Handling Distinct Correlated Effects with CCE

The Common Correlated Effects (CCE) estimator is a popular method to estimate panel data regression models with interactive effects. Due to its simplicity in approximating the common factors with cross-section averages of the observables, it lends itself to a wide range of applications. They include static and dynamic models, homogeneous or heterogeneous coefficients or possibly very general types of factor structure. Despite such flexibility, with very few exceptions, CCE properties are usually examined under a restrictive assumption that all the observed variables load on the same set factors, which ensures joint identification of the factor space. In this paper, we explore an empirically relevant scenario when the dependent and explanatory variables are driven by distinct but correlated factors. In doing this, we consider panel dimensions such that T/N is finite even in large samples, which is known to induce an asymptotic bias in CCE setting. We subsequently develop a toolbox to perform asymptotically valid inference in homogeneous and heterogeneous panels.