The impact of a Hausman pretest, applied to panel data, on the coverage probability of confidence intervals

In the analysis of panel data that includes a time-varying covariate, a Hausman pretest is commonly used to decide whether subsequent inference is made using the random effects model or the fixed effects model. We consider the effect of this pretest on the coverage probability of a confidence interval for the slope parameter. We prove three new finite sample theorems that make it easy to assess, for a wide variety of circumstances, the effect of the Hausman pretest on the minimum coverage probability of this confidence interval. Our results show that for the small levels of significance of the Hausman pretest commonly used in applications, the minimum coverage probability of the confidence interval for the slope parameter can be far below nominal.