A dynamic analysis of the global timber market under global warming: an integrated modeling approach.

Lyon, Kenneth S.

1. Introduction

Scientists and policymakers alike are concerned about global warming caused by the accumulation of carbon dioxide in the atmosphere. A significant number of studies have built comprehensive assessment models of carbon dioxide concentrations in the atmosphere over long time periods; however, most of these are deficient in the sense that they do not develop integrated assessment models that capture economic effects associated with global warming. In this vein, our research, as shown here, contributes to a growing body of literature that attempts to develop dynamic integrated models of ecosystem and economic system interactions that arise from predictions of global warming. We focus on the global timber market as a particular inquiry of global warming.

As global warming forces ecosystems to migrate toward the poles, the distribution of ecosystem types and the productivity of ecosystems will be altered. The transformation and adjustment of ecosystems resulting from climate change also change the environmental conditions under which natural resources, including forest products, are extracted and regenerated. It has been discussed and predicted that changes of forest types occur along two dynamic paths: dieback and regeneration (Shugart et al. 1986; Solomon 1986; King and Neilson 1992). As climate change causes forest types to change along these dynamic paths, the global timber market will adjust as timber availability is altered.

In this context, we have developed an integrated modeling approach that identifies the effect of global warming on the global timber market. Most literature that studied this objective have only investigated the effect of global warming on timber markets in limited regions. Binkley (1988) studied the impact of global warming on boreal forests. Joyce et al. (1995), Burton et al. (1998), and Sohngen and Mendelsohn (1998) focused only on the United States. Perez-Garcia et al. (1997) and Sohngen et al. (1997) extended the effect of global warming on the global timber market. Except for Sohngen and Mendelsohn (1998) and Sohngen et al. (1997), these studies use comparative static analysis and compare steady-state equilibria. They consider neither dynamic ecological change nor dynamic economic behavior of the timber market.

For our integrated modeling approach, we use the Timber Supply Model (TSM) developed by Sedjo and Lyon (1990) and extend it to include additional global timber market components. BIOME 3 (Haxeltine and Prentice 1996), an equilibrium terrestrial biosphere model based on ecophysiological constraints, resource availability, and competition among plant functional types, is adopted as our steady-state ecological model and Hamburg (Claussen 1996) as our general circulation model (GCM) to investigate the change of climate variables when carbon dioxide is doubled in the atmosphere. Because there are no dynamic ecological models that span the globe, we impose linearity assumptions about ecosystem adjustment to climate change. We do this to derive a predicted time path of relevant ecological changes such as forest dieback hectares and regeneration hectares and to predict the dynamic productivity change. We modify the extended TSM (which is referred to as TSM 2000) to reflect these dynamic ecological changes. Then we simulate a non-climate change base scenario and a climate change scenario using TSM 2000 to predict the effect of global warming on the global timber market. We perform these procedures for three different timber demand scenarios to observe the sensitivity of the conclusions to the level of timber demand. These include normal timber demand growth, high timber demand growth, and very high timber demand growth. First, we specify and formulate TSM 2000. Second, we develop our procedures for estimating the relevant dynamic ecological changes caused by global warming. These include dynamic forestland area changes and productivity changes. Third, the simulation results are reported and discussed for each scenario. This includes a discussion of the sensitivity results and welfare implications.

2. Dynamic Timber Supply Model

Alternative dynamic economic models of timber market behavior include (Berck 1979; Brazee and Mendelsohn 1990; Adams et al. 1996; Sohngen and Mendelsohn 1998; Sohngen, Mendelsohn, and Sedjo 1999) and the TSM (Sedjo and Lyon 1990, 1996). We use TSM because it has the relevant characteristics, we understand it, and we can modify it to fit the problem at hand. In general, the volume harvested in the TSM is affected by seven types of adjustments. These are (i) rotation length of age; (ii) the rate of drawdown of old growth inventories; (iii) the number of forested land classes that are utilized in the harvest; (iv) the level of regeneration input applied to the various land classes; (v) the rate at which new industrial plantations are added to the world's timber-producing regions; (vi) the rate of technical change-wood-extending, wood-growing, and wood-saving; and (vii) changes in production from nonresponsive regions of the world (Lyon and Sedjo 1992). (1) The TSM provides economically efficient solutions in the sense that it maximizes total benefit to the society as a whole, not the net income stream of an individual landowner.

Description of TSM 2000

To develop TSM 2000, we modify TSM in the following ways. First, the TSM 2000 considers the former Soviet Union to be a part of the responsive region. We postulate that the former Soviet Union will participate in the global timber market and that it will play a critical role in supplying stumpage to the global timber market since it contains approximately 25% of worldwide forest growing stock (Backman and Waggener 1991). For this research, we subdivide the former Soviet Union into three subregions: European USSR, West Siberia, and East Siberia. Also, we subdivide these three regions according to ecosystem type and the degree of accessibility for harvesting; hence, these three subregions consist of 16 land classes: eight land classes for European USSR and four land classes for West Siberia and East Siberia, respectively. These are identified more concretely later.

Second, we include more plantation forests in the emerging region in the TSM 2000. (2) Plantation forests in India, Asia-Pacific region, and subregions in Africa except South Africa are not included in the TSM as the emerging region. According to Sedjo (1994), both tropical and subtropical regions have experienced an increase in plantation forest. Land areas in these regions, which are exploited for agricultural production or were being conserved for the future use, are now being turned into plantation forest. About six million hectares had been planted in the emerging region by 1980 (Sedjo and Lyon 1990); however, it is estimated that plantation forest acreage included in these areas were about 38 million hectares in 1990 (UNFAO 1993a, 1993b, 1995).

