Simulation-based tests for heteroskedasticity in linear regression models: Some further results

As shown by the results of Dufour, Khalaf, Bernard and Genest (2004, Journal of Econometrics 122, 317--347), exact tests for heteroskedasticity in linear regression models can be obtained, by using Monte Carlo (MC) techniques, if either (i) it is assumed that the true form of the error distribution under homoskedasticity is known, or (ii) the null hypothesis specifies both homoskedasticity and the form of the error distribution. Non-parametric bootstrap tests of homoskedasticity alone are only asymptotically valid, but do not require specification of the error law. Since information about the precise form of the error distribution is not often available to applied workers, two questions merit attention. First, if the primary purpose is to check for heteroskedasticity, how sensitive are MC tests to incorrect assumptions/claims about the error distribution? Second, what can be said about the relative merits of MC tests and non-parametric bootstrap tests? Theoretical results relevant to these two questions are derived using asymptotic analysis and evidence is provided from simulation experiments.