The Impact of a Hausman Pretest on the Size of a Hypothesis Test: the Panel Data Case

Abstract

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-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 depends on the degree of time variation in the regressors and on the variance of the error term relative to the variance of the individual specific effect and equals 1 for empirically relevant specifications of the parameter space. Monte carlo simulations document that the size distortion is well reflected in finite samples. The size distortion is caused mainly by the poor power properties of the pretest that lead to frequent unjustified inference based on the random effects estimator in the second stage. However, it is also shown that the conditional size of the test, conditional on the Hausman pretest rejecting the pretest null hypothesis, exceeds the nominal level of the test. Given the results in the paper, the recommendation then is to use a t-tatistic based on the fixed effects estimator instead of using the two-stage procedure.

JEL codes