Cross-Sectional Independence Test for a Class of Parametric Panel Data Models

Abstract

This paper proposes a new statistic to conduct cross-sectional independence test for the residuals involved in a parametric panel data model. The proposed test statistic, which is called linear spectral statistic (LSS), is established based on the characteristic function of the empirical spectral distribution (ESD) of the sample correlation matrix of the residuals. The main advantage of the proposed test statistic is that it can capture nonlinear cross-sectional dependence. Asymptotic theory for a general class of linear spectral statistics is established, as the cross-sectional dimension N and time length T go to infinity proportionally. This type of statistics covers many classical statistics, including the bias-corrected Lagrange Multiplier (LM) test statistic and the likelihood ratio test statistic. Furthermore, the power under a local alternative hypothesis is analyzed and the asymptotic distribution of the proposed statistic under this local hypothesis is also established. Finite sample performance shows that the proposed test statistic works well numerically in each individual case and it can also distinguish some dependent but uncorrelated structures, for example, nonlinear MA(1) models and multiple ARCH(1) models.