When implemented using forecasts, inflation is the 4-quarter inflation rate 3 quarters ahead, and Δu is the 4quarter change in the unemployment rate 3 quarters ahead. See Athanasios Orphanides (2003), “Historical Monetary Policy Analysis and the Taylor Rule,” Journal of Monetary Economics, vol. 50 (July), pp. 9831022.
27 While the natural rate of interest may be changing over time and the first-difference rule does not take these changes into account, Orphanides and Williams (2007) argue that rules like the first-difference rule can deliver good economic performance even when there is uncertainty about those changes.