A note on Michelacci and Zaffaroni, long memory, and time series of economic growth

In a recent paper in The Journal of Monetary Economics, Michelacci and Zaffaroni (2000) estimate long memory parameters for GDP per capita of 16 OECD countries. In this note we argue that these estimations are questionable for the purposes of clarifying the time series properties of these data (presence of unit roots, mean reversion, long memory) because the authors a) filter out a deterministic linear-in-logs trend instead of first-differencing in logs, and manipulate the data in other highly questionable ways, b) rely on the semiparametric Geweke and Porter-Hudak (GPH) method as modified by Robinson, which is known to be highly biased in small samples. We re-examine these results using Beran’s nonparametric FGN estimator and Sowell’s exact maximum likelihood ARFIMA estimator. These methods avoid the small-sample bias and arbitrariness of the cut-off parameters of Robinson’s method and allow us to control for short memory effects, although the parametric ARFIMA estimator introduces specification problems of its own. We also look at the influence of the choice of sub-periods on the results. Finally, we apply Robinson’s method to our treatment of the data and show that MZ’s results no longer hold, nor are their cut-off parameter and filtering insensitivity claims substantiated.