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 m 2 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 p th-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 m 2 test and has high power when the overidentifying restrictions test does not, under a variety of alternatives including slope heterogeneity and cross section dependence.