Effects on inference of pretesting the exogeneity of a regressor

This paper investigates, via simulation, the performance of the inference of a pretest estimator based on a Hausmanʹs test of exogeneity. I find that an inference based on conventional pretest procedure leads to a substantial size distortion. A bootstrap-based inferential procedure is proposed to take into account the pretesting effect on the small sample distribution of the pretest estimator in independently (possibly non-identically) distributed samples. My simulation shows that the bootstrap-based inference improves substantially over the conventional procedure.