Decomposing risk in dynamic stochastic general equilibrium

We analyze the theoretical moments of a nonlinear approximation to a model of business cycles and asset pricing with stochastic volatility and recursive preferences. We find that heteroskedastic 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. Our method decomposes moments into contributions from realized shocks and differing orders of approximation and from shifts in the distribution of future shocks, enabling us to identify the common channel through which stochastic volatility in isolation operates and through which conditional asset pricing measures vary.