Job Market Paper

"Nonparametric Analysis of Time-Inconsistent Preferences"

Abstract

What are the necessary and sufficient nonparametric/revealed preference empirical conditions for quasi-hyperbolically discounted consumption behaviour? This paper explores this question for standard consumption data in the elementary, choice-revealed preference tradition of Samuelson (1948), Houthakker (1950) and Afriat (1967). We describe conditions for the leading forms of the model: the sophisticated agent who recognises his future behaviour will be at odds with his current wishes, and the naive agent who does not. We find, perhaps surprisingly, that, without further restrictions, the conditions for the data satisfying quasi-hyperbolic discounting (sophisticated or naive) are simply that they satisfy the generalised axiom of revealed preference (GARP). We explore what extra assumptions we can make in order to get additional restrictions beyond GARP.
We discuss how to implement tests of these restrictions and also how to make sensible empirical comparisons with alternative models including the standard exponential discounting model. The hyperbolic model or GARP necessarily fit the data at least as well as the exponential model because they are less restrictive, and so claiming a better fit is not a rational way to compare models. We consider this problem in some detail and suggest a different way of comparing models using their empirical informational content. We provide an empirical application investigating how the quasi-hyperbolic discounting model performs compared to the exponential model using a large, consumption panel data set.