Discounted Utility and Present Value—A Close Relation

Abstract

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.

Does Willingness to Pay for Rate Conditions Depend on the Booking Window? A Novel Time-Dependent Conjoint Analysis Approach

“…The idea of a preference, impatience, or impulsivity for advancing the timing of future satisfaction has been central to research on intertemporal choice. Building on the classical exponential discounted utility (EDU) model, a plethora of different models of intertemporal choice have been developed over the years (Dhami, 2016), each challenging the critical preference conditions of the EDU model, most notably time consistency and intertemporal separability (Bleichrodt, Keskin, Rohde, Spinu, & Wakker, 2015). First, the rejection of constant (exponential) discounting, although some empirical studies found support for consistent impatience over time (e.g., Benhabib, Bisin, & Schotter, 2010;Harrison, Lau, & Williams, 2002), has led to the development and testing of hyperbolic (Loewenstein & Prelec, 1992), quasi-hyberbolic (Laibson, 1997), and subadditive (Read, 2001;Read & Roelofsma, 2003) models.…”

“…These inconsistencies do not only result from procedural differences (e.g., elicitation tasks, time frames), showing why consumer can exhibit decreasing (or even increasing) impatience, but also from various framing effects such as whether the decision concerns a gain or a loss (i.e., sign effect), or a large or a small amount (i.e., magnitude effect). Second, intertemporal separability, which embodies the assumption that consumer preferences in any period are independent of consumption in any other period, is frequently relaxed empirically as it ignores effects such as habit formation, satiation, addiction, and sequencing (Bleichrodt et al, 2015).…”