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This study explores the mechanism behind the persistent effects of monetary policy shocks, resolving a discrepancy between an assumption in typical macroeconomic models and micro evidence. While standard macro models often rely on a large demand kink (a micro real rigidity) to generate persistent real effects of monetary policy shocks, micro-empirical studies find this kink to be modest. I show that this discrepancy can be resolved by focusing on a previously underexplored interaction: the effects of this modest, empirically consistent micro real rigidity are amplified when combined with the macro real rigidities inherent in production linkages. A stylized production-chain model first clarifies the mechanism, showing how upstream micro rigidities are transformed into downstream macro rigidities. A large-scale production-network model, disciplined by empirical data, then demonstrates that this combined mechanism is quantitatively important for macroeconomic persistence.