Dynamic Economics with Quantile Preferences

This paper studies the dynamic quantile model for intertemporal decisions under uncertainty, in which the decision maker maximizes the τ-quantile, for τ ∈ (0, 1) of the stream of future utilities. We present two sets of contributions. First, we generalize existing results in directions that are important for applications. Second, we illustrate the simplicity and usefulness of this approach by applying it to five standard models in macroeconomics, development, finance and labor. In the first model, we construct an intertemporal consumption model with one asset and derive its properties. We obtain closed-form expressions for the value function, the optimal asset allocation and consumption, as well as for the consumption path. Second, we revisit the one-sector growth model. We compare and contrast the results with the corresponding expected utility case. We also investigate two models of investment under uncertainty, one with convex costs and another with demand uncertainty. We derive the corresponding quantile Euler equations and show that the purchase price of capital is the τ-quantile of the discounted present value of marginal profits. Finally, we discuss a quantile-based version of the job-search model. As mentioned, the paper generalizes the settings where one can use the dynamic quantile model. First, the future state is not determined exclusively by agent’s choice, but can be determined by the choice and shocks. Second, we allow choice variables and shocks to be either discrete or continuous. Under these generalizations, we show that the intertemporal quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, this value function is concave and differentiable, and the principle of optimality holds. Additionally, we derive the corresponding Euler equation. These extensions broaden substantially the scope of applications for dynamic quantile models