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Econometrica Vol. 88 No. 2 2020

Time Lotteries and Stochastic Impatience

Patrick DeJarnette1; David Dillenberger2; Daniel Gottlieb3; Pietro Ortoleva4

1 Faculty of Political Science and Economics, Waseda University · 2 Department of Economics, University of Pennsylvania · 3 Department of Management, London School of Economics and Political Science · 4 Department of Economics, Woodrow Wilson School, Princeton University

Abstract

We study preferences over lotteries in which both the prize and the payment date are uncertain. In particular, a time lottery is one in which the prize is fixed but the date is random. With Expected Discounted Utility, individuals must be risk seeking over time lotteries (RSTL). In an incentivized experiment, however, we find that almost all subjects violate this property. Our main contributions are theoretical. We first show that within a very broad class of models, which includes many forms of nonexpected utility and time discounting, it is impossible to accommodate even a single violation of RSTL without also violating a property we termed Stochastic Impatience, a risky counterpart of standard Impatience. We then present two positive results. If one wishes to maintain Stochastic Impatience, violations of RSTL can be accommodated by keeping Independence within periods while relaxing it across periods. If, instead, one is willing to forego Stochastic Impatience, violations of RSTL can be accommodated with a simple generalization of Expected Discounted Utility, obtained by imposing only the behavioral postulates of Discounted Utility and Expected Utility.

DOI
10.3982/ecta16427
Volume
88
Issue
2
Pages
619-656
Language
en
Sources
bibtex:phds-export.bib openalex crossref

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