The consensus among central bankers is that higher inflation expectations can drive up inflation today, requiring tighter policy. We assess this by devising a novel method for identifying shocks to inflation expectations, estimating a semi-structural VAR where an expectation shock is identified as that which causes measured expectations to diverge from rationality. Using data for the United States, we find that a positive inflation expectations shock is deflationary and contractionary: inflation, output, and interest rates all fall. These results are inconsistent with the standard New Keynesian model, which predicts inflation and interest rate hikes. We discuss possible resolutions to this new puzzle.