Panel Data Models with Interactive Fixed Effects and Relatively Small $T$

Abstract: This paper studies the estimation of a linear panel data model with interactive fixed effects. A transformation is introduced which, after having been applied, enables the least squares (LS) estimator of \cite{bai_panel_2009} to produce estimates that are consistent and asymptotically unbiased when $n$ is large and $T$ is fixed. This is termed the \textit{transformed} least squares (TLS) estimator. Going further, these properties are shown to also carry over to the large $n$, large $T$ setting, provided $T / n \rightarrow 0$. This contrasts sharply with the usual case where the LS estimator is, in general, inconsistent when $n$ is large and $T$ is fixed, and is asymptotically biased when both $n$ and $T$ are large.