Third, there has been a trend to withdraw forestland from timber harvesting and conserve it for wilderness, ecological reserves, parks, scenic corridors, and other purposes in many major timber-producing countries. Recent publications of the International Union Conservation of Nature and Natural Resources (IUCN 1990, 1994) included all the areas designated to be protected by individual governments as well as the international organizations. Yan (1996) calculated the conserved hectares of forest for seven responsive regions being included in the TSM since 1981 (1980 for Asia-Pacific region) based on publication of IUCN (1994). He designated nine scenarios of the forest conservation by combining these calculations with more information on conservation actions for each responsive region. Current trends to promote conservation of forest for environmental protection suggest that conservation patterns modeled in TSM 2000 will be an important factor affecting worldwide timber supply. In this respect, we model conservation of forest for each land class in each region by adopting Yan's (1996) scenario 5. Here we discuss the forest conservation ratios that we use for the subregions of the former Soviet Union. (3)

Fourth, the TSM (1990, 1996) considered only 22 land classes in seven responsive regions to project the optimal time profile of important endogenous variables in the model. To meet our research objective, we consider the change of distribution of ecosystem type (vegetation pattern) and change of productivity of ecosystem type after climate change. When we examine the change of distribution of ecosystem types on the basis of BIOME 3 predictions using Hamburg as our GCM, we observe that in some regions a large portion of an ecosystem type would be transformed into other ecosystem types after climate change. This reflects the fact that some species die out from the area where they are currently standing and new species are regenerated naturally or planted by human beings for economic benefit. In this respect, we subdivide land classes in more detail in the TSM 2000 in order to include the ecological detail acquired from the BIOME 3 predictions on ecosystem change. Consequently, TSM 2000 includes 42 land classes in 10 responsive regions.

Formulation of TSM 2000

We now describe the model. Net surplus in the year j is defined as

(2.1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [Q.sub.j] is the quantity or volume of timber for solid wood harvested in year j, [D.sup.s.sub.j]([Q.sub.j]) is the inverse demand function of industrial solid wood in year j, [[??].sub.j] is the volume of timber for pulpwood harvested in year j, [D.sup.p.sub.j]([[??].sub.j]) is the demand function of industrial pulpwood in inverse form, and [C.sub.j] is the total cost in year j. The total costs are the summation of harvest, access, transportation costs (C[H.sub.j]), and regeneration cost (C[R.sub.j]). Harvesting and transportation costs in year j depend on the total volumes harvested by land class, and regeneration costs depend on hectares harvested (regenerated) and the level of regeneration inputs used.

For the formulation, define [x.sub.hj] to be a vector of hectares of trees in each age-group for land class h in year j with elements [x.sub.hij]. The subscripts h, i, and j correspond to land class, age-group, and the year, respectively. Let [z.sub.hj] be the vector of state variables for the regeneration input with elements [z.sub.hij], which is the level of regeneration input associated with age-group i in year j for land class h. Next, [u.sub.hj] is the control vector of portions of hectares harvested. The elements of [u.sub.hj] denote for land class h the portion of the hectares of trees in age-group i harvested in year j. Let [w.sub.hj] be the level of regeneration input per hectare for those hectares regenerated in year j and [p.sub.wh] be the price of regeneration input for land class h. The merchantable volume of timber per hectare for land class h in time period j for a stand regenerated i time periods ago depends on i and on the magnitude of the regeneration input used on this stand ([z.sub.hij]). We denote this merchantable volume as follows:

(2.2) [q.sub.hij] = [f.sub.h] (i, [z.sub.hij]).

This volume is divided between solid wood and pulpwood using variable proportions that vary by land class, with [[phi].sub.h] the portion going to solid wood and (1 - [[phi.sub.h]) the portion going to pulpwood. The proportion [[phi].sub.h] is a constant elasticity function of the price of solid wood relative to the price of pulpwood ([p.sup.s.sub.j]/[p.sup.p.sub.j]). It is given by

[[phi].sub.hj] = [A.sub.h] [([p.sup.s.sub.j]/[p.sup.p.sub.j]).sup.[epsilon]],

where [p.sup.s] and [p.sup.p] are solid-wood and pulpwood price, respectively; [epsilon] is the elasticity of [phi] with respect to relative price, which is the same for all land classes; and [A.sub.h] is a scaling factor that varies by land class. For the base case and the several scenarios to be considered, we use an elasticity, [epsilon], of 0.6, and select the scaling factors so that the reference percents solid wood would exist at a relative price of 1.5.

With these definitions, the volume of commercial timber harvested for solid wood and pulpwood from land class h in year j, [Q.sub.hj] and [Q.sub.hj] is given by

(2.3a) [Q.sub.hj] = [[phi].sub.hj] [u'.sub.hj] [X.sub.hj][q.sub.hj]

(2.3b) [[??].sub.hj] = (1 - [[phi].sub.hj][u'.sub.hj] X.sub.hj][q.sub.hj]

and

[Q.sub.j] = [summation over (h)] [Q.sub.hj], [[??].sub.j] = [summation over (h)] [[??].sub.hj]

where [X.sub.hj] is a diagonal matrix using the elements of [x.sub.hj] and the total volume harvested in the responsive regions is the summation of these over all land classes. Costs including harvest, access, and transportation cost for land class h is a function of the volume harvested in that land class,

(2.4) C[H.sub.hj] = [C.sub.h]([Q.sub.hj] + [[??].sub.hj]),

and regeneration cost for land class h in time period j is given by

(2.5) C[R.sub.hj] = ([u'.sub.hj][x.sub.hj] + [v.sub.hj])[p.sub.wh][w.sub.hj],

where the inner product in parentheses gives the hectares harvested in land class h, [v.sub.hj] is the exogenously determined number of hectares of new forestland in land class h, and the product of the last two terms gives expenditure per hectare. This yields total cost of

C[R.sub.hj] = [summation over (h)] (C[H.sub.hj] + C[R.sub.hj).

