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.     

The Ethics of Intertemporal Distribution in a Warming Planet

This paper evaluates, from the ethical viewpoint, current work by economists on intergenerational resource allocation in the presence of global warming. We begin by attempting to elucidate the debate that has recently occurred on the appropriate choice of the discount rate. We offer three justifications for maximizing the discounted sum of generational utilities, and find only one of these to be a satisfactory justification of that practice: the possibility that the human species may become extinct. This implies that a very small discount rate (large discount factor) should be used. We argue that the justification for discounting, inherent in the approaches taken by many economists, is that of ‘the present generation of hegemon,’ which is unacceptable. The role of the Ramsey equation in deducing the discount rate in these theories is explained. As an alternative to discounted utilitarianism, we propose a principle of sustainability; we describe optimal paths that have been calculated for the sustainabilitiarian (Rawlsian) objective function, and paths that will sustain growth in welfare, at a positive rate. We report results concerning optimal paths when the uncertainty of existence of future generations is taken into account. In sharp contrast to the utilitarian model, it turns out that under some conditions, the ‘sustainabilitarian’ can ignore the uncertainty regarding the date at which humans become extinct. There is a striking difference between the solutions of the discounted utilitarian program and the sustainabilitarian program under uncertainty.     

Declining Discount Rates: The Long and the Short of it

The last few years have witnessed important advances in our understanding of time preference and social discounting. In particular, several rationales for the use of time-varying social discount rates have emerged. These rationales range from the ad hoc to the formal, with some founded solely in economic theory while others reflect principles of intergenerational equity. While these advances are to be applauded, the practitioner is left with a confusing array of rationales and the sense that almost any discount rate can be justified. This paper draws together these different strands and provides a critical review of past and present contributions to this literature. In addition to this we highlight some of the problems with employing DDRs in the decision-making process, the most pressing of which may be time inconsistency. We clarify their practical implications, and potential pitfalls, of the more credible rationales and argue that some approaches popular in environmental economics literature are ill-conceived. Finally, we illustrate the impact of different approaches by examining global warming and nuclear power investment. This includes an application and extension of Newell and Pizer [‘Discounting the benefits of climate change mitigation : how much do uncertain rates increase valuations?’ Journal of Environmental Economics and Management 46 (2003) 52] to UK interest rate data.     

Valuation and management of wetland ecosystems

We recently completed a study of wetland values in coastal Louisiana that employed both willingness-to-pay and energy analysis-based methodologies and were able to bracket a range of values within which we feel fairly confident the true value lies. However, a large amount of uncertainty remains. Our current estimates of the total prsent value of an average acre of natural wetlands in Louisiana are US$2429–6400 per acre (assuming an 8% discount rate) to $8977–17000 per acre (assuming a 3% discount rate). At the lowest value, the current annual rate of loss of Louisiana wetlands (50 sq miles per year) is worth about $77 million. At the largest value it is worth about $544 million.In this paper we (a) discuss the fundamental theoretical and practical problems underlying natural resources valuation; (b) summarize our methods and findings for Louisiana wetlands; and (c) elaborate on some of the more recalcitrant problems attending applied natural resource valuation, including discounting and dealing with uncertainty and imprecision.The discount rate makes more difference in the final result than any other one factor, and yet there is much disagreement about the appropriate approach to discounting natural resources. We discuss the discounting problem as applied to natural resources and argue for lower discount rates for valuing renewable natural resources than apply for other aspects of the economy.It now seems clear that no reasonable amount of effort will produce very precise estimates of wetland values, and we suspect this is also the case for several other classes of natural resources. We elaborate a Wetlands Asurance Bonding System to address these problems.     

The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process

The long term discount rate is critically dependent upon projections of future growth rates that are fuzzier in proportion to the remoteness of the time horizon. This paper models such increasing fuzziness as an evolving hidden-state stochastic process. The underlying trend growth rate is an unobservable random walk hidden by noisy transitory shocks and recoverable only as a probability distribution via Bayesian updating. A simple expression is derived for the time-declining Ramsey discount rate. The components of this hidden-state Ramsey discounting formula are then analyzed, followed by a few remarks about possible implications and applications.     

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.     

