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After the Great Recession several central banks started setting negative nominal interest rates in an expansionary attempt, but the effectiveness of this measure remains unclear. Negative rates can stimulate the economy by lowering the rates that commercial banks charge on loans, but they can also erode bank profitability by squeezing deposit spreads. This paper studies the effects of negative rates in a new DSGE model where banks intermediate the transmission of monetary policy. I use bank-level data to calibrate the model and find that monetary policy in negative territory is between 60 and 90 percent as effective as in positive territory.