Complete Theory for CCE Under Heterogeneous Slopes and General Unknown Factors

A recent study of Westerlund (CCE in Panels with General Unknown Factors, The 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. Specifically, the common factors can have much more general time series properties than stationarity. This helps to alleviate the uncertainty over deterministic model components (e.g. trends) since they can be treated as unknown, similarly to unobserved stochastic (possibly non‐stationary) factors. While very promising, these theoretical results concern only the baseline scenario of the pooled (CCEP) estimator in the restrictive case of homogeneous model parameters, which is asymptotically biased and requires bias correction. Economic theory often hints at individuals exhibiting slope heterogeneity, which is a more realistic case when CCE is unbiased. Therefore, it is natural to extend the findings on general unknown factors to the case of unit‐specific slopes and understand if unbiasedness still holds, which would be an empirically handy feature. 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. Hence, the current study introduces more completeness in 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.