OPTIMAL FOREST STAND MANAGEMENT WHEN BENEFITS ARE DERIVED FROM CARBON

The management of second-growth and old-growth forest stands has important implications for the global carbon cycle. This paper considers the optimal forest rotation when flows of CO₂ to carbon have positive value. If benefits are derived only from carbon, then typically it will never be optimal to harvest any forest stands. This result is a formalization and extension of Harmon et al. [1990]. Private forest owners will often maximize net returns to timber, ignoring benefits from carbon sequestration. Thus, the privately and socially optimal rotations will not generally coincide. We show that the socially optimal rotation is always greater than the privately optimal rotation and less than or equal to the rotation when only carbon is valued.     

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

Optimal forest rotation age when carbon captured is considered: theory and applications

Carbon dioxide (CO₂) is the gas most responsible for the greenhouse effect. Since trees absorb CO₂ during growth, some authors have argued for the importance of considering forests not only as timber producers but also as carbon pools. The consideration of carbon uptake as a public good generates a divergence between the private and social optima. This paper presents a methodology to determine optimal forest rotation ages in this context of multiple use and to remove the divergence between these two optima. A theoretical framework, based upon compromise programming, is applied to a case study of a beech forest in Spain, within the context of the current European financial aid for afforestation programs.     

VALUING A TIMBER HARVEST CONTRACT AS A HIGH‐DIMENSIONAL AMERICAN CALL OPTION VIA LEAST‐SQUARES MONTE CARLO SIMULATION

Abstract Industrial timberland ownership in the United States has shifted substantially in the last 20 years. Having sold their fee‐owned timberlands, forest products companies relied heavily on the open market for raw timber. To reduce their exposure to market risks, however, forest products companies have been using a number of supply chain instruments, such as timber harvest contracts. As these vehicles become increasingly important to the forest industry, it is necessary and important to determine their economic values. In this study, we treated a 3‐year timber harvest contract on a 30‐year‐old loblolly pine plantation as a high‐dimensional American call option and calculated its value by the least‐squares Monte Carlo simulation technique. The estimated values of such a contract ranged from $1,693/ac to $1,984/ac under two timber price assumptions. With reasonable starting timber prices and strike price in the simulation, random timber prices led to higher contract values. Results from this study can help private landowners, timber brokers, and forest products companies better manage their business risks.     

RANDOM ENTRY FORESTRY: TIMBER MANAGEMENT IN A TIME OF SPECIES CONSERVATION

In this paper we propose a timber management scheme which mimics the patchy stand structure of a fire climax forest and has the desirable characteristic of retaining stands of trees of very old ages. We go on to do a preliminary economic analysis and determine that if management is taking place under the restriction that a certain fraction of the forest must be of at least some given age then this approach may be far superior to standard single age rotation schemes.     

TIMBER SUPPLY UNDER DEMAND UNCERTAINTY: WELFARE GAINS FROM PERFECT COMPETITION WITH RATIONAL EXPECTATIONS

ABSTRACT. This paper presents a noneconometric approach to estimating the short‐run timber supply function based on optimal harvest decisions. Determination of optimal harvest levels and estimation of supply function coefficients are integrated into one step by incorporating a parametric short‐run timber supply function into the harvest decision model. In this manner we convert the original harvest decision model into a new optimization problem with the supply function coefficients functioning as “decision variables.” Optimal solution to the new decision model gives the coefficients of the short‐run supply function and, indirectly, the optimal harvest levels. This approach enables us to develop stochastic models of the timber market that are particularly useful for forest sector analysis involving comparison of alternative institutional regimes or policy proposals and when the timber market is affected by stochastic variables. For demonstration purposes, we apply this method to compare the performances of two timber market regimes (perfect competition and monopoly) under demand uncertainty, using the Swedish data. The results show that the expected timber price is 22 percent lower and the expected annual timber supply is 43 percent higher in the competitive market than in the monopoly market. This confirms the theoretical result that monopoly reduces supply and increases price. The expected social welfare gain from perfect competition over monopoly is about 24 percent.     

OPTIMAL HARVESTING OF FOREST AGE CLASSES UNDER PRICE UNCERTAINTY AND RISK AVERSION

ABSTRACT. . We analyze optimal forest harvesting under mean reverting and random walk timber price and include multiple age classes, forest owners' consumption‐savings decisions and risk aversion. This framework generalizes existing studies that assume a single stand and risk neutrality or include ad hoc risk aversion and obtain the result that uncertainty lengthens the optimal rotation. Including planting cost implies that price stochasticity may shorten the rotation period. Under the mean reverting price process, optimal harvesting becomes more sensitive to periodic price level, as compared to the random walk case. Including risk aversion completely changes the harvesting policy in the sense that, if the forest initially consists of just one age class, it is optimal to smooth the age class structure and have more frequent cuttings from younger age classes. With risk aversion, optimal cuttings depend on price level, even under a random walk price and zero replanting and harvesting costs. In addition, harvesting decisions become dependent on subjective time preference and forest owners' wealth.     

