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.     

Further generalization of Faustmann's formula for stochastic interest rates

Markov decision process (MDP) models generalize Faustmann's formula by recognizing that future stand states, prices, and interest rates, are not known exactly. Buongiorno (Forest Science 47(4) 2001) presents a dynamic programming and a linear programming formulation of the MDP model with a fixed interest rate. Both formulations are generalized here to account for a stochastic interest rate. The objective function is the expected present value of returns over an infinite horizon. It gives, like Faustmann's formula, the value of the land and the eventual standing trees. The changes between stand states, prices, and interest rate, are represented by Markov chains. Faustmann's formula is a special case where the change from one state to another has 0 or 1 probability, and the interest rate is constant. The MDP model applies to any stand state, even- or uneven-aged, and the best decisions are tied uniquely to the current system state. An example shows the effects of recognizing variations in interest rate on the land expectation value, and the cost of ignoring them.     

Optimal forest harvest age considering carbon sequestration in multiple carbon pools: A comparative statics analysis

We present an analytical model for determination of the economically optimal harvest age of a forest stand considering timber value, and the value of carbon fluxes in living biomass, dead organic matter, and wood products pools. Through comparative statics analysis, we find that consideration of timber value and fluxes in biomass carbon increase harvest age relative to the timber only solution, and that the effect on optimal harvest age of incorporating fluxes in the dead organic matter and wood products pools is indeterminate.We also present a numerical example to examine the magnitudes of these effects. In general, incorporating the dead organic matter and wood products pools have the effect of reducing rotation age. Perhaps more interestingly, when initial stocks of carbon in dead organic matter or wood products pool are relatively high, consideration of these pools can have a highly negative effect on net present value.     

The multiple effects of carbon values on optimal rotation

Non-consumptive benefits which increase with crop age, like keeping carbon sequestered, lengthen optimal rotation compared with rotation for timber alone. High proposed carbon prices may extend rotation indefinitely. Carbon storage in wood products reduces this tendency. Biomass as an energy source displacing fossil fuels favours rotations near those of maximum biomass productivity. Use of sawn timber to displace structural materials with high embodied carbon favours somewhat longer rotations. Effects of rotation on soil carbon, and fossil carbon volatilised in harvesting operations, are further complications. Including all carbon effects results in optimal rotations somewhat longer than those based only on timber value, but shorter than those based on timber plus forest carbon. To include all factors intuitively is not possible: balanced appraisal needs economic calculations.     

Economics of carbon sequestration under fluctuating economic environment,forest management and technological changes: An application to forest stands in the southern United States

This study presents a model that determines the effect of current and future payments for carbon sequestration, proportion of wood that sequesters carbon in long-lived product and landfills, and amount of carbon in the wood, on the optimal current forest harvest age. Increased current and future prices of carbon would lead to a longer and shorter harvest age, respectively. Higher current prices of carbon could increase the supply of carbon at a decreasing rate due to longer harvest ages. Moderate prices of carbon would encourage landowners to maintain standing timber. Policies focused then on stimulating landowners to hold timber on forestlands may not necessarily imply higher amounts of sequestered carbon. Increased future values of carbon could imply a reduction of the current supply of carbon.     

Faustmann and the climate

The paper presents an adjusted Faustmann Rule for optimal harvest of a forest when there is a social cost of carbon emissions. The theoretical framework takes account of the dynamics and interactions of forests’ multiple carbon pools and assumes an infinite time horizon. Our paper provides a theoretical foundation for numerical model studies that have found that a social cost of carbon implies longer optimal rotation periods and that if the social cost of carbon exceeds a certain threshold value the forest should not be harvested. At the same time we show that it could be a net social benefit from harvesting even if the commercial profit from harvest is negative. If that is the case, the optimal harvest age is decreasing in the social cost of carbon.     

Could the Faustmann model have an interior minimum solution?

