Testing under a special form of heteroscedasticity

In the presence of heteroscedasticity, conventional standard errors (which assume homoscedasticity) can be biased up or down. The most common form of heteroscedasticity leads to conventional standard errors that are too small. In this study, we discuss the conditions under which conventional standard errors are too large. In such settings, standard tests of heteroscedasticity may fail and leave the heteroscedasticity undetected. This is particularly problematic as power gains can be achieved when testing for the causal effect in such settings.