Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 5

There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedasticity. One possibility not covered in the text is to run the regression
where the h. are the OLS residuals and the i. are the OLS fitted values. Then, we would test joint significance of x i1 , x i2 , …, x ik and i 2. (Of course, we always include an intercept in this regression.)
(i) What are the df associated with the proposed F test for heteroskedasticity
(ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test.
(iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP or special case of the White statistic Explain.
(iv) Suppose someone suggests also adding i. to the newly proposed test. What do you think of this idea