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We show that firms' market power dampens the response of their output to monetary policy shocks, using firm‐level data for the USA and a large cross‐country firm‐level dataset for 14 advanced economies. We also find some evidence that the role of markups in monetary policy transmission, while independent from other channels, is greater for firms whose characteristics—notably size and age—are likely to be associated with greater financial constraints. [ABSTRACT FROM AUTHOR]