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

TL;DR

This paper extends the Lagrange multiplier test for cross-section independence in large panels, accommodating non-normal errors and large dimensions, and introduces a more powerful test statistic based on fourth powers of correlations.

Contribution

It develops an enlarged test with new asymptotic normality for large panels with non-normal errors and proposes a novel, more powerful test statistic based on fourth powers.

Findings

The new asymptotic normality holds when both n and T grow large.

The fourth power-based test outperforms existing tests in simulations.

Real data analysis confirms the advantages of the proposed methods.

Abstract

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.