We examine the differential impact of monetary policy and macroprudential policy on bank lending rates in the euro area, using granular corporate loan-level data for the period 2019-2023. We find three results: First, consistent with the predictions of a stylized theoretical model of bank lending rates, monetary policy exerts an order of magnitude larger impact on lending rates than macroprudential policy. Second, the effectiveness of monetary policy transmission weakens when interest rates are close to or below zero. Third, the impact of macroprudential policy on lending rates increases when banks have limited capital headroom above capital buffer requirements, indicating cautious lending behavior when banks get close to regulatory constraints. Our findings have important policy implications for the joint conduct of monetary and macroprudential policy.