Robust Comparative Statics for the Elasticity of Intertemporal Substitution

TL;DR

This paper develops a general framework to determine how consumption responds to shocks in models with recursive preferences, linking the response to the elasticity of intertemporal substitution and the marginal value of wealth.

Contribution

It characterizes the sign of consumption responses in recursive preference models using two key statistics, providing new insights for empirical identification and classical economic problems.

Findings

Sign of consumption response depends on EIS and REMV

Under homotheticity, REMV equals one, simplifying analysis

Provides empirical strategies for estimating EIS and its relation to unity

Abstract

We study a general class of consumption-savings problems with recursive preferences. We characterize the sign of the consumption response to arbitrary shocks in terms of the product of two sufficient statistics: the elasticity of intertemporal substitution between contemporaneous consumption and continuation utility (EIS), and the relative elasticity of the marginal value of wealth (REMV). Under homotheticity, the REMV always equals one, so the propensity of the agent to save or dis-save is always signed by the relationship of the EIS with unity. We apply our results to derive comparative statics in classical problems of portfolio allocation, consumption-savings with income risk, and entrepreneurial investment. Our results suggest empirical identification strategies for both the value of the EIS and its relationship with unity.