Assignment #10 Heteroskedasticity

Assignment #10 Heteroskedasticity

Reading:  Wooldridge Ch 8

1. Using data on students, the following equation was estimated:

Here, trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken, cumgpa is GPA prior to the current semester, tothrs is total credit hours prior to the semester, sat is SAT score, hsperc is graduating percentile in high school class, female is a gender dummy, and season is a dummy variable equal to unity if the student’s sport is in season during the fall. The usual and heteroskedasticity-robust standard errors are reported in parentheses and brackets, respectively.

(i)  Do the variables crsgpa, cumgpa, and tothrs have the expected estimated effects? Which of these variables are statistically significant at the 5% level? Does it matter which standard errors are used?

(ii)  Why does the hypothesis H₀: β_crsgpa = 1 make sense? Test this hypothesis against the two-sided alternative at the 5% level, using both standard errors. Describe your conclusions.

(iii)  Test whether there is an in-season effect on term GPA, using both standard errors. Does the significance level at which the null can be rejected depend on the standard error?

2.  The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. We estimate a linear probability model for smokes:

The variable white equals one if the respondent is white, and zero otherwise; the other in- dependent variables are defined in Example 8.7 on p.285. Both the usual and heteroskedasticity- robust standard errors are reported.

(i)  Are there any important differences between the two sets of standard errors?

(ii)  Holding other factors fixed, if education increases by four years, what happens to the estimated probability of smoking?

(iii)  At what point does another year of age reduce the probability of smoking?

(iv)  Interpret the coefficient on the binary variable restaurn (a dummy variable equal to

one if the person lives in a state with restaurant smoking restrictions).

(v)  Person number 206 in the data set has the following characteristics: cigpric =67.44, income = 6,500, educ =16, age = 77, restaurn=0, white =0, and smokes = 0. Compute the predicted probability of smoking for this person and comment on the

result.