In standard macroeconomic models, the two objectives in the Federal Reserve’s dual mandate—full employment and price stability—are closely intertwined. We motivate and estimate an alternative model in which long-term unemployment varies endogenously over the business cycle but does not affect price inflation. In this new model, an increase in long-term unemployment as a share of total unemployment creates short-term tradeoffs for optimal monetary policy and a wedge in the dual mandate. In particular, faced with high long-term unemployment following the Great Recession, optimal monetary policy would allow inflation to overshoot its target more than in standard models.