What to Expect from the Lower Bound on Interest Rates: Evidence from Derivatives Prices

This paper analyzes the effects of the lower bound for interest rates on the distributions of expectations for future inflation and interest rates. We study a stylized New Keynesian model where the policy instrument is subject to a lower bound to motivate the empirical analysis. Two equilibria emerge: In the ``target equilibrium,'' policy is unconstrained most or all of the time, whereas in the ``liquidity trap equilibrium,'' policy is mostly or always constrained. We use options data on future interest rates and inflation to study whether the decrease in the natural rate of interest leads to forecast densities consistent with the theoretical model. We develop a lower bound indicator that captures the effects of the lower bound on the distribution of interest rates. Qualitatively, we find that evidence is largely consistent with the theoretical predictions in the target equilibrium and find no evidence in favor of the liquidity trap equilibrium. Quantitatively, while the lower bound has a sizable effect on the distribution of future interest rates, its impact on forecast densities for inflation is relatively modest.