Inference without smoothing for large panels with cross-sectional and temporal dependence

Abstract

This paper addresses inference in large panel data models in the presence of both cross-sectional and temporal dependence of unknown form. We are interested in making inferences without relying on the choice of any smoothing parameter as is the case with the often employed "HAC" estimator for the covariance matrix. To that end, we propose a cluster estimator for the asymptotic covariance of the estimators and a valid bootstrap which accommodates the nonparametric nature of both temporal and cross-sectional dependence. Our approach is based on the observation that the spectral representation of the fixed effect panel data model is such that the errors become approximately temporal uncorrelated. Our proposed bootstrap can be viewed as a wild bootstrap in the frequency domain. We present some Monte-Carlo simulations to shed some light on the small sample performance of our inferential procedure and illustrate our results using an empirical example