Testing serial correlation in semiparametric panel data models

We propose three test statistics for testing serial correlation in a semiparametric partially linear panel data model that could allow lagged dependent variables as explanatory variables. The first is for testing zero first-order serial correlation, the second for testing higher-order serial correlations and the third testing for individual effects. The test statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of a martingale difference error process. We conduct some Monte Carlo experiments to examine the finite sample performances of the proposed tests. We also discuss the generalization to testing serial correlation in a nonparametric framework.