Computing Time-Consistent Markov Policies for Quasi-Hyperbolic Consumers Under Uncertainty

Abstract:     
We study the question of existence and computation of time-consistent Markov policies of quasi-hyperbolic consumers under a stochastic transition technology and borrowing constraints. Under standard assumptions on preferences, as well as a mild geometric condition on a transition probabilities, we prove existence of the greatest and the least time-consistent policies, and provide conditions for (Lipschitz) continuous and monotone equilibria. We show how our methods extend the results of Harris and Laibson (2001). We present a simple approximation scheme for extremal equilibrium, and provide some monotone equilibrium comparative statics results in the model's deep parameters.

Number of Pages in PDF File: 32

Keywords: time consistency, Markov equilibria, stochastic games, constructive methods

JEL Classification: C62, C73

working papers series