Optimal rotation with declining discount rate

In recent years it has been argued, from many perspectives, that the further into the future a value flow occurs, the lower is the appropriate discount rate for it. National governments are now beginning to authorise such declining discount rates. This viewpoint can be, and has been, formalised in various ways, and has been applied to evaluating forestry investments of given durations. When the optimal duration of investment is itself the issue, new problems arise. Lower discount rates make subsequent rotations longer than earlier ones, and for a given length more valuable than they would otherwise be. This affects the optimal length of earlier rotations, which in turn may affect the discount rate profile applicable to later ones. In the absence of analytical solutions for the optimal sequence of rotations, numerical protocols are needed. The results arising are mostly in accord with expectations. If the change of discount rate is due to expected changes of circumstance that are actually realised, then the optimal sequence of rotations will remain as initially determined. If, however, it is due merely to the particular time perspective of the present generation, rotations will be revised by future generations. This will lead to a sequence of rotations similar to that deemed optimal at the current short-term discount rate. The most important reductions in profitability caused by choosing the “wrong” discounting protocol arise from the “wrong” rate, rather than by using declining rates as such.     

Decision-making Criteria for Purchasing Milk Quota at the Individual Farm Level

Dairy farmers wishing to contemplate purchases of additional quota should first consider what the appropriate time horizon on their investment should be. If the chosen time horizon is one year or less, the problem of estimating how much they can afford to bid for quota can be solved with simple budgeting techniques. On the other hand, if the time horizon is taken as several years, and this would seem rational, then capital budgeting techniques are required. However, in either case, investment in additional quota should be compared with alternative investment opportunities before a final decision is made. Where capital budgeting techniques are used, a modification of the net present value approach permits the farmer to take account of his time preference for money, and allows calculation of the break-even price, or the maximum affordable price to pay for additional quota. This approach necessitates the provision of estimates of the expected net returns from investing in quota for each year of the selected time horizon, as well as provision of estimates of the salvage value of the quota and an appropriate discount rate. The calculation of the expected net returns figures represents the most difficult task for the farmer. If expansion of milk shipments rests upon increasing output of milk per cow, then the short-run production function and marginal cost curve provide the appropriate reference points. The expected net return on investment in quota is then given by the area under the marginal revenue line and above the relevant portion of the marginal cost curve. If, however, all short-run variable input decisions have already been implemented at the optimum level, and expansion of milk shipments depends upon expanding the number of cows, or the “fixed” plant and equipment, or both, then the average total cost curve is the appropriate reference point. The expected net return on investment in quota is then represented by the difference between total net revenue at the new planned level of output and total net revenue at the existing level of output.     

Optimal rotation with negative discount rates: completing the picture

While the rotation of maximum forest rent (no discounting of revenues and costs) is sometimes discussed conceptually and calculated practically, forest economists have almost invariably focused on optimal rotation with a positive discount rate. Some circumstances, especially related to increasing marginal utility with decreasing availability per head of products, would justify use of a negative discount rate. For a logically complete suite of conditions, a means of identifying optimal rotation with such a rate is needed. Applying the usual formulation for land expectation value then produces a meaningless result. Two approaches seem to give a solution. One uses the first-order conditions for an optimum. Another uses inversion of time perspective to produce sensible-seeming results. However, for cases where the world, or the value of forest production, ends suddenly at an unpredictable time, the optimal rotation is, surprisingly, that of maximum forest rent. Where the cause of negative discount rates is of limited duration before stability or growing affluence is re-established, this “provisional optimum” can be modified responsively.     

Regulating Nitrogen Pollution with Risk Averse Farmers under Hidden Information and Moral Hazard

We consider a model of pollution regulation for a risk averse farmer involving hidden information, moral hazard, and risk-sharing. The representative farmer faces a production risk originating from nitrogen leaching, and privately observes the soil capacity in retaining nitrogen only after the regulation contract is signed. The latter specifies a transfer and a nitrogen quota, whose decomposition by the farmer among different production stages is unknown to the regulator. We first characterize the optimal solution to the regulator's problem. The sequential decision model is estimated on French crop production data, and the results are used to calibrate and simulate the optimal contract.     