The growth of an even-aged stand usually follows a S-shaped pattern, implying that the growth function is convex when stand age is low and concave when stand age is high. Given such a growth function, the Faustmann model could in theory have multiple optima and hence an interior local minimum solution. To ensure that the rotation age at which the first derivative of the land expectation value equals zero is a maximum, it is often assumed that the growth function is concave in stand age. Yet there is no convincing argument for excluding the possibility of conducting the final harvest before the growth function changes to concave. We argue that under normal circumstances the Faustmann model does not have any interior minimum. It is neither necessary nor proper to assume that the growth function is concave in the vicinity of the optimal rotation age. When the interest rate is high, the optimal rotation may lie in the interval on which the growth function is convex, i.e. before volume or value growth culminates.     

The effect of site quality on economically optimal stand management

This paper proposes a discrete-time type timber harvesting model for simultaneously determining (i) the optimal quantity of seedlings to be planted, (ii) the optimal quantities of timber harvested by thinnings, and (iii) the optimal rotation age. With the help of Microsoft Excel Solver, a generalized reduced gradient algorithm, numerical examples are developed to evaluate the impact of the variations in the quality level of a forest site on the optimal harvest strategy. It is shown that the level of optimal rotation age and optimal quantity of seedlings to be planted can individually exhibit non-monotonicity to the increase in site quality.     

Annual use, economic life and residual value of cut-to-length harvesting machines

Recognizing the absence of up-to-date empirical data on the economic life, the annual use and the residual value of dedicated cut-to-length (CTL) harvesting machinery, the authors gathered a large database of second-hand machine sale offers containing over 1000 records, coming from Europe and North America. The statistical analysis of these data pointed at an economic life in the vicinity of 18,000 h for both harvesters and forwarders, which confirms previous assumptions. The average annual use for the machines in the database is 1424 and 1581 h year⁻¹, respectively for the harvesters and the forwarders. Nordic users achieve a higher annual use than central European users, and the difference is statistically significant. Nevertheless, the average annual use recorded for both groups falls below the levels commonly adopted in current estimates, which may therefore represent ideal reference figures rather than actual averages. Residual value is strongly related to machine age, and the authors calculated some simple functions for estimating it. The study points at a better retention of the original value, compared to the figures reported in previous literature. At 5 years of age the harvesters and forwarders in the study keep respectively 38% and 44% of the new value. The information contained in the study is crucial to machine rate calculation, which has often been based on rule-of-thumb assumptions, in the absence of empirical data.     

Taxation, life-time uncertainty and non-industrial private forest-owner's decision-making

The nonindustrial private forest (NIPF) owner's consumption and harvesting decisions are investigated under inheritance and capital income taxes using a two-period model. The impact of the forest-owner's age is introduced into the analysis through a parameter of perceived probability of surviving through a future period. This allows us to study the impacts of ageing on consumption and harvesting decisions as well as to see how the impact of taxes changes among different age groups of forest-owners. The results show that current consumption first decreases and then increases when moving from younger to older individuals regardless of whether non-timber assets are more or less heavily taxed through bequests than consumption. In general, we find that tax effects are dependent on the forest-owner's age. Age tends to intensify the increasing effect of the forest bequest tax on harvesting. The same is true with respect to the decreasing effect on harvesting of the inheritance tax imposed on non-forest assets. Furthermore, the forest-owner's age tends to intensify the effect on harvesting of the capital income tax imposed on forest assets, but diminishes the effect on harvesting of the capital income tax imposed on non-forest assets.     

The emergence of forest age structures as determined by uneven-aged stands and age class forests

This article explores the question under which conditions trees are managed in even- or uneven-aged stands or age class forests, respectively. The problem of uneven-aged management within stands and forests can be reduced to the analysis of simultaneous optimal times of harvest and regeneration of interdependently growing trees. Restricting attention to a market environment, a forest investment model is developed which accounts for the opportunity to manage trees or stands individually. As a consequence, age class forests evolve as the optimal compromise between two opposing effects. They allow for a combination of the advantages of uneven-aged management by utilizing differences in tree growth on a larger scale and of even-aged management by exploiting locally effective positive inter-tree dependencies on a smaller scale. Accordingly, the emergence of the forest structure is determined by the dynamics in the balance of value growth and impact rate differences.     

