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Fixed $T$ Estimation of Linear Panel Data Models with Interactive Fixed Effects$^*$
\title{Fixed $T$ Estimation of Linear Panel Data Models with Interactive Fixed Effects$^*$}
\author{Ayden Higgins$^{\dagger}$\\University of Cambridge}
\date{\today}
\maketitle
\begin{abstract}
This paper studies the estimation of linear panel data models with interactive fixed effects, where one dimension of the panel, typically time, may be fixed. To this end, a novel transformation is introduced that reduces the model to a lower dimension, and, in doing so, relieves the model of incidental parameters in the cross-section. The central result of this paper demonstrates that transforming the model and then applying the principal component (PC) estimator of \cite{bai_panel_2009} delivers $\sqrt{n}$ consistent estimates of regression slope coefficients with $T$ fixed. Moreover, these estimates are shown to be asymptotically unbiased in the presence of cross-sectional dependence, serial dependence, and with the inclusion of dynamic regressors, in stark contrast to the usual case. The large $n$, large $T$ properties of this approach are also studied, where many of these results carry over to the case in which $n$ is growing sufficiently fast relative to $T$. Transforming the model also proves to be useful beyond estimation, a point illustrated by showing that with $T$ fixed, the eigenvalue ratio test of \cite{horenstein} provides a consistent test for the number of factors when applied to the transformed model. \\
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\textbf{Keywords:} interactive fixed effects, dynamic panels, factor models.\\
\textbf{JEL classification:} C13, C33, C38.\\
\end{abstract}
\vspace{-0.1in}
\xdef\@thefnmark{}\@footnotetext{\hspace{-0.2in}$^*$This work was supported by the European Research Council through the grant ERC-2016-STG-715787-MiMo. I am grateful to Valentina Corradi, Koen Jochmans, Federico Martellosio, Jo$\tilde{\text{a}}$o Santos Silva and Martin Weidner for their comments and suggestions.}
\xdef\@thefnmark{}\@footnotetext{\hspace{-0.2in}$^{\dagger}$Email: [email removed].}
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\begin{thebibliography}{15}
\bibitem[{Ahn and Horenstein(2013)}]{horenstein}
Ahn, S.~C., Horenstein, A.~R., 2013. Eigenvalue ratio test for the number of
factors. Econometrica 81~(3), 120 -- 1227.
\bibitem[{Ahn et~al.(2013)Ahn, Lee, and Schmidt}]{ahn_panel_2013}
Ahn, S.~C., Lee, Y.~H., Schmidt, P., 2013. Panel data models with multiple
time-varying individual effects. Journal of Econometrics 174~(1), 1 -- 14.
\bibitem[{Bai(2003)}]{baifac}
Bai, J., 2003. Inferential theory for factor models of large dimensions.
Econometrica 71~(1), 135 -- 171.
\bibitem[{Bai(2009)}]{bai_panel_2009}
Bai, J., 2009. Panel data models with interactive fixed effects. Econometrica
77~(4), 1229 -- 1279.
\bibitem[{Balestra and Nerlove(1966)}]{balestra_nerlove}
Balestra, P., Nerlove, M., 1966. Pooling cross section and time series data in
the estimation of a dynamic model: The demand for natural gas. Econometrica
34~(3), 585--612.
\bibitem[{Barbosa and Moreira(2020)}]{moriera_dynamic}
Barbosa, J.~D., Moreira, M.~J., 2020. Likelihood inference and the role of
initial conditions for the dynamic panel data model. Journal of econometrics
(in press).
\bibitem[{Chamberlain(1984)}]{chamberlain}
Chamberlain, G., 1984. Chapter 22: Panel data. In: Griliches, Z., Intriligator,
M. (Eds.), Handbook of {Econometrics}. Vol.~2. Elsevier, pp. 1247 -- 1318.
\bibitem[{Hayakawa(2016)}]{hayakawa}
Hayakawa, K., 2016. Identification problem of {GMM} estimators for short panel
data models with interactive fixed effects. Economics Letters 139, 22 -- 26.
\bibitem[{Latala(2005)}]{latala}
Latala, R., 2005. Some estimates of norms of random matrices. Proceedings of
the American Mathematical Society 133~(5), 1273--1282.
\bibitem[{Moon and Weidner(2015)}]{moon_linear_2015}
Moon, H.~R., Weidner, M., 2015. Linear regression for panel with unknown number
of factors as interactive fixed effects. Econometrica 83~(4), 1543 -- 1579.
\bibitem[{Moon and Weidner(2017)}]{moon_dynamic_nodate}
Moon, H.~R., Weidner, M., 2017. Dynamic linear panel regression models with
interactive fixed effects. Econometric Theory 33~(1), 158 -- 195.
\bibitem[{Neyman and Scott(1948)}]{neyman}
Neyman, J., Scott, E.~L., 1948. Consistent estimates based on partially
consistent observations. Econometrica 16~(1), 1--32.
\bibitem[{Nickell(1981)}]{nickell}
Nickell, S., 1981. Biases in dynamic models with fixed effects. Econometrica
49~(6), 1417--1426.
\bibitem[{Onatski(2009)}]{onatski}
Onatski, A., 2009. Testing hypotheses about the number of factors in large
factor models. Econometrica 77~(5), 1447 -- 1479.
\bibitem[{Pesaran(2006)}]{pesaran_estimation_2006}
Pesaran, H., 2006. Estimation and inference in large heterogeneous panels with
a multifactor error structure. Econometrica 74~(4), 967 -- 1012.
\end{thebibliography}