Individual and social discounting in a viscous population

Social discounting in economics involves applying a diminishing weight to community-wide benefits or costs into the future. It impacts on public policy decisions involving future positive or negative effects, but there is no consensus on the correct basis for determining the social discount rate. This study presents an evolutionary biological framework for social discounting. How an organism should value future benefits to its local community is governed by the extent to which members of the community in the future are likely to be its kin. Trade-offs between immediate and delayed benefits to an individual or to its community are analysed for a modelled patch-structured iteroparous population with limited dispersal. It is shown that the social discount rate is generally lower than the individual (private) discount rate. The difference in the two rates is most pronounced, in ratio terms, when the dispersal level is low and the hazard rate for patch destruction is much smaller than the individual mortality rate. When decisions involve enforced collective action rather than individuals acting independently, social investment increases but the social discount rate remains the same.     

基于生态系统服务价值的湿地恢复工程效益分析——以北京市延庆县蔡家河为例

根据实地测量数据,以中国陆地生态系统单位面积生态服务价值当量表为基础,应用经济学原理将静态的生态系统服务价值转化为动态的资金流量,核算了考虑货币时间价值的资金净现值,对北京市一处面积为37 hm2的湿地恢复工程进行了效益分析研究。结果表明,研究区域的生态系统服务价值在湿地恢复工程实施后由584478元增加至3579713元。在所考察的9项生态系统服务功能中废物处理、气候调节和水源涵养对价值变化的贡献率较大,食物生产和原材料的贡献率为负值。以3a和5a为收益期计算所得的内部收益率分别为-26.81%和-4.67%,此时湿地恢复工程亏损;以10a为收益期计算所得的内部收益率为11.43%,湿地恢复工程取得良好收益。在设定折现率为4.2%,只计算可用直接市场法核算的生态系统服务情况下,湿地恢复工程的投资回收期为14.96年。为合理评估湿地恢复工程效益,应适当延长工程验收时间。在当前基准利率水平下,湿地恢复工程具有潜在盈利能力。     

The ecology and evolution of patience in two New World monkeys

Decision making often involves choosing between small, short-term rewards and large, long-term rewards. All animals, humans included, discount future rewards--the present value of delayed rewards is viewed as less than the value of immediate rewards. Despite its ubiquity, there exists considerable but unexplained variation between species in their capacity to wait for rewards--that is, to exert patience or self-control. Using two closely related primates--common marmosets (Callithrix jacchus) and cotton-top tamarins (Saguinus oedipus)--we uncover a variable that may explain differences in how species discount future rewards. Both species faced a self-control paradigm in which individuals chose between taking an immediate small reward and waiting a variable amount of time for a large reward. Under these conditions, marmosets waited significantly longer for food than tamarins. This difference cannot be explained by life history, social behaviour or brain size. It can, however, be explained by feeding ecology: marmosets rely on gum, a food product acquired by waiting for exudate to flow from trees, whereas tamarins feed on insects, a food product requiring impulsive action. Foraging ecology, therefore, may provide a selective pressure for the evolution of self-control.     

Measuring Impatience in Intertemporal Choice

In general terms, decreasing impatience means decreasing discount rates. This property has been usually referred to as hyperbolic discounting, although there are other discount functions which also exhibit decreasing discount rates. This paper focuses on the measurement of the impatience associated with a discount function with the aim of establishing a methodology to compare this characteristic for two different discount functions. In this way, first we define the patience associated with a discount function in an interval as its corresponding discount factor and consequently we deduce that the impatience at a given moment is the corresponding instantaneous discount rate. Second we compare the degree of impatience of discount functions belonging to the same or different families, by considering the cases in which the functions do or do not intersect.     

Discounting and the environment should current impacts be weighted differently than impacts harming future generations?

