The role of score and information bias in panel data likelihoods

We show why reducing information bias can improve the performance of likelihood based estimators and confidence regions in small samples, and why it seems to matter more for inference than for estimation. The insights in this paper are helpful in explaining several simulation findings in the panel data literature. E.g., we can explain the well documented phenomenon that reducing the score bias alone often reduces the finite sample variance of estimators and improves the coverage of confidence regions in small samples, and why confidence regions based on conditional (on sufficient statistics) likelihoods can have excellent coverage even in very short panels. We can also explain the simulation results in Schumann, Severini, and Tripathi (2021), who find that, in short panels, estimators and confidence regions based on pseudolikelihoods that are simultaneously first-order score and information unbiased perform much better than those based on pseudolikelihoods that are only first-order score unbiased.