OPERATIONS RESEARCH Vol. 63, No. 6, November–December 2015, pp. 1420–1430 ISSN 0030-364X (print)  ISSN 1526-5463 (online) http://dx.doi.org/10.1287/opre.2015.1433 © 2015 INFORMS Discounted Utility and Present Value—A Close Relation Han Bleichrodt Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, 3000 DR, the Netherlands, bleichrodt@ese.eur.nl Umut Keskin Department of Economics, Istanbul Bilgi University, 34060 Eyup Istanbul, Turkey, umut.keskin@bilgi.edu.tr Kirsten I. M. Rohde, Vitalie Spinu, Peter Wakker Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, 3000 DR, the Netherlands {rohde@ese.eur.nl, spinuvit@gmail.com, wakker@ese.eur.nl} We introduce a new type of preference condition for intertemporal choice, which requires present values to be independent of various other variables. The new conditions are more concise and more transparent than traditional ones. They are directly related to applications because present values are widely used tools in intertemporal choice. Our conditions give more general behavioral axiomatizations, which facilitate normative debates and empirical tests of time inconsistencies and related phenomena. Like other preference conditions, our conditions can be tested qualitatively. Unlike other preference conditions, our conditions can also be directly tested quantitatively, and we can verify the required independence of present values from predictors in regressions. We show how similar types of preference conditions, imposing independence conditions between directly observable quantities, can be developed for decision contexts other than intertemporal choice and can simplify behavioral axiomatizations there. Our preference conditions are especially efficient if several types of aggregation are relevant because we can handle them in one stroke. We thus give an efficient axiomatization of a market pricing system that is (i) arbitrage-free for hedging uncertainties and (ii) time consistent. Keywords : intertemporal optimization; present value; discounted utility; time inconsistency; arbitrage-free; preference axiomatization; decision analysis: sequential; utility: multi-attribute; mathematics: functions. Subject classifications : decision analysis: sequential; utility/preference: multiattribute; mathematics: functions. Area of review : Decision Analysis. History : Received February 2015; revision received June 2015; accepted August 2015. Published online in Articles in Advance November 5, 2015. 1. Introduction Debates about appropriate models of intertemporal choice, both for the normative purpose of making optimal decisions and for the descriptive purpose of fitting decisions, usually focus on the critical preference conditions that distinguish these models. The two most discussed conditions are time consistency, which plays a role in distinguishing constant and hyperbolic discounting, and intertemporal separability, which pertains to habit formation, satiation, addiction, and sequencing effects. 1 Both time consistency and intertempo- ral separability are assumed in the classical models but they are usually violated empirically. Their normative status has also been questioned. 2 To shed new light on the appropriateness of intertem- poral decision models, we introduce a new kind of prefer- ence conditions to distinguish them, stated directly in terms of present values (PVs). PVs are simple and tractable and have been widely used in intertemporal choice, both when reflecting the preferences of the financial market 3 and when reflecting subjective preferences of individuals. 4 They relate to the indifferences most commonly encountered in every- day life. We often have to decide on whether to pay up front for goods consumed later, whether to pay a price now for a financial product with future financial consequences, or whether to choose a savings plan that requires the money to be delivered now. For these reasons, present values are widely used in experimental measurements of intertemporal preferences. People can more easily relate to independence conditions imposed on present values than to independence preference conditions. “For your present value of this extra payment on day 10, the payments on the other days do (not) matter” is easier to relate to for most people than the usual pref- erence conditions (see Equation (16) in §7, for instance). In general, PVs can depend on many variables, such as the periods of the receipt of future outcomes, the initial wealth levels at those periods, and the wealth levels at other periods. Our preference conditions will impose indepen- dence of PVs from some of those other variables. We show that many models can be characterized by the appropriate independencies. Like all preference conditions, our conditions can be tested qualitatively. Unlike other preference conditions, our conditions can also be directly tested quantitatively. 1420 Downloaded from informs.org by [130.115.158.153] on 05 February 2016, at 10:23 . For personal use only, all rights reserved.