The White test, with squares and cross-products

Question

You run the White test for heteroskedasticity on $n = 300$ observations. The auxiliary regression puts the squared residuals on the regressors, their squares, and their cross-products, a total of 9 terms, and returns $R^2 = 0.10$ .

Compute the White test statistic and decide at the 5 percent level. How does it differ from Breusch-Pagan?

Accepted Answer

Same machinery, richer auxiliary regression. The White test uses the same statistic, 	ext{LM} = n \cdot R^2{	ext{aux}} = 300 	imes 0.10 = 30.0, but its auxiliary regression includes not just the regressors but also their squares and cross-products. This lets it catch heteroskedasticity that depends on the regressors nonlinearly, at the cost of using more degrees of freedom. Degrees of freedom and cutoff. There are 9 terms in the auxiliary regression, so the null distribution is chi-square with 9 degrees of freedom, 5 percent critical value 16.919. Decision. 30.0 16.919, so we reject homosk…

The White test, with squares and cross-products

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