Service contracts, rate discounting, and the future of shipping conferences

The objective of this paper is to assess the impact of service contracts and rate discounting on the future of ocean linear shipping conferences. As a result of increased competition between ocean liner conference carriers and nonconference carriers and excess shipping capacity in the ocean liner container industry, conference carriers on many shipping lanes are engaging in rate discounting and negotiating service contracts with large shippers to obtain additional business. Often, these service contracts are entered into without the prior approval of the conference. Will the use of discounting and service contracts lead to the end of shipping conferences? Using economic theory, the conclusion is drawn that shipping conferences are likely to be weakened but not eliminated as a result of these practices.     

On the neoclassical growth model with non-constant discounting

We study the neoclassical growth model with non-constant discounting. We do not assume specific functional forms for discounting and demonstrate that the competitive economy always performs better than the planning economy.     

Developments in discounting: With special reference to future health events

Research on time preferences and discounting has two main motivations: to inform decision making by providing a basis for the comparison of future costs and benefits; to explain the influence of the future on current behaviour. This paper introduces the wide range of discount functions which have been advocated in addition to the standard constant rate exponential model. The different approaches taken to estimating the parameters of the discount function are reviewed. The issues raised by discounting in the longer term are discussed. Particular attention is given to time preferences with respect to future health events which have for a number of reasons been a fruitful area for research on time preferences. Specifically the paper examines: the distinctive issues raised when discounting future health events; the methods which have been used to discount health events; the relationship between time preferences and health-affecting behaviour.     

On the microeconomics of food and malnutrition under endogenous discounting

This paper explores the microeconomics and dynamics of food and nutrition. It examines the linkages between malnutrition and the incentive to invest and accumulate capital. The analysis focuses on a dynamic model where preferences about the future depend on nutrition and health. Situations of malnutrition cover both ends of the spectrum: from nutrient deficiency to obesity. The model involves preferences that are not time-additive and exhibit endogenous discounting. This provides a framework to investigate the factors affecting consumption and investment behavior. The adverse investment incentives of malnutrition are examined.     

Ecological discounting

Which rates should we use to discount costs and benefits of different natures at different time horizons? We answer this question by considering a representative agent consuming two goods whose availability evolves over time in a stochastic way. We extend the Ramsey rule by taking into account the degree of substitutability between the two goods and of the uncertainty surrounding the economic and environmental growths. The rate at which environmental impacts should be discounted is in general different from the one at which monetary benefits should be discounted. We provide arguments in favor of an ecological discount rate smaller than the economic discount rate. In particular, we show that, under certainty and Cobb-Douglas preferences, the difference between the economic and the ecological discount rates equals the difference between the economic and the ecological growth rates. Using data about the link between biodiversity and economic development, I estimate that the rate at which changes in biodiversity should be discounted is 1.5%, whereas changes in consumption should be discounted at 3.2%.     

Energy discounting

The procedure described allows comparison of various energy transformation processes, including those using fossil fuels, solar energy, and conservation. The procedure allows a determination of the relative feasibility and desirability of each process for producing a surplus of energy beyond the output that could be obtained directly from the process energy (i.e., the energy needed for self-reproduction). The analysis includes all energy directly or indirectly committed to the process, throughout the entire economy.To quantify the feasibility of energy transformation, an input-output ratio was calculated for 44 processes. The calculations exclude fuels transformed directly into energy output. Adjustments were made for differences in quality, end use, and time of use. A low ratio means that the process should receive further research and development funding or else should be dropped from consideration. The input-output ratio of a feasible transformation process may decline with time because of a resource scarcity, indicating a falling desirability. Highly desirable processes, ones with ratios that show the least signs of declining, should also be compared for future use on the basis of their relative effects on labor needs, capital requirements, the demand for critical material, and their environmental impact. Policy conclusions are hampered by an unevenness in the quality of the available data. Nevertheless, a useful and comprehensive method of energy analysis is demonstrated.     

Exponential discounting bias

We address intertemporal utility maximization under a general discount function that nests the exponential discounting and the quasi-hyperbolic discounting cases as particular specifications. Under the suggested framework, the representative agent adopts, at some initial date, an optimal behavior that shapes her consumption trajectory over time. This agent desires to take a constant discount rate to approach the optimization problem, but bounded rationality, under the form of a present bias, deviates the individual from the intended goal. As a result, decreasing impatience will end up dominating the agent’s behavior. The individual will not be aware of her own time inconsistency and, therefore, she will not revise her plans as time elapses, what makes the problem relatively simple to address from a computational point of view. The general discounting framework is used to approach a standard optimal growth model in discrete time. Transitional dynamics and stability properties of the corresponding dynamic setup are studied. An extension of the standard utility maximization model to the case of habit persistence is also considered.     

Over-savings and hyperbolic discounting

Hyperbolic discounting models are widely seen as implying that consumers do not save enough, in accordance with the observed low rates of savings of some households. This paper qualifies this view by showing that hyperbolic consumers may ‘oversave’ in the short run. The result extends to uncertainty on future income and does not depend on whether preferences are present-biased or future-biased. A generalized comparative statics analysis of self-control is introduced, and its relationship to the analysis of uncertainty on discount factors is emphasized.     

Expropriation risk and discounting

This paper focuses on time preference and individual measures of expropriation risk. We use survey data on Italian households and on the 50+ population in eleven European countries. The surveys provide measures of discount rate and proxies for expropriation due to criminal offenses. We show that impatience increases with expropriation risk.     

