More Uncertainty About the Unit Root in U.S. Real Gnp

Abstract

Since the seminal work by Nelson and Plosser (1982), ubiquitous evidence in favor of the integration hypothesis across a wide range of macroeconomic and financial time series has been reported in the literature. These results have recently come under attack, however, along several fronts. For example, some researchers have challenged the widespread acceptance of the difference stationary (DS) model on the basis of the low power of the unit root tests against stationary alternatives. The low power of the Dickey-Fuller tests was extensively documented, for example, by DeJong, et al. (1992). Rudebusch (1993) went further and showed that there is low power against trend stationary (TS) alternatives which are not "local in economic terms" to the DS null, for TS and DS models estimated for U.S. real GNP. The results of his Monte Carlo simulations led him to conclude that the existence of a unit root for U.S. real GNP is uncertain.

Several refinements of the Dickey-Fuller test have appeared in the literature. In Dickey-Fuller type tests, a unit root is set up as the null hypothesis to be tested. A reverse approach is taken by Kwiatkowski, Phillips, Schmidt and Shin (KPSS) (1992). That is, KPSS base their test on a TS null hypothesis. Choosing a components representation in which the time series under consideration is written as the sum of a deterministic trend, a random walk and a stationary error, the TS null corresponds to the hypothesis that the variance of the random walk equals zero.

KPSS argue that in trying to distinguish between stochastic and deterministic trends by classical hypothesis testing, it is useful to test both the TS and DS null hypotheses. This is especially important in light of the low power of Dickey-Fuller type tests against stationary alternatives.

The purpose of this paper is to directly test the TS null hypothesis for post-war U.S. real GNP via the KPSS test. The possible distinction between the DS and TS nulls for this time series is important, since the estimated DS and TS models display notably different macroeconomic behavior over business cycle frequencies, i.e., neither model is an economically local alternative of the other. Accordingly, this paper is very similar to Rudebusch (1993), except that it focuses on the KPSS test instead of the Dickey-Fuller test. The paper's analysis complements that in Rudebusch (1993) by testing the TS null hypothesis for quarterly U.S. post-war real GNP instead of the DS null hypothesis.

When appropriately sized, the KPSS test fails to reject the trend stationary null. This provides an important counter-example to the generic inability to reject the difference stationary null hypothesis for output by classical hypothesis testing. The evidence in favor of the trend stationary representation is weakened, however, by showing that such size correction dramatically reduces power.

Note: This is a description of the paper and not the actual abstract.

JEL Classification: C22, E30