Background  In Life-Cycle Assessment (LCA), decision makers are often faced with tradeoffs between current and future impacts. One typical example is waste incineration, where immediate emissions to the air from the incineration process have to be weighted against future emissions of slag landfills. Long-term impacts are either completely taken into account or they are entirely disregarded in case of a temporal cut-off. Temporal cutoffs are a special case of discounting. Objective  In this paper, discounting is defined as valuing damages differently at different points of time using a positive or negative discount rate. Apart from temporal cut-offs, discounting has rarely been applied in LCA so far. It is the goal of this paper to discuss the concept of discounting and its applicability in the context of LCA. Methods  For this purpose, we first review the arguments for discounting and its principles in economic sciences. Discounting in economics can be motivated by pure time preference, productivity of capital, diminishing marginal utility of consumption, and uncertainties. The nominal discount rate additionally includes changes in the price level. These arguments and their justification are discussed in the context of environmental impacts harming future generations. Results and Discussion  It is concluded that discounting across generations because of pure time preference contradicts fundamental ethical values and should therefore not be applied in LCA. However, it has to be acknowledged that in practice decision makers often use positive discount rates because of pure time preference — either because they might profit from imposing environmental damage on others instead of themselves or because people in the far future are not of immediate concern to them. Discounting because of the productivity of capital assumes a relationship between monetary values and environmental impact. If such a relationship is accepted, discounting could be applied. However, future generations should be compensated for the environmental damage. It is likely that they would demand a higher compensation if the real per capita income increases. As both the compensation and the discount rate are related to economic growth, the overall discount rate might be close to zero. It is shown that the overall discount rate might even be negative considering that the required compensation could increase (even to infinite) if natural assets remain scarce, whereas the utility of consumption diminishes with increasing income. Uncertainties could justify both positive and negative discount rates. Since the relationship between uncertainties and the magnitude of damage is generally not exponential, we recommend to model changes in the magnitude of damage in scenario analysis instead of considering it in discounting (which requires an exponential function of time in the case of a constant discount rate). We investigated the influence of discounting in a case study of heavy metal emissions from slag landfills. It could be shown that even small discount rates of less than 1 % lead to a significant reduction of the impact score, whereas negative discount rates inflate the results. Conclusions and Recommendations  Discounting is only applicable when temporally differentiated data is available. In some cases, such a temporal differentiation is necessary to take sound decisions, especially when long emission periods are involved. An example is the disposal of nuclear or heavy metal-containing waste. In these cases, the results might completely depend on the discount rate. This paper helps to structure arguments and thus to support the decision about whether or not discounting should be applied in an LCA.     

Time,space, place,and the Bonn Challenge global forest restoration target

The Bonn Challenge, a global effort to begin restoring 350 million hectares of degraded forest landscapes by 2030, was launched in 2011. To date countries have committed to restore more than 60 million hectares as part of the Bonn Challenge. As global decision‐makers, governments, and communities join the effort to restore degraded land, new questions about the economics of restoration have emerged. Critics argue that restoration takes too long, costs too much, and produces too few benefits to justify public or private expenditures. This paper addresses these concerns by presenting a methodology for valuing the net benefits of large‐scale ecosystem restoration initiatives by estimating the net benefit of achieving the Bonn Challenge. This paper also estimates the net benefit of achieving the Bonn Challenge restoration target under different social discounting regimes, different valuations of public goods, and different time horizons to see how they affect the argument for investing society's scarce resources in restoration. The results suggest that achieving the Bonn Challenge would generate a net benefit of between U.S.$0.7 and U.S.$9 trillion. The results show that restoration can create benefits that exceed its costs and that the value of these benefits might differ depending on the discount rate. The results show that lower social discount rates correspond to higher restoration rates. This suggests that the Bonn Challenge target is more likely to be met when a low social discount rate is used to discount the benefits and costs of restoration.     

三江平原湿地生态系统生物多样性保护价值

生物多样性保护是三江平原湿地生态系统提供的一项重要的生态服务功能,具有重要的经济价值。应用M.Hoel和T.Sterner提出的经济模型,分析了贴现率和边际价格变化综合影响下的三江平原湿地生态系统生物多样性保护价值变化过程,研究了收入边际效用弹性和替代弹性对贴现率和边际价格变化综合效应的影响,并通过对比传统贴现方法揭示了三江平原湿地生态系统生物多样性保护所蕴含的巨大经济价值。研究结果表明,在贴现率和边际价格变化的综合影响下,三江平原湿地生态系统生物多样性保护价值曲线呈现出先增长再下降的变化趋势,总经济价值为人均19438.9元;收入边际效用弹性和替代弹性的取值对价值评估结果的影响较大,不同参数条件下的价值评估结果将最终作用于湿地生态系统保护相关决策的制定;价值评估结果同样证明了在保持经济较快速度发展的同时提高三江平原湿地生态系统生物多样性保护功能的恢复速率对于促进地区经济协调发展和提高社会福祉状况具有重要的现实意义。     

Commodity specific rates of temporal discounting: Does metabolic function underlie differences in rates of discounting?

