The Dynamic Behavior of Efficient Timber Prices

The problem of when to optimally harvest trees when timber prices evolve according to an exogenous stochastic process has been studied extensively in recent decades. However, little attention has been given to the appropriate form of the stochastic process for timber prices, despite the fact that the choice of a process has important effects on optimal harvesting decisions. We develop a simple theoretical model of a timber market and show that there exists a rational expectations equilibrium in which prices evolve according to a stationary ARMA(1,1) process. Simulations are used to analyze a model with a more general representation of timber stock dynamics and to demonstrate that the unconditional distribution for rational timber prices is asymmetric. Implications for the optimal harvesting literature are: 1) market efficiency provides little justification for random walk prices, 2) unit root tests, used to analyze the informational efficiency of timber markets, do not distinguish between efficient and inefficient markets, and 3) failure to recognize asymmetric disturbances in time-series analyses of historical timber prices can lead to sub-optimal harvesting rules.

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

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,

Optimal Advertisement Scheduling in Breaks of Random Lengths

Broadcasters generate a large part of their revenue through advertising, especially in live sports. Scheduling advertisements can be challenging in live broadcasting, however, for sports such as Cricket that have breaks of random lengths and number during which the ads are shown. This uncertainty, coupled with the high price of spots for major competitions, means that improving ad scheduling can add significant value to the broadcaster. This problem shares similarities with the stochastic cutting stock problem and the dynamic stochastic knapsack problem, with applications in the wood, steel and paper industry and the transportation industry respectively. This dissertation adds to the existing literature on advertising scheduling by taking stochasticity in break sizes into consideration. We propose an optimal scheduling rule under simplifying assumptions and prove that our policy outperforms traditional scheduling methods. We also study the performance of several heuristics, and find that a flexible heuristic that does not depend on creating bundles performs the best

Climate Change Mitigation Policy: The Effect of the New Zealand Emissions Trading Scheme on New Radiata Pine Forest Plantations in New Zealand

Climate change is one of the toughest challenges facing the world today. Putting a price on carbon emissions is an important step towards climate change mitigation. A cap and trade system is one of the ways to create a carbon price. The New Zealand Emissions Trading Scheme (NZETS) is the world’s first economy-wide cap and trade system that covers all sectors and all 6 greenhouse gases. Forestry is a major part of the NZETS, allowing foresters to earn carbon credits for new forests planted on and after 1st January 1990 (afforestation and reforestation). At the same time, the NZETS also makes foresters liable for harvesting new forests planted on and after 1st January 1990, and deforesting forests existing on and before 31st December 1989. In this paper, we perform an economic analysis of how a carbon price will likely affect the returns and forestry management behaviour in new forests in New Zealand. Previous works have used the NPV/LEV (fixed harvesting) analysis where the forest is assumed to be harvested (in future) at the estimated optimal rotation age regardless of timber prices at that time. Other works have employed the Real Options approaches (flexible harvesting) where sophisticated models such as Partial Differential Equations and simulations analyse the effects of bringing forward the harvest decision if timber prices are favourable, and deferring the harvest decision if timber prices are unfavourable. Often, these methods tend to have higher data requirements, employ different assumptions and are much more complex to estimate. Because of these differences, it may be difficult to compare the results of NPV/LEV analysis with Real Options. Our work here applies the binomial tree method, which is a relatively simple method that can generate both LEV (fixed harvesting) and Real Options (flexible harvesting) results on a common model with the same data requirements and assumptions. This allows for better comparability of forestry management behaviour and effects of carbon price. The forestry valuations are analysed under a stochastic timber price and a constant carbon price. This paper concludes with some implications on policy in New Zealand.Environmental Economics and Policy,