A DSGE model of downside risk

Abstract

This paper develops a DSGE model with recursive quantile preferences and rare disaster risk. In this economy, infinitely lived households maximize the discounted value of the stream of future τ-quantile utilities for τ ∈ (0, 1). The quantile parameter τ captures the households’ downside risk attitude, independent of the elasticity of intertemporal substitution. We establish central properties of the model, including: (i) existence and uniqueness of a fixed point for household value functions, (ii) envelope condition, and the quantile Euler equation. We define the quantile recursive competitive equilibrium and establish its existence and uniqueness. Quantitatively, following a one-standard-deviation positive technology shock, output, consumption, and investment increase on impact and gradually return to baseline. In contrast, labor adjusts differently under recursive quantile preferences: initial labor hours decline, indicating that a preference-based tilt toward downside outcomes alters intratemporal tradeoffs even in an otherwise frictionless setting. Similar qualitative responses arise following rare-disaster shocks.