Minimax regret discounting

The paper considers an environmental policy decision in which the appropriate approach for discounting future costs and benefits is unknown. Uncertainty about the discount rate is formulated as a decision under Knightian uncertainty. To solve this, we employ minimax regret, a decision criterion that is much less conservative then the related criterion maximin—in particular, it can be shown to implement a “proportional response” in that it equally balances concern about the mistake of doing too little with that of doing too much. Despite the criterion's balanced nature, the minimax regret solution mimics a policy that maximizes the present discounted value of future net benefits with an effective (certainty-equivalent) discount rate that declines over time to the lowest possible rate. In addition to reinforcing Weitzman's (1998) original limiting result, the approach generates concrete policy advice when decision makers are unable to specify a prior over possible discount rates. We apply it to the Stern–Nordhaus discounting debate and find that the effective discount rate converges to the Stern rate in just under 200 years.     

The endowment effect,discounting and the environment

There is a considerable body of evidence showing that our preferences exhibit both reference dependence and loss aversion, a.k.a. the endowment effect. In this paper, we consider the implications of the endowment effect for discounting, with a special focus on discounting future improvements in the environment. We show that the endowment effect modifies the discount rate via (i) an instantaneous endowment effect and (ii) a reference-updating effect. Moreover we show that these two effects often combine to dampen the preference to smooth consumption over time. What this implies for discounting future environmental benefits may then depend critically on whether environmental quality is merely a factor of production of material consumption, or whether it is an amenity. On an increasing path of material consumption, dampened consumption smoothing implies a lower discount rate. But on a declining path of environmental quality and where we derive utility directly from environmental quality, it implies a higher discount rate. On non-monotonic paths, loss aversion specifically can give rise to substantial discontinuities in the discount rate.     

环境风险知觉和评价的整体框架

环境风险通常发生在一定时间之后,以某种可能性发生在某个特定的地方,使得某些人群受到影响。因此,环境风险是典型的多维度事件,它涵盖四个基本的偏好维度：时间、空间、概率与社会性,每个维度都可能导致环境风险知觉和评价出现折扣（discount）现象。但是,传统视角往往关注单一维度,主要是时间,因而割裂了维度的整体性。基于环境风险的多维度特征,提出了一个统一的多维度偏好框架,为环境风险知觉及评价提供整体性视角。这四个偏好维度统一的内在原因是心理距离。维度共性意味着时间维度上的折现机制能够应用到其它维度,为此,对环境风险跨期评价中关于折现率热点问题的研究进展进行了一个关键的梳理。未来有必要在此整体框架下,重点关注三个方面的问题：（1）环境折现率,对环境折现率的要素及其关系进行规范性分析,进而分析环境贴现率与经济贴现率之间的关系,及双率折现对可持续发展的涵义;（2）基于维度共性,将时间维度上的研究结论应用到其它维度;（3）研究多重维度复合情形下的偏好和评价问题,建立综合性描述模型,依托具体案例探讨有效的环境风险沟通策略、环境政策和制度设计。     

Accounting for Uncertainty in Making Species Protection Decisions

Abstract:  Uncertainty gives rise to two decision errors in implementing the U.S. Endangered Species Act: listing species that are not in danger of extinction and delisting species that are in danger of extinction. I evaluated four methods (minimum standard, precautionary principle, minimax regret criterion, adaptive management) for deciding whether to list or delist a species when there is uncertainty about how those decisions are likely to influence survival of the species. A safe minimum standard criterion preserves some minimum amount or safe standard (population) of a species unless maintaining that amount generates unacceptable social cost. The precautionary principle favors not delisting a species when there is insufficient evidence on the efficacy of state management plans for protecting them. A minimax regret criterion selects the delisting decision that minimizes the maximum loss likely to occur under alternative ecosystem states. When the cost of making a correct decision is less than the cost of making an incorrect decision, the minimax regret criteria indicates that delisting is the optimal decision. Active adaptive management employs statistically valid experiments to test hypotheses about the likely impacts of delisting decisions. Safe minimum standard and minimax regret criterion are not compatible with the U.S. Endangered Species Act. The precautionary principle comes closest to describing how federal agencies make delisting decisions. Active adaptive management is scientifically superior to the other methods but is costly and time consuming and may not be compatible with the U.S. National Environmental Policy Act.     

