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%.     

Time Preference and Income Convergence in a Dynamic Heckscher–Ohlin Model

This paper shows that income convergence in an open‐economy setting hinges upon how the time discount rate of the households is determined. As opposed to the case of constant time discount rate where cross‐country income divergence may emerge, the small open economy may catch up with the rest of the world if the time discount rate increases with consumption. In contrast, if the time discount rate decreases with consumption, then the small open economy fails to catch up with the rest of the world under free trade of commodities.     

The government's time discount rate: Choices and consequences in a dynamic framework

This paper considers a closed macroeconomy where the monetary authority pursues an inflation target and policy outcomes are the consequence of a Nash game between fiscal and monetary authorities. The specification of the macroeconomic framework is characterized by nonlinearities which lead to multiple equilibria with differing stability properties. Employing a calibrated model and simulations derived using the Mathematica package, the stability properties of the economy and the likely choice of equilibrium are examined. Within this framework, the dynamic consequences of different time discount rates for the fiscal authority are investigated, both in a world of certainty and also in a world of uncertainty. It is shown that, in a world of certainty, it will be optimal to choose the fiscal authority's time discount rate equal to the market rate of interest. However, depending on the degree of uncertainty in evaluating the time discount rates of consumers and of the fiscal authority, it may be appropriate to bias the fiscal authority's discount rate above or below the expected interest rate.     

The Equivalency Principle for Discounting the Value of Natural Assets: An Application to an Investment Project in the Basque Coast

Making decisions about optimal investments in green infrastructure necessitates setting social discount rates. This paper suggests a practical way for determining the discount rate for projects or programmes in which one of the options is to maintain or restore land to an undeveloped state. We propose an “equivalency principle” to derive a simple rule that sets the discount rate. The rule is based on the premise that the long term value of a piece of undeveloped land ought to be at least the same as the value of an identical piece of land in the vicinity to which permission has been granted for development. We illustrate this principle with various case studies and we apply it to a contentious investment project in the Basque Country associated with the regeneration of a large scale harbour that involves reclaiming undeveloped land that has important ecological values, including for the conservation of a marine ecosystem.     

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.     

Joint estimation of discount rates and willingness to pay for public goods

We analyze willingness to pay (WTP) for environmental programs whose time periods of benefit and repayment differ, using a net present value framework that identifies parameters of both WTP and personal discount rates. Respondents to a contingent valuation survey focusing on protection of critical habitat buffer zones for the endangered Steller Sea Lion in Alaska were asked their willingness to pay for 1-, 5-, and 15-year repayment periods. We jointly estimate the personal discount rates and WTP via maximum likelihood, and compare with a model assuming a fixed, market discount rate.     

The Evolutionary Theory of Time Preferences and Intergenerational Transfers

At each age an organism produces energy by foraging and allocates this energy among reproduction, survival, growth, and intergenerational transfers. We characterize the optimal set of allocation decisions that maximizes fitness. Time preference (the discount rate) is derived from the marginal rate of substitution between energy obtained at two different times or ages, holding fitness constant. Time preference varies with age in different ways depending on whether an individual is immature or mature, and during the transition between these stages. We conclude that time preference and discount rates are likely to be U-shaped across age.     

Challenging the human crisis: “The trilemma”

The great increase in world population in the coming century will result in a human crisis of worldwide proportions. A new concept for describing and proposing solutions to this crisis, called the Trilemma, is described by the authors. To feed large and growing populations, humankind is now being forced to make the difficult choice between producing sufficient food for the world population and preserving the environment, or generating economic growth, requiring the consumption of energy and natural resources. These difficult choices present the Trilemma, a new concept that is composed of three dimensions: economic growth, resources such as energy and food, and the environment. None of these three dimensions can be optimized individually as they are mutually interdependent.This paper describes a possible world energy condition in the 21st century. Three scenarios of this energy consumption are presented and compared with the possible energy supply at that time. This supply is estimated from the extrapolation of the renewable energy development of the past and the possible fossil fuel supply. The comparison of the energy supply and the energy consumption indicates that the annual rate of economic growth in the developed region would be only 1% if the gross national product (GNP) per capita of the developing region increases gradually from 1/26 of the GNP of the developed regions in 1990, to 1/10 in 2020, and finally to 1/3 in 2100.Another possibility is that if the GNP per capita of the developing region remains 1/26 of the GNP of the developed regions between 1990 and 2100, the economic growth rate in the developed region could be as large as 3%. In the latter case, an energy shortage would develop in the middle of the 21st century, even if the fast breeder reactor were fully operational by the year 2030. Energy technological developments in Japan are also described as a part of the possible countermeasures against the Trilemma.     

