Heteroskedasticity Testing Through Comparison of Wald-Type Statistics

A test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The resulting statistic is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of this test is sensitive to the choice of parametric restriction on which the Wald statistics are based, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version, easier to implement, does not have a known asymptotic null distribution, so the bootstrap is employed in order to assess its behaviour and enable meaningful conclusions from its use in applied work. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A small simulation study illustrates the implementation and finite-sample performance of both versions of the test.