Evidence of variable discount rates and non-standard discounting in mortality risk valuation

Time discounting is central to the valuation of future health and mortality risks in public sector allocative decision-making, particularly for environmental policies with delayed health impacts. Using a Risk-Risk trade-off survey, we elicit discount rates for fatality risks and establish discounting functional forms on both a sample and an individual level. We find wide variation in implicit discount rates for fatality risk between individuals, as well as between-individual heterogeneity in discounting functional forms. In aggregate, the sample is best characterised by subadditive discounting. Our work has implications for the academic investigation of intertemporal choice involving mortality risks, and potentially for the evaluation of policy options with delayed mortality risk outcomes. A thought experiment cautions against the standard practice of assuming that exponential discounting characterises society's time preferences.     

Time perspective and climate change policy

The tendency to foreshorten time units as we peer further into the future provides an explanation for hyperbolic discounting at an inter-generational time scale. We study implications of hyperbolic discounting for climate change policy, when the probability of a climate-induced catastrophe depends on the stock of greenhouse gasses. We characterize the set of Markov perfect equilibria (MPE) of the inter-generational game amongst a succession of policymakers. Each policymaker reflects her generation's preferences, including its hyperbolic discounting. For a binary action game, we compare the MPE set to a “restricted commitment” benchmark. We compare the associated “constant-equivalent discount rates” and the willingness to pay to control climate change with assumptions and recommendations in the Stern Review on Climate Change.“…My picture of the world is drawn in perspective…. I apply my perspective not merely to space but also to time”—Ramsey.     

Discounting for personal and social payments: Patience for others,impatience for ourselves

The market rate of return on private investment is often used as the discount rate when conducting cost-benefit analysis (CBA) of public projects. I argue that the decision to invest pits current consumption against future consumption, both of which accumulate to the private decision maker. Public projects, on the other hand, provide benefits that accrue to society in general. To examine the appropriateness of discount rates based on returns to private investment, this paper considers lab experiments designed to test whether individuals discount personal and social benefits at different rates. Personal benefits are captured through personal monetary payments, while social benefits are captured through anonymous donations to charitable organizations. I jointly elicit time and risk preferences and find that subjects discount charitable contributions at significantly lower rates than personal payments.     

Discounting for personal and social payments: Patience for others,impatience for ourselves

The market rate of return on private investment is often used as the discount rate when conducting cost-benefit analysis (CBA) of public projects. I argue that the decision to invest pits current consumption against future consumption, both of which accumulate to the private decision maker. Public projects, on the other hand, provide benefits that accrue to society in general. To examine the appropriateness of discount rates based on returns to private investment, this paper considers lab experiments designed to test whether individuals discount personal and social benefits at different rates. Personal benefits are captured through personal monetary payments, while social benefits are captured through anonymous donations to charitable organizations. I jointly elicit time and risk preferences and find that subjects discount charitable contributions at significantly lower rates than personal payments.     

Time discounting and the decision to protect areas that are near and threatened or remote and cheap to acquire

Should conservation organizations focus on protecting habitats that are at imminent risk of being converted but are expensive or more remote areas that are less immediately threatened but where a large amount of land can be set aside? Variants of this trade‐off commonly arise in spatial planning. I used models of land‐use change near a deforestation frontier to examine this trade‐off. The optimal choice of where to protect was determined by how decisions taken today accounted for ecological benefits and economic costs of conservation actions that would occur sometime in the future. I used an ecological and economic discount rate to weight these benefits and costs. A large economic discount rate favored protecting more remote areas, whereas a large, positive ecological discount rate favored protecting habitat near the current deforestation frontier. The decision over where to protect was also affected by the influence economic factors had on landowners' decisions, the rate of technological change, and ecological heterogeneity of the landscape. How benefits and costs through time are accounted for warrants careful consideration when specifying conservation objectives. It may provide a niche axis along which conservation organizations differentiate themselves when competing for donor funding or other support.     

