Time-specific disturbances in a panel stationarity test

Abstract

In this article, we investigate the performance of a panel data stationarity test when cross-sectional correlation is modelled by a time-specific factor. Size distortions, that occur especially when the number of cross sections is small, are documented. To eliminate these distortions, a new set of critical values is supplied. When investigating the rejection frequency under the alternative hypothesis, it is found that the panel data stationarity test that uses the supplied critical values maintain good power characteristics even when only a subset of the cross-sectional units have a unit root.

Acknowledgements

The author is grateful for the help obtained from discussions with Tommy Andersson. Financial support, from The Crafoord Foundation, The Royal Swedish Academy of Sciences and The Jan Wallander and Tom Hedelius Foundation, research grant number P2005-0117:1, is gratefully acknowledged. All the simulations in the current article are performed in GAUSS and run on the LUNARC cluster.

Notes

¹ Recent surveys of this rapidly developing research field can be found in Breitung and Pesaran (2008) and Choi (2006).

² Examples of empirical applications where panel unit root tests have been utilized are Lee and Wu (2004), Carrion-I-Silvestre et al. (2004) and Holmes (2002).

³ From here on, the Kwiatkowski et al. (1992) test will be referred to as the KPSS test.

⁴ T is used to indicate the number of time-series observations, while N is used to denote the number of cross-sectional units.

⁵ Here, and in the remainder of this article, we let i denote the cross-sectional dimension and t denote the time-series dimension. Throughout we will also assume that i∈{1,…,N} and t∈{1,…,T}.

⁶ It is important to note that Hadri (2000) allows for the covariance stationary disturbance to be serially correlated, while Hadri and Larsson (2005) consider the case where the disturbance is serially independent.

⁷ It should be noted, however, that other forms of CSD might not be addressed by demeaning the data (see, e.g. Strauss and Yigit, 2003).

⁸ The final specification in Equation 9 was obtained after trying out various specifications for the response surface regressions. The final specification was chosen on the basis of in-sample fit.

⁹ In Equation 9, TS and CS refer to ‘time series’ and ‘cross section’, respectively.

¹⁰ To reduce the influence of the initial condition, ξ_{i ,0} = 0, where i∈{1,…,N ^{H ₁} }, for the random walk component, T + 100 time series observations are generated, while only the last T are used to construct the time series.

¹¹ We have also investigated other time-series dimensions than the ones presented in the tables. The main conclusions that follow from the tables remain unchanged also when the time-series dimensions are chosen outside the set used for fitting the response surface regressions.