Discounting rates vary as a function of commodity type. Previous studies suggest five potential characteristics of the commodity that could explain these differences: type of reinforcer (primary or secondary), if the commodity is perishable, if the commodity is satiable, if the commodity can be directly consumed, and immediacy of consumption. This paper suggests that these characteristics may best be viewed as related to a more fundamental characteristic: metabolic processing. In order to explore the possibility that metabolic processing underlies changes in discount rates, the difference in discounting between food, money, music CDs, DVDs, and books are compared. Music CDs, DVDs, and books share many characteristics in common with food, including gaining value through a physiological process, but are not directly metabolized. Results are consistent with previous findings of commodity specific discount rates and show that metabolic function plays a role in determining discount rates with those commodities that are metabolized being discounted at a higher rate. These results are interpreted as evidence that the discount rate for different commodities lies along a continuum with those that serve an exchange function rather than a direct function (money) anchoring the low end and those that serve a direct metabolic function capping the high end (food, alcohol, drugs).     

Time discounting and the body mass index: Evidence from the Netherlands

In many Western countries, the relative weight of people -- measured by the body mass index (BMI) -- has increased substantially in recent years, leading to an increasing incidence of overweight and related health problems. As with many forms of risky behavior, it is plausible that overweight is related to the individual discount rate. Increases in credit card debts, the rise in gambling and the development of a more hedonic life style, suggest that the average discount rate has increased over time. An increase in time discounting may be a contributing factor in the rise in BMI. Applying a large set of indicators for the individual discount rate from a Dutch survey, this paper analyzes whether changes in time discounting can account for differences in body mass between individuals at a given point in time and whether changes in the average individual discount rate can explain the remarkable increase in BMI experienced in recent years in the Netherlands. We find some evidence for a link between time discounting and differences in BMI between people, but this relationship depends strongly on the choice of the proxy for the discount rate. Giving our hypothesis the best chance, we analyze the development of the time discounting proxies that are most strongly related to BMI. We find no evidence for a change of these proxies over time. Our main conclusion therefore is that overweight might be related to the way people discount future health benefits, but the increase in BMI is more likely explained by shifts in other parameters that determine the intertemporal decisions regarding the trade-off of current and future health and satisfaction.     

On hyperbolic discounting and uncertain hazard rates

The value of a future reward should be discounted where there is a risk that the reward will not be realized. If the risk manifests itself at a known, constant hazard rate, a risk-neutral recipient should discount the reward according to an exponential time-preference function. Experimental subjects, however, exhibit short-term time preferences that differ from the exponential in a manner consistent with a hazard rate that falls with increasing delay. It is shown here that this phenomenon can be explained by uncertainty in the underlying hazard. The time-preference function predicted by this analysis can be calculated by means of either (i) a direct superposition method, or (ii) Bayesian updating of the expected hazard rate. The observed hyperbolic time-preference function is consistent with an exponential prior distribution for the underlying hazard rate. Sensitivity of the predicted time-preference function to variation in the probability distribution of the underlying hazard rate is explored.     

生物产品的经济效益优化

为了优化经济效益，许多文献一般以现值作为目标函数，其贴现率的主观性很大．本文以内部收益率作为目标函数，从根本上排除了主观性，与实际目标较为相符．     

最大可允许填海面积模拟——厦门西海域案例研究

填海造地在解决海岸带地区发展空间短缺问题的同时,严重损害了人类赖以生存和发展的海洋与海岸带生态系统。如何控制大规模填海造地是我国面临的重大课题。构建了估算海湾最大可允许填海造地面积的分析框架和模型。填海造地的各种收益和成本,包括环境和生态成本被系统性地量化并嵌入到框架和模型之中。模型的估算结果可以为实施控制填海造地的约束机制提供科技支撑。利用建立的框架和模型对厦门西海域模拟的结果显示:当贴现率为4.5%时,厦门西海域最大可允许填海面积是89.44 hm2,其面积至少应该保持在44.52 km2;即便是使用8%的高贴现率,最大可允许填海面积也只占规划填海面积的35.83%;如果采用更加重视环境与生态效益的低贴现率2%,则厦门西海域最大可允许填海面积是0。     

