On the harm that ignoring pretesting can cause

In econometrics the same data set is typically used to select the model and to estimate the parameters in the selected model. In applied econometrics practice, however, one typically acts as if the model had been given a priori, thus ignoring the fact that the estimators are in fact pretest estimators. Hence one assumes incorrectly that the estimator is unbiased, and that the reported variance, conditional on the selected model, is equal to its unconditional variance. In this paper, we find the unconditional first and second moments of the pretest estimator (in fact, of a more general estimator, the WALS estimator), taking full account of the fact that model selection and estimation are an integrated procedure, and show that the error in not reporting the correct moments can be large. We also show that this error can vary substantially between different model selection procedures. Finally, we ask how the error increases when the number of auxiliary regressors increases.