A Lagrange-Multiplier Test for Large Heterogeneous Panel Data Models

This paper introduces a new test for error cross-sectional independence in large panel data models with exogenous regressors having heterogenous slope coefficients. The proposed statistic, LM_{RMT}, is based on the Lagrange Multiplier (LM) principle and the sample correlation matrix R_{N} of the model's residuals. Since in large panels R_{N} poorly estimates its population counterpart, results from Random Matrix Theory are used to establish the high-dimensional limiting distribution of LM_{RMT} under heteroskedastic normal errors and assuming that both the panel size N and the sample size T grow to infinity in comparable magnitude. Simulation results support our theoretical findings, with LM_{RMT} being correctly sized (except for some small values of N and T). Further, the small sample size and power outcomes show robustness of our statistic to deviations from the assumptions of normality for the error terms and regressors, of strict exogeneity for the regressors, as well as of heterogeneity for their slope coefficients. The test has comparable small sample properties to related tests in the literature which have been developed under different asymptotic theory