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

Abstract:

Dealing with nonstationary panel models with the error term following the AR(1) process, we examine cross-sectional effects of regressors on the asymptotic properties of panel unit root tests. For this purpose we consider various types of common and heterogeneous regressors and compute limiting local powers of tests as T goes to infinity for each N, where T is the time series dimension, whereas N is the cross section dimension. Among the unit root tests considered are those based on the OLSE, GLSE, and other residual-based tests. It is theoretically and graphically shown that the existence of common regressors does not affect the asymptotic properties of these tests, although that of heterogeneous regressors does affect. We also derive the limiting power envelopes of the most powerful invariant tests, which yields the conclusion that the GLSE-based tests are asymptotically efficient, unlike the time series case. It is also shown that the effect of regressors on the envelopes is shown to be the same as in the tests mentioned above.