Optimal harvesting of fish stocks under a time-varying discount rate

Optimal control theory has been extensively used to determine the optimal harvesting policy for renewable resources such as fish stocks. In such optimisations, it is common to maximise the discounted utility of harvesting over time, employing a constant time discount rate. However, evidence from human and animal behaviour suggests that we have evolved to employ discount rates which fall over time, often referred to as “hyperbolic discounting”. This increases the weight on benefits in the distant future, which may appear to provide greater protection of resources for future generations, but also creates challenges of time-inconsistent plans. This paper examines harvesting plans when the discount rate declines over time. With a declining discount rate, the planner reduces stock levels in the early stages (when the discount rate is high) and intends to compensate by allowing the stock level to recover later (when the discount rate will be lower). Such a plan may be feasible and optimal, provided that the planner remains committed throughout. However, in practice there is a danger that such plans will be re-optimized and adjusted in the future. It is shown that repeatedly restarting the optimization can drive the stock level down to the point where the optimal policy is to harvest the stock to extinction. In short, a key contribution of this paper is to identify the surprising severity of the consequences flowing from incorporating a rather trivial, and widely prevalent, “non-rational” aspect of human behaviour into renewable resource management models. These ideas are related to the collapse of the Peruvian anchovy fishery in the 1970's.     

海洋工程生态损害评估与补偿——以厦门杏林跨海大桥为例

随着海岸带地区经济的发展、人口的增加和城市化程度的加快,日益增多的各类海洋工程已经或者正在损害海洋与海岸带生态系统为人类提供各种产品和服务的能力,严重威胁到人类健康和海洋经济的可持续发展。实施海洋生态损害补偿制度,即让生态损害责任方承担生态损害的全部成本,是解决海洋生态损害问题的有效途径之一。建立了海洋工程生态损害评估框架和生态损害补偿标准估算模型,并成功运用于厦门杏林跨海大桥的案例研究。结果表明,在2%的贴现率下,杏林大桥生态补偿标准为1739万元,远高于政府实际征收的补偿金额600万元。该评估框架信息需求量小,成本低且简单易行,在小规模海洋工程的生态损害评估与补偿方面有良好的应用前景。     

When Should Communities and Conservationists Monitor Exploited Resources?

Both conservationists and harvesters may be willing to contribute to participatory monitoring of exploited species. However, this can be costly and stakeholders need to choose whether monitoring programs or other alternatives, such as a moratorium or unmonitored exploitation, meet their objectives most efficiently. We discuss when, and how much, stakeholders may be willing to contribute to monitoring of exploited resources. We predict that communities’ contributions will usually be much less than the annual value of the harvest, and will be affected by their dependency upon it; their discount rate; its cultural importance, vulnerability to overexploitation and amenability to monitoring. ‘Efficient’ conservationists’ willingness to contribute should be similar to that of communities’, since monitoring and management programs must compete with compensated moratoria. The combined willingness to contribute of both stakeholder groups will usually be much less than twice the annual revenue from the resource. Applying this framework to a case-study of crayfish harvesting in Madagascar, we find that the total willingness to contribute to monitoring is likely to be insufficient to support conventional monitoring efforts. We conclude that conservation planners must be realistic about what stakeholders are willing to contribute to monitoring programmes and consider low cost methods or negotiated moratoria.     

在矿山废弃地上发展可再生能源的潜力——以辽宁省为例

在国内外碳减排压力和我国能源结构调整需求下,我国可再生能源的开发压力较大.矿山具有丰富的废弃土地,发展可再生能源的潜力巨大,在矿山废弃地上开发可再生能源对我国的能源战略具有重要意义.本研究以辽宁省矿山废弃地为例,提出矿山废弃地的生物质能与太阳能发展预案,估算辽宁省矿山废弃地的可再生能源发展潜力.结果表明:辽宁省1227.6 km2的矿山废弃地面积发展可再生能源的潜力较大,不同预案的潜力差异显著.预案1以光伏发电最大化为目标模式,总计可发电量为79.4 TWh,折标煤量32.1 Mt,碳减排量为79.1Mt CO2.预案2以生物质能源利用最大化为目标模式,光伏与生物质能总的发电量可达到31.2~33.1 TWh,折标煤量12.7~13.4 Mt,碳减排量为31.1~33.0 Mt CO2.预案3以矿山能源综合利用最大化为目标并兼顾生态修复的发展模式,光伏与生物质能总的发电量可达到62.3~63.7 TWh,折标煤量25.1~25.7 Mt,碳减排量为62.1~63.5 Mt CO2.3种预案的发电量在31.2~79.4 TWh,占辽宁省2016年总电力消费量的15.3%~38.9%,折标煤量12.7~32.1 Mt,碳减排量为31.1~79.1 Mt CO2.本研究对在矿山废弃地上发展可再生能源潜力及其替代化石能源能力的评估,对于碳减排、能源结构的调整以及矿山废弃地的生态修复具有重要的研究意义.     