Modelling carbon storage in highly fragmented and human-dominated landscapes: Linking land-cover patterns and ecosystem models

To extend coupled human–environment systems research and include the ecological effects of land-use and land-cover change and policy scenarios, we present an analysis of the effects of forest patch size and shape and landscape pattern on carbon storage estimated by BIOME-BGC. We evaluate the effects of including within-patch and landscape-scale heterogeneity in air temperature on carbon estimates using two modelling experiments. In the first, we combine fieldwork, spatial analysis, and BIOME-BGC at a 15-m resolution to estimate carbon storage in the highly fragmented and human-dominated landscape of Southeastern Michigan, USA. In the second, we perform the same analysis on 12 hypothetical landscapes that differ only in their degree of fragmentation. For each experiment we conduct four air-temperature treatments, three guided by field-based data and one empirically informed by local National Weather Service station data. The three field data sets were measured (1) exterior to a forest patch, (2) from the patch edge inward to 60 m on east-, south-, and west-facing aspects, separately, and (3) interior to that forest patch. Our field-data analysis revealed a decrease in maximum air temperature from the forest patch edge to a depth of 80 m. Within-patch air-temperature values were significantly different (α = 0.01) among transects (c.v. = 13.28) and for all measurement locations (c.v. = 30.58). Results from the first experiment showed that the interior treatment underestimated carbon storage by ～8000 Mg C and the exterior treatment overestimated carbon storage by 30,000 Mg C within Dundee Township, Southeastern Michigan, when compared to a treatment that included within-patch heterogeneity. In the second experiment we found a logarithmic increase in carbon storage with increasing fragmentation (r² = 0.91). While a number of other processes (e.g. altered disturbance frequency or severity) remain to be included in future experiments, this combined field and modelling study clearly demonstrated that the inclusion of within-patch and landscape heterogeneity, and landscape fragmentation, each have a strong effect on forest carbon cycling and storage as simulated by a widely used ecosystem process model.     

The effects of summer heat on academic achievement: A cohort analysis

This paper analyzed the effect of summer heat on academic achievement. Summer heat can negatively affect student learning, as previous studies have shown that high temperatures in laboratory settings have a negative effect on cognitive abilities. For this analysis, the test scores of five different cohorts were combined with city-level daily temperature data. To control for unobserved heterogeneity, the test scores of students within the same school were compared over time (school-fixed effects estimation). Summer heat negatively affected student test scores. Specifically, an additional day with a maximum daily temperature exceeding 34 °C (93.2 °F) during the summer, relative to a day with a maximum temperature between 28 °C (82.4 °F) and 30 °C (86 °F), decreased the scores of math and English tests by 0.0042 and 0.0064 standard deviations, respectively. No significant effects were found on the reading test scores. In addition, these effects were larger in relatively cooler cities, but did not differ based on gender. Finally, the previous year's summer also had negative effects on the current year's test scores.     

Modeling and coupling of soil respiration and soil water content in fenced Leymus chinensis steppe,Inner Mongolia

Soil respiration was measured with the enclosed chamber method during 2 years in fenced Leymus chinensis steppe, Inner Mongolia, China. Soil water content at 0–10 cm depth was a major limited factor of soil respiration in semi-arid grassland, accounting for 76.4% of the variation. The temperature-dependent exponential function could only explain 38.7% of the variation in soil respiration. With 246 data over the entire experimental period, multiple linear stepwise regressions of soil respiration rate were analyzed with the influencing factors, including soil water content at 0–10 cm depth, air temperature, air pressure, air humidity, total radiation and their interactions. With soil water content at 0–10 cm depth (W) and air temperature (T_h) as combined factors, the twice linear regression (F = 1.68WT_h − 109.09) was simple and its coefficients were significant, accounting for 83.1% of the variation in soil respiration. Due to the lack of long-term and continuous soil water content, a water sub-model based on precipitation and evapotranspiration was introduced, which could provide better fits with the measured values (R² = 0.813). The magnitudes of soil respiration calculated from the twice linear regression equation and water sub-model were 439.58 and 463.06 g CO₂ m⁻² in 2001 (19 June–23 September) and in 2002 (1 June–24 September), respectively. The mean hourly soil respiration rates were in the range of the previous studies in the adjacent region and the world's major temperate grasslands.     

