Unit root testing using covariates: Some theory and evidence

This paper analyzes the conditions under which power gains can be achieved using the Covariate Augmented Dickey-Fuller test (CADF) rather than the con ventional Augmented Dickey-Fuller (ADF), and argues that this method has th e advantage, relative to univariate unit root tests, of increasing power wi thout suffering from the large size distortions affecting the latter. The i nclusion of covariates affects unit root testing by: (a) reducing the stand ard error of the estimate of the autoregressive parameter without affecting the estimate itself, and/or (b) reducing both the standard error and the a bsolute value of the estimate itself. Conditions in terms of contemporaneou s correlation and Granger causality are derived for case (a) or (b) to aris e. As an illustration, it is shown that applying the more powerful CADF (ra ther than the ADF) test reverses the finding of a unit root for many US mac roeconomic series.