Using GMM when testing for a unit root in panels where the time-series dimension is fixed

In this paper we investigate GMM-based unit root inference in an autoregressive panel data model with individual-specific levels. We consider tests based on GMM estimators of the AR parameter and moment condition tests. The limiting distributions of the corresponding test statistics are derived when the AR parameter is unity and local-to-unity. This provides information about which statistics lead to valid test procedures. The performance of the valid tests in terms of their local power can then be compared. The results show that the GMM estimator of the AR parameter based on the Arellano-Bover type moment conditions, expressing that lagged differences are used as instruments for the equations in levels, can be used to detect a unit root. On the other hand, the widely used GMM estimator of the AR parameter based on the Arellano-Bond type moment conditions, expressing that lagged levels are used as instruments for the equations in first-differences, can not be used for this purpose. Instead a moment condition test of the hypothesis that the Arellano-Bond type moment conditions do not identify the AR parameter is valid as a unit root test. Finally, a simulation study demonstrates that the local power of the tests provides good approximations of their actual power in finite samples.