Population growth versus population spread of an ant-dispersed neotropical herb with a mixed reproductive strategy

In plants that produce seeds with contrasting genetic background (selfed versus outcrossed), the question arises whether the ecological function of the two types of progeny differ. This paper addresses this issue for the ant-dispersed Calathea micans by introducing a novel application of the Neubert–Caswell model for analysis of wave speed for structured populations. Because dispersal as well as vital rates are structured, the model allows for distinct dispersal kernels for different types of progeny and thus permits comparisons of the sensitivity to changes in demographic and dispersal parameters of in situ population growth rate versus population spread across space. The study site was a lowland, evergreen tropical rain forest at La Selva Biological station, Costa Rica, where the species is commonly found throughout the forest. In C. micans, seeds produced by open flowers (potentially outcrossed) or by closed flowers (selfed) bear oily arils and are dispersed by ants. Five life-history stages were used to characterize the population: seedlings originating from seeds produced by open flowers, seedlings originating from seeds produced by closed flowers, juvenile vegetative plants, reproductive plants without new shoots and reproductive plants with new shoots. Demography varied seasonally. Transitions were estimated from marking and following the fate of plants (N = 400) in a natural population over a dry and a wet season. The population dynamics was described by a 10 × 10 matrix, with five life-history stages and two habitat states. The habitat states cycle repeatedly, dry–wet–dry–wet. To estimate dispersal kernels for each seed type, individual seeds (N = 225 and 306 seeds produced by open and closed flowers, respectively) were color-coded and placed in depots, allowing the ants to redistribute them. Five months later, seedlings with an attached seed coat bearing the intact color-coding, were surveyed around the depots. Radial distances and angles were recorded for each seedling (N = 67 and 81 seedlings arising from open and closed flowers, respectively). The results of the model give an asymptotic growth rate of 1.06 per season and an asymptotic rate of spread of 8.36 cm per season. There is a high correlation (r = 0.99) between elasticity of growth rate and elasticity of rate of spread of the population. Both rates are most sensitive to changes in stasis of juveniles during the dry season. However, most interesting is the analysis that revealed that population spread is more sensitive than in situ population growth to demographic rates of seedlings arising from open flowers. The analysis suggests a new way of thinking about ecological functions of multiple modes of reproduction.     

Modelling CO2 and energy exchanges in a northern semiarid grassland using the carbon- and nitrogen-coupled Canadian Land Surface Scheme (C-CLASS)

The development of carbon (C) and nitrogen (N) simulations is one of the ongoing efforts in the land surface schemes of climate models. The C- and N-coupled Canadian Land Surface Scheme (C-CLASS) was recently modified to better represent grassland ecosystems. Improvements include revised plant growth and senescence calculations that are driven by the plant C balance between fixation and respiration, and leaf-out and leaf-fall schemes that are regulated by the seasonal dynamics of C and N reserves. These revisions were developed to better simulate the stress-related senescence and regrowth of perennials. The model was tested with observations of surface carbon and energy fluxes, soil temperature and moisture, and plant growth during 3 years of declining precipitation at a northern semiarid grassland near Lethbridge, Alberta, Canada. The R² and standard deviations between the simulated and observed half-hourly fluxes were 0.95 and 22.5 W m⁻² for net radiation, 0.82 and 42.1 W m⁻² for sensible heat, 0.66 and 29.2 W m⁻² for latent heat, and 0.63 and 0.95 μmol C m⁻² s⁻¹ for net CO₂ exchange. The model and observations both showed a strong impact of declining precipitation on annual carbon budgets in this semi-arid grassland. In a wet year (1998, precipitation = 482 mm), the ecosystem acted as a strong C sink (92 g C m⁻² modelled and 109 g C m⁻² measured from June 20th to December 31st). In a near-normal year (1999, precipitation = 341 mm), a smaller C sink was indicated (24 g C m⁻² modelled and 21 g C m⁻² measured). In a dry year (2000, precipitation = 276 mm), the ecosystem acted as a small C source (−18 g C m⁻² modelled and −17 g C m⁻² measured).     

