A Locally Optimal Test for No Unit Root in Cross-Sectionally Dependent Panel Data

This paper develops a simple test for the null hypothesis of no unit root for 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 Kwiatkowski et al. (1992) test with the regression augmented by cross-sectional average of the observations, and hence, we call it the augmented KPSS test. We also develop a Lagrange multiplier (LM) test allowing for cross-sectional dependence and compare it with the augmented KPSS test under the null of no unit root, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. We show that the augmented KPSS test is asymptotically optimal in the sense that the two tests have the same asymptotic local power, although the optimality of the augmented KPSS test is not guaranteed under a wide range of the fixed alternative.