The impact of a Hausman pretest on the size of a hypothesis test: The panel data case

The size properties of a two-stage test in a panel data model are investigated where in the first stage a Hausman (1978) specification test is used as a pretest of the random effects specification and in the second stage, a simple hypothesis about a component of the parameter vector is tested, using a t$t$-statistic that is based on either the random effects or the fixed effects estimator depending on the outcome of the Hausman pretest. It is shown that the asymptotic size of the two-stage test equals 1 for empirically relevant specifications of the parameter space. The size distortion is caused mainly by the poor power properties of the pretest. Given these results, we recommend using a t$t$-statistic based on the fixed effects estimator instead of the two-stage procedure.