CCE in fixed-T panels

The presence of unobserved heterogeneity and its likely detrimental effect on inference has recently motivated the use of factor-augmented panel regression models. The workhorse of this literature is based on first estimating the unknown factors using the cross-section averages of the observables, and then applying ordinary least squares conditional on the first-step factor estimates. This is the common correlated effects (CCE) approach, the existing asymptotic theory for which is based on the requirement that both the number of time series observations, T, and the number of cross-section units, N, tend to infinity. The obvious implication of this theory for empirical work is that both N and T should be large, which means that CCE is impossible for the typical micro panel where only N is large. In the current paper, we put the existing CCE theory and its implications to a test. This is done by developing a new theory that enables T to be fixed. The results show that many of the previously derived large-T results hold even if T is fixed. In particular, the pooled CCE estimator is still consistent and asymptotically normal, which means that CCE is more applicable than previously thought. In fact, not only do we allow T to be fixed, but the conditions placed on the time series properties of the factors and idiosyncratic errors are also much more general than those considered previously.