Introduction to Econometrics
Professor Alexei Onatski
Problem Set 9 – December 7
Problem 1) [
Stock and Watson 11.1
]
(a) The
t
statistic for the coefficient on
Experience
is 0.031/0.009
=
3.44, which is significant at the
1% level.
(b)
0.712
0.031 10
1.022;
(1.022)
0.847
Matthew
z
=
+
×
=
Φ
=
(c)
=
+
×
=
Φ
=
0.712
0.031
0
0.712;
(0.712)
0.762
Christopher
z
(d)
=
+
×
=
Φ
=
0.712
0.031
80
3.192;
(3.192)
0.999,
Jed
z
this is unlikely to be accurate because the
sample did not include anyone with more that 40 years of driving experience.
Problem 2) [
Stock and Watson 11.6
]
(a) For a black applicant having a P/I ratio of 0.35, the probability that the application will be
denied is
Φ
(

2.26
+
2.74
×
0.35
+
0.71)
=
Φ
(

0.59)
=
27.76%.
(b) With the P/I ratio reduced to 0.30, the probability of being denied is
Φ
(

2.26
+
2.74
×
0.30
+
0.71)
=
Φ
(

0.73)
=
23.27%. The difference in denial probabilities compared to (a) is 4.4
percentage points lower.
(c) For a white applicant having a P/I ratio of 0.35, the probability that the application will be
denied is
Φ
(

2.26
+
2.74
×
0.35)
=
9.7%. If the P/I ratio is reduced to 0.30, the probability of
being denied is
Φ
(

2.26
+
2.74
×
0.30)
=
7.5%. The difference in denial probabilities is 2.2
percentage points lower.
(d) From the results in parts (a)–(c), we can see that the marginal effect of the P/I ratio on the
probability of mortgage denial depends on race. In the probit regression functional form,
the marginal effect depends on the level of probability which in turn depends on the race
of the applicant. The coefficient on
black
is statistically significant at the 1% level.
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Problem 3) [
Stock and Watson 11.7
]
(a) For a black applicant having a P/I ratio of 0.35, the probability that the application will be
denied is
0.9805
1
1
( 4.13
5.37
0.35
1.27)
27.28%.
e
F
+

+
×
+
=
=
(b) With
the
P/I
ratio
reduced
to
0.30,
the
probability
of
being
denied
is
+

+
×
+
=
=
1.249
1
1
( 4.13
5.37
0.30
1.27)
22.29%.
e
F
The difference in denial probabilities compared
to (a) is 4.99 percentage points lower.
(c) For a white applicant having a P/I ratio of 0.35, the probability that the application will be
denied is
2.2505
1
1
( 4.13
5.37
0.35)
9.53%.
e
F
+

+
×
=
=
If the P/I ratio is reduced to 0.30, the
probability of being denied is
2.519
1
1
( 4.13
5.37
0.30)
7.45%.
e
F
+

+
×
=
=
The difference in denial
probabilities is 2.08 percentage points lower.
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 Fall '09
 Natski
 Econometrics, Conditional Probability, Normal Distribution, Probability theory, Likelihood function, Smoking ban

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