Testing AR(1) against MA(1) disturbances in an error component model

This paper derives three LM statistics for an error component model with first-order serially correlated errors. The first LM statistic jointly tests for zero first-order serial correlation and random individual effects, the second LM statistic tests for zero first-order serial correlation assuming fixed individual effects, and the third LM statistic tests for zero first-order serial correlation assuming random individual effects. In all three cases, the corresponding LM statistic is the same whether the alternative is AR(1) or MA(1). This paper also derives two extensions of the Burke, Godfrey, and Termayne (1990) test from the time-series to the panel data literature. The first tests the null of AR(1) disturbances against MA(1) disturbances, and the second tests the null of MA(1) disturbances against AR(1) disturbances in an error component model. These tests are computationally simple requiring only OLS or within residuals. The small sample performance of these tests are studied using Monte Carlo experiments.