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This paper investigates the macroeconomic risks associated with undesirably low inflation using a medium-sized New Keynesian model. We consider different causes of persistently low inflation, including a downward shift in long-run inflation expectations, a fall in nominal wage growth, and a favorable supply-side shock. We show that the macroeconomic effects of persistently low inflation depend crucially on its underlying cause, as well as on the extent to which monetary policy is constrained by the zero lower bound. Finally, we discuss policy options to mitigate these effects.