An alternative to confidence intervals constructed after a Hausman pretest in panel data

Abstract

Consider panel data modelled by a linear random intercept model that includes a timevarying covariate. Suppose that our aim is to construct a confidence interval for the slope parameter. Commonly, a Hausman pretest is used to decide whether this confidence interval is constructed using the random effects model or the fixed effects model. This post-model-selection confidence interval has the attractive features that it (a) is relatively short when the random effects model is correct and (b) reduces to the confidence interval based on the fixed effects model when the data and the random effects model are highly discordant. However, this confidence interval has the drawbacks that (i) its endpoints are discontinuous functions of the data and (ii) its minimum coverage can be far below its nominal coverage probability. We construct a new confidence interval that possesses these attractive features, but does not suffer from these drawbacks. This new confidence interval provides an intermediate between the post-model-selection confidence interval and the confidence interval obtained by always using the fixed effects model. The endpoints of the new confidence interval are smooth functions of the Hausman test statistic, whereas the endpoints of the post-model-selection confidence interval are discontinuous functions of this statistic.