Theory and practice of monetary policy

Summary. We consider an optimally managed renewable resource with stochastic non-concave growth function. We characterize the conditions under which the optimal policy leads to global extinction, global conservation and the existence of a safe standard of conservation. Our conditions are specified in terms of the economic and ecological primitives of the model: the biological growth function, the welfare function, the distribution of shocks and the discount rate. Our results indicate that, unlike deterministic models, extinction and conservation in stochastic models are not determined by a simple comparison of the growth rate and the discount rate; the welfare function plays an important role.Received: 20 October 2004, Revised: 28 February 2005, JEL Classification Numbers: D90, O11, O41, Q32.Santanu Roy: Correspondence toResearch on this paper was completed when the second author visited Cornell University in July, 2003. We thank the Center for Analytic Economics and the Department of Economics at Cornell University for making this research visit possible. The current version has gained considerably from the comments made by an anonymous referee.     

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.     

“Economics and Psychology”? The Case of Hyperbolic Discounting*

The article questions the methodology of “economics and psychology” in its focus on the case of hyperbolic discounting. Using some experimental results, I argue that the same type of evidence, which rejects the standard constant discount utility functions, can just as easily reject hyperbolic discounting as well. Furthermore, a decision‐making procedure based on similarity relations better explains the observations and is more intuitive. The article concludes that combining “economics and psychology” requires opening the black box of decision makers instead of modifying functional forms.     

Discounting the Distant Future: An Experimental Investigation

We use a laboratory experiment to elicit discount rates over a 20-year time horizon using government savings bonds as a payment vehicle. When using a constant (exponential) discount rate function, we find an implied average discount rate of 4.9 %, which is much lower than has been found in previous experimental studies that used time horizons of days or months. However, we also find strong support for non-constant, declining discount rates for longer time horizons, with an extrapolated implied annual discount rate approaching 0.5 % in 100 years. There is heterogeneity in discount rates and risk preferences in that people with more optimistic beliefs about technological progress have higher discount rates. These findings contribute to the debate over the appropriate discount rate to use in comparing the long-term benefits of climate change mitigation to the more immediate costs.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

Efficiency with Non-Convexities: Extending the “Scandinavian Consensus” Approaches

There are two distinct “Scandinavian consensus” approaches to public good supply, both based on agents' willingness to pay. A Wicksell–Foley public competitive equilibrium arises from a negative consensus in which no change of public environment, together with associated taxes and subsidies which finance it, will be unanimously approved. Alternatively, in a Lindahl or valuation equilibrium, charges for the public environment induce a positive consensus. To allow general non-convexities to be regarded as aspects of the public environment, we extend recent generalizations of these equilibrium notions and prove counterparts to both the usual fundamental efficiency theorems of welfare economics.     

Insiders,outsiders, and the adaptability of informal rules to ecological shocks

The history of the world is strewn with the remains of societies whose institutions failed to adapt to ecological change, but the determinants of institutional fragility are difficult to identify in the historical record. We report a laboratory experiment exploring the impact of an exogenous ecological shock on the informal rules of property and exchange. We find that geographically-induced tribal sentiments, which are unobservable in the historical record, impede adaptation post shock and that inequality declines as wealth and sociableness increase. Quantitative measures of individual and group sociality account for some of the differences in successful or failed adaptation.     

