Estimation and Inference for Unbalanced Panel Data Models with Interactive Fixed Effects

Abstract

This paper establishes the inferential theory for unbalanced panel data models with interactive fixed effects. We propose a two-step estimation algorithm with the first step obtaining an initial consistent estimator followed by an alternating maximization procedure. We prove that the alternating maximization procedure is a contractionary mapping and the final estimator is asymptotically normal, as long as the initial estimator is consistent. We also develop analytical bias corrections according to the derived asymptotic bias expressions and the observed missing pattern. Our results cover important missing patterns such as completely exogenous missing, selection on regressors/factors/loadings and block/staggered missing, and we also show that our results can be readily extended to cases with a Heckman correction term or more general settings. An empirical analysis of the U.S. state-level tax rates from 1951 to 2000 with missing data reveals persistence in tax rates, while state income influences different taxes in varying ways.

Keywords: Dynamic Panel, Gauss-Seidel Algorithm, Interactive Effects, Missing Not At Random, Unbalanced Panel