A New Diagnostic Test for Cross-Section Uncorrelatedness in Nonparametric Panel Data Models

In this paper, we propose a new diagnostic test for residual cross-section uncorrelatedness in a nonparametric panel data model. The proposed nonparametric cross-section uncorrelatedness (CU) test is a nonparametric counterpart of an existing parametric cross-section dependence (CD) test proposed in Pesaran (2004) for the parametric case. We establish asymptotic distributions of the proposed test statistic for several different cases. Without assuming cross-section independence, we establish asymptotic distributions for the proposed test for the case where both the cross-section dimension and the time dimension go to infinity simultaneously. We then analyze the power function of the proposed test under a sequence of local alternatives that involve a nonlinear multi-factor model. We also provide several numerical examples. The small sample studies show that the nonparametric CU test associated with an asymptotic critical value works well numerically in each individual case. An empirical analysis of a set of CPI data in Australian capital cities is given to examine the applicability of the proposed nonparametric CU test