Econ 371
Problem Set #5
Answer Sheet
8.2 This question focuses on the hedonic regression model results in Table 8.2.
a. The first part of this question asks you to predict the change in the price of a home from building a
500square addition to the house. According to the regression results in column (1), the house price is
expected to increase by 21% (= 100%
×
0
.
00042
×
500), assuming all other factors are held constant.
The 95% confidence interval for the percentage change is 100%
×
500
×
(0
.
00042
±
1
.
96
×
0
.
000038) or
[17.276% to 24.724%].
b. Because the regressions in columns (1) and (2) have the same dependent variable,
¯
R
2
can be used to
compare the fit of these two regressions.
The loglog regression in column (2) has the higher so it is
better so use ln(Size) to explain house prices.
c. With the addition of a swimming pool, the house price is expected to increase by 7.1% (= 100%
×
0
.
071
×
1). The 95% confidence interval for this effect is 100%
×
(0
.
071
±
1
.
96
×
0
.
034) or [0.436% to 13.764%].
d. The addition of a single bedroom is expected to increase the price of a house by 0.36% (= 100%
×
0
.
0036
×
1). However, the effect is not statistically significant at a 5% significance level (with a corresponding
tstatistic of only
t
act
=
0
.
0036
0
.
037
= 0
.
097
<
1
.
96).
Note that this coefficient measures the effect of an
additional bedroom holding the size of the house constant.
e. The quadratic term
ln
(
Size
)
2
is not statistically significant at a 5% significance level (with a correspond
ing tstatistic in column (4) of only
t
act
=
0
.
0078
0
.
14
= 0
.
056
<
1
.
96).
f. The expected change in the price when a pool is added to a house with a view is 7.1% (= 100%
×
0
.
071
×
1)
when a swimming pool is added to a house without a view and other factors are held constant. The
house price is expected to increase by 7.32% (= 100%
×
(0
.
071
×
1 + 0
.
0022
×
1) when a swimming pool
is added to a house with a view and other factors are held constant.
The difference in the expected
percentage change in price is 0.22%. The difference is not statistically significant at a 5% significance
level (with a corresponding tstatistic of only
t
act
=
0
.
0022
0
.
10
= 0
.
022
<
1
.
96)
8.4 This question focuses on the returns to education.
a. In this first part of the question, you are asked to predict the impact of an additional year of experience
on the logarithm of average hourly earnings (
AHE
) for a male with 16 years of education and 2 years
of experience who is from a western state. Using the ideas from the Key Concept 8.1, we have that:
Δ
ln
(
AHE
)
=
£
1
.
215 + 0
.
0899(0)

0
.
521(0) + 0
.
0207(0)(16) + 0
.
0232(3)

0
.
000368(3
2
)

0
.
058(0)

0
.
078(0)

0
.
030(1)]

£
1
.
215 + 0
.
0899(0)

0
.
521(0) + 0
.
0207(0)(16) + 0
.
0232(2)

0
.
000368(2
2
)

0
.
058(0)

0
.
078(0)

0
.
030(1)]
=
2
.
60

2
.
578
=
0
.
022
( or 2.2%)
b. Repeating this exercise for someone with 10 years of experience, we get that:
Δ
ln
(
AHE
)
=
£
1
.
215 + 0
.
0899(0)

0
.
521(0) + 0
.
0207(0)(16) + 0
.
0232(11)

0
.
000368(11
2
)

0
.
058(0)

0
.
078(0)

0
.
030(1)]

£
1
.
215 + 0
.
0899(0)

0
.
521(0) + 0
.
0207(0)(16) + 0
.
0232(10)

0
.
000368(10
2
)

0
.
058(0)

0
.
078(0)

0
.
030(1)]
=
2
.
744

2
.
729
=
0
.
015
( or 1.5%)
c. The results in (a) and (b) are different because the model is nonlinear, including a quadratic expression
in experience.
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 Spring '08
 Jeon
 Econometrics

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