Inference Problems under a Special Form of Heteroskedasticity

Abstract

In the presence of heteroskedasticity, conventional standard errors (which assume homoskedasticity) can be biased up or down. The most common form of heteroskedasticity leads to conventional standard errors that are too small. When Wald tests based on these standard errors are insignificant, heteroskedasticity ro- bust standard errors do not change inference. On the other hand, inference is conservative in a setting with upward-biased conventional standard errors. We discuss the power gains when using robust standard errors in this case and also potential problems of heteroskedasticity tests. As a solution for the poor performance of the usual heteroskedasticity tests in this setting, we propose a modification of the White test which has better properties. We illustrate our findings using a study in labor economics. The correct standard errors turn out to be around 15 percent lower, leading to different policy conclusions. Moreover, only our modified test is able to detect heteroskedasticity in this application.

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