Time Lotteries and Stochastic Impatience

39 Pages Posted: 20 Sep 2018

See all articles by Patrick DeJarnette

Patrick DeJarnette

University of Pennsylvania - The Wharton School

David Dillenberger

University of Pennsylvania - Department of Economics

Daniel Gottlieb

Washington University in St. Louis

Pietro Ortoleva

Princeton University - Department of Economics

Date Written: June 13, 2018

Abstract

We study preferences over lotteries that pay a xed prize at an uncertain future date: what we call time lotteries. The standard model of risk and time preferences, Expected Discounted Utility, implies that individuals must be risk seeking towards such lotteries (RSTL). In contrast, we show experimentally that almost all subjects violate this property. Our main contributions are theoretical. First, we show that risk aversion over time lotteries can be captured by a generalization of Expected Discounted Utility that is obtained by keeping the behavioral postulates of Discounted Utility and Expected Utility. Second, we introduce a new property termed Stochastic Impatience, a risky counterpart of standard Impatience, and show that not only the model above, but also substantial generalizations that allow for non-Expected Utility and non-exponential discounting, cannot jointly accommodate it and even a single instance of risk aversion over time lotteries (or, equivalently, any violation of RSTL), showing a fundamental tension between the two.

Keywords: Expected Discounted Utility, Separation of Risk and Time preferences, Time Lotteries, Stochastic Impatience

JEL Classification: C91, D81, D90

Suggested Citation

DeJarnette, Patrick and Dillenberger, David and Gottlieb, Daniel and Ortoleva, Pietro, Time Lotteries and Stochastic Impatience (June 13, 2018). PIER Working Paper No. 18-021, Available at SSRN: https://ssrn.com/abstract=3252514 or http://dx.doi.org/10.2139/ssrn.3252514

Patrick DeJarnette

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

David Dillenberger (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-1503 (Phone)

Daniel Gottlieb

Washington University in St. Louis ( email )

One Brookings Drive
Campus Box 1208
St. Louis, MO MO 63130
United States

Pietro Ortoleva

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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