CCE estimation of factor-augmented regression models with more factors than observables

This paper considers estimation of factor-augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross-section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross-section combinations. Asymptotic properties of the resulting combination-augmented CCE (C3E) estimator are provided and tested in small samples using both simulated and real data.