With these definitions, the objective function of TSM 2000 will be the sum of discounted present value of the net surplus as follows:

(2.6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [rho] is the discount factor, [e.sup.-r], with r the market interest rate; J is the last time period of the modeled time horizon; u is any admissible set of control vectors, [u.sub.0], [u.sub.1], ..., [u.sub.J-1] (including all land classes); w is any set of admissible control scalars, [w.sub.0], [w.sub.1], ..., [w.sub.J-1] (also covering all land classes); and [S.sup.*.sub.J](*,*) is the optimal terminal value function. Equation 2.6 is to be maximized over the control variables subject to the laws of motions of the state variables and the constraints. The portions of hectares harvested are constrained to be nonnegative and less than or equal to 1, and the regeneration inputs are constrained to be nonnegative:

(2.7a) 0 [less than or equal to] [u.sub.hij] [less than or equal to] 1 for all h, i, j

(2.7b) 0 [less than or equal to] [w.sub.hj] for all h, j.

The laws of motion for the given system are given by

(2.8a) [x.sub.hj+1] = (A + B[U.sub.hj])[x.sub.hj] + [v.sub.hj]e for all h, j

(2.8b) [z.sub.hj+1] = A[z.sub.hj] + [w.sub.hj]e for all h, j,

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

A, B, and U are M-square matrices, [U.sub.hj] is a diagonal matrix using the elements of [u.sub.hj], and e is a M-vector where M is equal to or greater than the index number of the oldest age-group in the problem.

Solution Techniques

The problem of maximizing objective function (Eqn. 2.6), subject to the constraint Equations 2.7a through 2.8b, is a discrete time, optimal control problem that can be solved by the discrete time maximum principle. The maximum principle is a theorem that states that the constrained maximization of Equation 2.6 can be decomposed into a series of subproblems. In each time period, the following Hamiltonian is maximized with respect to [u.sub.hj] and [w.sub.hj] subject to the constraints. The Hamiltonian for year j is

(2.9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where

(2.10a) [[lambda].sub.hj] = [rho][d[S.sup.*] [sub.j]([x.sub.j], [z.sub.j])/d[x.sub.hj]] (j = 1, ..., J) [[lambda].sub.hj] = [rho][(d[s.sup.*.sub.j]/d[x.sub.hj] + (A + B[U.sup.*.sub.hj])'[[lambda].sub.h, j+1]] (j = 1, ..., J - 1)

and

(2.10b) [[psi].sub.hj] = [rho][d[S.sup.*.sub.j]([x.sub.j], [z.sub.j])/d[z.sub.jh]] (j = 1, ..., J) [[psi].sub.jh] = [rho][d[s.sup.*.sub.j]/d[z.sub.hj]) + A'[[psi].sub.h, j+1] (j = 1, ..., J - 1).

The derivatives with respect to vectors are gradient vectors, and [S.sup.*.sub.j+1] (.,.) is the solution function in j + 1. The solution function in year j + 1 can be conceptualized as the result of an application of Bellman's optimality principle and backward recursion. The [[lambda].sub.hj] and [[psi].sub.hj] are costate (adjoint) vectors and identify the shadow values of the hectares of forest and the regeneration input, respectively, in each age-group in year j. The Lagrangian function and the Kuhn-Tucker necessary conditions of this optimization problem are

(2.11) [L.sup.H.sub.j] = [H.sub.j] + [summation over (h)] [[xi]'.sub.hj] (1 - [u.sub.hj])

(2.12a) [differential][L.sup.H.sub.j]/[differential][u.sub.hj] = [[[phi].sub.hj][D.sup.s.sub.j]([Q.sub.j]) + (1 - [[phi].sub.hj]) [D.sup.P.sub.j]([[??].sub.j]) - [c'.sub.h] ([Q.sub.hj] + [[??].sub.hj])][X.sub.hj][q.sub.hj] - [x.sub.hj][p.sub.wh][w.sub.hj]

+ [X'.sub.hj] B'[[lambda].sub.hj+1] = [[xi].sub.hj] [less than or equal to] 0 for all h

(2.12b) ([differential][L.sup.H.sub.j]/[differential][u.sub.hij] = 0 for all h and i

(2.12c) [differential][L.sup.H.sub.j]/[differential][w.sub.hj] = -[u'.sub.hj][x.sub.hj][p.sub.wh] + [[psi].sub.h, 1, j+1] [less than or equal to] 0 for all h

(2.12d) ([differential][L.sup.H.sub.j]/[differential][w.sub.hj]) [w.sub.hj] = 0 for all h

(2.12e) [differential][L.sup.H.sub.j]/[differential][[xi].sub.hj] = (1 - [u.sub.hj]) [greater than or equal to] 0 for all h

(2.12f) ([differential][L.sup.H.sub.j]/[differential][[xi].sub.hij])[[xi].sub.hij] = 0 for all h and i.

These Kuhn-Tucker conditions, the laws of motion for the state variables (Eqns. 2.8a and 2.8b), and the laws of motion for costate variables (Eqns. 2.10a and 2.10b) identify a two-point boundary value problem that can be used to solve both theoretical and numerical problems. These are the equations that we solve to find the optimal time paths for the scenario analyses.

