Finite-sample distribution of a recursively mean-adjusted panel data unit root test

Abstract

In this paper, we investigate the finite-sample distribution of the recursively mean-adjusted panel data unit root test of Shin et al. [Shin, D.W., Kang, S. and Oh, M.-S., 2004, Recursive mean adjustment for panel unit root tests. Economics Letters, 84, 433–439.]. More precisely, we provide response surface parameters that can be used to calculate small-sample critical values for the test. Furthermore, we supply standardizing moments that can be used to calculate a test statistic that has an asymptotic standard normal distribution. The asymptotic standard normal distribution, which follows when the cross-sectional dimension increases, enables easy calculation of critical values and p-values. Hence, it is of interest to study how large the cross-sectional dimension has to be in order for the normal approximation to be valid for inference. By performing a Monte Carlo simulation, we find that the normal approximation works well, at conventional significance levels, even when the cross-sectional dimension is as small as 2. We also supply critical values and moments for the panel unit root test that can be used when the baseline model is augmented to account for serially correlated disturbances. Finally, we investigate the finite-sample size and power properties of the test and find that the test performs well even when disturbances display serial correlation.