Department of Economics
Spring 2009
University of California
Prof. Woroch
Economics 140:
Problem Set 5
ANSWER SHEET
Instructions:
Include the names/SIDs of members of your study group (maximum of 3) and the
name of your common GSI. Staple your answer sheets—otherwise it will not be accepted.
I.
True/False/Uncertain and Explain.
Below are statements that may be true or false, or
possibly ambiguous.
State which one you believe to be the case, and more importantly, give a
detailed but concise explanation for your answer.
1.
Suppose that using data on mortgage application decisions, estimation of a probit model of
denial generated the following results:
Pr(
deny
= 1|
P/I Ratio
,
black
) =
(–2.26
+ 2.74
P/I
ratio
+ 0.71
black
).
Given this probit specification, and the probit coefficient estimates, the
effect of increasing the P/I (“payment to income”) ratio from 0.3 to 0.4 for a white person
amounts to 2.74 percentage points.
Answer
: False.
It is found by evaluating the estimated probit model at the two hypothesized
situations: Pr(
deny
=1|
P/I
=0.4,
white
) - Pr(
deny
=1|
P/I=
0.3,
white
) =
(–2.26 + 2.74×0.4) -
(–2.26
+ 2.74×0.3) =
(–1.164) -
(–1.143) =
0.1222 - 0.0752 = 0.046995, or 4.7%
increase in probability of mortgage denial.
(Alternatively, one could approximate the effect
of this change using the derivative of the denial probability with respect to P/I:
∂
Pr(
deny
=1|
P/I
,
white
)/
∂
(P/I)×
Δ
(P/I)
=
∂
/
∂
(P/I)×
Δ
(P/I) =
φ
(–2.26+2.74×0.3)×2.74×
Δ
(P/I) =
0.1419×2.74×0.1 = 0.03889, or about 3.9%.
This is quite a bit different than the discrete
comparison we made because the denial probability is highly nonlinear in the vicinity of the
change in
P/I
.)
2.
When calculating the standard errors of TSLS coefficient estimates you do not have to worry
about heteroskedasticity because it will be taken into account in the first stage OLS
estimation.
You cannot, however, be certain that the standard errors reported by OLS
estimation of the second stage regression where fitted values of endogenous regressors from
the first stage are used in place of the regressors’ original values are consistent.
Answer
: True and false.
Heteroskedasticity robust estimation in the first stage of TSLS will
accommodate heteroskedasticity of the error in the relation between the instruments and the
endogenous regressors.
However, it does not address possible heteroskedasticity in the error
of the relation between the fitted values from that first stage and the dependent variable, i.e.,
the second stage.
It is true, however, that when the research simply runs that second
regression taking the fitted values as exogenous, the standard errors are not good estimates of
the standard deviation of the original regressor.
After all, the second stage regression ignores
the sampling error introduced into those fitted values, instead taking those values as
exogenous in the second stage.
A good econometric software package will not make that
mistake; it will generate standard errors that take account of sampling error introduced in first
stage.