Rewarding carbon sequestration in South-Western French forests: A costly operation?

The extension of rotation lengths in forests has been proposed as an option for increasing carbon storage and contributing to climate change mitigation. This paper presents the results of a case study conducted on forests located in the southwest of France. The aim of this research was to assess the cost effectiveness of a subsidy/tax system on carbon fluxes. First, it is shown that such a mechanism leads forest owners to extend rotation lengths. However, cost effectiveness analysis shows that: (1) marginal social costs are more expensive than the private marginal costs of carbon sequestration; (2) marginal costs are higher when carbon stocks are discounted, ranging from 170.1 €/tC to 719.8 €/tC with discounted carbon stocks; and from 38.8 €/tC to 78.4 €/tC with undiscounted carbon stocks; (3) marginal costs are in the range of measures of the social value of carbon for France; (4) marginal costs increase with timber prices and increase with discount rate.     

Compliance Monitoring and Agri-Environmental Policy

This paper examines the issue of compliance monitoring in agri-environmental policy when a farmer is risk-neutral and risk-averse. The optimal contract model presented here significantly extends and generalises the results and conclusions of Choe and Fraser (1998). In this paper the environmental agency explicitly chooses monitoring accuracy and monitoring costs as well as rewards for farmers. It is found that, by modelling the environmental agency as being cost-conscious optimal monitoring accuracy may or may not be higher for a risk-averse farmer than for a risk-neutral farmer. Essentially, the environmental agency faces an explicit trade-off between monitoring costs and incentive payments as a means to ensure the desired behaviour from the farmer. The importance of the results derived are discussed in the context of agri-environmental policy design and implementation     

Potential demand for hedging by Australian wheat producers

The potential for hedging Australian wheat with the new Sydney Futures Exchange wheat contract is examined using a theoretical hedging model parametised from previous studies. The optimal hedging ratio for an ‘average’ wheat farmer was found to be zero under reasonable assumptions about transaction costs and based on previously published measures of risk aversion. The estimated optimal hedging ratios were found by simulation to be quite sensitive to assumptions about the degree of risk aversion. If farmers are significantly more risk averse than is currently believed, then there is likely to be an active interest in the new futures market.     

Intergenerational equity and the social discount rate

Recent modelling of the costs and benefits of climate change has renewed debate regarding assumptions for the social discount rate in analysing the impacts of environmental change. Previous literature suggests two key factors influence estimates of the social discount rate: the rate of pure time preference and the elasticity of marginal utility of future consumption. These components of the social discount rate reinforce the linkages between the choice of social discount rate and intergenerational distribution. This paper addresses the question of the relationship between intergenerational equity and the social discount rate and promotes the application of intergenerational distributional weights as a means of incorporating intergenerational equity preferences in policy analysis. Intergenerational equity‐adjusted social discount rates are derived as a means of decomposing the intergenerational equity aspect of the social discount rate. The work has significant policy implications for projects with long time frames given the sensitivity of Cost Benefit Analysis outcomes to decisions regarding the social discount rate.     

Estimation of a Social Rate of Interest for India

This paper estimates a social discount rate in India for the purpose of economic evaluation of investment projects, such as those aimed at improving the nation's agricultural performance. The component parameters of this rate are: the growth rate of per capita consumption in real terms, the elasticity of the marginal utility of consumption and the mortality‐based discount rate. Based upon time series data, the overall figure turns out to be 5.2 percent. This, it is contended, is reasonable and may be used in cost benefit analysis in that country.     

THE SOCIAL DISCOUNT RATE FOR LAND-USE PROJECTS IN INDIA

The social discount rate is derived from an inter-temporal social utility model for land-use projects in India. The social discount rate is a function of two parameters: the elasticity of social marginal utility of consumption and the growth rate of per capita real consumption. The final results for the social discount rate and the elasticity of social marginal utility of consumption are 2 per cent and -1.4 respectively. These values are plausible and comparable with other estimates found in the literature.     

