In Exercise 7.7 we considered a model designed to provide information to mortgage lenders. They want to determine borrower and loan factors that may lead to delinquency or foreclosure. In the file lasvegas.dat are 1000 observations on mortgages for single-family homes in Las Vegas, Nevada during 2008. The variable of interest is DELINQUENT, an indicator variable ¼ 1 if the borrower missed at least three payments (90þ days late), but zero otherwise. Explanatory variables are LVR ¼ the ratio of the loan amount to the value of the property; REF ¼ 1 if purpose of the loan was a ‘‘refinance’’ and ¼ 0 if loan was for a purchase; INSUR ¼ 1 if mortgage carries mortgage insurance, zero otherwise; RATE ¼ initial interest rate of the mortgage; AMOUNT ¼ dollar value of mortgage (in $100,000); CREDIT ¼

credit score, TERM ¼ number of years between disbursement of the loan and the date it is expected to be fully repaid, ARM ¼ 1 if mortgage has an adjustable rate, and ¼ 0 if mortgage has a fixed rate.

(a) Estimate the linear probability (regression) model explaining DELINQUENT as a function of the remaining variables. Use the White test with cross-product terms included to test for heteroskedasticity. Why did we include the crossproduct terms?

(b) Use the estimates from

(a) to estimate the error variances for each observation.

How many of these estimates are at least one? How many are at most zero? How many are less than 0.01?

(c) Prepare a table containing estimates and standard errors from estimating the linear probability model in each of the following ways:

(i) Least squares with conventional standard errors.

(ii) Least squares with heteroskedasticity-robust standard errors.

(iii) Generalized least squares omitting observations with variances less than 0.01.