Do You Save More or Less in Response to Bad News? A New Identification of the Elasticity of Intertemporal Substitution

We define the elasticity of intertemporal substitution (EIS) for general recursive preferences and identify a sharp comparative static from a general dynamic portfolio choice problem. In the homothetic case, if the EIS is smaller (larger) than 1, an investor will increase (decrease) current consumption in response to bad news about the future. Examples of bad news include if (i) she becomes more risk averse, (ii) investment opportunities shrink, (iii) investment returns become riskier, or (iv) she becomes more uncertain about the distribution of returns. Bad news effectively raises the price of future continuation utility, which produces the same qualitative changes in savings rates as lowering the interest rate.