A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence

This paper develops a simple test for the null hypothesis of stationarity in heterogeneous panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. Our test is basically the same as the KPSS test but the regression is augmented by cross-sectional average of the observations. We also develop a Lagrange multiplier (LM) test allowing for cross-sectional dependence and, under restrictive assumptions, compare our augmented KPSS test with the extended LM test under the null of stationarity, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. The latter results are derived using the joint asymptotic limits where T and N-> infinity simultaneously (under the additional condition that N/T -> 0) and the limiting distributions under the null are shown to be standard normal. We also extend our test to the more realistic case where the shocks are serially correlated. We use Monte Carlo simulations to examine the finite sample property of the augmented KPSS test.