Cross-Sectional Effects of Common and Heterogeneous Regressors on Asymptotic Properties of Panel Autoregressive Unit Root Tests

The present paper deals with nonstationary panel autoregressive （AR） models, and examines cross-sectional effects of regressors on the asymptotic properties of panel unit root tests for the AR（1） coefficient. We consider various types of common and heterogeneous regressors and compute limiting local powers of tests as T →∞ for each N, where T and N are the time and cross section dimensions, respectively. Dealing with tests based on the ordinary least squares estimator （OLSE） and the generalized LSE（GLSE）, we examine how common and heterogeneous regressors affect the tests as N becomes large. It is shown that the existence of common regressors does not affect the tests asymptotically as N →∞. This means that the power of the tests remains the same even if the model contains common regressors. We further derive the limiting power envelopes of the most powerful invariant （MPI） tests, which yields the conclusion that the GLSE-based tests are asymptotically efficient, unlike the time series case.