Testing slope homogeneity in panel data models with a multifactor error structure

Based on the common correlated effects (CCE) method and the Lagrange multiplier (LM) principle, this paper proposes a slope homogeneity test in a panel data model with a multifactor error structure that allows unobserved factors to be correlated with explanatory variables. The CCE method is first used to transform the regression equation to control for the unobserved common factors. Then, we adopt the idea of an LM-type test to conduct a homogeneity test. Our asymptotic analysis indicates that the test statistic is asymptotically normally distributed under the null hypothesis of homogeneity, regardless of the errors’ normality or homoskedasticity, as both N and T go to infinity, with \(T^{2/3}N^{-1}\rightarrow 0\) and \(T^{2}N^{-1}\rightarrow \infty \). It is also proved that the test is asymptotically powerful under a sequence of Pitman local alternatives. Monte Carlo simulations indicate that the test has good finite sample properties for all combinations of N and T, with the exception of a large N / T. The simulation results also suggest that the proposed test is robust to the errors’ non-normality and conditional heteroskedasticity.