A New Way to Quantify the Effect of Uncertainty

Abstract

This paper develops a new way to quantify the effect of uncertainty and other higher-order moments. First, we estimate a nonlinear model using Bayesian methods with data on uncertainty, in addition to common macro time series. This key step disciplines the model and allows us to generate data-driven policy functions for any higher-order moment. Second, we use the Euler equation to analytically decompose consumption into several terms--expected consumption, the ex-ante real interest rate and the ex-ante variance and skewness of future consumption, technology growth, and inflation--and then use the policy functions to filter the data and generate a time series for the effect of each term. We apply our method to a familiar New Keynesian model with a zero lower bound constraint on the nominal interest rate and two stochastic volatility shocks, but it is adaptable to any dynamic model. Over a 1-quarter horizon, uncertainty has a very small effect on consumption, similar to the volatility shocks in our model. Over horizons that remove the influence of expected consumption, the effect of uncertainty is an order of magnitude larger. Other higher-order moments have much smaller effects.