Testing for Correlated Factor Loadings in Panels with Interactive Effects
A large literature on modelling cross-section dependence in panels has been developed through interactive effects. However, there are areas where research has not really caught on yet. One such area is the one concerned with whether the factor loadings are correlated with the regressors or not. This is an important hypothesis to be tested because if the loadings are uncorrelated with the regressors, we can simply use the consistent two-way fixed effects (FE) estimator without employing any fancy econometrics such as the principal component (PC) or the common correlated e¤ects estimators. As the main contribution, we propose the novel test that determines the validity of uncorrelated factor loadings. Further, we develop two nonparametric variance estimators for the FE and PC estimators as well as their difference, that are robust to the presence of heteroscedasticity, autocorrelation and slope heterogeneity. The proposed test follows the X2 distribution, asymptotically. Monte Carlo simulation results confirm satisfactory size and power performance of the test even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings. In this situation, the FE estimator would provide a simple and well-established estimation strategy by avoiding nontrivial computational issues associated with the PC estimator.