In the textbook CGG model (1999), augmented with a hybrid Phillips curve that features an inertial backward-looking component, the equilibrium persistence of inflation is an endogenous function of the monetary policy rule such that the more aggressively the central bank leans against exogenous shocks that push inflation away from target, the less persistent are inflation deviations from target in equilibrium.
In the simple case in which equilibrium inflation is a first-order autoregressive process (as it is in the CGG (1999)  7  This view has also long been shared by fellow monetary policymakers. See, for example, Bernanke (2007b) and Powell (2018).