Alternative estimation approaches for the factor augmented panel data model with small T
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Alternative estimation approaches for the factor augmented panel data model with small T Jörg Breitung1 · Philipp Hansen1 Received: 1 February 2020 / Accepted: 19 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Panel data · Interactive fixed effects · CCE estimator · GMM JEL Classification C23 · C38
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00181020-01948-7) contains supplementary material, which is available to authorized users.
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Jörg Breitung [email protected] Institute of Econometrics, University of Cologne, Albertus Magnus Platz, 50923 Köln, Germany
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J. Breitung, P. Hansen
1 Introduction The seminal work of Holtz-Eakin et al. (1988) has provided two important contributions to the statistical analysis of panel data. First, it proposes a GMM framework for estimating dynamic panel data models that were further developed and popularized by Arellano and Bond (1991). This approach has become standard in the dynamic analysis of panel data. The second contribution, the introduction of time varying individual effects, was less influential and went largely unnoticed for many years. For example, the excellent monograph of Baltagi (2005)—as all other textbooks on panel data analysis of the early 2000s—does not consider time varying individual effects or any other factor structure. Bai (2009) pointed out that time varying individual effects are just a special case of a factor structure and provided a general framework for estimating a panel data model with “interactive fixed effects”, which is also referred to as the factor-augmented panel data model. With the work of Ahn et al. (2001, 2013), Pesaran (2006), and Bai (2009) the interest in models that account for time varying heterogeneity and cross-sectio
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