Decomposing Risk in Dynamic Stochastic General Equilibrium

We analyze the theoretical moments of a nonlinear approximation to real business cycle model with stochastic volatility and recursive preferences. We nd that the conditional heteroskedasticity of stochastic volatility operationalizes a time-varying risk adjustment channel that induces variability in conditional asset pricing measures and assigns a substantial portion of the variance of macroeconomic variables to variations in precautionary behavior, both while leaving its ability to match key macroeconomic and asset pricing facts untouched. We calculate the theoretical moments directly and decomposes these moments into contributions from shifts in the distribution of future shocks (i.e., risk) and from realized shocks and differing orders of approximation, enabling us to identify the common channel through which stochastic volatility in isolation operates and through which conditional asset pricing measures vary over time. Under frictional investment and varying capital utilization, output drops in response to an increase in risk, but the contributions to the variance of macroeconomic variables from risk becomes negligible.