Behaviour-based price discrimination with cross-group externalities

Two platforms compete for heterogeneous firms and consumers. Platforms are allowed to discriminate prices on the consumers’ side according to their past purchase behaviour. The findings of the paper depend on two dimensions: the relative cross-side externalities and the consumer discounting relative to platform discounting. Price competition is strengthened in the poaching phase compared to the case where a uniform price is charged in both sides, whereas the early price competition is relaxed if firms exhibit weaker externalities than consumers and if the latter discount sufficiently the future. The overall effect on inter-temporal profits of platforms is negative, but consumers might be harmed by BBPD when they discount sufficiently the future. Finally, depending on consumers’ discounting, total welfare may increase or decrease going from the uniform pricing to the discriminatory pricing.     

Discounting in a world of limited growth

This paper explores the consequences fordiscounting of assuming limits to growth. One of the main determinants of the discount rate is the rate of economic growth. If growth rates decline in the future then the discount rate should not be constant but also decline over time. In fact, we would then need not a single discount rate but rather a variable discount schedule. This would imply higher present values for the distant future. The paper analyses how discount rates would vary with different assumptions about the patterns of growth and the pure rate of time preference.An earlier version of this paper was presented at the conference ECOLOGICAL ECONOMICS, Stockholm, August 1992. I am grateful for valuable comments from Partha Dasgupta, Gunnar Köhlin, Karl-Göran Mäler, Mike Young and two anonymous referees.     

Discounting and altruism to future decision-makers

Is discounting of future decision-makers’ consumption utilities consistent with “pure” altruism toward those decision-makers, that is, a concern that they are better off according to their own, likewise forward-looking, preferences? It turns out that the answer is positive for many but not all discount functions used in the economics literature. In particular, “hyperbolic” discounting of the form used by Phelps and Pollak (Rev. Econ. Studies 35 (1968) 201) and Laibson (Quart. J. Econ. 112 (1997) 443) is consistent with exponential altruism towards future generations. More generally, we establish a one-to-one relationship between discount functions and altruism weight systems, and provide sufficient, as well as necessary, conditions for discount functions to be consistent with pure altruism.     

Hyperbolic Discounting,Borrowing Aversion and Debt Holding

Analysis of an original Internet‐based survey reveals that debt holding is related to time discounting through: (i) present bias, measured by the degree of declining impatience in the generalized hyperbolic discount function; (ii) borrowing aversion, captured by a sign effect in that future losses are discounted at lower rates than future gains; and (iii) impatience, measured by the overall discount rate. Hyperbolic respondents are classified naïve if their answers reveal them to be time‐inconsistent procrastinators, and otherwise sophisticated. Naïve respondents with more steeply declining impatience are more likely to be debtors. The sign effect relates negatively to borrowing. Survey responses indicative of high or declining impatience are associated with credit card borrowing and other overborrowing indicators.     

Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting

The derivation of the correct discount rate for intergenerational projects in Cost Benefit Analysis is particularly contentious. Public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in Britain and the USA. This is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic (rather than an exponential) function. There is also empirical evidence for this hypothesis. The hyperbolic nature of discounting is also a standard finding in the behavioural sciences. For intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost-benefit sensitivity analyses.Sincere thanks to Maureen Cropper and Paul Portney for supplying their survey results and to Elaine Barrow and Phillip Judge for graphics assistance. Two anonymous referees also provided valuable comments.     

Reconciling sustainability, systems theory and discounting

Most definitions of sustainability imply that a system is to be maintained at a certain level, held within certain limits, into the indefinite future. Sustainability denies run-away growth, but it also avoids any decline or destruction. This sustainability path is hard to reconcile with the renewal cycle that can be observed in many natural systems developing according to their intrinsic mechanisms and in social systems responding to internal and external pressures. Systems are parts of hierarchies where systems of higher levels are made up of subsystems from lower levels. Renewal in components is an important factor of adaptation and evolution. If a system is sustained for too long, it borrows from the sustainability of a supersystem and rests upon lack of sustainability in subsystems. Therefore by sustaining certain systems beyond their renewal cycle, we decrease the sustainability of larger, higher-level systems. For example, Schumpeter's theory of creative destruction posits that in a capitalist economy, the collapse and renewal of firms and industries is necessary to sustain the vitality of the larger economic system. However, if the capitalist economic system relies on endless growth, then sustaining it for too long will inevitably borrow from the sustainability of the global ecosystem. This could prove catastrophic for humans and other species. To reconcile sustainability with hierarchy theory, we must decide which hierarchical level in a system we want to sustain indefinitely, and accept that lower level subsystems must have shorter life spans. In economic analysis, inter-temporal discount rates essentially tell us how long we should care about sustaining any given system. Economists distinguish between discount rates for individuals based on personal time preference, lower discount rates for firms based on the opportunity cost of capital, and even lower discount rates for society. For issues affecting even higher-level systems, such as global climate change, many economists question the suitability of discounting future values at all. We argue that to reconcile sustainability with inter-temporal discounting, discount rates should be determined by the hierarchical level of the system being analyzed.     

