Bias Reduction in Nonlinear and Dynamic Panels in the Presence of Cross-Section Dependence, with a GARCH Panel Application

Abstract

Nonlinear and dynamic panel models that contain individual-specific parameters are well-known to suffer from the incidental parameter bias. This bias and methods for correcting it have been studied extensively for panels with time-series dependence. However, a general analysis under cross-section dependence is missing. This paper extends the literature to dependence across both dimensions in large-N large-T panels. Our analysis is based on the integrated likelihood method which nests many common estimation approaches. We show that the composition of the first-order bias changes only under strong cross-section dependence, but not under weak or cluster-type dependence. Using bias correction techniques, we also propose a novel estimation approach for GARCH-type financial volatility modelling in small samples. Simulation analysis and a forecast exercise suggest that this method achieves success with as little as 150 time-series observations, which is much less than what is required by standard volatility estimation methods. We also use this approach to analyse the volatility characteristics of monthly hedge fund returns.