Test for serial correlation in panel data models with interactive fixed effects

This article considers a consistent test for serial correlation of unknown form in the residual of panel data models with interactive fixed effects and possibly lagged dependent variables. Following the spirit of Hong, we construct a test statistic based on the comparison of a kernel-based spectral density estimator and the null spectral density. Under the null hypothesis, our test statistic is asymptotically N(0, 1) as both N and T tend to infinity. In contrast to existing tests for serial correlation, there is no need to specify the order of serial correlation about the alternative. We further examine the local and global power properties of test. A simulation study shows that our test performs well in finite samples. In the empirical application, we apply the test to study the impact of the divorce law reform on divorce rate. We find strong evidence of serial correlation in the residual, and our results show that the divorce law reform has permanent positive effects on divorce rates.