An LM Test for the Conditional Independence between Regressors and Factor Loadings in Panel Data Models with Interactive Effects

A huge literature on modelling cross-sectional dependence in panels has been developed using interactive effects (IE). One area of contention is the hypothesis concerned with whether the regressors and factor loadings are correlated or not. Under the null hypothesis that they are conditionally independent, we can still apply the consistent and robust two-way fixed effects estimator. As an important specification test we develop an LM test for both static and dynamic panels with IE. Simulation results confirm the satisfactory performance of the LM test in small samples. We demonstrate its usefulness with an application to a total of 22 datasets, including static panels with a small T and dynamic panels with serially correlated factors, providing convincing evidence that the null hypothesis is not rejected in many datasets.