On the performance of tests by Wu and by Hausman for detecting the ordinary least squares bias problem

We first consider the performance of the Wu (1973) - Hausman (1978) (W-H) specification error test as a test for the existence of ordinary least squares (OLS) bias. We discuss power properties of the test under alternative null hypotheses, one of which has not previously been considered. We next consider how the W-H test performs as an indicator of the extent (rather than the existence) of an OLS bias problem, since this usage of the test seems common in applied studies. Finally Monte Carlo methods are used to evaluate Wu's two-step estimation procedure involving the W-H test as a pretest.