Experimental and statistical considerations to avoid false conclusions in proteomics studies using differential in-gel electrophoresis

In quantitative proteomics, the false discovery rate (FDR) can be defined as the number of false positives within statistically significant changes in expression. False positives accumulate during the simultaneous testing of expression changes across hundreds or thousands of protein or peptide species when univariate tests such as the Student's t test are used. Currently most researchers rely solely on the estimation of p values and a significance threshold, but this approach may result in false positives because it does not account for the multiple testing effect. For each species, a measure of significance in terms of the FDR can be calculated, producing individual q values. The q value maintains power by allowing the investigator to achieve an acceptable level of true or false positives within the calls of significance. The q value approach relies on the use of the correct statistical test for the experimental design. In this situation, a uniform p value frequency distribution when there are no differences in expression between two samples should be obtained. Here we report a bias in p value distribution in the case of a three-dye DIGE experiment where no changes in expression are occurring. The bias was shown to arise from correlation in the data from the use of a common internal standard. With a two-dye schema, where each sample has its own internal standard, such bias was removed, enabling the application of the q value to two different proteomics studies. In the case of the first study, we demonstrate that 80% of calls of significance by the more traditional method are false positives. In the second, we show that calculating the q value gives the user control over the FDR. These studies demonstrate the power and ease of use of the q value in correcting for multiple testing. This work also highlights the need for robust experimental design that includes the appropriate application of statistical procedures.     

Optimal harvesting with exponential growth in an environment with random disasters and bonanzas

The optimal discounted present value of an exploited population under constant effort harvesting in an environment with random disasters and bonanzas is investigated. The deterministic component of growth is density independent (also called Malthusian or exponential). The disasters and bonanzas are random, occurring at the times of events of a Poisson process. The density independent properties of the model and the constant effort open loop policy lead to an exact solution for the expected present value. The optimal expected present value is compared with those in deterministic models with and without deterministic type jumps. Both deterministic and random jumps can have a significant influence on the optimal present value. However, the effort to achieve the optimal is not sensitive to variations in the total jump frequency or in the discount rate. The average random jump model is much easier to apply than the deterministic jump model. Bonanzas can have much more of an effect on the present value than disasters given similar jump rates.     

Optimal harvesting of a logistic population in an environment with stochastic jumps

Dynamic programming is employed to examine the effects of large, sudden changes in population size on the optimal harvest strategy of an exploited resource population. These changes are either adverse or favorable and are assumed to occur at times of events of a Poisson process. The amplitude of these jumps is assumed to be density independent. In between the jumps the population is assumed to grow logistically. The Bellman equation for the optimal discounted present value is solved numerically and the optimal feedback control computed for the random jump model. The results are compared to the corresponding results for the quasi-deterministic approximation. In addition, the sensitivity of the results to the discount rate, the total jump rate and the quadratic cost factor is investigated. The optimal results are most strongly sensitive to the rate of stochastic jumps and to the quadratic cost factor to a lesser extent when the deterministic bioeconomic parameters are taken from aggregate antarctic pelagic whaling data.Research supported in part by the National Science Foundation under grants MCS 81-01698 and MCS 83-00562.     

Temporal estimates of effective population size in species with overlapping generations

The standard temporal method for estimating effective population size (N(e)) assumes that generations are discrete, but it is routinely applied to species with overlapping generations. We evaluated bias in the estimates N(e) caused by violation of this assumption, using simulated data for three model species: humans (type I survival), sparrow (type II), and barnacle (type III). We verify a previous proposal by Felsenstein that weighting individuals by reproductive value is the correct way to calculate parametric population allele frequencies, in which case the rate of change in age-structured populations conforms to that predicted by discrete-generation models. When the standard temporal method is applied to age-structured species, typical sampling regimes (sampling only newborns or adults; randomly sampling the entire population) do not yield properly weighted allele frequencies and result in biased N(e). The direction and magnitude of the bias are shown to depend on the sampling method and the species' life history. Results for populations that grow (or decline) at a constant rate paralleled those for populations of constant size. If sufficient demographic data are available and certain sampling restrictions are met, the Jorde-Ryman modification of the temporal method can be applied to any species with overlapping generations. Alternatively, spacing the temporal samples many generations apart maximizes the drift signal compared to sampling biases associated with age structure.