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This paper considers fixed effects (FE) estimation for linear panel datamodels under possible model misspecification when both the number ofindividuals, $n$, and the number of time periods, $T$, are large. We firstclarify the probability limit of the FE estimator and argue that thisprobability limit can be regarded as a pseudo-true parameter. We then establishthe asymptotic distributional properties of the FE estimator around thepseudo-true parameter when $n$ and $T$ jointly go to infinity. Notably, we showthat the FE estimator suffers from the incidental parameters bias of which thetop order is $O(T^{-1})$, and even after the incidental parameters bias iscompletely removed, the rate of convergence of the FE estimator depends on thedegree of model misspecification and is either $(nT)^{-1/2}$ or $n^{-1/2}$.Second, we establish asymptotically valid inference on the (pseudo-true)parameter. Specifically, we derive the asymptotic properties of the clusteredcovariance matrix (CCM) estimator and the cross section bootstrap, and showthat they are robust to model misspecification. This establishes a rigoroustheoretical ground for the use of the CCM estimator and the cross sectionbootstrap when model misspecification and the incidental parameters bias (inthe coefficient estimate) are present. We conduct Monte Carlo simulations toevaluate the finite sample performance of the estimators and inference methods,together with a simple application to the unemployment dynamics in the U.S.

Estimation and inference for linear panel data models under misspecification when both $n$ and $T$ are large