Further Evidence on the Uncertain (Fractional) Unit Root in Real GNP


In an interesting paper Diebold and Senhadji (1996) showed that U.S. GNP data was not as uniformative as many believed as to whether trend was better described as deterministic (trend-stationarity) or stochastic (unit root). By using long data spans and new econometric techniques, they showed that the unit root hypothesis could be rejected with high power. Using the same data set we first show that, if the hypotheses are reversed, also the trend stationary model can be easily rejected. This suggests that neither model provides a good characterization of this data. Long memory (ARFIMA) as well as non-linear models are considered as alternatives. Economic as well as statistical justification for the presence of these features in the data is provided. It turns out that the latter models and in general preferred to the former. Finally, a new technique is also applied to discriminate between these the long memory and the structural break models. It is shown that for both real GNP and real GNP per capita the preferred model turns out to be a fractionally integrated model with a memory parameter, d; around 0.7. This implies that these series are non-stationary, highly persistent but with no permanent shocks. Some macroeconomic implications of these findings are also discussed.

Published as: Further Evidence on the Statistical Properties of Real Gnp in Oxford Bulletin of Economics and Statistics , Vol. 68, No. Suppl.1, 901--920, January, 2006