Unified and Robust Lagrange Multiplier Type Tests for Cross-Sectional Independence in Large Panel Data Models

This paper revisits the Lagrange multiplier type test for the null hypothesis of no cross-sectional dependence. We propose a unified test procedure and its power enhancement version, which show robustness for a wide class of panel model contexts. Specifically, the two procedures are applicable to both heterogeneous and fixed effects panel data models with the presence of weakly exogenous as well as lagged dependent regressors, allowing for a general form of non-normal error distribution. With the tools from Random Matrix Theory, the asymptotic validity of the test procedures is established under the simultaneous limit scheme. The derived theories are accompanied by detailed Monte Carlo experiments, which confirm the robustness of the two tests and also suggest the validity of the power enhancement technique. Additionally, we apply the proposed test to detect the cross-sectional dependence in the residuals of the CAPM model and its Fama-French factor extensions from S&P 500 securities over the period Sept 1998 - Sept 2010. Both the simulation results and empirical analysis indicate the reliability of the two procedures