Poor identification and estimation problems in panel data models with random effects and autocorrelated errors

A dramatically large number of corner solutions occur when estimating by (Gaussian) maximum likelihood a simple model for panel data with random effects and autocorrelated errors. This can invalidate results of applications to panel data with a short time dimension, even in a correctly specified model. We explain this unpleasant effect (usually underestimated, almost ignored in the literature) showing that the expected log-likelihood is nearly flat, thus rising problems of poor identification.