Homework answers / question archive / ECT316D Use the data in HPRICE1 to obtain the heteroskedasticity-robust standard errors for the equation: ????? = ?0 + ?1??????? + ?2????? + ?3????? Discuss any important differences with the usual standard errors

ECT316D Use the data in HPRICE1 to obtain the heteroskedasticity-robust standard errors for the equation: ????? = ?0 + ?1??????? + ?2????? + ?3????? Discuss any important differences with the usual standard errors

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ECT316D Use the data in HPRICE1 to obtain the heteroskedasticity-robust standard

errors for the equation:

????? = ?0 + ?1??????? + ?2????? + ?3?????

Discuss any important differences with the usual standard errors.

(ii) Repeat part (i) for the equation:

log (?????) = ?0 + ?1log (???????) + ?2log (?????) + ?3?????

(iii) What does this example suggest about heteroskedasticity, and the

transformation used for the dependent variable?

(iv) Apply the full White test for heteroskedasticity the previous equation. Using

the chi-square form of the statistic, obtain the p-value. What do you

conclude?

QUESTION 2

(i) Use the data in LOANAPP 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 white, a dummy

variable equal to one if the applicant was white. The other applicants in the

data set are black and Hispanic. To test for discrimination in the mortgage

loan market, a linear probability model can be used:

??????? = ?0 + ?1????? + ????? ???????

If there is discrimination against minorities, and the appropriate factors have

been controlled

for, what is the sign of ?1?

(ii) Regress approve on white and report the results in the usual form. Interpret

the coefficient on white. Is it statistically significant? Is it practically large?

(iii) As controls, add the variables hrat, obrat, loanprc, unem, male, married,

dep, sch, cosign, chist, pubrec, mortlat1, mortlat2, and vr. What happens to

the coefficient on white? Is there still evidence of discrimination against

nonwhites?

(iv) Estimate the equation in part (iii), computing the heteroskedasticity-robust

standard errors. Compare the 95% confidence interval on bwhite with the

nonrobust confidence interval.

(i) Obtain the fitted values from the regression in part (iv). Are any of them less

than zero? Are any of them greater than one? What does this mean about

applying weighted least squares?

QUESTION 3

Consider the following model to explain sleeping behavior:

????? = ?0 + ?1?????? + ?2??? + ?3??? + ?4???2 + ?5??????

+ ?6???? + ?

(i) Write down a model that allows the variance of u to differ between men and

women. The variance should not depend on other factors.

(ii) Use the data in SLEEP75 to estimate the parameters of the model for

heteroskedasticity. (You have to estimate the sleep equation by OLS, first,

to obtain the OLS residuals.) Is the estimated variance of u higher for men

or for women?

(iii) Is the variance of u statistically different for men and for women?