What Makes Mountain Pine Beetle a Tricky Pest? Difficult Decisions when Facing Beetle Attack in a Mixed Species Forest

The pine forest of British Columbia is undergoing its largest recorded pest epidemic. The damage caused by native mountain pine beetle creates difficulties for the public owner of the resource, which is interested in protecting future timber supply while salvaging dead and dying pine. This paper addresses two problems that have often been over-looked: the variability and timing of beetle attack, and the variability of pine inventory in each stand. Management controls are limited to the annual rate of harvest and timber product outputs are based on shelf life – the length of time infested timber can still be used to produce lumber. Using mathematical programming to schedule harvest, we introduce a novel objective function based on the maximization of the net returns of the timber portfolio at the end of the 20 year time horizon under harvest and product flow constraints implemented by the public landowner to insure stability in the forest sector, and especially a stable supply of feedstock (bushchips) for bio-energy production, while recovering value from stands that would otherwise become uneconomical to harvest. The optimal short-run response is to increase harvests over the baseline harvest without beetle. The use of future net returns as the optimization objective ensures that harvest during the 20 year time horizon occurs in stands that would otherwise be economically unharvestable and also the harvest is generally above 70% pine in aggregate. Net returns do not exceed those of the baseline harvest without beetle, regardless of the scenario, as the harvest of low value bushchips must be subsidized by the harvest of timber that can be converted into lumber. Shelflife provides significant changes in NPV as more timber can be converted to lumber if shelflife is longer. The government has a difficult fiscal management problem. Employing an evenflow of total harvest can yield higher net gains but at the risk of relying more heavily on the harvest of damaged timber and reduced future harvests of quality timber for dimensional lumber. This strategy would produce a “feast” of short term revenue followed by a “famine” when bushchip harvest is subsidized by the harvest of better quality timber. Alternatively, managing the individual forest products could yield some minimum government revenues but this strategy could also lead to the need to deplete reserves that could be reserved for future timber supply. Regardless of the strategy, to optimize for future timber supply potential means that a large percentage (25% in this study) of the damaged pine should only be harvested in the future and will not be of a quality to produce lumber

INTERNAL CONSISTENCY IN MODELS OF OPTIMAL RESOURCE USE UNDER UNCERTAINTY

For several decades, economists have been concerned with the problem of optimal resource use under uncertainty. In many studies, researchers assume that prices evolve according to an exogenous stochastic process and solve the corresponding dynamic optimization problem to yield an optimal decision rule for exploitation of the resource. This study is motivated by our attempt to understand the relationship between efficiency in resource markets and optimal harvest decisions in which price is an exogenous state variable. The literature on optimal commodity storage finds that in a rational expectations equilibrium commodity prices are stationary and serially correlated. Yet recent papers on optimal timber harvesting that assume exogenous stationary prices generate harvest rules inconsistent with the price processes on which they are based. In this study, we investigate the appropriate form of the stochastic process governing prices of renewable resources. We develop a model in which timber is supplied by profit-maximizing managers with rational expectations and aggregate timber demand is subject to independent exogenous shocks. In contrast to earlier studies, prices are endogenously determined. Managers know the structure of the timber market and form expectations of future market equilibria in making optimal harvesting decisions. We show under general conditions that efficient timber prices are stationary and serially correlated. Stationarity and serial correlation are shown to arise from two sources: the occurrence of stock-outs (i.e., depletion of the inventory) and stock-dependent growth of the resource. Further, we show that prices retain these properties even in the absence of stock-outs. Simulations are used to further illustrate the analytical results. Our findings have implications for a large number of economic analyses of optimal resource use. First, our results reveal why extraction rules for renewable resources based on exogenous price specifications are internally inconsistent, even when the specification conforms to the stochastic behavior of prices generated by an efficient market. These prices arise in a particular structural environment, and if large numbers of resource managers adopt the harvesting rule, the underlying structural environment would change, and the price process would deviate from that used to derive the harvesting rule. Second, we show that there can be no gains from exploiting the stochasticity of resource prices in a rational expectations world, a finding that challenges the prescriptive policies for resource use found in many studies, including those on option values. Third, our results show that time-series analyses designed to test for the efficiency of renewable resource markets cannot distinguish prices generated in an efficient market from those generated in an inefficient market. Finally, we extend the literature on optimal storage. Previous models of commodity storage models are shown to be a special case of our model involving age-independent depreciation of the inventory.Resource /Energy Economics and Policy,

A simple OPT + 1 algorithm for cutting stock under the modified integer round-up property assumption

We present a simple algorithm for the cutting stock problem with a constant number d of object sizes that produces solutions of value at most OPT +1 in time d^{O(d)} log^7 n, where OPT is the value of an optimum solution. This algorithm works under the assumption that the modified integer round-up property of Scheithauer and Terno for the cutting stock problem holds

Stochastic Dominance Portfolio Analysis of Forestry Assets

We consider the forestry decision-making and harvesting problem from the perspective of financial portfolio management, where harvestable forest stands constitute one of the liquid assets of the portfolio. Using real data from Finnish mixed borealis forests and from the Helsinki stock exchange, we investigate the effect of trading the timber stock together with the forest land, or without the land (i.e., harvesting), on the portfolio efficiency. As our research methodology, we utilize the general Stochastic Dominance (SD) criteria, focusing on the recent theoretical advances in analyzing portfolio diversification within the SD framework. Our findings shed some further light on the question of how to model the forestry planning problem, and provide some comparative evidence of the applicability of the alternative SD test approaches.Forest Management, Portfolio Optimization, Stochastic Dominance, Diversification

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

The Evolution of an Industrial Sector with a Varying Degree of Roundaboutness of Production

The evolutionary model presented in this paper depicts an industrial sector with a varying degree of economic roundaboutness, i.e. vertical division of labour between producers and users of different types of intermediate products that are ultimately used for the production of a single final product. To include this vertical aspect of industrial dynamics, the model adds the concept of production trees to the evolutionary models of Schumpeterian competition. The specification of this concept suggests the use of the notions of graph theory and the related algorithms of computer science in the treatment of industrial novelty, including structural innovations. Although the model is developed within the Nelson and Winter tradition, the introduction of the 'Austrian' issue of roundaboutness implies a major extension of the research agenda, including production- structure innovations, the emergence and functioning of markets for intermediate products, ways of coping with the instability of upstream markets, the spread of the effects of an upstream innovation, and the measurement of the degree of roundaboutness and of overall productivity. The model reflects a Schumpeterian version of the Böhm-Bawerkian vision of the emergence of increased long-term roundaboutness of production. The Schumpeterian approach implies an innovation- and entrepreneur-driven process of vertical disintegration and reintegration.Roundaboutness, production graphs, evolutionary economic modelling, Nelson and Winter

A note on the split rank of intersection cuts

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that ! log 2(l)mixed integer programming, split rank, intersection cuts.