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Title: Extension of the Lagrange multiplier test for error cross-section independence to large panels with non-normal errors Authors:  Zhaoyuan Li - The Chinese University of Hong Kong, Shenzhen (China) [presenting]
Jeff Yao - The University of Hong Kong (Hong Kong)
Abstract: The aim is to reexamine 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 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 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 compared to the existing procedures.