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This paper reexamines the seminal Lagrange multiplier test for cross-sectionindependence in a large panel model where both the number of cross-sectionalunits n and the number of time series observations T can be large. The firstcontribution of the paper is an enlargement of the test with two extensions:firstly the new asymptotic normality is derived in a simultaneous limitingscheme where the two dimensions (n, T) tend to infinity with comparablemagnitudes; second, the result is valid for general error distribution (notnecessarily normal). The second contribution of the paper is a new teststatistic based on the sum of the fourth powers of cross-section correlationsfrom OLS residuals, instead of their squares used in the Lagrange multiplierstatistic. This new test is generally more powerful, and the improvement isparticularly visible against alternatives with weak or sparse cross-sectiondependence. Both simulation study and real data analysis are proposed todemonstrate the advantages of the enlarged Lagrange multiplier test and thepower enhanced test in comparison with the existing procedures.

Extension of the Lagrange multiplier test for error cross-section independence to large panels with non normal errors