Unit Root Tests with Smooth Breaks: An Application to the Nelson-Plosser Data Set

Abstract

This paper reconsiders the nature of the trends (i.e. deterministic or stochastic) in the Nelson and Plosser (1982) series, both for the original and for an extended data set. For this purpose, I employ two tests that have been recently introduced by Enders and Lee (2006) and Becker et. al. (2006), respectively. These new tests display robustness to structural breaks of unknown forms, irrespective of the date and/or location of the breaks. Both Enders and Lee (2006) and Becker et al. (2006) approximate structural changes via Flexible Fourier transforms. Applied to the original dataset, these tests confirm the hypothesis of deterministic trends in the unemployment rate and the monetary aggregates. Moreover, both tests confirm the presence of stochastic trends in nominal GNP, the GNP deflator, consumer prices, wages, velocity, bond yields, and stock prices. However, real GNP, real per capita GNP, industrial production, employment, and real wages display mixed evidence of both a stochastic and a deterministic trend, although results are more conclusive for the extended data set. For the latter, the tests deliver strong evidence in favor of a nonlinear deterministic trend for real GNP, real per capita GNP, employment, the unemployment rate, and stock prices. Further, the two tests confirm the existence of stochastic trends in nominal GNP, consumer prices, real wages, monetary aggregates, velocity, and bond yields. Additionally, this conclusion appears to be verified for the GNP deflator and nominal wages. Industrial production is the only inconclusive result. In general, it appears that real variables are stationary while nominal ones have a unit root.