3. Ecological Change Impacted by Global Warming

Because a dynamic ecological model that covers the globe has not yet been developed, we use a steady-state ecological model to predict the steady-state ecological equilibrium before and after climate change and then linearize the variables between the end points. The Intergovernmental Panel of Climate Change (IPCC) predicts a linear increase of temperature from 1990 to 2060, when the carbon dioxide concentration in the atmosphere is predicted to be doubled; hence, we use 1990 and 2060 as our end points. We first use a general circulation model (GCM) to estimate the effects of a doubling of atmospheric carbon on global climate. Then, using these climate results as inputs, the steady-state ecological model is simulated. The output of this is the distribution of ecosystems by type and the productivity of ecosystems across the globe. In general, steady-state ecological models are classified into two categories. Biogeographical distribution models (Prentice et al. 1992; Neilson and Marks 1994; Woodward, Smith, and Emanuel 1995) predict the distribution of ecosystem types, and biogeochemical cycle models (Patton, Stewart, and Cole 1988; Running and Coughland 1988; Running and Gower 1991; Melillo et al. 1993) predict the productivity of the ecosystems. In our research, we adopt BIOME 3 to observe steady-state ecological change using Hamburg as our GCM. BIOME 3 includes both a biogeographical distribution model and a biogeochemical cycle model within a single global framework. The output of BIOME 3 consists of a quantitative vegetation state description in terms of the dominant plant function types, the total leaf index, and the net primary productivity. (4) This output is then used to generate our predictions for 2060. We generate data for the 1990 end point in the same way, except that we use the current climate situation. To simulate the dynamic effects, we linearize the change between these end points. This linearization is consistent with the IPCC (1990) prediction of linear temperature change and with Sohngen et al. (1997). Sohngen et al. assume that climate variables are linearly increasing from 1990 to 2060 (5) and that, after 2060, climate variables stabilize, with ecosystems doing the same. Within our model, this yields dynamic ecological changes that decompose into dynamic land area change, hectares of forest by land class, and dynamic productivity change of ecosystem types, productivity of these forests. The implementation of the linearity assumptions is detailed later.

Dynamic Land Area Change

Biospheric scientists (Shugart et al. 1986; Solomon 1986; King and Neilson 1992) suggest that there are two processes of dynamic ecosystem type change as climate changes over time. One is dieback, and the other is regeneration. Dieback occurs when environmental conditions of the forest significantly deviate from those to which the current growing trees are accustomed. Changing climate conditions continuously harass growing trees and cause standing trees to stop growing. Eventually, the standing trees die out. The regeneration process occurs slowly through the gradual competitive displacement of forest types or through plantation management. As existing forests are harvested or die out naturally, however, old species are not regenerated. Instead, new species naturally migrate into the sites with a time lag or are planted by human beings for economic benefit. In this context, we first identify the change in potential forest for each of 41 geographic land areas (land classes) around the globe. We identify changes in both land area and dominant species. The BIOME 3 simulation results provide us with predictions of plant functional types and total leaf index for all land areas on the globe. We eliminate nonforestland areas from the BIOME 3 results and collate the results with our 41 geographic land classes. Nonforest areas include farmland and settlement, city complexes, paddy, cropland and pasture, coastal, and water and islands. (6) Using these hectares of potential forest for before and after climate change, we calculated the dieback ratio and the regeneration ratio for each ecosystem type. We did this for the land area in each of our 41 geographic land classes. (7) We consider two factors in choosing ecosystem types in each responsive region. These factors include dominant forest types for commercial use as well as the degree of ecological transformation after climate change. Each land class in the TSM 2000 is classified according to its biological and geographical characteristics, such as ecosystem type, as well as the degree of harvesting accessibility. Using our linearity assumptions, we estimate dynamic land area change for each of our 41 geographic land classes. This includes forest dieback hectares per year and regeneration hectares per year by land class.

Dynamic Productivity Change

As part of our dynamic ecological specification, we assume that net primary productivity (NPP) adjustment occurs proportionally to climate change. The NPP is a steady-state concept in the sense that the biogeochemical cycle model predicts the equilibrium NPP at a given time; hence, the dynamic path of NPP is assumed to be linear over the period of climate change. NPP is the net amount of carbon garnered for plant growth; hence, we assume that tree growth per unit time is proportional to NPP. Letting t = 0 for 1990 and t = 70 for 2060, we linearize the effects of climate change using

[[kappa].sub.h](t) = 1 + [kappa] * t,

where [kappa] = ((NP[P.sub.70]/NP[P.sub.0]) - 1)/70. The non-climate change yield function per hectare was defined as [q.sub.hij] = [f.sub.h](i, [z.sub.hij]) for land class h in time period j and the standing trees regenerated i years ago. To capture the effects of NPP change, we modify the yield function for trees for the time period during which climate change occurs. These modifications are developed in Appendix A.

4. Simulation Results of the Global Timber Market

To examine the impact of global warming on the global timber market, we simulate intertemporal values of the endogenous variables for both the non-climate change base scenario and the climate change scenario under normal timber demand growth over a time horizon of 90 years, starting in 1995. (8) For the simulation of climate change scenarios, we modify the TSM 2000 to reflect the dynamic ecological changes discussed previously. The estimations obtained for the base scenario and the climate change scenario allow us to predict the effect of global warming on the global timber market. In addition, to assess the sensitivity of the results to different assumptions of timber demand growth, we also simulate the model under both high timber demand growth and very high timber demand growth scenarios.

An Analysis of the Base Scenario

In our modeling framework, the base scenario results are considered to be our best predictions of what will occur if there is no climate change and will be used as the baseline to compare with and to contrast the other scenarios against. The assumptions used for model simulation of the base scenario under normal demand scenario are as follows:

(i) World demand schedule for industrial wood (combined pulpwood and solid-wood products) will increase at an annual growth rate of 1.0% in the first year and decrease in a linear fashion each successive year until growth rate is zero in the 90th year.

(ii) World demand schedule for pulpwood initially increases at an annual growth rate of 2.27% in the first year and decreases in a linear fashion each successive year until the growth rate is zero in the 90th year.

(iii) New forest plantations are established in the emerging region at an annual rate level of 2.80 million hectares for 10 years.

