The standard new Keynesian model predicts that economies behave differently at the zero lower bound: completely wasteful government spending or forward guidance is very stimulative, and capital destruction or oil supply shocks are expansionary. I provide empirical evidence on this prediction and find it wanting: The Great East Japan Earthquake and oil supply shocks are contractionary at the zero lower bound. Modifications of the model that are consistent with this evidence also overturn other unusual policy predictions, such as large fiscal multipliers. My results suggest that many of the usual rules of economics continue to hold at zero nominal interest rates.