Testing For Stationarity With a Break in Panels Where the Time Dimension is Finite

In this paper, we consider the case of finite time dimension in the panel stationarity tests with structural breaks. By fixing T; the finite sample properties of the tests for both micro (T small and N large) and macro (both T and N large) panel data are generally greatly improved. More importantly, the derivation of the tests for finite T and N -> infinity, as opposed to joint asymptotic where N and T -> infinity simultaneously, avoids the imposition of the rate condition N/T -> 0; making the test valid for any (T;N) blend. Four models corresponding to the usual combination of breaks are considered. The asymptotic distributions of the test are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically employing two approaches. The first method is based on the Laplace Transform and the second derivation is based on Ghazal’s (1994) corollary. The case with unknown breaks is also considered. The proposed tests have generally empirical sizes that are very close to the nominal size. The Monte-Carlo simulations show that the power of the test statistics increases substantially with N and T.