Nonparametric Estimation of Smooth Coefficients in Fixed-Effect Panel Data Models

We propose a kernel-based nonparametric estimator for a smooth coefficient panel data model with fixed effects. Without requiring a zero sum of fixed effects, we propose an estimator that is easy to construct and computationally efficient. Eliminating the fixed effects through a local within transformation, we perform a local linear estimation for the coefficient functions associated with time varying variables and associated derivatives. We further estimate the intercept coefficient function, if present, through a difference of kernel weighted averages. We characterize the estimator’s asymptotic properties under a large-n and large-T framework. We demonstrate that the estimator is not asymptotically equivalent to the standard kernel estimator that ignores fixed effects. Through extensive simulation studies, we highlight the estimator’s encouraging numerical performance and computational advantages over existing kernel estimators in the literature. We showcase the empirical applicability by estimating a smooth coefficient model for the Environmental Kuznets Curve through a panel of OECD countries.