(iv) The dollar exchange rate is assumed to remain at an intermediate level throughout the period of analysis. (9)

In the formulation of TSM 2000, the former Soviet Union as well as plantation forests in India, African countries, and Asia-Pacific are included as a part of responsive regions. As a result, we need to estimate the new demand function for the responsive regions. The initial solid-wood and pulpwood demand functions are also estimated as follows:

[P.sup.s] = 162 - 0.001215 * [Q.sup.s]

[P.sup.p] = 118 - 0.001215 * [Q.sup.P].

By extending land classes from 22 land classes contained in TSM to 42 land classes in TSM 2000, we need to include not only the cost functions but also the yield functions for new land classes. Components of cost function for new land classes such as harvest, access, and domestic and international transportation costs are estimated from the previous works of Sedjo and Lyon (1990) and Sohngen et al. (1996). Yield functions for the new land classes were selected to have the same basic equations as those in Sedjo and Lyon (1990). The coefficients of yield functions of new land classes are selected to reflect characteristics of the region, such as climate and topography, in which each land class is located. The variable proportions of production in solid wood, [[phi].sub.h], for new land classes were constructed from those given in Sedjo and Lyon (1996) by considering land classes with similar geographical characteristics, ecosystem type, climate, NPP, and so on. In general, the annual market discount rate would fluctuate over the simulation period, but in this research we used an interest rate of 4% for the entire simulation time period. Given the initial commercial timber stock inventory for each land class, we simulate the base TSM 2000 scenario and identify the optimal time profile of harvesting volumes and prices of solid wood and pulpwood, respectively.

Simulation Results of the Base Scenario

Simulation results of the base scenario are shown in Figures 1-4 and summarized in Table 1. These data indicate that total industrial wood production increases 31%, pulpwood production increases 55%, and solid-wood production increases only 4.6%. Increased pulpwood production accounts for 93% and solid wood for 7% of the increase in total industrial wood production over the 90-year period. Figure 4 shows estimated price changes for solid wood and pulpwood over the simulation period, with the price of pulpwood increasing 44% and the price of solid wood increasing 21%. The more rapid growth for pulpwood volume and price is due primarily to the more rapid growth of pulpwood demand. To accommodate this rapid growth of pulpwood demand, the price of pulpwood rises relative to that of solid wood, which signals producers to switch production away from solid wood to pulpwood.

[FIGURES 1-4 OMITTED]

Simulation of timber production by regions, which is presented as Table B.1 in Appendix B, suggests that the dominant production regions currently and in 2085 are in the emerging region, the U.S. South, and East Siberia. Over 90 years, the emerging region increases production by a factor of three, while the U.S. South and the East Siberia regions roughly double their timber production. Most timber production of these regions contributes to the increase of pulpwood production. Eastern Canada and European USSR also increase timber production, mostly in supplying pulpwood. Nordic Europe maintains fairly substantial timber production over the first 70 years, and after that timber production declines slightly. The U.S. Pacific Northwest, Western Canada, West Siberia, and Asia-Pacific are only modest producers of timber and experience a minimal change over the 90-year period. Prior to the initial simulation year, both the U.S. Pacific Northwest and Western Canada experienced increasing government oversight directed at the withdrawal of public forestlands from commercial forests. These conservation efforts allow these regions to show only modest timber production over the entire simulation period.

An Analysis of the Climate Change Scenario

In order to simulate the climate change scenario, we modify the laws of motion of TSM 2000 to incorporate the effects of dieback and regeneration. In addition, we modify the yield functions to incorporate the effects of changes in NPP. To track the effects of dieback on the hectors of trees by land class and age-group, we assume that the age-groups are affected proportionally within each land class. Previously we discussed the calculation of dieback hectares by land class, which is then linearized to yield dieback hectares per year. To distribute this proportionally across the age-groups, we use the portion of the commercial land area of the land class that is not affected by dieback:

[d.sub.j] = 1 - dieback per [year.sub.h]/[SIGMA] [x.sub.h,i,j].

For the land area where standing trees are expected to die out, we modify Equation 2.8a, which denotes the law of motion of the hectares of trees by age, to be

[x.sub.h,j+1] = (C + D[U.sub.hj])[x.sub.hj] for all h, j,

This equation can also be expressed as

[x.sub.h,1,j+1] = [d.sub.j][u'.sub.hj][x.sub.hj]

[x.sub.h,2,j+1] = [x.sub.h,1,j] for all h, j

[x.sub.h,i+1,j+1] = [d.sub.j]([x.sub.h,i,j - [u.sub.h,i,j][x.sub.h,i,j])

for all h, j

(i = 2, 3, ..., M - 1).

For the land areas where standing trees are not expected to die out, Equation 2.8a is changed to

[x.sub.h,j+1] = (A + B[U.sub.hj])[x.sub.hj] + ([v.sub.hj] + [R[R.sub.h])e for all h, j,

where R[R.sub.h] denotes the regeneration hectares per year for land class h and A, B, [U.sub.hj], [v.sub.hj], and e are the same as defined in the Equations 2.8a and 2.8b. This equation can be expressed as

[x.sub.h,1,j+1] = [u'.sub.hj][x.sub.hj] + [v.sub.hj] + R[R.sub.h] for all, h, j

[x.sub.h,i+1j+1] = [x.sub.h,i,j] - [u.sub.h,i,j][x.sub.h,i,j] (i = 1, 2, ..., M - 1)

Next, the volume of commercial timber harvested for the total industrial wood after climate change is modified by identifying three harvesting categories. The first category is where commercial harvesting occurs in the land areas where standing trees are expected to die out after climate change. The second category accounts for the possibility that some portion of dieback trees is salvaged from dieback areas. The third category considers commercial harvesting in the land areas in which standing trees are not expected to die out after climate change. For the salvage of dieback trees, the salvage rate of dieback trees is assumed to be 60% of normal merchantable volume on average for both accessible and inaccessible land areas and 70% of merchantability ratio for all salvage operations. (10) The merchantability ratio is defined as the minimum age of salvage trees divided by the optimal harvest age.

