ECMT6007/6702: Econometric Applications Problem Set 5

Question 1. Computer Exercise: Racial Discrimination in the US Market for Home Loans            Use the data in loanapp5 .dta for this exercise. The binary variable to be explained is approve, which is equal to one (1) if a mortgage loan to an individual was approved and zero (0) otherwise. The key explanatory variable is white, an indicator (i.e. dummy) variable equal to one if the appli- cant was white. The other applicants in the data set are black or Hispanic.

To test for discrimination in the mortgage loan market, a linear probability model (LPM) can be used:

approve = β0 + β1 white + other factors

(i) If there is discrimination in loan approvals against minorities, and the appropriate factors have been controlled for, what is the sign of β1 ?

(ii) Regress approve on white using OLS and report the results in the usual form. Interpret the coefficient on white. Is it statistically significant at the 1% level of significance (against the appropriate one-sided alternative)? Is it practically large? Would you conclude that there is discrimination (or no discrimination) in the market for loans? Explain your reasoning.

(iii) As controls, add the variables obrat, loanprc, unem, male, married, dep, sch and cosign. Is there still evidence of discrimination against nonwhites?

(iv) Re-estimate the model in (iii) using heteroskedasticity-robust standard errors. [Note: In STATA use the vce(robust) option with the regress command]. Report the robust standard er- rors. Compare the 95% confidence intervals for β1 using the non-robust and robust standard

errors.

(v) Based on the model specification in (iii) – with 9 explanatory variables – test for the presence of heteroskedasticity using the Breusch-Pagan test and a 5% significance level. What do you conclude?

(vi) Repeat the test for heteroskedasticity using the White test procedure: what is your conclusion?

(vii) Obtain the fitted values from the regression in part (iii). Are there any less than zero? Are

there any greater than one? What does this mean for applying Weighted Least Squares?

(viii) Make any necessary adjustments to the fitted values in (iii), and re-estimate the model using

Weighted Least Squares (WLS) for the LPM. Report the results in the usual form. Comment on any differences between these estimates and those based on OLS with robust standard errors.