A DSGE model of downside risk

This paper presents a new dynamic stochastic general equilibrium (DSGE)framework based on recursive quantile preferences (quantile certainty equivalent),in which household downside risk attitudes are a model primitive. In this economy,infinitely lived households maximize the discounted value of the stream offuture τ-quantile utilities for τ ∈ (0, 1) with standard consumption and disutility oflabor. The quantile parameter τ captures the households’ downside risk attitude,independent of the elasticity of intertemporal substitution. Representative firmsare price takers, and prices are determined endogenously. We establish centralproperties of the model, including: (i) existence and uniqueness of a fixed pointfor household value functions, (ii) envelope condition, and the quantile Euler equation.We define the quantile recursive competitive equilibrium and establish itsexistence and uniqueness. We also provide an algorithm and numerically computethe quantile DSGE procedure. Lastly, we employ nonlinear impulse responsefunctions and present empirical results for the varying one-time technology shockimpulse response functions for augmented MaCurdy and KPR utility functions.We find significant heterogeneity in downside risk attitudes with the potentialfor countercyclical labor responses for a shallow shock in an otherwise frictionlessenvironment. Rates of dissipation of the shock also vary with the configuration.