Following the crisis of 2008, several central banks engaged in a new experiment by setting negative policy rates. Using aggregate and bank level data, we document that deposit rates stopped responding to policy rates once they went negative and that bank lending rates in some cases increased rather than decreased in response to policy rate cuts. Based on the empirical evidence, we construct a macro-model with a banking sector that links together policy rates, deposit rates and lending rates. Once the policy rate turns negative, the usual transmission mechanism of monetary policy through the bank sector breaks down. Moreover, because a negative policy rate reduces bank profits, the total effect on aggregate output can be contractionary. A calibration which matches Swedish bank level data suggests that a policy rate of-0.50 percent increases borrowing rates by 15 basis points and reduces output by 7 basis points. * This working paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank. This paper replaces an earlier draft titled Are Negative Nominal Interest Rates Expansionary? We are grateful to compricer.se and Christina Soderberg for providing bank level interest rate data. We are also grateful to seminar and conference participants at Bundesbanken, Brown University, CEF 2018, the European Central Bank,