The introduction of a firm or product life cycle into New Keynesian frameworks fundamentally alters the design of optimal monetary policy. Economic welfare and the Phillips curve then depend on the gap between inflation and a time-varying inflation target that arises endogenously from turnover. The inflation target is positive on average and shifts in response to productivity disturbances. As a result, steady-state price stability is no longer desirable and the dynamics make it optimal for monetary policy to “look through” certain productivity disturbances. The latter requires keeping nominal rates unchanged even though both output and inflation move. This complicates the empirical distinction between supply, demand, and policy shocks. Our results highlight that accounting for supply side turnover delivers a rich set of policy-relevant results for inflation targeting and shock identification.