Optimal Experimentation in a Changing Environment

This paper studies optimal experimentation by a monopolist who faces an unknown demand curve subject to random changes, and who maximizes profits over an infinite horizon in continuous time. We show that there are two qualitatively very different regimes, determined by the discount rate and the intensities of demand curve switching, and the dependence of the optimal policy on these parameters is discontinuous. One regime is characterized by extreme experimentation and good tracking of the prevailing demand curve, the other by moderate experimentation and poor tracking. Moreover, in the latter regime the agent eventually becomes "trapped" into taking actions in a strict subset of the feasible set.     

Reconciling sustainability and discounting in Cost–Benefit Analysis: A methodological proposal

The incorporation of the intergenerational equity objective has rendered the traditional Cost–Benefit Analysis (CBA) approach obsolete for the evaluation of projects presenting an important number of environmental externalities and for those whose impacts extend throughout a long period of time.Based on the assumption that applying a discount rate rewards current consumption and, therefore, that it is only possible to introduce a certain intergenerational equity in a Cost–Benefit Analysis, in this work we propose an approach to discounting based on a different rationale for tangible and intangible effects. We designed two indicators of environmental profitability: a) the Intergenerational Transfer Amount (ITA), which quantifies in monetary units what the current generation is willing to pass on future generations when an environmental restoration project is carried out, and b) the Critical Environmental Rate (CER), measures the implicit environmental profitability.These concepts were tested through an empirical case study pertaining to the assessment of an Erosion Control Project in the southeast of Spain. The results yield traditional profitability indicators that are higher — and probably closer — to the real values set by the contemporary society. The information provided by the environmental profitability indicators proposed renders more transparency to the quantification of the levels of intergenerational equity applied, thereby facilitating the difficult reconciliation of the CBA technique with the objective of sustainability.     

Conditions for Sustainable Optimal Economic Development

This paper shows that, for dynamic optimizing economies with different types of natural resource, environmental, and human‐made capital stocks, a necessary and sufficient condition for permanently sustaining an optimal utility/consumption level is the stationarity of the current‐value Hamiltonian. For economies whose development is not exogenously and directly affected by time (i.e., time‐autonomous economies), this stationarity condition generalizes Dixit et al.’s (1980 ) “zero‐net‐aggregate‐investment” rule of sustain‐ability, which in turn generalizes Solow‐Hartwick’s sustainability rule. For non‐autonomous economies, the stationarity condition is not generally fulfilled, and the current‐value Hamiltonian under (over) estimates the true welfare level by an amount equal to the discounted value of the net “pure time effect.” For the non‐autonomous case of a time‐dependent utility discount rate, a general condition on the discount rate function (of which the hyperbolic discount rate function is a special case) upholds the results obtained for autonomous cases. The paper concludes with a discussion of policies that promote both optimality and sustainability objectives.     

“(MA)LINGERING ON THE DISABLED LIST”

In this article, we examine two offsetting incentives that may affect a baseball player's willingness to play with injuries. We allow for the usual disincentive effects associated with long‐term contracts, while also incorporating the importance of the incentives associated with contract renewal. Our results are consistent with the previous work that showed those likely to retire at the end of their current contracts have an increased incentive to shirk. For those who expect to re‐sign a subsequent contract, however, we find that players tend to step up their effort as they approach the final year of their contract. (JEL L83)     

Discounting,Distribution and Disaggregation: Discount Rates for the Rich and the Poor with Climate as a Source of Utility

To consider the implications of disaggregated consumption and discounting in the context of climate change, we study discounting in a world composed of the rich and the poor; a standard setting in the literature of cost–benefit analysis with distributional considerations. We derive several discount rates for different numéraires, which allow us to discuss intergenerational and intragenerational equity in common terms. In the example of CES‐CRRA utility, we also show that disaggregated discount rates may vary owing to several factors. One important parameter, inequality aversion, can be determined in the weighting of intergenerational and intragenerational concerns.