ECON 414
SOLUTION TO HOMEWORK 8
Spring 2011
7.2
(i) If
∆
cigs
= 10 then
·
log(
)
bwght
∆
=

.0044(10) =

.044, which means about a 4.4% lower
birth weight.
(ii) A white child is estimated to weigh about 5.5% more, other factors in the first equation
fixed.
Further,
t
white
≈
4.23, which is well above any commonly used critical value.
Thus, the
difference between white and nonwhite babies is also statistically significant.
(iii) If the mother has one more year of education, the child’s birth weight is estimated to be .
3% higher.
This is not a huge effect, and the
t
statistic is only one, so it is not statistically
significant.
(iv) The two regressions use different sets of observations.
The second regression uses fewer
observations because
motheduc
or
fatheduc
are missing for some observations.
We would have
to reestimate the first equation (and obtain the
R
squared) using the same observations used to
estimate the second equation.
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
β
+
1
log(
sales
) +
2
roe
+
1
δ
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
.
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View Full DocumentC7.4
(i) The two signs that are pretty clear are
3
β
< 0 (because
hsperc
is defined so that the
smaller the number the better the student) and
4
> 0.
The effect of size of graduating class is
not clear.
It is also unclear whether males and females have systematically different GPAs.
We
may think that
6
< 0, that is, athletes do worse than other students with comparable
characteristics.
But remember, we are controlling for ability to some degree with
hsperc
and
sat
.
(ii) The estimated equation is
·
colgpa
=
1.241

.0569
hsize
+
.00468
hsize
2

.0132
hsperc
(0.079)
(.0164)
(.00225)
(.0006)
+
.00165
sat
+ .155
female
+ .169
athlete
(.00007)
(.018)
(.042)
n
= 4,137,
R
2
= .293.
Holding other factors fixed, an athlete is predicted to have a GPA about .169 points
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 Spring '11
 CARRILLO
 Economics, Statistics, colGPA, average looks

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