Nonparametric multidimensional fixed effects panel data models

Multidimensional panel datasets are routinely employed to identify marginal effects in empirical research. Fixed effects estimators are typically used to deal with potential correlation between unobserved effects and regressors. Nonparametric estimators for one-way fixed effects models exist, but are cumbersome to employ in practice as they typically require iteration, marginal integration or profile estimation. We develop a nonparametric estimator that works for essentially any dimension fixed effects model, has a closed form solution and can be estimated in a single step. A cross-validation bandwidth selection procedure is proposed and asymptotic properties (for either a fixed or large time dimension) are given. Finite sample properties are shown via simulations, as well as with an empirical application, which further extends our model to the partially linear setting.