At year j, the three cases of commercial harvesting volume are specified as follows: Commercial harvesting volume in the land area where standing trees are expected to die out after climate change is

[u'.sub.hj][d.sub.j][X.sub.hj][q.sub.hj] for all h, j,

where [X.sub.hj] is a diagonal matrix using the elements of [x.sub.hj], the vector of hectares of trees in this land area, and [q.sub.hj] is the vector of non-climate change yield function. Salvage volume of dieback trees is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where s is the salvage rate and age k is the margin for the salvage of dead trees. Commercial harvesting volume in the land area where standing trees are not expected to die out after climate are

[u'.sub.hj][X.sub.hj][[??].sub.hj] for all h, j [member of] [1995, 2060]

and

[u'.sub.hj][X.sub.hj][[??].sub.hj] for all h, j [member of] [2061, [infinity],

where both [[??].sub.hj] and [[??].sub.hj] are vectors of modified yield functions of trees when climate change occurs (see Eqns. A.1 and A.2 in Appendix A). The total volume harvested of industrial wood after climate change is the sum of harvesting volume of these three cases. Harvesting volume for solid wood and for pulpwood are calculated by multiplying the total harvested volume of industrial wood by [[PHI].sub.h], and (1 - [[phi].sub.h]), respectively.

Simulation Results of the Climate Change Scenario

Output projections of the climate change scenario are shown in Figures 5-7 and summarized in Table 1. The increase in total industrial wood is 65% over the entire simulation period. Relative to the base scenario, production is larger by 625 million cubic meters in 2085, and it reflects 30% larger production than in the base scenario. Estimated gains in timber production due to climate change are the result of two important factors: First, BIOME 3 predicts an increase in net primary productivity for all land classes; second, BIOME 3 predicts that there will be an increase in hectares of faster-growing tree species. As a result, the climate change scenario shows that global timber supply grows faster than global timber demand, resulting in declining timber prices.

[FIGURES 5-7 OMITTED]

The increase in pulpwood production is 82% over the simulation period. Pulpwood production in 2085 is 20%, or 261 million cubic meters, larger than in the base scenario. In addition, solid-wood production increases 46% over the 90-year period. Estimates for the climate change scenario indicate that solid-wood production in 2085 is 45%, or 364 million cubic meters, larger than in the base scenario. Figure 8 shows that the supply response induces a substantial price decrease for both solid wood and pulpwood. Solid-wood price is estimated to decrease about 34% from $73 per cubic meter in 1995 to $48 in 2085. Pulpwood price will decrease about 25% from $40 in 1995 to $30 in 2085. This simulation suggests that global warming will have a positive effect on the global timber market through increasing timber production and decreasing the prices of solid wood and pulpwood.

[FIGURE 8 OMITTED]

Regional variations in timber production, which are presented in Table B.2 in Appendix B, suggest that the dominant production region over 90 years is East Siberia, followed by the U.S. South and the emerging region. In East Siberia, the total volume of industrial wood increases 107% over the simulation period, and unlike the base scenario, this region has an increase in the production for both pulpwood and solid wood. The volume of pulpwood and solid wood increase 107% and 106%, respectively. In the U.S. South, the total volume of industrial wood increases 126%, and the volume of pulpwood and solid wood increases 208% and 82%, respectively. In the emerging region, the total volume of industrial wood increases 29% over the 90-year period. The volume of pulpwood and solid wood increase 34% and 20% over the simulation period, respectively. The increase of timber production in the emerging region after climate change is relatively less than in the other dominant regions. Also, most of the production increase in total industrial wood is in pulpwood. Unlike other dominant regions, the increase in production of solid wood in the emerging region is very modest, mainly because the trees have short rotation periods and fast-growing trees (Sedjo 1995).

Regional production estimates indicate that East Siberia and the U.S. South are greatly impacted by global warming, mostly through the increase in hectares of faster-growing species and the increase in NPP. In these regions, global warming increases timber production for both pulpwood and solid wood. Other regions also show increased pulpwood and solid-wood production over the simulation period. Both Eastern Canada and European USSR show substantial timber production over 90 years, while Nordic Europe shows fairly substantial timber production over the earlier portion of the simulation time period. The remaining regions show modest increases of timber production as discussed in the base scenario.

A Sensitivity Analysis of Timber Demand Growth Scenarios

We analyze model results under two different timber demand scenarios: high timber demand growth scenario and very high timber demand growth scenario. The high timber demand growth scenario is based on recent FAO forecasts. FAO forecasts the demand of total industrial wood to increase by 1.8% annually and pulpwood to increase at a rate of 2.5% annually to the year 2010. For this research, we extended the growth period to 2085, with the timber demand growth declining linearly to zero in 2085. For the very high timber demand growth scenario, we double these growth rates to 3.6% and 5%, respectively. Tables 2 and 3 present the results of the sensitivity analyses for these two scenarios. These sensitivity analyses provide significant information on the direction, magnitude, and natures of various adjustment mechanisms in the global timber market. In summary, the economic system responds to increasing growth of timber demand through changes in timber production and prices. Differences in timber production and prices are highly related to differences in the growth rate of timber demand and in the potential capacity to produce and expand available supply. Also, if growth of pulpwood demand increases at a significantly higher rate than solid-wood demand, the production of solid wood increases at a very modest rate or decreases in the later part of the simulation period. This trend results from the fact that higher growth of pulpwood demand relative to solid-wood demand switches industrial wood from solid wood to pulpwood. Finally, if timber demand grows at a higher rate than that in the normal demand scenario, the initial timber production is lower, but timber production is ultimately larger than in the normal timber demand scenario. This structure suggests that rational forward-looking producers postpone the initial timber production with the anticipation of higher price in the future.