The nature of discounting

From monetary policies to the climate change problem, from the burden of private credit card debts to the evaluation of public projects, discount rate is the central issue, yet there is little clear understanding about the nature of discounting. In this paper, applying a newly developed production theory, we discuss how discount rate is related to other factors in social systems, such as risk, duration of production, fixed cost in production and market size. The relations among different factors in a social system put constraints on the ranges of discount rate that are viable in particular environments. Our findings have strong policy implications. In a world of increasing cost of extracting natural resources, the continuation of low discount rate policy will generate wide gyration of social systems that we have witnessed in recent years.     

Quasi-hyperbolic discounting and retirement

Some people have self-control problems regularly. This paper adds endogenous retirement to Laibson’s quasi-hyperbolic discounting savings model [Quarterly Journal of Economics 112 (1997) 443–477]. Earlier selves think that the deciding self tends to retire too early and may save less to induce later retirement. Still earlier selves may think the pre-retirement self does this too much, saving more to induce early retirement. The consumption pattern may be different from that with exponential discounting. Other observational non-equivalence includes the impact of changing mandatory retirement rules or work incentives on savings and a possibly negative marginal propensity to consume out of increased future earnings. Naive agents are briefly considered.     

Non-constant discounting in continuous time

This paper derives the dynamic programming equation (DPE) to a differentiable Markov Perfect equilibrium in a problem with non-constant discounting and general functional forms. Beginning with a discrete stage model and taking the limit as the length of the stage goes to 0 leads to the DPE corresponding to the continuous time problem. The note discusses the multiplicity of equilibria under non-constant discounting, calculates the bounds of the set of candidate steady states, and Pareto ranks the equilibria.     

A counterexample to the folk theorem with discounting

The ‘folk theorem’ formalizes the theme that ‘repetition leads to cooperation’. We present an example showing that, even with perfect monitoring, the set of Nash equilibria of the discounted games does not have to converge to the feasible, individually rational set, i.e., this version of the ‘folk theorem’ can break down.     

Spatial discounting of ecosystem services

The impact of conservation efforts targeted at preserving ecosystem services largely depend on the welfare implications associated with spatial variations in the provision of ecosystem services. While there is ample empirical evidence of spatial discounting or decay of the valuation of ecosystem services, there are still few underpinnings based on welfare economic theory. We establish a theory of spatial discounting that closely follows the concept of time discounting pertaining to climate change, and show spatial discount rates in the consumption, ecosystem service, and willingness to pay (WTP) numeraires. We consider the role of key parameters such as pure rate of spatial preference, consumption change, ecosystem services change, population density, and elasticity of marginal utility. We find that the spatial discount rate of WTP for ecosystem services that frequently appears in the empirical literature is the difference between the ecosystem service discount rate and consumption discount rate, where the ecosystem service discount rate includes both physical distance decay and welfare effects. Finally, we use numerical simulations to illustrate how the three different spatial discount rates vary with the spatial distance from the source of ecosystem services and with consumption patterns, implying many more possible spatial variations of WTP.     

Credibility and endogenous societal discounting

We consider a dynamic moral hazard economy inhabited by a planner and a population of privately informed agents. We assume that the planner and the agents share the same discount factor, but that the planner cannot commit. We show that optimal allocations in such settings solve the problems of committed planners who discount the future less heavily than agents. Thus, we provide micro-foundations for dynamic moral hazard models that assume a societal discount factor in excess of the private one. We extend the analysis to allocations that are reconsideration-proof in the sense of Kocherlakota [Kocherlakota, N., 1996. Reconsideration-proofness: A refinement for infinite horizon time inconsistency. Games and Economic Behavior 15, 33–54]. We show that these allocations solve the choice problem of a committed planner with a unit discount factor.     

Consistent planning under quasi-geometric discounting

We study properties of stationary Markov-perfect equilibria in a general model of intertemporal choice under quasi-geometric discounting. The dynamics generated by stationary Markov-perfect equilibria can be very complicated, even if the model satisfies strict convexity and smoothness properties and the decision maker is arbitrarily patient. If there exist multiple stationary Markov-perfect equilibria, then it is in general possible to construct infinitely many non-degenerate stationary sunspot equilibria as well.     

Multiple solutions under quasi-exponential discounting

Infinite horizon dynamic optimization problems with non-exponential time preferences may not only exhibit time inconsistency but may also have multiple solutions with distinct payoffs. We here show that such multiplicity is generic in the sense that it occurs in an open set of such decision problems, even with small state- and action-spaces. Non-exponential discounting allows for an “addictive” equilibrium alongside a “virtuous” equilibrium. We also provide a sufficient condition for uniqueness in infinitely repeated decision problems with general action spaces. Authors thank Philippe Jehiel, Maria Saez-Marti and Bill Sandholm for comments to an earlier version, and the Knut and Alice Wallenberg Research Foundation for financial support.     

Endogenous discounting and the domain of the felicity function

The objective is to show that endogenous discounting models should use a felicity function constrained to a positive domain. A variety of articles use the Mangasarian or Arrow and Kurz condition as a sufficient condition for optimality, which restricts felicity to a negative domain. Since the level of the felicity function shows up in the optimal path it leads to qualitatively different solutions when one uses a negative or positive felicity function. We suggest reasons why the domain should be positive. We furthermore derive sufficiency conditions for concavity of a transformed Hamiltonian if the felicity function is assumed to be positive.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.