Testing for a Deterministic Trend when there is Evidence of Unit-Root

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This paper proposes a formal statistical procedure to distinguish between the null hypothesis of unit root and that of unit root with drift. Our procedure is asymptotically robust with regard to autocorrelation and takes into account a potential single structural break. Empirical results show that most of the macroeconomic time series originally analysed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend.