A Robust Test for Serial Correlation in Panel Data Models

We consider a new nonparametric test for serial correlation of unknown form in the estimated residuals of a panel regression model, where individual and time effects can be fixed or random, and the panel data can be balanced or unbalanced. Our test is robust against potential weak error cross-sectional dependence and error serial dependence in higher-order moments. This is in contrast to existing tests for serial correlation in panel data models, which assume error components to be cross-sectionally and serially independent. Our test has an asymptotic N(0, 1) distribution under the null hypothesis and is consistent against serial correlation of unknown form. No common alternative is assumed and hence our test allows for substantial inhomogeneity in serial correlation across individuals. A simulation study highlights the merits of the proposed test relative to a variety of existing tests in the literature. We apply the new test to the empirical study of Wolfers on the relationship between unilateral divorce laws and divorce rates and find strong evidence against serial uncorrelatedness even controlling for the fixed effect.