Do Real Interest Rates Really Contain a Unit Root? More Evidence from a Bootstrap Covariate Unit Root Test

Abstract

This paper re‐examines the empirical finding that international real interest rates usually have a unit root. This conclusion is put forth in Rapach and Weber (2004), using the Ng and Perron (2001) tests. We use Rudebusch's (1993) approach to construct the small sample distributions of the Ng and Perron tests, and calculate their asymptotic sizes, size‐adjusted powers and rejection rates. These numbers show that the lack of power in the Ng and Perron tests might account for the findings of Rapach and Weber (2004): that the unit root null cannot be rejected for most OECD countries. Size distortions are mild in the case of Ng and Perron tests for two series, but are serious for the Phillips and Perron Z‐test on inflation rates. We then apply a powerful covariate augmented Dickey–Fuller unit root test to examine the series for which stationarity cannot be determined with the Ng and Perron tests. The bootstrap technique is also used to control possible size distortions. In contrast to the results of Rapach and Weber (2004), the bootstrap covariate augmented Dickey–Fuller test yields striking evidence that real interest rates are stationary for 14 of 16 OECD countries, because nominal interest rates are stationary for the 14 countries, while inflation rates are stationary for all countries.