Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes

The asymptotic null distribution of the nonlinear IV panel unit root test due to Chang (2002, Journal of Econometrics 110, 261-292) is examined under the assumption of an invertible general linear process with a weak summability condition. An autoregressive approximation of order p, with p growing to infinity jointly with the sample size T is employed in the test regression. The conditions under which the analysis is conducted are fairly similar to those usually assumed for the augmented Dickey-Fuller test, with the exception of the conditions imposed on the innovations of the general linear process; these satisfy much stricter conditions needed for the nonlinear IV framework. The asymptotic normality of the nonlinear IV (panel) unit root test is established when p is of a magnitude order lower than the square root of T. Furthermore, the convergence rate of the nonlinear IV estimator of the coefficient associated to the lagged level is found to be lower than square root T, thus leading to inconsistency of the residual variance estimator. Two simple solutions to this problem are suggested.