A Monte Carlo study on the size and power of panel unit root tests: Limitations in small data sets

Abstract

The aim of this paper is to explore the properties of various panel unit root tests in terms of their power and size regarding different panel data structures, with a special focus on small data samples. In particular, different values of the cross-sectional and time dimensions for both heterogeneous and homogeneous data settings with intercept and with and without time trend are observed. We examine and compare the results of five commonly used first-generation panel unit root tests: Levin, Lin and Chu test, Im Pesaran and Shin test, Harris–Tzavalis test, Breitung test and a Fischer type test. The results are derived using Monte Carlo simulations and show that all the observed panel unit root tests suffer from a serious lack of power and tend to either over or under reject the null hypothesis when the time dimensions are small. It is evident that the results of conducting panel unit root tests for data with $T<30$ are erroneous and unreliable, and it is therefore concluded that panel unit root tests should not be conducted for such samples in the first place. This is even more pronounced when there is a time trend or heterogeneity.