˆ
)
.020.
The coefficient has fallen by some margin because we are now controlling for factors that
should affect loan approval rates, and some of these clearly differ by race.
(On average, white
people have financial characteristics – such as higher incomes and stronger credit histories – that
make them better loan risks.)
But the race effect is still strong and very significant (
t
statistic
6.45).
(iv) When we add the interaction
white
obrat
to the regression, its coefficient and
t
statistic
are about .0081 and 3.53, respectively.
Therefore, there is an interactive effect:
a white