  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.
