基于广义Faustmann模型的营林管理决策方法学研究前沿及展望

doi:10.11707/j.1001-7488.LYKX20220833

摘要/Abstract

摘要：

可持续营林及相关联的最优轮伐期决策是缓解全球气候变化的重要途径。经典Faustmann模型关于“所有参数在不同轮伐期内保持一致”的基本假设无法得到满足，有必要以广义Faustmann模型为基础探求多因素影响下的最优轮伐期决策问题。本研究围绕广义Faustmann模型，归纳总结其理论扩展及前沿应用，梳理可持续营林决策方法学中广义Faustmann模型的最新研究进展。研究发现：1）广义Faustmann模型已在碳汇效益、异龄林管理、自然风险和税收政策4个方向得到拓展，其中土地期望值及相应的利润最大化一阶条件能够帮助林地所有者制定合理的营林管理方案；2）利用广义Faustmann模型，能够将Pressler指示率中的数量增长率、质量增长率和价格增长率具体化，允许林地所有者在不知道未来价格的情况下，结合自身风险偏好使用事前决策的方法决定当年是否采伐林分；3）林分的土地价值和木材价值在广义Faustmann模型下能够被明确区别开来，从而在转让一片未成熟林分时，实现对林分的土地和木材准确估值，并在不同税收政策下确定其各自税率。广义Faustmann模型在未来最优轮伐期决策研究中的拓展方向还包括以下几个方面：1）将碳汇效益由地上生物量碳库扩展至完整林业碳库；2）将税收政策由国外政策扩展至中国特色林业税费体系；3）将模型假设由确定环境扩展至随机环境；4）将研究尺度由林分层面扩展至森林层面；5）将生态效益由碳汇效益扩展至森林生态系统服务。

关键词: 广义Faustmann模型, 最优轮伐期, 碳汇效益, 风险管理, 林业税收与估值, Pressler指示率

Abstract:

Sustainable forest management and related optimal rotation decision are important ways to mitigate global climate change. Due to the basic assumption of the classical Faustmann model that all parameters are consistent in different rotation cycles cannot be satisfied, it is necessary to explore the optimal rotation decision-making problem under the influence of multiple factors based on the generalized Faustmann model. This study focuses on the generalized Faustmann model, summarizes its theoretical expansion and frontier application, and analyses the research frontier of the generalized Faustmann model in sustainable forest management decision-making methodology. The research finds that: 1) The generalized Faustmann model has been expanded in four directions, carbon sequestration benefits, uneven-aged forest management, natural risk and tax policy, among them, the land expectation value and the corresponding first-order conditions for profit maximization can help forest owners to formulate a reasonable forest management plan. 2) By using the generalized Faustmann model, the quantity growth rate, quality growth rate and price growth rate in the Pressler indicator rate can be specified, it allows forest owners to make decision in advance in conjunction with their own risk preferences to decide whether to cut the stand in the current year. 3) The land value and timber value of the forest can be clearly distinguished under the generalized Faustmann model, so that when transferring an immature forest, the accurate valuation of forest land and timber can be achieved, and their respective tax rates can be determined under different tax policies. The extension direction of the generalized Faustmann model in the future optimal rotation decision-making research also includes the following aspects: 1) Expanding carbon sequestration benefits from aboveground biomass carbon pool to complete forestry carbon pools. 2) Expanding tax policies from foreign policies to the forestry tax and fee system with Chinese characteristics. 3) Extending model assumptions from deterministic environments to stochastic environments. 4) Expanding the research scale from stand-level to forest-level. 5) Expanding ecological benefits from carbon sequestration benefits to forest ecosystem services.

Key words: generalized Faustmann model, optimal rotation period, carbon sequestration benefits, risk management, forestry taxation and valuation, Pressler indicator rate

中图分类号:

S7-9
F307.2

余智涵,杨红强. 基于广义Faustmann模型的营林管理决策方法学研究前沿及展望[J]. 林业科学, 2024, 60(9): 170-182.

