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How important is the risk‐taking channel for monetary policy? To answer this question, we develop and estimate a quantitative monetary DSGE model where banks choose excessively risky investments, due to an agency problem that distorts banks' incentives. As the real interest rate declines, these distortions become more important and excessive risk taking increases, lowering the efficiency of investment. We show theoretically that this novel transmission channel generates a new monetary policy trade‐off between inflation and real interest rate stabilization, whereby the central bank may prefer to tolerate greater inflation volatility in order to lower excessive risk taking.