Testing for Correlated Factor Loadings in Cross Sectionally Dependent Panels

A large strand of the literature on panel data models has focused on explicitly modelling the cross-section dependence between panel units. Factor augmented approaches have been proposed to deal with this issue. Under a mild restriction on the correlation of the factor loadings, we show that factor augmented panel data models can be encompassed by a standard two-way fixed effect model. This highlights the importance of verifying whether the factor loadings are correlated, which, we argue, is an important hypothesis to be tested, in practice. As a main contribution, we propose a Hausman-type test that determines the presence of correlated factor loadings in panels with interactive effects. Furthermore, we develop two nonparametric variance estimators that are robust to the presence of heteroscedasticity, autocorrelation as well as slope heterogeneity. Via Monte Carlo simulations, we demonstrate desirable size and power performance of the proposed test, even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings in panels with interactive effects.