Fixed Effect Estimation of Large T Panel Data Models

TL;DR

This paper reviews recent methods for fixed effect estimation in large T panel data models, emphasizing bias correction techniques and the impact of many fixed effects on estimation accuracy.

Contribution

It provides a comprehensive overview of advances in fixed effect estimation for long panels, including bias correction and models with both individual and time effects.

Findings

Bias order is p/n for all models discussed.

Split-panel Jackknife effectively reduces bias.

Extensions include unbalanced panels and distribution effects.

Abstract

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.