Testing for stationarity in heterogeneous panel data where the time dimension is finite

Abstract

This paper expands the tests of Hadri (2000, Econometrics Journal 3, 148–161) for the null of stationarity against the alternative of a unit root in panel data to the case where the time dimension of the panel is finite. This improves the finite sample properties of the tests for micro and macro panels. More importantly, the derivation of the tests for finite T as opposed to joint asymptotic where N and T→∞ simultaneously avoids the imposition of the rate condition N/T→ 0 and hence makes the test valid for any (T, N) combination. The asymptotic distributions of the tests are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically using Ghazal's (1994, Statistics and Probability letters 20, 313–319)1 lemma 1. Finite sample size and power are considered in a Monte Carlo experiment. The proposed tests have empirical sizes that are very close to the nominal 5% level. The Monte Carlo results clearly show that the power of the test statistics increases substantially with N, T and ω (ω being the number of unit root processes under the alternative). The results indicate that the assumption that T is asymptotic rather than fixed leads to tests that are substantially oversized particularly for relatively short panels with large N.