A joint serial correlation test for linear panel data models

This paper proposes a joint error serial correlation test to be applied to linear panel data models after generalised method of moments estimation. This new test is an alternative inferential tool to both the m2 test of [Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277-297] and the overidentifying restrictions test. The proposed test, called the m(2,p)2 test, involves an examination of the joint significance of estimates of second to pth-order (first differenced) error serial correlations. The small sample properties of the m(2,p)2 test are investigated by means of Monte Carlo experiments. The evidence shows that the proposed test mostly outperforms the conventional m2 test and has high power when the overidentifying restrictions test does not, under a variety of alternatives including slope heterogeneity and cross section dependence.