Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate

Abstract

Tests of the null hypothesis of stationarity against the unit root alternative play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asymptotic critical values for stationarity tests may cause extreme size distortions, if the model under the null hypothesis is highly persistent. This fact calls into question the use of these tests in empirical work. We illustrate the practical importance of this point for tests of long-run purchasing power parity under the recent float. We show that the common practice of viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions and in spurious rejections of long-run PPP. While the size distortions may be overcome by the use of finite-sample critical values, the resulting tests tend to have low power under economically plausible assumptions about the half-life of deviations from PPP. Thus, the fact that stationarity is not rejected cannot be interpreted as convincing evidence in favor of mean reversion. Only in the rare case that stationarity is rejected do size-corrected tests shed light on the question of long-run PPP.

Aluminum Consumption and Economic Growth: Evidence from Rich Countries

“…These show LALC it $ I(1) while LGDP it is integrated of an order higher than one. Following Caner and Kilian (2001), unit root tests for the H 0 of stationarity tend to have serious size distortions when the H 0 is close to the alternative of a unit root. Moreover, Choi (2001) argues about the loss of power of the LLC and IPS tests when a linear trend is included and proposes some alternative tests.…”

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

“…Italy, the nonstationary covariates are the growth rate of home country income, and the 7 The Bartlett kernel and lag truncation of 12 are used to allow comparison with Caner and Kilian (2001). Lag truncation of T is used to maintain consistency with Jansson (2002).…”

“…Univariate stationarity tests are demonstrated to have large size distortions in highly persistent stationary processes as documented by Caner and Kilian (2001). Since most processes in empirical macroeconomics tend to be highly persistent, very little is learned from the test except in the case of a rejection of stationarity.…”

Panel data tests of PPP: a critical overview

“…Provided that this assumption holds, one can use the central limit theorem and derive the asymptotic distribution for 28 Different methods have been suggested to deal with this problem. For example, Carner and Kilian (1999) report extreme size distortions for the Leybourne and McCabe (1994) test and the KPSS test. They consider a highly persistent model under the null of stationarity, and a unit root process under the alternative.…”