State-dependent pricing, de-anchored expectations, and the cost of looking through inflation shocks

We extend an estimated euro-area Smets-Wouters (2007) model with endogenous price-adjustment hazards and a credibility-weighted expectations channel and study the interaction between state-dependent pricing (SDP) and inflation-expectation de-anchoring as complementary sources of second-round inflation dynamics. We establish four results. First, the two channels are super-additive: the long-run price-level cost of a large cost-push shock exceeds the sum of individual effects when both channels are active. Second, de-anchoring is material only when routed through the forward expectation term, not through backward indexation. Third, a formal Kalman-filter state-space estimation using ECB Survey of Professional Forecasters (SPF) and Consumer Expectations Survey (CES) data finds that professional forecasters remained fully anchored while households de-anchored significantly once inflation crossed approximately 5% during 2021-2024 inflation surge, consistently with rational inattention. Fourth, looking through a large cost-push shock is costly because the supply-side and expectations-side risks compound.