沙县杉木人工林经验收获表的编制及应用研究

对杉木人工林的单位面积蓄积量、平均胸径、平均树高以及株数的生长模型采用民理查德方程来进行计算，并结合了相关公式编制了一份收获表，收获表在经检验后表明据有一定的科学依据，非常适宜，对林分生长收获的预估和小班资源数据更新有着非常重要的作用，文中最后给出了应用经验收获表进行生长收获预估的实例。     

杉木人工林经济成熟龄的研究

利用杉木人工林标准地材料建立生长收获预估模型,根据技术经济指标采用净现值法研究经济成熟。结果表明:在现有技术经济指标的情况下,利率为5%时杉木人工林经济成熟龄为17年。若其它条件保持不变,木材价格或成本每增减20%,杉木人工林经济成熟龄将推迟或提前1年。利率对经济成熟龄的到来有显著影响,利率每增加1个百分点,经济成熟龄将提前1年。     

林业现代化评价方法探讨

论述了林业现代化评价指标数据的来源与取得方法、指标设计的基本思路，并且建立了林业现代化的评价模型。认为林业现代化评价指标的标准值应该以中等发达国家相应指标的实际值平均数为主，以专家咨询法（Delphi）定为辅；林业现代化评价指标的权重必须采用层次分析法（AHP）和专家咨询法确定。此外，还详细阐述了林业现代化评价指标权重的计算过程、计算公式和国内外常见的5种现代化评价标准。     

Do Formula or Competitive Grant Funds Have Greater Impacts on State Agricultural Productivity?

This article examines the impact of public agricultural research and extension on agricultural total factor productivity at the state level. The objective is to establish whether federal formula or competitive grant funding of agricultural research has a greater impact on state agricultural productivity. A pooled cross-section time-series model of agricultural productivity is fitted to annual data for forty-eight contiguous states over 1970–1999. Our results show that public agricultural research and agricultural extension have statistically significant positive impacts on state agricultural productivity. In addition, Hatch formula funding has a larger impact on agricultural productivity than federal competitive grant funding, and a reallocation of Hatch formula funds to competitive grant funding would lower agricultural productivity. This seems unlikely to be a socially optimal policy. Furthermore, from a cost–benefit perspective, our study shows that the social marginal annualized real rate of return to public resources invested in agricultural research is 49–62%, and to public agricultural extension, the rate is even larger.     

Optimal harvest age considering multiple carbon pools – A comment

In two recent papers, Asante and Armstrong (2012) and Asante et al. (2011) considered the question of optimal harvest ages. They found that the larger are the initial pools of dead organic matter (DOM) and wood products, the shorter is the optimal rotation period. In this note, it is found that this conclusion follows from the fact that the authors ignored all release of carbon from decomposition of DOM and wood products after the time of the first harvest. When this is corrected for, the sizes of the initial stocks of DOM and wood products do not influence the optimal rotation period. Moreover, in contrast to the conclusions in the two mentioned papers, our numerical analysis indicates that inclusion of DOM in the model leads to longer, not shorter, rotation periods.     

Integrating neighbourhood effects in the calculation of optimal final tree diameters

Modern silvicultural treatments are based on single trees whereas classic forest economics look at the stand level. To accompany each other it is necessary to transfer the established economic models to the single tree level. This paper is an approach to use the Faustmann model and the corresponding marginal rate of return (Pressler percent) to derive value increment rates of single trees taking into account neighbourhood effects due to competition between individual trees. Furthermore, optimal rotation periods and optimal final diameters for future trees will be calculated.     

A DYNAMIC PROGRAMMING MODEL OF EARLY POTATO HARVESTING

A vegetable producer often faces complex harvest decisions where yield increases through time and varies across crop area, price is determined in erratic seasonal markets, and harvest rate is constrained. In this paper, a simplified two-period potato harvest problem is developed to define a set of marginal conditions for an optimum. The model is then extended to the multi-period case and numerical solutions are generated for a representative farm in South Wales using dynamic programming. The model provides a general framework for analysing crop harvesting systems and prescribing marginal changes, such as adjustments in the harvest capacity, which improve profitability over myopic harvest patterns.     

