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How much ability does the Fed have to stimulate the economy by cutting interest rates? We argue that the presence of substantial debt in fixed-rate, prepayable mortgages means that the ability to stimulate the economy by cutting interest rates depends not just on their current level but also on their previous path. Using a household model of mortgage prepayment matched to detailed loan-level evidence on the relationship between prepayment and rate incentives, we argue that recent interest rate paths will generate substantial headwinds for future monetary stimuli.