Time-specific disturbances and cross-sectional dependency in a small-sample heterogeneous panel data unit root test

In their seminal work, Im et al. (1997, 2003) suggested that time series for several cross-sectional units could be used to increase the power of the Dickey-Fuller unit root test. They argued that when cross-sectional correlation is a problem that can be modelled by a time-specific factor, demeaning across the cross-sectional units can solve the problem. In this study, this proposition is proven valid, but it is also shown that previously supplied standardizing moments are inappropriate when the number of cross-sections are small, causing size to differ from the significance level. To correct this size distortion, the current paper supplies response surface parameters that can be used to obtain moments that are valid when a time-specific factor suffices for modelling cross-sectional correlation in the heterogeneous panel data unit root framework. The correct size of the panel data unit root test comes at the cost of a somewhat lower power against a stationary alternative.