MODELING CATASTROPHIC RISK IN ECONOMIC ANALYSIS OF FOREST CARBON SEQUESTRATION

ABSTRACT. The effect of risk from catastrophic tree mortality, such as fire, insect outbreaks and hurricanes, on selling credits for carbon sequestration from a slash pine plantation is modeled. We achieve this task by developing a modified Hartman model and applying it to a slash pine plantation. It is found that risk decreases the land expectation value and the optimal rotation age on a forest stand producing timber and carbon sequestration benefits. This decrease is greater with higher prices of carbon. Furthermore, risk increases the amount of pulpwood produced from the stand and decreases the amount of sawtimber produced. Since pulpwood has a shorter life span than sawtimber this reduces the amount of carbon sequestered. This effect is greater for higher prices of carbon suggesting that risk dampens the effect that a carbon market would have in inducing landowners to sequester more carbon.     

LAND DEVELOPMENT AND WILDERNESS CONSERVATION POLICIES UNDER UNCERTAINTY: A SYNTHESIS

The effects of uncertainty and irreversibility on land management are examined in an infinite horizon Arrow-Fisher-Henry conservation model with non-linear land-use welfare function which accounts for the possible role of breakthrough benefits stemming from the genetic resources of wilderness. The effects of uncertainty on optimality and certainty-equivalent development strategies are examined. Crucially, “jump” decision rules are shown to be generally non-optimal for managing wilderness areas.     

ENVIRONMENTAL AND FINANCIAL SUSTAINABILITY OF FOREST MANAGEMENT PRACTICES

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or nondeclining flow of services from the forest is socially desirable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber-productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforestation and rehabilitation costs, and the impact of the system on the productivity of the site. An application of the model is presented for lodgepole pine in Alberta. We conclude that, at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for more intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvesting on soil productivity.     

Portfolio management with background risk under uncertain mean-variance utility

This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain mean-variance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented.

     

The impact of environmental constraints on short term harvesting: Use of planning tools and mathematical models

Both in New Zealand and Chile there exist important forest industries based mostly on pine plantations. The management of harvesting requires a series of activities such as building access roads, harvesting with skidders on flat terrain and cable logging for steep terrain, transportation from forest origins to destinations, such as a port, pulp plant and sawmills.These harvesting activities imply some potentially harmful environmental impacts such as water sedimentation, erosion and loss of scenic beauty. This has led to the proposal of several mitigating actions, such as creating riparian strips along rivers, avoiding the use of heavy machinery on fragile soils and minimizing road building.The degree of implementation of these mitigating actions differs in Chile and New Zealand. In New Zealand, the 1991 Resource Management Act regulated the implementation of environmental protection measures. In Chile a series of such measures have been implemented, but a set of definite regulations has not been defined yet and there is a need to develop an economic evaluation of the implementation of environmental measures in terms of reduced timber production and high harvesting costs, together with the benefits to the environment. To support decisions at tactical and operational levels, mathematical models have been developed both in Chile and New Zealand and are being used successfully by the timber industries. These models can be modified to consider diverse environmental protection measures. We analyze the implementation of these modifications and how the new models can help evaluate the economic impact of the protection measures. We show some preliminary results.     

Design of insurance contracts using stochastic programming in forestry planning

This work addresses a tactical planning problem faced by a forestry firm, deciding which timber units to harvest and what roads to build to obtain the greatest possible benefits. We include uncertainty in prices by means of utility theory. This enables solutions to be found that the firm finds preferable to those obtained when risk aversion is ignored and makes it possible to design insurance contracts that benefit the firm while also being attractive to an insurer. Two types of contract are designed; one dependent on the firm’s operating result and the other independent of it. Metrics are then developed to quantify the benefits conferred by a contract, demonstrating that the latter contract type dominates the former. These results are then illustrated by applying them to a simplified planning problem of a forest owned by the Chilean forestry operator Millalemu.     

A TUTORIAL ON EVALUATING EXPECTED RETURNS FROM RESEARCH FOR FISHERY MANAGEMENT USING BAYES' THEOREM

Traditional methods for evaluating potential or actual returns from research and development include scoring methods, cost-benefit analysis and production-function approaches. The research reported in the present paper complements these traditional methods with the use of statistical decision analysis and Bayesian methods to account explicitly for risk and uncertainty and to capture some of the effects of information evolution. Measurement of the expected returns from research for fishery management is detailed. Both ex post and ex ante evaluation of expected returns are illustrated by deliberately simplified example.     

