Optimal Harvesting of Timber: Valuing Timberland with Stochastically Evolving Timber Volume and Prices Using Linked Biological/Geographical Data from British Columbia

在环境和自然资源经济学中，经济学家对可再生自然资源的管理非常感兴趣，因为永远管理资源的前景具有实际重要性和现实意义。此外，由于过去未能妥善管理某些可再生自然资源，导致若干物种灭绝，因此制定管理剩余可再生自然资源的切实可行的战略既及时又有用。 本项目详细调查了加拿大不列颠哥伦比亚省的一种可再生自然资源--木材的管理情况。 对于不列颠哥伦比亚省的一个木材供应区（TSA），调查人员获得了非常详细的现场级数据的独特访问权，这些数据被不列颠哥伦比亚省森林部的木材供应经理在做出采伐决策时使用。特别是，他们可以在网格一级以地理信息系统的形式获得详细的相关生物和地理数据，在这种情况下，网格是一公顷或100平方米。因此，弗雷泽TSA位于不列颠哥伦比亚省的温哥华附近，占地数十万公顷，森林部的官员为调查人员提供了与采伐木材有关的各种生物、工程和地理信息。此外，他们还可以获得建议的采伐战略，在某些情况下，还可以获得森林部长执行的决定，因此他们可以将我们的估计决定与实际决定进行比较。在开发木材的实际采伐解决方案时，他们应用了随机动态规划的方法。 该项目的目标是做出以下贡献：首先，该项目认真对待地理学，无论是在平面意义上还是在三维意义上。第二，它认真对待特定地点的异质性，无论是在成本方面的砍伐和运输方面，在生长和产量方面的异质林分的木材。第三，它模拟初始条件。特别地，它不以稳态分配或甚至最优分配作为起点。相反，它需要现有的非均匀年龄的木材林，并得出最佳的政策功能，最佳的木材采伐配置文件，在这个年龄分布。第四，该项目使用最佳实践生物方法来模拟异龄森林生长和产量的动态。第五，在过去，经济学家和林业学家通常通过对木材价格和木材量的随机性做出非常简单的假设来证明他们的方法，以便解决封闭形式的例子。 这项研究实现了计算方法的最新发展，使从业者可以在现实的生物，经济和空间环境中数值求解最优政策函数。

In environmental and natural resource economics, the management of renewable natural resources is of considerable interest to economists because the prospect of stewarding a resource forever has practical importance and real-world relevance. Moreover, because past failures in managing certain renewable natural resources properly have lead to the extinction of several species, developing practical strategies for managing remaining renewable natural resources is both timely and useful. This project investigates in detail the management of one renewable natural resource, timber, in the province of British Columbia, Canada. For a Timber Supply Area (TSA) in British Columbia the investigators have obtained unique access to extremely detailed site-level data, which are used by timber-supply managers in the British Columbia Ministry of Forests when making harvesting decisions. In particular, they have access to elaborate linked biological and geographical data in the form of a Geographical Information System (GIS) at the grid level which, in this case, is a hectare or 100 meters square. Thus, for every hectare in the Fraser TSA, which is located near Vancouver, British Columbia and contains several hundreds of thousands hectares, officials at the Ministry of Forests provide the investigators with a wide variety of biological, engineering, and geographical information relevant to harvesting timber. In addition, they also have access to the harvesting strategies proposed and, in some cases, the decisions implemented by the Minister of Forests, so they can compare our estimated decisions with actual ones. In developing practical harvesting solutions for timber, they apply the method of stochastic dynamic programming. The goal of the project is to make the following contributions: First, this project takes geography seriously, both in the planar sense and in the three-dimensional sense. Second, it takes site-specific heterogeneity seriously both on the cost side in terms of felling and transportation and on the growth and yield side in terms of heterogeneous stands of timber. Third, it models initial conditions. In particular, it does not take as the starting point a steady-state allocation, or even an optimal allocation. Instead, it takes the existing uneven-aged timber stand as given and derives the optimal policy function, the optimal timber-harvesting profile, in terms of this age distribution. Fourth, this project uses best-practice biological methods to model the dynamics of uneven-aged forest growth and yield. Fifth, in the past economists and foresters have typically demonstrated their methods by making extremely simple assumptions concerning the stochastic nature of timber prices and volumes so that closed-form examples could be solved. This research implements recent developments in computational methods so that practitioners can solve numerically for the optimal policy function in realistic biological, economic, and spatial environments.