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.     

How certain are we about the certainty-equivalent long term social discount rate?

Theoretical arguments for using a term structure of social discount rates (SDR) that declines with the time horizon have influenced government guidelines in the US and Europe. The certainty equivalent discount rate that often underpins this guidance embodies uncertainty in the primitives of the SDR, such as growth. For distant time horizons the probability distributions of these primitives are ambiguous and the certainty equivalent itself is uncertain. Yet, if a limited set of characteristics of the unknown probability distributions can be agreed upon, ‘sharp’ upper and lower bounds can be defined for the certainty-equivalent SDR. Unfortunately, even with considerable agreement on these features, these bounds are widely spread for horizons beyond 75 years. So while estimates of the present value of intergenerational impacts, including the social cost of carbon, can be bounded in the presence of this ambiguity, they typically remain so imprecise as to provide little practical guidance.     

Sustainability, limited substitutability, and non-constant social discount rates

The paper shows how limited substitutability in consumption between different classes of goods affects the magnitude and time development of social discount rates. It decomposes the discount rates into an absolute growth and a relative growth or substitutability effect. The paper relates between-good and intertemporal substitutability to the notions of weak and strong sustainability. It analyzes under which circumstances low as opposed to high between-good substitutability increases the weights given to long-run environmental services.     

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。     

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.     

The derivation of discount rates with an augmented measure of income

Most developed economies invest in public goods such as national defense, education, infrastructure, and the environment. Discount rates used to evaluate such projects should reflect the rate of return on the current mix of investment opportunities. Rates derived from the productivity of private capital neglect returns beyond the market boundary. The present paper derives discount rates using an augmented measure of national income inclusive of non-market goods. In an empirical application focusing on air pollution and climate damages in the United States economy, the paper reports that the difference between augmented and market discount rates averages 0.3 percentage points from 1999 to 2014.     

Numerical analysis of non-constant pure rate of time preference: A model of climate policy

When current decisions affect welfare in the far-distant future, as with climate change, the use of a declining pure rate of time preference (PRTP) provides potentially important modeling flexibility. The difficulty of analyzing models with non-constant PRTP limits their application. We describe and provide software (available online) to implement an algorithm to numerically obtain a Markov perfect equilibrium for an optimal control problem with non-constant PRTP. We apply this software to a simplified version of the numerical climate change model used in the Stern Review. For our calibration, the policy recommendations are less sensitive to the PRTP than widely believed.     

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.     

Integrating soil carbon cycling with that of nitrogen and phosphorus in the watershed model SWAT: Theory and model testing

In this paper we describe and test a sub-model that integrates the cycling of carbon (C), nitrogen (N) and phosphorus (P) in the Soil Water Assessment Tool (SWAT) watershed model. The core of the sub-model is a multi-layer, one-pool soil organic carbon (S_C) algorithm, in which the decomposition rate of S_C and input rate to S_C (through decomposition and humification of residues) depend on the current size of S_C. The organic N and P fluxes are coupled to that of C and depend on the available mineral N and P, and the C:N and N:P ratios of the decomposing pools. Tillage explicitly affects the soil organic matter turnover rate through tool-specific coefficients. Unlike most models, the turnover of soil organic matter does not follow first order kinetics. Each soil layer has a specific maximum capacity to accumulate C or C saturation (S_x) that depends on texture and controls the turnover rate. It is shown in an analytical solution that S_x is a parameter with major influence in the model C dynamics. Testing with a 65-yr data set from the dryland wheat growing region in Oregon shows that the model adequately simulates the S_C dynamics in the topsoil (top 0.3 m) for three different treatments. Three key model parameters, the optimal decomposition and humification rates and a factor controlling the effect of soil moisture and temperature on the decomposition rate, showed low uncertainty as determined by generalized likelihood uncertainty estimation. Nonetheless, the parameter set that provided accurate simulations in the topsoil tended to overestimate S_C in the subsoil, suggesting that a mechanism that expresses at depth might not be represented in the current sub-model structure. The explicit integration of C, N, and P fluxes allows for a more cohesive simulation of nutrient cycling in the SWAT model. The sub-model has to be tested in forestland and rangeland in addition to agricultural land, and in diverse soils with extreme properties such high or low pH, an organic horizon, or volcanic soils.