THE ROLE OF STOCHASTIC MONOTONICITY IN THE DECISION TO CONSERVE OR HARVEST OLD-GROWTH FOREST

The problem of when, if ever, a stand of old-growth forest should be harvested is formulated as an optimal stopping problem, and a decision rule to maximize the expected present value of amenity services plus timber benefits is found analytically. This solution can be thought of as providing the “correct” way in which cost-benefit analysis should be carried out. Future values of amenity services provided by the standing forest and or timber are considered to be uncertain and are modeled by Geometric Poisson Jump (GPJ) processes. This specification avoids the ambiguity which arises with Geometric Brownian Motion (GBM) models, as to which form of stochastic integral (Itô or Stratonovich) should be employed, but more importantly allows for monotonic (yet stochastic) processes. It is shown that monotonicity (or lack of it) in the value of amenity services relative to timber values plays an important part in the solution. If amenity values never go down (or never go up) relative to timber values, then the certain-equivalence cost-benefit procedure provides the optimal solution, and there is no option value. It is only to the extent that the relative valuations can change direction that the certainty-equivalence procedure becomes sub-optimal and option value arises.     

Logging damage and injured tree mortality in tropical forest management

Using insights from the forest ecology literature, we analyze the effect of injured trees on stand composition and carbon stored in above‐ground biomass and the implications for forest management decisions. Results from a Faustmann model with data for a tropical forest on Kalimantan show that up to 50% of the basal area of the stand before harvest can consist of injured trees. Considering injured trees leads to an increase in the amount of carbon in above‐ground biomass of up to 165%. These effects are larger under reduced impact logging than under conventional logging. The effects on land expectation value and cutting cycle are relatively small. The results suggest that considering injured trees in models for tropical forest management is important for the correct assessment of the potential of financial programs to store carbon and conserve forest ecosystem services in managed tropical forests, such as reducing emissions from deforestation and forest degradation and payment for ecosystem services. Recommendations for Resource Managers

• Considering the role of injured trees is important for managing tropical forests
• These trees can cover up to 50% of basal area and contain more than 50% of the carbon stored in above‐ground biomass
• Reduced impact logging leads to a larger basal area of injured trees and more carbon stored in injured trees than conventional logging
• Injured trees play an important role when assessing the potential for carbon storage in the context of payment for forest ecosystem services.

     

A note on issues of over-conservatism in robust optimization with cost uncertainty

We identify and discuss issues of hidden over-conservatism in robust linear optimization, when the uncertainty set is polyhedral with a budget of uncertainty constraint. The decision-maker selects the budget of uncertainty to reflect his degree of risk aversion, i.e. the maximum number of uncertain parameters that can take their worst-case value. In the first setting, the cost coefficients of the linear programming problem are uncertain, as is the case in portfolio management with random stock returns. We provide an example where, for moderate values of the budget, the optimal solution becomes independent of the nominal values of the parameters, i.e. is completely disconnected from its nominal counterpart, and discuss why this happens. The second setting focusses on linear optimization with uncertain upper bounds on the decision variables, which has applications in revenue management with uncertain demand and can be rewritten as a piecewise linear problem with cost uncertainty. We show in an example that it is possible to have more demand parameters equal their worst-case value than what is allowed by the budget of uncertainty, although the robust formulation is correct. We explain this apparent paradox.     

THE OPTIMAL MANAGEMENT OF TRANSBOUNDARY FISHERIES: GAME THEORETIC CONSIDERATIONS

One of the most ubiquitous of the fishery management problems to have arisen as a result of E.F.J. is that of managing transboundary resources. Economic analysis of this problem rests upon models blending the standard dynamic economic analysis of fisheries with game theory. The analysis reveals that noncooperation is likely to have severe economic consequences and that cooperative arrangements must deal with possible conflicting goals of management, as well as the division of economic returns from the fishery. While the existing economic analysis of transboundary fishery management is far from complete, it can be shown that the analysis is capable of providing important insights into existing real world cases of transboundary resource management.     

Inventory control with product returns: The impact of imperfect information

Product returns are characterized by considerable uncertainty on time and quantity. In the literature on inventory management for product return environments best forecasts of future returns are associated with methods that use the most information regarding product return history. In practice, however, data is often scarce and unreliable, while forecasts based on historical data, reliable or not, are never perfect. In this paper we therefore investigate the impact of imperfect information with respect to the return process on inventory management performance. We show that in the case of imperfect information the most informed method does not necessarily lead to best performance. The results have relevant implications regarding investments in product return information systems.     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.