We study monetary policy where the price and wage Phillips curves exhibit true curvature. To this end, we propose a New Keynesian (NK) model featuring endogenous adjustment of price and wage setting frequencies, moving beyond the quasi-linear structure of the standard nonlinear NK Phillips curves (NKPC). Using euro area data spanning 1999Q1 to 2024Q4, we estimate and simulate the non-linear model. We then study the recent inflation surge and the implications of state-dependent prices and wages

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