A Welfare Change in the Global Timber Market

In order to examine the effect of global warming on the global timber market in the economic welfare sense, we measure the welfare change between the base scenario and the climate change scenario under each of timber demand scenarios. As already stated, the welfare level in TSM 2000 is the sum of discounted present value of net surplus over the simulation period. Under the normal timber demand growth scenario, we calculate the welfare levels for both the base scenario and the climate change scenario. The welfare level for the base scenario is about $336 million, while that for the climate scenario is about $352 million. The welfare level in the climate change scenario is $16 million (4.8%) larger than in the base scenario. This amount of welfare increase suggests that the society will experience an economic benefit through the global timber market when climate change occurs. Also, in Tables 2 and 3, the welfare level for both the base scenario and the climate change scenario are illustrated under the high timber demand growth and the very high timber demand growth.

5. Conclusion

To capture the economic effects in the global timber market that arise from the prediction of global warming, we develop an integrated assessment model of the ecosystem and the economic system. TSM 2000, BIOME 3, and Hamburg are used as suitable economic and ecological models to perform this objective. The TSM 2000 is developed to model dynamic economic behavior in the global timber market. BIOME 3 is utilized as our steady-state ecological model and Hamburg as our general circulation model. In particular, the TSM 2000 not only incorporates the important additional components in the global timber market but also disaggregates the total industrial wood production into pulpwood production and solid-wood production by responsive region. We estimate dynamic ecological change based on the simulation results of BIOME 3 using Hamburg and the linearity assumption on climate change and ecosystem. The projected dynamic ecological changes, dynamic land area changes, and productivity changes are run through the TSM 2000 to identify the economic effects of dynamic climate change on the global timber market. We simulate a non-climate change base scenario and a climate change scenario. With the simulation results for both scenarios, we identify that the increase of total industrial wood production, pulpwood production, and solid-wood production in the climate change scenario are larger than in the base scenario by 30%, 20%, and 45%, respectively. In particular, we note that these estimated gains in timber production due to climate change are caused by an expansion of hectares of faster-growing tree species and an increase in net primary productivity, the rate at which carbon is garnered for plant growth. As a result, the climate change scenario shows that for normal timber demand growth, global timber supply grows faster than global timber demand, resulting in declining timber prices. In this sense, we conclude that global warming has a positive effect on the global timber market through an increase of timber production causing stumpage prices to be lower than they otherwise would have been. In addition, we calculate the sum of discounted present value of net surplus for both scenarios over the simulation period to estimate the welfare level. In comparing the welfare level between the two scenarios, the welfare level in the climate change scenario is larger than that in the base scenario by 4.8%; thus, global warming is economically beneficial to society through the global timber market. Furthermore, there are many avenues for future research to improve our research results. We feel that the most promising would be the sensitivity of these results to the ecological and general circulation models used.

Appendix A

Climate Change Yield Function

We use the yield function of merchantable volume per hectare formulated in Sedjo and Lyon (1990, pp. 208-9) as our non-climate change yield function and a modification of it for our climate change yield function. Since changes in NPP cause changes in the rate at which the trees grow we start with the non-climate change yield function and modify its rate of tree growth to reflect the increase in NPP. This gives us a differential equation whose solution is the climate change yield function. The non-climate change yield function consists of functional components such as age of trees and management of practices (regeneration input). This yield function is as follows:

q = [q.sup.1] (z) * [q.sup.2] (age),

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For the simplicity of deriving the climate change yield function, this yield function can be written as

[q.sub.hij] = [alpha][e.sup[beta]/(i-[gamma])],

where [alpha] = [q.sup.1]([z.sub.hj]) * [c.sup.2] * exp([c.sup.3]), [beta] = [c.sup.4], y = [c.sup.5]. This non-climate change yield function implies that the growth due to aging of the trees is

dq/di = - [beta]/[(i - [gamma]).sup.2] * [alpha] * [e.sup.[beta]/(i - [gamma])].

While climate change is occurring (j [member of] [1995, 2060]) the growth due to aging at year j is given as

(A.1) d[??]/di = - [beta]/(i - [[gamma]).sup.2] * [alpha] * [e.sup.[beta]/(i-[gamma])] * (1 + [kappa] (i - a)) = - [beta]/(i - [[gamma]).sup.2] * [alpha] * [e.sup.[beta]/(i-[gamma]) - [beta]/[(i - [gamma]).sup.2] * [alpha] * [kappa](i - a) * [e.sup.[beta]/(i-[gamma]),

where i = a + (j - [j.sup.*]) and a is the age of tree at year [j.sup.*] at which time climate change begins to occur and 1 + [kappa] (i - a) denotes the change of NPP during the time period of j - [j.sup.*]. This makes the change in the growth of trees proportional to the change in NPP. Thus, the yield function is the solution to the differential Equation A.1. In addition, the yield function for j [member of] [2061, [infinity]] would be the solution to

(A.2) d[??]/di = - [beta]/(i - [[gamma]).sup.2] * [alpha] * [e.sup.[beta]/(i-[gamma]) * [bar][kappa],

where [kappa] = 1 + [kappa] * 70 = NP[P.sub.70]/NP[P.sub.0]. We use these yield functions to reflect the growth of trees associated with the increment of net primary productivity.

Appendix B

This Appendix presents the simulation results by responsive region for both the base scenario and the climate change scenario under normal timber demand growth. These are summarized in Tables B.1 and B.2.