Analyzing and modelling spatial distribution of summering lesser kestrel: The role of spatial autocorrelation

In modelling spatial distribution of species, ignoring spatial autocorrelation (SA) and multicollinearity may lead to false ecological conclusions. Here we take into account both issues for examining and modelling the spatial pattern of abundance of the globally threatened lesser kestrel (Falco naumanni) during summer in a 38,400 ha area of northwestern Spain where large premigratory aggregations of the species occur. Spatial pattern was examined using Moran's correlogram, and models were built including geographical coordinates and autocovariate terms (which account for SA) in generalized linear models (GLM) and hierarchical partitioning (HP) models. HP models allow to alleviate multicollinearity. A grid-based approach was used by dividing the study area in 24 contiguous 4 km × 4 km squares where birds were counted in 2–3 visits per square (response variable). Environmental coarse-grained variables were extracted from a geographic information system (GIS) at three spatial extents. Moran's correlogram showed that lesser kestrel mean abundance per square was spatially autocorrelated up to 4–8 km. The results from both GLM and HP analyses were roughly compatible. The GLM models explained 80.0% of the variation in kestrel abundance and were the same at the three spatial extents. Lesser Kestrel abundance was not significantly explained by landscape variables, but was negatively related to both the distance to the nearest communal roost and distance to the nearest breeding colony with more of 10 breeding pairs of lesser kestrel. An autocovariate term added later in the GLM models improved both their explanatory power (from 74.5 to 80.0%) and model residuals, which were not longer spatially autocorrelated, fulfilling thus the statistical assumption of independent errors. Findings suggest that the spatial distribution of abundance of summering lesser kestrel is, at least, partially driven by endogenous causes, such as conspecific attraction. Exogenous causes such as finer-scale variables (e.g. type of crops and food available) are yet likely needed for lesser kestrel-environment relationships.     

Effect of risk aversion on prioritizing conservation projects

Conservation outcomes are uncertain. Agencies making decisions about what threat mitigation actions to take to save which species frequently face the dilemma of whether to invest in actions with high probability of success and guaranteed benefits or to choose projects with a greater risk of failure that might provide higher benefits if they succeed. The answer to this dilemma lies in the decision maker's aversion to risk—their unwillingness to accept uncertain outcomes. Little guidance exists on how risk preferences affect conservation investment priorities. Using a prioritization approach based on cost effectiveness, we compared 2 approaches: a conservative probability threshold approach that excludes investment in projects with a risk of management failure greater than a fixed level, and a variance‐discounting heuristic used in economics that explicitly accounts for risk tolerance and the probabilities of management success and failure. We applied both approaches to prioritizing projects for 700 of New Zealand's threatened species across 8303 management actions. Both decision makers’ risk tolerance and our choice of approach to dealing with risk preferences drove the prioritization solution (i.e., the species selected for management). Use of a probability threshold minimized uncertainty, but more expensive projects were selected than with variance discounting, which maximized expected benefits by selecting the management of species with higher extinction risk and higher conservation value. Explicitly incorporating risk preferences within the decision making process reduced the number of species expected to be safe from extinction because lower risk tolerance resulted in more species being excluded from management, but the approach allowed decision makers to choose a level of acceptable risk that fit with their ability to accommodate failure. We argue for transparency in risk tolerance and recommend that decision makers accept risk in an adaptive management framework to maximize benefits and avoid potential extinctions due to inefficient allocation of limited resources. El Efecto de la Aversión de Riesgo sobre la Priorización de Proyectos de Conservación     

Nitrogen controls on ecosystem carbon sequestration: a model implementation and application to Saskatchewan,Canada

