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.     

Justifying social discounting: The rank-discounted utilitarian approach

The discounted utilitarian criterion for infinite horizon social choice has been criticized for treating generations unequally. We propose an extended rank-discounted utilitarian (ERDU) criterion instead. The criterion amounts to discounted utilitarianism on non-decreasing streams, but it treats all generations impartially: discounting becomes the mere expression of intergenerational inequality aversion. We show that more inequality averse ERDU societies have higher social discount rates when future generations are better off. We apply the ERDU approach in two benchmark economic growth models and prove that it promotes sustainable policies that maximize discounted utilitarian welfare.     

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.     

The prevalence of hyperbolic discounting: some European evidence

Experimental matching data are used from the 2000 Bank of Italy Survey of Household Income and Wealth (SHIW) and the 2000 wave of the Center for Economic Research (CentER) Savings Survey at Tilburg University to compare the relative frequencies of hyperbolic and exponential discounters. Among 3200 Italian respondents and 1400 Dutch respondents, less than a quarter exhibited hyperbolic discounting. This finding is both statistically significant and robust with respect to various assumptions regarding utility; moreover, it holds across a wide variety of economic, social and demographic characteristics. The youngest, poorest, most urban and least educated individuals are the most likely to be hyperbolic discounters. In addition, it is found that hyperbolic discounters accumulate less wealth and are somewhat less likely than exponential discounters to utilize commitment devices to constrain their future choices.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen in J Polit Econ 89:841?C864, 1981). We find that it is often optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (1) R is small relative to P (where R is risk aversion and P is absolute prudence); (2) the distribution of shocks to output is asymmetric and the asymmetry takes a particular form; (3) the principal faces a limited liability constraint; and (4) there is agent heterogeneity of a particular form.     

Permanence discounting for land-based carbon sequestration

One major concern regarding land-based carbon sequestration involves the issue of permanence. Sequestration may not last forever and may either be released in the future or require expenditures to maintain the practices that keep it sequestered. In this paper, we investigate the differential value of offsets in the face of impermanent characteristics by forming a price discount that equalizes the effective price per ton between a “perfect offset” and one possessing some with impermanent characteristics. We find this discount to be a function of the future needs to replace offsets (in the face of lease expiration quantity or volatilization upon activities such as timber harvest) and the magnitude of any needed maintenance costs. We investigate the magnitude of the discounts under alternative agricultural tillage and forest management cases. In those studies, we find that permanence discounts in the range of 50% are not uncommon. This means that in the market place an impermanent sequestration offset may only receive payments amounting to 50% of the market carbon price. Furthermore, we find that in the face of escalating carbon prices that offsets may prove to be worthless.     

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.     

Hyperbolic discounting and uniform savings floors

Previous research suggests that, in partial equilibrium, individuals whose decision-making exhibits a present-bias – such as hyperbolic discounters who tend to over-consume – will be in favor of having a floor imposed on their savings. In this paper, I show it is quite difficult for the introduction of a savings floor to be Pareto improving in general equilibrium. Indeed, a necessary condition for the floor to be Pareto improving is that it is high enough to be binding for all individuals. Even in that case, because the equilibrium interest rate adjusts with the level of the savings floor, some individuals may prefer to commit to a future time path of consumption by facing a high interest rate (and no floor) rather than a high floor. An essential insight for understanding this result is to note that even those with little self-control (in an absolute sense) will choose to save a lot when the interest rate is high enough.     

Quasi-hyperbolic discounting and social security systems

Hyperbolic discounting has become a common assumption for modeling bounded rationality with respect to individual savings decisions. We examine the effects of hyperbolic discounting on the comparison of alternative social security systems. We show that this form of bounded rationality breaks the equivalence between funded and pay-as-you-go (PAYG) systems established in Sheshinski and Weiss [Sheshinski, E., Weiss, Y., 1981. Uncertainty and optimal social security. Quarterly Journal of Economics 95, 189-206]. Intergenerational transfers within a PAYG economy are usually secured by the social security system and independent of longevity, whereas this is not the case for the funded economy. The savings level under hyperbolic discounting is lower than under exponential discounting [Laibson et al., 1998], but the ratio between the savings level under hyperbolic discounting within a funded economy and a PAYG economy depends on the effectiveness of the commitment devices. It is shown that if individuals are hyperbolic discounters, then in a PAYG economy any change in the mandated level of intergenerational transfers is neutralized by individuals’ voluntary bequests. This does not apply to a funded system.