Table B.1. Simulation Results by Regions: The Base Scenario

 Total Volume Solid-Wood Pulpwood Volume
 Volume

 1995 2085 1995 2085 1995 2085

Emerging region 262.93 668.09 97 227.64 165.93 440.45
U.S. Pacific 57.21 67.34 39.15 34.92 18.06 32.42
Western Canada 123.81 87.25 77.89 45.42 45.92 41.83
Nordic Europe 222.32 102.37 86.69 37.06 135.63 65.31
U.S. South 281.85 449.67 169.07 205.22 112.78 244.45
Eastern Canada 116.7 109.96 62.74 40.01 53.96 69.95
European USSR 133.99 110.82 55.78 38.72 78.21 72.1
West Siberia 81.97 62.37 33.81 22.94 48.16 39.43
East Siberia 260.91 378.01 104.8 124.41 156.11 253.6
Asia Pacific 44.56 40.92 37.77 24.02 6.79 16.9

All regions 1586.25 2076.8 764.7 800.36 821.55 1276.44

Unit is million cubic meters.

Table B.2. Simulation Results by Regions: The Climate Change Scenario

 Total Volume Solid-Wood Pulpwood
 Volume Volume

 1995 2085 1995 2085 1995 2085

Emerging region 435.5 562.05 167.79 201.99 267.71 360.06
U.S. Pacific 61.08 86.47 41.81 49.87 19.27 36.6
Western Canada 64.78 31.79 43.59 18.07 21.19 13.72
Nordic Europe 96.35 128.28 45.02 48.39 51.33 79.89
U.S. South 267.63 605.55 173.65 316.24 93.98 289.31
Eastern Canada 95.34 92.66 47.84 35.9 47.5 56.76
European USSR 73.98 144.38 32.63 58.76 41.35 85.62
West Siberia 76.98 104.62 32.3 39.81 44.68 64.81
East Siberia 412.82 854.07 163.11 336.65 249.71 517.42
Asia Pacific 53.91 91.55 44.87 58.35 9.04 33.2

All regions 1638.37 2701.42 792.61 1164.03 845.76 1537.39

Table 1. Simulation Results of Normal Timber Demand Growth Scenario

 Base Climate
 Scenario Change Scenario

 1995 2085 1995 2085

Total volume 1589 2076 1638 2701
Solid-wood volume 765 800 793 1164
Pulpwood volume 821 1276 846 1537
Solid-wood price 76 92 73 48
Pulpwood price 43 62 40 30

Welfare level 336 352

Unit of harvested volume is million cubic meters: unit of price
is dollars and welfare level is million dollars.

Table 2. Simulation Results of High Timber Demand Growth Scenario

 Base Climate
 Scenario Change Scenario

 1995 2085 1995 2095

Total volume 1150 2180 1390 3470
Solid-wood volume 484 759 645 1473
Pulpwood volume 665 1420 750 2015
Solid-wood price 126 166 107 81
Pulpwood price 76 125 64 53

Welfare level 385 450

Unit of harvested volume is million cubic meters; unit of price
is dollars and welfare level is million dollars.

Table 3. Simulation Results of Very High Timber Demand Growth Scenario

 Base Climate
 Scenario Change
 Scenario

 1995 2085 1995 2085

Total volume 1740 2710 2880 4190
Solid-wood volume 761 741 529 1420
Pulpwood volume 943 1970 780 2780
Solid-wood price 137 430 166 368
Pulpwood price 81 409 101 292
Welfare level 750 878

Unit of harvested volume is million cubic meters: unit of price
is dollars and welfare level is million dollars.

We are indebted to two referees for helpful comments on earlier drafts of this paper. This research was supported by the Department of Economics and the Utah Agricultural Experiment Station, Utah State University, Logan, Utah.

(1) In the TSM, responsive regions include U.S. South, U.S. Pacific Northwest, Eastern Canada, Western Canada, Nordic Europe. Asia-Pacific, and the emerging region.

(2) Emerging region in the TSM includes Brazil, Chile, Venezuela, New Zealand, Australia, South Africa, Spain, and Portugal.

(3) For more details about Yan's scenario 5, see chapter 4 of Yan's (1996) dissertation. For the former Soviet Union, the conservation ratio of forest for European USSR, West Siberia, and East Siberia are 29%, 16%, and 14%, respectively.

(4) For more detail about the plant functional types, see Haxeltine and Prentice (1996). In BIOME 3, nine legends denote the forests.

(5) These references at least partially justify our linearity assumption. We expect that the biological effects will occur with a lag; hence, we include a five-year lag for the effects on forests. This is detailed here. The logistic curve (learning curve) is an alternative to a linear adjustment and would push the growth further into the future. The optimization would take this later growth into account and would shift harvests toward the present. We therefore feel that linearization is a good first approximation, and we leave it to further research to refine the results.

(6) We chose nonforest areas from the world map created by Olson (1989-1991), which displays 74 ecosystem categories across the globe within [0.5.sup.9] x [0.5.sup.0] and 10 min x 10 min grid cells.

(7) We use 42 land classes, but one of them, the emerging region, is not bound to a single geographic area.

(8) We assume a fire-year time lag; hence. 1990 for climate becomes 1995 for forests.

(9) These four conditions were also used in the analysis of the climate change scenario.

(10) In reality, both salvage rate and the merchantability ratio are not fixed as we assume here, but they change as timber prices change.

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Received February 2001; accepted January 2003.

Dug Man Lee * and Kenneth S. Lyon ([dagger])

* Department of Economics, Sungkyunkwan University, 53 3-ka, Myungryun-dong, Chongro-ku, Seoul, South Korea 110-745; E-mail [email protected].

([dagger]) Department of Economics, Utah State University, Logan, UT 84321. USA; E-mail [email protected]; corresponding author.