This paper considers estimation of truncated.and censored regression models with fixed effects. Up until now, no estimator has been shown to be consistent as the cross-section dimension increases with the time dimension fixed. Trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two, and it is proven that they are consistent and asymptotically normal. It is not necessary to maintain parametric assumptions on the error terms to obtain this result. A small scale Monte Carlo study demonstrates that these estimators can perform well in small samples.