Alternative estimation approaches for the factor augmented panel data model with small T

Abstract

In this paper, we compare alternative estimation approaches for factor augmented panel data models. Our focus lies on panel data sets where the number of panel groups (N) is large relative to the number of time periods (T). The principal component (PC) and common correlated effects (CCE) estimators were originally developed for panel data with large N and T, whereas the GMM approaches of Ahn et al. (J Econ 728 174:1–14, 2013) and Robertson and Sarafidis (J Econ 185(2):526–541, 2015) assume that T is small (that is T is fixed in the asymptotic analysis). Our comparison of existing methods addresses three different issues. First, we analyze the possibility of an inappropriate normalization of the factor space (the so-called normalization failure). In particular we propose a variant of the CCE estimator that avoids the normalization failure by adapting a weighting scheme inspired by the analysis of Mundlak (Econometrica 46(1):69–85, 1978). Second, we analyze the effects of estimating versus fixing the number of factors in advance. Third, we demonstrate how the design of the Monte Carlo simulations favors some estimators, which explains the conflicting findings from existing Monte Carlo experiments.