Testing for stationarity using covariates: an application to purchasing power parity

Abstract

We examine the evidence for Purchasing Power Parity (PPP) using post-Bretton Woods exchange rate data for 20 industrialized countries. The two tests used are the covariate tests for stationarity where the null hypothesis of stationarity is tested against the unit root alternative. These tests are generalizations of existing univariate stationarity tests and improve the power of univariate tests by utilizing the information contained in related stationary covariates. We conclude that PPP holds for 17 out of the 20 countries tested.

Acknowledgement

I thank Michael Jansson for the MATLAB program that implements the tests described in this study.

Notes

¹The most restrictive form of PPP, absolute PPP, states that international arbitrage will cause the relative prices of a common basket of goods to be equalized when expressed in the same currency. The relative form of PPP, which is what we measure, emphasizes that the exchange rate will adjust to reflect the movement in the price levels between countries.

²Multivariate tests, such as the panel unit root tests, increase the power of unit root tests without having to mix exchange rate regimes by exploiting cross section and time series variation of the data. However, the issue with panel unit root tests is that the rejection of the unit root null does not indicate which individual exchange rates are mean reverting.

³Even though the tests allow for a null hypothesis of trend or level stationarity, we apply the null of level stationarity to exchange rate data. This is consistent with the implication that relative PPP is the reversion of the exchange rate to a constant mean.

⁴For the univariate tests, the Bartlett kernel and lag truncation are used to allow comparison with Caner and Kilian (2001). The quadratic spectral kernel, with Andrews (1991) bandwidth selector, and pre-whitening are used for Jansson's stationarity tests.