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

This paper considers estimation of factor-augmented panel data regression models with homogenous slope coefficients. One of the most popular approaches towards this end is the pooled common correlated effects CCE estimator of Pesaran 2006. For this estimator to be consistent at the usual sqrt-NT rate, where N and N denote the number of cross-section and time series observations, respectively, the number of factors cannot be larger than the number of observables. This is a problem in the typical application involving only a small number of regressors. The current paper proposes a simple extension to the CCE procedure by which the requirement 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. The asymptotic properties of the resulting combination-augmented CCE C3E estimator are provided and verified in small samples using Monte Carlo simulation.