Editorial - Multiple-use forestry

The problem of multiple-use forestry arises because (1) a forest can be managed to provide a wide range of products and services, (2) the different uses are not perfectly compatible with each other, and (3) some products are not priced in markets and many of the services a forest provides have the characteristics of public goods. Examples of major forest products include, in addition to timber, edible berries, fungi, and hunting games. Forests also provide recreation opportunities and various environmental services (such as regulating local climate, reducing soil erosion, reducing pollutants in the atmosphere, regulating the global climate, providing habitats for wildlife, etc.). The outputs of nontimber goods in general depend on the quantity and structure of the forest, which can be changed by various forest management activities. However, a forest state most suitable for the production of one good is usually not optimal with respect to another good. Typically, there does not exist a set of management activities that simultaneously maximize the outputs of timber and all other goods.Another way to understand the conflicts between different uses is to view standing timber as an intermediate product of forestry investment, which is employed as an “input” for the production of timber products and nontimber goods. Thinking in this way, the conflicts arise partly because timber production and nontimber uses compete for the same input, and partly because of the differences in the “production technology” among different nontimber goods. A change in the standing timber may have positive impacts on some nontimber uses, but have negative effects on others. Because of the conflicts among different uses, it requires that both timber products and nontimber goods should be explicitly incorporated into forestry decision-making in order to achieve the greatest benefits to the forest owner and/or the public.Most of the economic analyses of multiple-use forestry decisions have explicitly or implicitly adopted the view that multiple-use should be achieved in individual stands. Each stand should be managed to produce an optimal mix of timber products and nontimber goods. Another view of multiple-use forestry is to manage each stand for a primary use, whereas multiple-use concerns are addressed by allocating different stands in a forest to different uses. A general argument in support of the primary-use view is that specialization makes for efficiency. The production of timber and nontimber goods is a joint process, however. Strictly speaking, one cannot separate timber production and the production of different nontimber goods. For example, managing a stand for timber production does not exclude the possibility of producing some nontimber goods in the stand. Since every stand usually produces more than one product, efficient multiple-use forestry requires that each stand should be managed for an optimal mix of timber and nontimber outputs. On the other hand, it may well be the case that the optimal multiple-use mix for a particular stand consists of a maximum output of one product. In this case the optimal multiple-use management decision would coincide with the optimal decision pertaining to a single use. In other words, it may be optimal to manage a particular stand for one primary use. Using the terminology of economics, primary-use may be efficient for stands in which the multiple-use production set is nonconvex. Recent research has explored several sources of nonconvexity in the multiple-use production set. However, there is no evidence supporting the argument that specialization is always more efficient than multiple-use management of individual stands. From an economics viewpoint, efficient primary-use is special cases of multiple-use stand management.A widely recognized limitation of multiple-use stand management is that, by considering each stand separately, one neglects the interdependence of nontimber benefits and ecological interactions among individual stands. The nontimber benefits of a stand depend on the output of nontimber goods from other stands. Likewise, the nontimber output from one stand affects the value of nontimber goods produced in the other stands. Ecological interactions among individual stands imply that the output of nontimber goods from two stands in a forest differs from the sum of the outputs from two isolated stands. These interdependence and interactions imply that the relationship between the nontimber benefits of a stand and the stand age (or standing timber stock) cannot be unambiguously determined - it depends on the flow of nontimber goods produced in the surrounding stands. Therefore, it is improper to determine optimal decisions for the individual stands independently. In stead, efficient multiple-use forestry decision should be analyzed by considering all the stands in a forest simultaneously.Another serious limitation of multiple-use stand management is that each stand is treated as a homogenous management unit to be managed according to a uniform management regime. One implicitly assumes that the boundaries of each stand is exogenously given and will remain unchanged over time. This assumption imposes a restriction on the multiple-use production set, thereby creates inefficiency. As an example, consider a large stand with a nonconvex production set. It may be possible to eliminate nonconvexity in the production set and push the production possibility frontier