Panel Unit Root Tests in the Presence of Cross-Sectional Dependencies: Comparison and Implications for Modelling

Abstract

Several panel unit root tests that account for cross section dependence using a common factor structure have been proposed in the literature recently, notably Pesaran (2003), Moon and Perron (2004) and Bai and Ng (2004). This paper is aimed at comparing these three proposed unit root tests for panels with dynamic factors. It makes fourcontributions: (1) it compares the three testing procedures in terms of similarities and difference in the data generation process, tests, null and alternative hypotheses considered,(2) it compares the small sample properties of the tests usingMonte Carlo results in models with up to two common factors, (3) it provides an application which illustrates the use of the tests, and (4) finally it discusses the use of the tests in modelling in general. The main conclusions are: Pesaran’s (2003) cross-sectionally augmented (CA)DF tests are designed for cases where cross-sectional dependence is due to a single factor. The Moon and Perron (2004) tests which use defactored data is similar in spirit but can account for mutiple common factors. The Bai and Ng (2004) tests allow to tests for unit roots in the common factors and/or the idiosyncratic factors. It would therefore be natural to use the Pesaran (2003) or Moon and Perron tests in a first step to find out whether there are unit roots in the data. Then in a second step of modelling, the Bai and Ng (2004) tests could be used to determine whether the unit roots arise in the common factors or in the idiosyncratic components. It is also found that the latter behave well when the observed nonstationarity in the data series comes exclusively from nonstationary common factors, e.g. when the series cointegrate along the cross sectional dimension of the panel.econometrics;