Focused Information Criterion and Model Averaging for Large Panels with a Multifactor Error Structure

This paper considers model selection and model averaging in panel data models with a multifactor error structure. We investigate the limiting distribution of the common correlated effects estimator (Pesaran, 2006) in a local asymptotic framework and show that the trade-off between bias and variance remains in the asymptotic theory. We then propose a focused information criterion and a plug-in averaging estimator for large heterogeneous panels and examine their theoretical properties. The novel feature of the proposed method is that it aims to minimize the sample analog of the asymptotic mean squared error and can be applied to cases irrespective of whether the rank condition holds or not. Monte Carlo simulations show that both proposed selection and averaging methods generally achieve lower expected squared error than other methods. The proposed methods are applied to analyze the consumer response to gasoline taxes