Uniform Theory for CCE under Heterogeneous Slopes and General Unknown Factors

A recent study proposed by Westerlund (CCE in Panels with General Unknown Factors, Econometrics Journal, 21, 264-276, 2018) showed that a very popular Common Correlated Effects (CCE) estimator is significantly more applicable than it was thought before. Contrary to the usual stationarity assumption, common factors can in fact be much more general and not unit root only. This also helps to alleviate the uncertainty over deterministic model components since they can be treated as unknown, similarly to unobserved stochastic factors. While very promising, these theoretical results concern only the pooled (CCEP) version of the estimator for the homogeneous parameters, which does no take heterogeneous effects into account. Therefore, it is natural to generalize these findings to the case of unit-specific slopes. It is especially interesting, because many previous studies on heterogeneous slopes did not rigorously account for the usual situation when the factors are proxied by more explanatory variables than needed. As a result, the current setup introduces more uniformity to the CCE theory. We demonstrate that save for some regularity conditions, CCEP and the mean group (CCEMG) estimators are asymptotically normal and unbiased under heterogeneous slopes and general unknown factors.