Median-based estimation of dynamic panel models with fixed effects

We propose outlier-robust estimators for linear dynamic fixed effects panel data models where the number of observations,N , is large and the number of time periods, T , is small. In the simple setting of estimating the AR(1) coefficient from stationary Gaussian panel data, the estimator is (a linear transformation of) the median ratio of adjacent first-differenced data pairs. Its influence function is bounded under contamination by independent or patched additive outliers. We derive the influence function and the gross-error sensitivity explicitly. When there are independent additive outliers, the estimator is asymptotically biased towards 0, but its sign remains correct, and it has a reasonably high breakdown point. When there are patched additive outliers with point mass distribution, the asymptotic bias is upward in nearly all cases; breakdown towards 1 can occur; and the associated breakdown point increases with the patch length.