The correlation between uncertainty shocks, as measured by changes in the VIX, and changes in breakeven inflation rates declined and turned negative after the Great Recession. This estimated time varying correlation is shown to be consistent with the predictions of a standard New Keynesian model with a lower bound on interest rates and a trend decline in the natural rate of interest. In one equilibrium of the model, higher uncertainty raises the probability of large shocks that leave the central bank constrained by the lower bound and unable to offset negative shocks. Resulting inflation shortfalls lower average inflation rates.