Dynamic Quantile Models of Rational Behavior∗

This paper develops a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of the future τ-quantile utilities, for τ ∈ (0, 1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, such as robustness and ability to capture heterogeneity. We provide an axiomatization of the recursive quantile preferences to motivate its use. Although quantiles do not have some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, establish its concavity and differentiability and show that the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well-known quantile regression methods for estimating and testing the economic model. In this way, the parameters of the model can be interpreted as structural objects. Therefore, the proposed methods provide microeconomic foundations for quantile regression models. To illustrate the developments, we construct an asset-pricing model and estimate the discount factor and elasticity of intertemporal substitution parameters across the quantiles. The results provide evidence of heterogeneity in these parameters.