  Consider panel data modelled by a linear random intercept model that includes
a time-varying covariate. Suppose that we have uncertain prior information that
this covariate is exogenous. We present a new confidence interval for the slope
parameter that utilizes this uncertain prior information. This interval has
minimum coverage probability very close to its nominal coverage. Let the scaled
expected length of this new confidence interval be its expected length divided
by the expected length of the confidence interval, with the same minimum
coverage, constructed using the fixed effects model. This new interval has
scaled expected length that (a) is substantially less than 1 when the prior
information is correct, (b) has a maximum value that is not too much larger
than 1 and (c) is close to 1 when the data strongly contradict the prior
information. We illustrate the properties of this new interval using an airfare
data set.
