Specification pre-test estimator

This paper is related to the specification test introduced by J. Hausman. A specification test is often used as a first step in an estimation procedure. In the case of the linear model the biases and the mean square errors of the classical and of the specification pre-test estimators are computed and compared. It is shown that the latter is not uniformly better than the former and conversely. In the case of a four-variables model, regions in the parameters space where the specification pre-test estimator outdoes the classical one are numerically settled.