Regulation of relationships between heterogeneous farmers and an aquifer accounting for lag effects

Many environmental problems are due to damage caused by pollutants that accumulate with a time lag following their emission. In this study, we focus on nitrates used in agriculture, which can pollute groundwater many years after their initial application. A dynamic optimal control problem with heterogeneous farmers is proposed. The usual structural parameters such as the discount rate, the natural clearing rate and the lagged time interval between the occurrence of soil‐level pollution and the impact on groundwater are taken into account. We also examine pollution as caused by a continuous set of farms characterised by their individual performance index and by their individual marginal contribution to the pollution. The issue is further investigated by taking account of change in the information context, successively related to perfect information and to asymmetric information. As a result, when the delay between the spreading of N‐fertilizer and the impact on the aquifer increases, that is, the longer the lag, the steady‐state pollution stock and the steady‐state shadow price of the stock both increase. Moreover, we show that the optimal regulation may require a decreasing amount of fertilizer over time, even in the case of initial underpollution.     

我国现代农业生产的碳排放变动趋势研究

现代农业生产中的碳排放是引起全社会高度关注的重大课题.本文构建了一个基于农户行为的碳排放评价体系和模型,测定和预测了我国现代农业生产中的碳排放变动水平与趋势.结果表明,改革开放以来我国农业生产碳排放以平均每年5%的速度持续增长,由于各因素变化率VAR检测值的分化,未来农业碳排放增长率表现为进一步升高的趋势.     

An Optimal Control Model of Forest Carbon Sequestration

This study develops an optimal control model of carbon sequestration and energy abatement to explore the potential role of forests in greenhouse gas mitigation. The article shows that if carbon accumulates in the atmosphere, the rental price for carbon sequestration should rise over time. From an empirical model, we find that carbon sequestration is costly, but that landowners can sequester substantial amounts of carbon in forests mainly by increasing forestland and lengthening rotations. Forest sequestration is predicted to account for about one-third of total carbon abatement. Tropical forests store over two-thirds of this added carbon.     

农户核桃交易契约链参与意愿分析——基于核桃种植农户的调查

以云南省180个农户调查问卷为样本,采用描述性统计分析方法和二元Logistic方法分析了农户核桃交易现状和农户契约链参与意愿的影响因素。研究表明,农户核桃种植规模较大,核桃销售方式以中间商为主,核桃销售的交易成本和风险较高,农户核桃销售的社会化服务需求强烈;户主个人特征变量对农户契约链参与意愿的影响不显著,家庭劳动力数对农户契约链参与意愿有显著负向影响,亲朋好友是否从事相关工作对农户契约链参与意愿有显著正向影响,人际关系资产专用性、交易风险和交易成本对农户契约链参与愿意有显著正向影响。     

Determining optimal forest rotation ages and carbon offset credits: Accounting for post-harvest carbon storehouses

Sequestering carbon in forest ecosystems is important for mitigating climate change. A major policy concern is whether forests should be left unharvested to avoid carbon dioxide (CO₂) emissions and store carbon, or harvested to take advantage of potential carbon storage in post-harvest wood product sinks and removal of CO₂ from the atmosphere by new growth. The issue is addressed in this paper by examining carbon rotation ages that consider commercial timber as well as carbon values. A discrete-time optimal rotation age model is developed that employs data on carbon fluxes stored in both living and dead biomass as opposed to carbon as a function of timber growth. Carbon is allocated to several ecosystem and post-harvest product pools that decay over time at different rates. In addition, the timing of carbon fluxes is taken into account by weighting future carbon fluxes as less important than current ones. Using simple formulae for determining optimal rotation ages, we find that: (1) Reducing the price of timber while increasing the price of carbon will increase rotation age, perhaps to infinity (stand remains unharvested). (2) An increase in the rate used to discount physical carbon generally reduces the rotation age, but not in all cases. (3) As a corollary, an increase in the price of carbon increases or reduces rotation age depending on the weight chosen to discount future carbon fluxes. (4) Site characteristics and the mix of species on the site affect conclusions (2) and (3). (5) A large variety of carbon offset credits from forestry activities could be justified, which makes it difficult to accept any.     

