Handling Distinct Correlated Effects with CCE

The common correlated effects (CCE) approach by Pesaran is a popular method for estimating panel data models with interactive effects. Due to its simplicity, i.e., unobserved common factors are approximated with cross-section averages of the observables, the estimator is highly flexible and lends itself to a wide range of applications. Despite such flexibility, however, the properties of CCE estimators are typically only examined under the restrictive assumption that all the observed variables load on the same set of factors, which ensures joint identification of the factor space. In this article, we take a different perspective, and explore the empirically relevant case where the dependent and explanatory variables are driven by distinct but correlated factors. Hence, we consider the case of Distinct Correlated Effects. Such settings can be argued to be relevant for practice, for instance in studies linking economic growth to climatic variables. In so doing, we consider panel dimensions such that as $(N,T)\to \infty$, which is known to induce an asymptotic bias for the pooled CCE estimator even under the usual common factor assumption. We subsequently develop a robust bootstrap-based toolbox that enables asymptotically valid inference in both homogeneous and heterogeneous panels, without requiring knowledge about whether factors are distinct or common.