Zhihan Yu,Hongqiang Yang. Research Frontier and Prospect of Forest Management Decision-Making Methodology Based on Generalized Faustmann Model[J]. Scientia Silvae Sinicae, 2024, 60(9): 170-182.

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参数发生变化的时间 Time of parameters change	发生“一次性增长”的参数名称 Parameter name where “one-time increase” occurs	最优轮伐期 Optimal rotation period
参数发生变化的时间 Time of parameters change		经典Faustmann模型	广义Faustmann模型
当前轮伐期 During the current rotation period	重置成本 Replacement cost（$ {C}_{k} $）	延长 Increase	不变 No change
	木材价格 Timber price（$ {P}_{k}） $	缩短 Decrease	延长 Increase
	折现率 Discount rate $ {（r}_{i}） $	缩短 Decrease	缩短 Decrease
	碳价格 Carbon price $ （P\mathrm{_c}） $	延长 Increase	延长 Increase
	碳转换系数 Carbon conversion factor $ （{\alpha }_{i}） $	延长 Increase	延长 Increase
	木材的长期储存比例 Long-term storage ratio of wood（$ {\beta }_{i} $）	缩短 Decrease	不确定 Uncertain
未来轮伐期 During the future rotation period	重置成本 Replacement cost（$ {C}_{k} $）	延长 Increase	延长 Increase
	木材价格 Timber price（$ {P}_{k} $）	缩短 Decrease	缩短 Decrease
	折现率 Discount rate（$ {r}_{i} $）	缩短 Decrease	延长 Increase
	碳价格 Carbon price（$ P\mathrm{_c} $）	延长 Increase	缩短 Decrease
	碳转换系数 Carbon conversion factor（$ {\alpha }_{i} $）	延长 Increase	缩短 Decrease
	木材的长期储存比例 Long-term storage ratio of wood（$ {\beta }_{i} $）	缩短 Decrease	延长 Increase

税收政策 Tax policy	公式类别 Formula category	公式 Formula
UPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[\dfrac{{r}_{1}+{y}_{1}}{\left({r}_{1}+{x}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-{x}_{1}+{y}_{1}}\right]\times \left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{({r}_{1}+{y}_{1})({t}_{1}-{s}_{1})}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\right]\end{array} $
UPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1}+{x}_{1} $
SVT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[\dfrac{{r}_{1}}{\left({r}_{1}+{x}_{1}\right){\mathrm{e}}^{{r}_{1}{t}_{1}-{x}_{1}}-{x}_{1}}\right]\times \left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}({t}_{1}-{s}_{1})}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\right]\end{array} $
SVT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
GFRPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\dfrac{\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}-{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\right]}{{e}^{{r}_{1}{t}_{1}}-1}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{r}_{1}}\end{array} $
GFRPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
NFRPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\dfrac{\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}-{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\right]}{{\mathrm{e}}^{{r}_{1}{t}_{1}}-1}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{r}_{1}}\end{array} $
NFRPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
FTP	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}\right]{\mathrm{e}}^{-{r}_{1}{t}_{1}}-{Y}_{1}\left(1-\dfrac{{\mathrm{e}}^{-{r}_{1}{t}_{1}}}{{r}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}{\mathrm{e}}^{-{r}_{1}{t}_{1}}\end{array} $
FTP	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{Y}_{1}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $

税收政策 Tax policy	价值类别 Value category	公式 Formula
UPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{s}_{1}\right)}}+\left(\dfrac{{y}_{1}-{x}_{1}}{{r}_{1}+{y}_{1}}\right){\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left[1-{\mathrm{e}}^{-\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
UPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){s}_{1}}-1\right)}{\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-1\right)} $
SVT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}}{{r}_{1}}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
SVT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
GFRPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
GFRPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
NFRPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
NFRPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
FTP	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{Y}_{1}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
FTP	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $

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