ANALYSIS OF RANGELAND DEGRADATION USING STOCHASTIC DYNAMIC PROGRAMMING

Degradation of arid rangeland, and efforts to control that degradation, have become topical issues. However, the inherent characteristics of the rangeland, and the intertemporal nature of the problem, complicate the analysis of degradation issues in the search for more appropriate rangeland policies. Stochastic dynamic programming is examined as one means of allowing for those complexities. Using the case of the Queensland mulga rangelands, optimal stocking rates are shown to rise with lower property sizes, higher discount rates, higher wool prices and declining risk aversion. Importantly, the analysis reveals that a strategy of high stocking rates with the potential for rangeland degradation is an optimal response to the economic and social factors that confront graziers and is not an intertemporal information problem alone.     

Managing basis risk with multiscale index insurance

Agricultural index insurance indemnifies a farmer against losses based on an index that is correlated with, but not identical to, her or his individual outcomes. In practice, the level of correlation may be modest, exposing insured farmers to residual, basis risk. In this article, we study the impact of basis risk on the demand for index insurance under risk and compound risk aversion. We simulate the impact of basis risk on the demand for index insurance by Malian cotton farmers using data from field experiments that reveal the distributions of risk and compound risk aversion. The analysis shows that compound risk aversion depresses demand for a conventional index insurance contract some 13 percentage points below what would be predicted based on risk aversion alone. We then analyze an innovative multiscale index insurance contract that reduces basis risk relative to conventional, single‐scale index insurance contract. Simulations indicate that demand for this multiscale contract would be some 40% higher than the demand for an equivalently priced conventional contract in the population of Malian cotton farmers. Finally, we report and discuss the actual uptake of a multiscale contract introduced in Mali.     

Optimal Area-Yield Crop Insurance Reconsidered

The implementability of area-yield insurance contracts in the presence of symmetric and asymmetric information about the farmer's "beta" linking his yield to the risk-pool's yield is examined. In the presence of fixed costs and symmetric information Mahul's result that optimality requires setting the slope of the indemnity schedule equal to each farmer's beta is confirmed. When there is asymmetric information between the insurer and the farmer, however, this full-insurance contract is vulnerable to adverse selection, and therefore may not be implementable for general cost structures. The optimal area-yield insurance contract under asymmetric information is characterized.     

Technical change and irreversible investment under risk

A stochastic dynamic model was constructed to analyze investment decisions of an individual farme under risk in the presence of legibilities, embedded technical change and indivisible capital. An analytical solution was obtained and its local behavior studied by numerical methods. Optimal investment is obtained by regulating the difference between the desired and actual capital stocks between two barriers that define an inaction interval. While the desired capital drifts between the barriers, no action is taken. If the desired capital touches the upper barrier, the farmer invests pushing the average efficiency of the actual capital stock up. This in turn raises the desired capital even higher and contracts the inaction interval. If these effects are strong enough, the farmer will invest again until the potential gains of the technological package are exhausted. If the desired capital falls enough, the farmer disinvests, pushing down the average productivity and expanding the inaction interval. Disinvestment continues until it slops either because the inaction interval becomes so wide that it is no longer optimal to disinvest or because the actual capital stock is so small that it is no longer profitable to produce.     

福建省生态公益林碳汇经济效益影响因子研究

根据对福建省6个样本县进行样地调查及其农户访谈式问卷调查的资料,首先应用因子分析法对影响福建省生态公益林碳汇效益的主要因子进行分析,然后将碳汇效益与主要因子进行逐步多元回归分析。结果表明:坡度、林龄、树种、蓄积量、碳汇量、重置成本、降水量、碳汇价格是影响福建省生态公益林碳汇效益的主要因子;碳汇价格、蓄积量和重置成本对福建省生态公益林碳汇效益影响显著;碳汇价格、蓄积量与碳汇效益呈正相关,重置成本与碳汇效益呈负相关。