Generalisations of Quasi-Hyperbolic Discounting

This paper proposes several time preference specifications that generalise quasi-hyperbolic discounting, while retaining its analytical tractability. We define their discount functions and provide a recursive formulation of the implied lifetime payoffs. A calibration exercise demonstrates that these specifications deliver better approximations to true hyperbolic discounting. We characterise the Markov-perfect equilibrium of a general intra-personal game of agents with various time preferences. When applied to specific economic examples, our proposals yield policies that are close to those of true hyperbolic discounters. Furthermore, these approximations can be used in settings where an exact solution for hyperbolic agents is not available. Finally, we suggest further generalisations which would provide an even better fit.