A plant–soil nitrogen (N) cycling model was developed and incorporated into the Integrated BIosphere Simulator (IBIS) of Foley et al. [Foley, J.A., Prentice, I.C., Ramankutty, N., Levis, S., Pollard, D., Sitch, S., Haxeltine, A., 1996. An integrated biosphere model of land surface process, terrestrial carbon balance and vegetation dynamics. Global Biogeochem. Cycles 10, 603–628]. In the N-model, soil mineral N regulates ecosystem carbon (C) fluxes and ecosystem C:N ratios. Net primary productivity (NPP) is controlled by feedbacks from both leaf C:N and soil mineral N. Leaf C:N determines the foliar and canopy photosynthesis rates, while soil mineral N determines the N availability for plant growth and the efficiency of biomass construction. Nitrogen controls on the decomposition of soil organic matter (SOM) are implemented through N immobilization and mineralization separately. The model allows greater SOM mineralization at lower mineral N, and conversely, allows greater N immobilization at higher mineral N. The model's seasonal and inter-annual behaviours are demonstrated. A regional simulation for Saskatchewan, Canada, was performed for the period 1851–2000 at a 10 km × 10 km resolution. Simulated NPP was compared with high-resolution (1 km × 1 km) NPP estimated from remote sensing data using the boreal ecosystem productivity simulator (BEPS) [Liu, J., Chen, J.M., Cihlar, J., Park, W.M., 1997. A process-based boreal ecosystem productivity simulator using remote sensing inputs. Remote Sens. Environ. 44, 81–87]. The agreement between IBIS and BEPS, particularly in NPP spatial variation, was considerably improved when the N controls were introduced into IBIS.     

A peaked function for modeling temperature dependence of plant productivity

We suggests that temperature response of plant productivity can be modeled by the Arrhenius function modified to describe the effect of temperature on enzyme activity: G_A(T) = 2f(T)/(1 + f²(T)), where f(T) = exp(E_a/RT_opt − E_a/RT), R the universal gas constant, E_a the activation energy and T_opt is the optimal temperature. In common with other functions used for modeling the temperature response of plant productivity, the curve of function G is almost symmetrical and bell-shaped. The special convenience of G_A is that it relates the width of the “bell” to thermodynamic concepts, such as activation energy of chemical reactions converting carbon dioxide and water to carbohydrates.     

Ambiguity,reasoned determination,and climate-change policy

This paper examines climate-change benefit-cost analysis in the presence of scientific uncertainty in the form of ambiguity. The specific issue addressed is the robustness of benefit-cost analyses of climate-change policy alternatives to relaxation of Savage's original axioms. Two alternatives to subjective expected utility (SEU) are considered: maximin expected utility (MEU) and incomplete expected utility (IEU). Among other results, it is demonstrated that polar opposite recommendations can emerge in an ambiguous decision setting even if all agree on Society's rate of time preference, Society's risk attitudes, the degree of ambiguity faced, and the scientific primitives. We show that, for a simple numerical simulation of our model, an MEU decision maker favors policies which immediately tackle climate change while an IEU decision prefers “business as usual”.“Each agency shall assess the costs and benefits of the intended regulation, and recognizing that some costs and benefits are difficult to quantify, propose or adopt a regulation only upon a reasoned determination that the benefits of the intended regulation justify its cost.” Executive Order 12866 of the US President.     

Optimal harvesting of a plant-hervibore system: lichen and reindeer in northern Finland

The optimal harvesting policy for a plant-herbivore system consisting of lichen and reindeer in Finnish Lapland is investigated. Using a discrete time model with no age structure it is shown that the optimal procedure to reach target levels for lichen and reindeer involves a possible initial harvest of reindeer and then a sequence of no-harvesting years until the lichen has recovered. After two adjusting harvests the system will settle to an equilibrium. The optimal solution is compared with the fastest possible approach to the target levels. The two solutions coincide if future yields are sufficiently discounted. With a discount factor near one there will be a heavier initial harvest in the optimal solution. It is seen that allowing some harvesting also in the no-harvesting years has no marked effect on the total yield. The target levels for lichen and reindeer are not unique but depend both on discounting and on the length of the planning period.