Approve is a binary dependent vari$-$ able, which equals one if individual i$$s mortgage loan was approved. The key explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the data set are black or Hispanic.

a$)$ To test for discrimination against nonwhites in the mortgage loan market, we can use the following linear probability model:

approvei $=$ $0+$ $1$whitei $+$ ui

If there is discrimination against nonwhites and the appropriate other factors have been controlled

for, what should the sign of $1$ be$?$

b$)$ Regress approve on white and report the results in the usual form. How should you estimate

the standard errors and why?

c$)$ Interpret the coefficient on white. Is it statistically significant? Is it economically significant $($i$.$e$.,$ large in magnitude$)?$

d$)$ Suppose you want to add the following control variables to the model: hrat, obrat, loanprc, unem, male, married, dep, sch$,$ cosign$,$ chist, pubrec, mortlat$1,$ mortlat$2,$ and vr$.$ Summarize them first. Notice if any variables have missing observations. Assume the observations are missing at random and estimate the model including all of the controls. What happens to the coefficient on white? Is there still evidence of discrimination against nonwhites?

e$)$ Consider whether there might be measurement error in any of the control variables in part $($d$).$ If you think there could be measurement error, discuss whether you think it is classical errors$-$in$-$ variables measurement error or some other type. Discuss any implications for bias or inconsistency in the model$$s estimates.

f$)$ Obtain the predicted values from the regression in part $($d$).$ Are any of the predicted values less than zero or greater than one? What does this imply about using weighted least squares in this context?

g$)$ Reset the predicted values to be bounded between $0$ and $1.$ Re$-$estimate the model in part $($d$)$ using weighted least squares. How do your results compare to the results in part $($d$)?$ Are there efficiency gains to using WLS$?$

h$)$ Perform the RESET test on the model in part $($g$).$ What do you conclude?

$1$

i$)$ Finally, consider whether the model might still have an omitted variable bias problem. If you think it does, which variable would you want to include? If you could not get data on that variable, can you think of a proxy variable that might be useful? Note: there are multiple correct answers to this question. Use your judgment and logic to answer.