Testing for serial correlation and random effects in a two-way error component regression model

In this paper, we test the existence of serial correlation and random effects in a two-way error component regression model with panel data. Under moment conditions alone, we suggest several easily implemented tests based on the parameter estimators for artificial autoregressions modeled by the differences in residuals. Under the null hypotheses, the tests for serial correlation are two-sided and asymptotically chi-square distributed, whereas those for random effects are one-sided, and are asymptotically standard normally distributed variables. Moreover, these methods can also be used similarly to construct tests for both serial correlation and individual effects jointly, whether or not time effects are present. The proposed tests are able to detect local alternatives that are distinct from the null at the parametric rate. Monte Carlo simulations and real data applications are carried out for purposes of illustration.