In Example 8.7, we computed the OLS and a set of WLS estimates in a cigarette demand equation.

(i) Obtain the OLS estimates in equation (8.35).

(ii) Obtain the h^

i used in the WLS estimation of equation (8.36) and reproduce equation (8.36).

From this equation, obtain the unweighted residuals and fitted values; call these u^i and y^i

, respectively. (For example, in Stata, the unweighted residuals and fitted values are given by default.)

(iii) Let u˘i 5 u^i

/"h^

i and y˘i 5 y^i

/"h^

i be the weighted quantities. Carry out the special case of the White test for heteroskedasticity by regressing u˘ 2 i on y˘i

, y˘

2 i , being sure to include an intercept, as always. Do you find heteroskedasticity in the weighted residuals?

(iv) What does the finding from part (iii) imply about the proposed form of heteroskedasticity used in obtaining (8.36)?

(v) Obtain valid standard errors for the WLS estimates that allow the variance function to be misspecified.