The Common Correlated Effects (CCE) methodology is now well established for the analysis of factor-augmented panel data models. Yet, it is often neglected that the pooled variant is biased unless the cross-section dimension ( ) of the dataset dominates the time series length ( ). This is problematic for inference with typical macroeconomic datasets, where is often equal or larger than . In response, we establish in this paper the theoretical foundation of the cross-section (CS) bootstrap for inference with CCE estimators in large and panels with . This resampling scheme is often used to estimate standard errors, yet without theoretical justification, and with unused potential, as we show it also provides a solution to the bias problem. We derive conditions under which the scheme replicates the distribution of the CCE estimators, such that bias can be eliminated and asymptotically valid inference can ensue. In so doing, we also spend attention to the case where factors need not be common across the dependent and explanatory variables, or when slopes are heterogeneous. Since we find that the CS-bootstrap applies in each case, researchers can stay agnostic on these issues. Simulation experiments show that the asymptotic properties also translate well to finite samples.

Stauskas, Ovidijus (2022)

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.