outwards by dividing the stand into several parts and managing each part for a primary-use. It may also be efficient to combine two adjacent stands into one to be managed following a uniform regime, because of the presences of fixed management costs, and/or because the relationship between some nontimber outputs and stand area is not linear.In contrast to income from timber production, nontimber goods produced at different time points are not perfect substitutes. The rate at which a forest owner is willing to substitute a nontimber good produced at one time point for that produced at another time point changes with the outputs of the nontimber good at the two time points. In general cases, the nontimber goods produced at one time point cannot be consumed at another time point, and the marginal utility of a nontimber good decreases when its output increases. This provides a motivation for reducing the variation in the output of nontimber goods over time. An effective approach to coordinating nontimber outputs over time is to apply different management regimes to different parts of a stand, or apply the same regime to adjacent stands, which would change the boundaries of the stands. Preserving the existing stand boundaries would limit the possibility of evening out the nontimber outputs over time, and thereby lead to intertemporal inefficiency in multiple-use management.In previous studies of multiple-use forestry decisions the nontimber outputs or benefits are usually modeled as functions of stand age or standing timber stock. Future flows of nontimber goods or benefits are incorporated into a stand/forest harvest decision model to explore the implications of nontimber uses for optimal harvest decisions. While stand age and standing timber stock may have significant impacts on nontimber outputs, other forest state variables, e. g. the spatial distribution of stands of different ages/species, may be of great importance to the production of nontimber goods. Recognition of such forest state variables could change the relationship between timber production and nontimber outputs and therefore change the optimal forest management decisions.In summary, multiple-use forestry is not simply an extension of timber management with additional flows of benefits to be considered when evaluating alternative management regimes. Recognition of multiple uses of a forest leads to two fundamental changes of the forestry decision problem. First, the optimal intertemporal consumption of forestry income is no longer separable from forest management decisions. In general, the optimal intertemporal consumption of forestry income depends on future flows of nontimber goods, implying that the consumption-saving decision should be made simultaneously with the decision on the production of timber and nontimber goods over time. Secondly, it is no longer appropriate to optimize the management regime for each stand separately. The nontimber outputs from a forest depend on the age distribution of individual stands, and on a wide range of other forest state variables such as the spatial distribution of stands of different ages and tree-species composition. Ecological interactions and interdependence among stands imply that management regimes for different stands should be optimized simultaneously. In addition to changing rotation ages and harvest levels, efficient multiple-use forestry requires optimizing the spatial allocation of harvests, redefining the boundaries of stands, coordinating the choices of tree species in regeneration of harvested area and so on.The lack of rigorous production functions for nontimber goods imposes a severe restriction on attempts to perform comprehensive economic analyses of multiple-use forestry decisions. This restriction in itself is no justification for ignoring many of the key aspects of multiple-use forestry problem and modeling the problem as one of determining the optimal rotation age or optimal harvest level. It requires that economic models of multiple-use forestry should be developed with special consideration of the vague and imprecise information regarding the relationships between nontimber outputs and forest state variables.Peichen GongDepartment of Forest EconomicsSE-90183 UmeåSweden     

Optimal management of the New Zealand longfin eel (Anguilla dieffenbachii)*

Annual recruitment of the New Zealand longfin eel (Anguilla dieffenbachii) has decreased by 75 per cent since significant levels of commercial fishing began in the early 1970s. This motivates application of a multiple‐cohort bioeconomic model to a New Zealand longfin eel fishery to investigate its optimal management and ascertain the suitability of existing regulatory policy. The use of historical harvest to calculate total allowable catch is asserted to be unsustainable based on recovery dynamics. In addition, individual transferable quota systems are argued to be fundamentally flawed for the protection of longfin fisheries because of high‐grading, low‐surplus production and a current lack of effective stock‐assessment procedures. Area closure and the spatial definition of harvest rights are attractive alternatives given the territoriality of longfins and high larval spillover. The importance of unfished reserves is reinforced when significant uncertainties regarding population strength, harvest intensity and growth dynamics are considered. Restriction of exploitation to older cohorts in fished areas is demonstrated to maximise economic yield.