This article 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 in a local asymptotic framework and show that the trade-off between bias and variance remains in 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 mean squared error than other methods. The proposed methods are applied to examine possible causes that lead to the increasing wage inequality between high-skilled and low-skilled workers in the U.S. manufacturing industries.