Orphanides and Williams (2005) make a case for monetary policy that responds less to imprecise movements in unemployment gaps and more to actual inflation in an estimated model with agents who learn over time.
Finally, even if, counterfactually, gap variables were observed without error, the reduced-form theoretical relationship between slack and price inflation will in general depend on the cyclical properties of markups and labor’s share, as is shown, for example, in the DSGE (dynamic stochastic general equilibrium) model of Ireland (2004).