Weak and strong cross-section dependence and estimation of large panels

This paper introduces the concepts of time-specific weak and strong cross-section dependence, and investigates how these notions are related to the concepts of weak, strong and semi-strong common factors, frequently used for modelling residual cross-section correlations in panel data models. It then focuses on the problems of estimating slope coefficients in large panels, where cross-section units are subject to possibly a large number of unobserved common factors. It is established that the common correlated effects (CCE) estimator introduced by Pesaran remains asymptotically normal under certain conditions on factor loadings of an infinite factor error structure, including cases where methods relying on principal components fail. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common effects.