Intertemporal choice and the magnitude effect

A robust …nding in experiments on time preference is the magnitude effect: subjects tend to be more patient towards larger rewards. Using a calibration theorem, we argue against standard curvature-based explanations for the …nding. We axiomatize a model of preferences over dated rewards that generalizes the standard exponential discounting model by permitting the discount factor to depend on the reward being discounted. The model is shown to behaviorally subsume the hyperbolic discounting model as a special case. When embedded in a sequential bargaining game the model gives rise to multiple stationary subgame perfect equilibria. There may exist equilibria in which the …rst mover gets a smaller share despite also being the more patient player. Keywords: Discounting, magnitude e¤ect, hyperbolic discounting, preference reversals, calibration theorem, bargaining. JEL classi…cation number : D11 Dept of Economics, Boston University, 270 Bay State Road, Boston MA 02215. Email: [email protected]. Thanks are due to Larry Epstein, Bart Lipman, Michael Luca, Michael Manove, Massimo Marinacci, Yusufcan Masatlioglu and audiences at Oxford University, Queen Mary University of London, University College London, Brown University, Arizona State University, the Econometric Society Winter 2008 Meeting (New Orleans) and the Canadian Economic Theory Conference 2008, and to a referee. This paper was previously circulated under the titles ‘Non-Separable Exponential Discounting’and ‘Magnitude-Dependent Impatience’. The usual disclaimer applies.