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.     

Hyperbolic discounting and the time-consistent solution of three canonical environmental problems

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open-access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.     

Once More on Intergenerational Discounting in Climate-Change Analysis: Reply to Partha Dasgupta

Discounting the utilities of future generations in many problems, such as climate-change analysis, has several justifications, only one of which can be supported by ethics which postulate that every individual, no matter when born, has an equal right to well-being. That justification is that future generations may not exist. In an earlier article published here, I explained this view, and criticized economists who deviate from it: the practical aspect of this deviation is to choose discount rates which are far too high, thus relegating future generations to lower utility than they a priori have a right to. As well, many economists continue to rely upon a utilitarian ethic, a reliance which is independent of the discounting issue, but which I also criticize. Dasgupta responded to my article; the present article is a response to Dasgupta.     

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.     

Preferences in the Future

Environmental economics has been much occupied with the discount rate, which is the value of future costs and benefits relative to present costsor benefits. But at least as important is the question of whatshould be discounted, that is, what the value of those future environmentalbenefits is to future generations. This paper analyzes the role for futurepreferences and discusses the state of knowledge. I argue that theappropriate discount rate is the market one, and that the real problemis determining future willingness-to-pay. This approach makes clearerthe connection between discounting and the valuation debate.This paper focuses on two features that have been prominent in that debate:existence value and reference dependence. I argue that thereis a vital connection between the two constructs and that this link yieldsimportant implications for future willingness-to-pay.     

The social value of carbon sequestered in Great Britain's woodlands

The economic value of carbon storage associated with British woodland is calculated. Models were developed to estimate C flux associated with live trees, forest floor litter, soils, wood products, harvest, fossil fuel used in manufacturing and C displacement from biofuels and products for representative British plantation species: Sitka spruce (Picea sitchensis) and beech (Fagus sylvatica). Map databases of publicly and privately owned woodlands were compiled for Great Britain. Carbon flux was determined for individual woodland sites, and monetised using candidate parameters for the social discount rate (1, 3, 3.5 or 5%) and social value of carbon (US$109.5, $1, $10 or $17.10/t). A conventional discount function was applied. Final results are expressed as Net Present Values, for the base year 2001, with discounting commencing in 2002. The minimum suggested NPV (discount rate = 3% and social value of carbon = $1) of GB woodlands already existing in 2001 is $82 million, with a further $72 million that might be added by future afforestation. These figures rise dramatically if a discount rate of 1% and social value of sequestered carbon = $109.5/t are assumed. The calculated total value of C stored in British woodland depends significantly on parameter assumptions, especially about appropriate discount rate and social value of sequestered carbon.     

A Note on Discounting an Increasingly Uncertain Future

This note clarifies the roles played by the wealth and precautionary effects in determining the socially efficient discount rate for public investment projects and how the rate should vary over time. We first give a general characterization of the effects of stochastic shifts in the consumption growth rate on the magnitude of the socially efficient discount rate. We then show that increasing uncertainty in the consumption growth rate provides a natural and compelling rationale for discounting more distant future consumption at a lower rate.     

Convex Time Budgets and Individual Discount Rates in the Long Run

The purpose of this study is to use experimental data to estimate individual discount rates and test for hyperbolic discounting over a long time horizon. To do this, we employ the convex time budget experimental approach with cash payments over a 20 year time horizon. To date, there are few experimental studies that explore discount rates beyond a 1 year time horizon. Previous experimental studies that focus on short time horizons find high discount rates, which may not be applicable to decisions that affect outcomes in the distant future. Our findings are quite similar to the average rate of 4.9% found by Grijalva et al. (Environ Resour Econ 59:39–63, 2014), who similarly use a 20 year time horizon, but use the multiple price list elicitation method along with payment via government savings bonds. We find annual discounts rates in the range of 1.9–5.5%, depending on the specific model used. We also find evidence for declining discount rates, and that this hyperbolic pattern of behavior is related to the confidence subjects have in receiving distant-future payments.