For example, if OLS is performed on a heteroscedactic data set, yielding biased standard error estimation, a researcher might fail to reject a null hypothesis at a given significance level, when that null hypothesis was actually uncharacteristic of the actual population (making a type II error).
He is noted for the Breusch–Pagan test from the paper (with Adrian Pagan) "A simple test for heteroscedasticity and random coefficient variation" (see Noted works, below).