Time Discounting and Time Consistency

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is exponential discounting. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that exponential time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as hyperbolic discounting. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs

Time discounting and time consistency

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is {\em exponential discounting}. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that exponential time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as {\em hyperbolic discounting}. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs

Hyperbolic discounting may be time consistent

Using dynamic programming methodology, the paper analyzes the most general conditions for an additive utility functional to represent time consistent preferences. It challenges the conventional wisdom of the domain, which, following Strotz(1956), assume that only exponential discounting is compatible with time consistent behavior. The paper gives some examples of special time consistent hyperbolic discount functions and also discuss the relation between time consistency and stationarity.intertemporal choice, consumption and saving, time consistency, time discounting, exponential discounting, hyperbolic discounting

Now or Never: Environmental Protection under Hyperbolic Discounting

In this paper, we extend the well known result that hyperbolically discounting agents tend to postpone costs into the future. In a simple model we show that, without commitment to the ex ante optimal plan, no investment in environmental protection is undertaken over the whole time horizon, no matter whether the decision makers are naive or sophisticated, although investment seems optimal in the long run from every generations point of view. This result questions the application of hyperbolic discounting in cost-benefit analysis and gives rise to concern, as it is consistent with unsatisfactory policy performance in solving long-term environmental problems.environmental policy, environmental protection, hyperbolic discounting, intertemporal decision theory, procrastination, time-(in)consistency

Rational Discounting for Regulatory Analysis

This Article examines the economic basis for what is termed rational discounting, which entails full recognition of policy effects over time and exponential discounting at a riskless rate of return. Policies often cannot be ranked unambiguously in terms of their present or future orientation. Both failure to discount and preferential intergenerational discounting generate inconsistencies and economic anomalies. Office of Management and Budget (OMB) discounting guidelines now stipulate more reasonable discount rates than earlier guidelines, but err in permitting open-ended preferential rates for intergenerational effects. This Article presents a methodology for monetizing the value of statistical life for people of different ages and at different points in time. Review of regulatory analyses indicates increased consistency of discounting practices. However, an examination of two policies with intergenerational effects, stratospheric ozone regulation and nuclear waste storage at Yucca Mountain, reveals failures to adopt a rational discounting approach. The influence of behavioral anomalies such as hyperbolic discounting may make full recognition of intertemporal effects in benefit-cost analysis more consequential than the use of preferential discount rates

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

In this paper we analyze a stochastic continuous time model in finite horizon in which agents discount the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with previous valuations in a way that cannot be explained by using a unique constant or a variable discount rate. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. For this class of time preferences, we study the classical consumption and portfolio rules model (Merton, 1971) for CRRA and CARA utility functions for time- consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of stochastic terminal time is also discussed.dynamic programming, consumption and portfolio rules, heterogeneous discounting, time consistency

Rational Discounting for Regulatory Analysis

This article examines the economic basis for what is termed %u201Crational discounting,%u201D which entails full recognition of policy effects over time and exponential discounting at a riskless rate of return. Policies often cannot be ranked unambiguously in terms of their present or future orientation. Both failure to discount and preferential intergenerational discounting generate inconsistencies and economic anomalies. Office of Management and Budget discounting guidelines now stipulate more reasonable discount rates than earlier guidelines, but err in permitting open-ended preferential rates for intergenerational effects. The article presents a methodology for monetizing the value of statistical life for people of different ages and at different points in time. Review of regulatory analyses indicates increased consistency of discounting practices. However, examination of two policies with intergenerational effects, stratospheric ozone regulation and nuclear waste storage at Yucca Mountain, reveal failures to adopt a rational discounting approach. The influence of behavioral anomalies such as hyperbolic discounting may make full recognition of intertemporal effects in benefit-cost analysis more consequential than the use of preferential discount rates.