  This paper reexamines the seminal Lagrange multiplier test for cross-section
independence in a large panel model where both the number of cross-sectional
units n and the number of time series observations T can be large. The first
contribution of the paper is an enlargement of the test with two extensions:
firstly the new asymptotic normality is derived in a simultaneous limiting
scheme where the two dimensions (n, T) tend to infinity with comparable
magnitudes; second, the result is valid for general error distribution (not
necessarily normal). The second contribution of the paper is a new test
statistic based on the sum of the fourth powers of cross-section correlations
from OLS residuals, instead of their squares used in the Lagrange multiplier
statistic. This new test is generally more powerful, and the improvement is
particularly visible against alternatives with weak or sparse cross-section
dependence. Both simulation study and real data analysis are proposed to
demonstrate the advantages of the enlarged Lagrange multiplier test and the
power enhanced test in comparison with the existing procedures.
