Unit Root Tests, Size Distortions, and Cointegrated Data

This paper demonstrates that unit root tests can suffer from inflated Type I error rates when data are cointegrated. Results from Monte Carlo simulations show that three commonly used unit root tests – the ADF, Phillips-Perron, and DF-GLS tests – frequently overreject the true null of a unit root for at least one of the cointegrated variables. The findings extend previous research which reports size distortions for unit roots tests when the associated error terms are serially correlated (Schwert, 1989; DeJong et al., 1992; Harris, 1992). While the addition to the Dickey-Fuller-type specification of the correct number of lagged differenced (LD) terms can eliminate the size distortion, I demonstrate that determining the correct number of LD terms is unachievable in practice. Standard diagnostics such as testing for serial correlation in the residuals, and using information criteria to compare different lag specifications, are unable to identify the requird number of lags. A unique feature of this study is that it includes programs (an Excel spreadsheet and Stata .do files) that allow the reader to simulate their own cointegrated data -- using parameters of their own choosing -- to confirm the findings reported in this paper.