On testing for heteroskedascity, some questions on the White test & Breusch-Pagan test

Question

1. Isn't the test statistic for both tests identical? The only difference I see is that the alternative hypothesis is different. Since you don't need to know the function h in the Breusch-Pagan test, what exactly is the difference between the two tests?

2. When would you use the White test, and when would you use the Breusch-Pagan test instead? What's the most important criteria to consider here when deciding which test to use?

Answer 1

In the Breusch-Pagan test, the predictors included in the so-called auxiliary regression were unspecified, but generally assumed to be only those from the original regression. White provided a specific set of predictors that should be included---those from the original regression, those predictors squared, and all of the pairwise interactions. The White test is really just a special case of the Breusch-Pagan test. White's contribution was to show the properties of his proposed case. His version is the one typically used, as far as I've seen.