Introductory Econometrics
Binary dependent variable
by Hieu Nguyen
Fall 2024
1.
Use the data in loanapp b.gdt for this exercise. The binary variable to be explained is approve, which
is equal to one if a mortgage loan to an individual was approved. The key explanatory variable is
whiteskin, a dummy variable equal to one if the applicant has light skin. The other applicants in the
data set are darkskin and Hispanic. To test for discrimination in the mortgage loan market, a LPM
can be used:
approve = β0 + β1whiteskin + other factors.
(a) Regress approve on whiteskin and report the results in the usual form. Interpret the estimated
coefficient on whiteskin. Is it significant? Is it practically large?
(b) As controls, add the variables hrat, obrat, loanprc, unem, male, married, dep, sch, cosign,
chist, pubrec, mortlat1, mortlat2, and vr. What happens to the estimated coefficient on
whiteskin? Is there still statistically significant evidence of discrimination against non-white
skin individuals?
(c) Estimate the equation in part (b) computing the White heteroskedasticity-consistent robust standard
errors. Compare the 95% confidence interval on βwhiteskin with the non-robust confidence
interval.
(d) Obtain the fitted values from the regression in part (c). Are any of them less than zero? Are any
of them greater than one?
(e) Estimate a Probit model of approve on whiteskin. Check the direction of the effect and the
statistical significance of whiteskin. Find the estimated probability of loan approval for both
whiteskin and non-white skin individuals. How do these compare with the LPM estimates?
(f) Now, add the variables hrat, obrat, loanprc, unem, male, married, dep, sch, cosign, chist,
pubrec, mortlat1, mortlat2, and vr. Is there still statistically significant evidence of discrimination
against non-white skin people? Interpret also other information from the Gretl output.
(g) Estimate the model from part (f) by Logit. Compare the estimated coefficient on whiteskin to
the Probit model.
(h) Estimate the sizes of the discrimination effects for Probit and Logit.
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