A Test for Autocorrelation in Dynamic Panel Data Models

This paper presents an autocorrelation test that is applicable to dynamic panel data models with serially correlated errors. Our residual-based GMM t-test (hereafter: t-test) differs from the m2 and Sargan's over-identifying restriction (hereafter: Sargan test) in Arellano and Bond (1991), both of which are based on residuals from the first-difference equation. It is a significance test which is applied after estimating a dynamic model by the instrumental variable (IV) method and is directly applicable to any other consistently estimated residual. Two interesting points are found: the test depends only on the consistency of the first-step estimation, not on its efficiency;and the test is applicable to both forms of serial correlation (i.e., AR(1) or MA(1)). Monte Carlo simulations are also performed to study the practical performance of these three tests, the m2, the Sargan and the t-test for models with first-order auto-regressive AR(1) and first-order moving-average MA(1) serial correlation. The m2 and Sargan test statistics appear to accept too often in small samples even when the autocorrelation coefficient approaches unity in the AR(1) disturbance. Overall, our residual based t-test has considerably more power than the m2 test or the Sargan test.