ECONOMIC EVALUATION OF BIOTECHNOLOGICAL PROGRESS: THE EFFECT OF CHANGING MANAGEMENT BEHAVIOR

Abstract

Abstract The paper assesses the welfare effects of biotechnological progress, as exemplified by tree improvements, using a partial equilibrium model. Timber demand is assumed to be stochastic and the distributions of its coefficients known. The coefficients of a log-linear supply function are determined by maximizing the expected present value of the total surplus of timber production, both in the presence and in the absence of genetically improved regeneration materials. The supply functions are then used to estimate the expected present values of the total surplus in different cases through simulation. These estimates enable us to assess the direct effect and the effect of changing harvest behavior on the expected present value of the total surplus. The main results of the study are (i) the presence of genetically improved regeneration materials has significant impacts on the aggregate timber supply function; (ii) the application of genetically improved regeneration materials leads to a significant increase in the expected present value of the total surplus; and (iii) a considerable proportion of the welfare gain results from the change in harvest behavior. A conclusion we draw from this study is that ignoring the influences of technological and policy changes on behavior can lead to significantly biased welfare estimates. We view the model as a potential approach to conducting counterfactual policy comparisons in economics without forward-looking data.

1. Introduction

Biotechnological progress in forestry has been relatively fast in the sense that the productivity of forestland has increased considerably in the past decades. In Sweden, for example, the current timber growth is 30% above what was considered to be the maximum level in the 1930s. The increase in forest growth is partly attributed to the improved silvicultural practices in general, but the use of genetically better materials in stand establishment is certainly one of the most important constituting factors.

Planting genetically improved trees is nowadays perceived as one of the most efficient methods to enhance timber yield and the income of forest owners (Simonsen et al. [2007]). Genetically improved trees can for example better resist damages, increase growth, and produces wood of higher quality. A higher survival rate of seedlings and higher production can in addition reduce the costs for stand establishment, management, and harvesting. In general, the cost of producing traditional seed-orchard seeds is very low compared to the great benefits, making the use of seed-orchard seedlings highly profitable and attractive to most forest owners. The logistics of seedling distribution from a small number of forest nurseries adds to the potential of widespread use of genetically improved trees. In Sweden, 80% of all Scots pine and 50% of all Norway spruce seedlings originate from seed orchards. In fact, all available seed-orchard seeds are used and new seed orchards are being established to cover the whole Swedish nursery market (Rosvall et al. [2002]). By using currently producing seed orchards and those that will be available in the future from already decided investments, the total timber harvest in Sweden is expected to increase by 9% in the future (Swedish Forest Agency [2008]). Rosvall (2007) estimates that future timber harvest can be increased by 14% through the use of new propagation techniques.

Research on economic valuation of new genetic materials in forestry started in the late 1960s. One of the first papers is Davis (1967), which focuses on the cost of producing genetically improved seeds through investment in loblolly pine clonal seed-orchard and on the increase in timber yield necessary to make the investment profitable. A number of similar studies were conducted in the early 1970s.¹ More recent empirical evaluations of different tree improvement programs include Fins and Moore (1984), Stier (1990), and Palmer et al. (1998). Löfgren (1985) investigates theoretically how different types of biotechnological progress affect optimal forest management and the economic value of forestry. Löfgren (1988, 1990, 1996) extend previous economic analyses of tree improvements by introducing a number of general results on the properties of the optimal value function, that is, the economic value of the forest under best practice associated with different types of biotechnology. Specifically, these works show how the economic gains from genetic progress can be given upper and lower bounds that, to a considerable extent, can be calculated based on current management practices.

In a general equilibrium setting, that is, when imbedded in the rest of the economy, the analysis shows how the valuation problem (the cost-benefit analysis) can be solved in a market economy under different institutional regimes (Löfgren [1990]). Here the impacts of consumer preferences are accounted for, as well as the effects of different sectors of the economy. The value generated by genetic progress, in the natural resource sector, emerges in terms of cost-benefit rules, which tell us which components have to be estimated empirically.

The purpose of this paper is to extend the previous economic analyses by explicitly considering the impact of accelerated forest growth, resulting from the use of improved seeds, on timber price and on harvesting decisions. We will draw heavily on a methodology developed in Gong (1994, 1995) and use a stochastic partial equilibrium model of the Swedish forest sector. This allows for counterfactual comparisons of old and new regeneration materials that are introduced gradually in the forest sector.

2. Overview

Tree improvement increases the productivity of forestland and, therefore, affects both forest owners and “timber consumers” (the timber processing industry and other users of timber). From the perspective of forest owners, access to genetically improved regeneration materials (IRMs) implies that forest stands established in the future will grow faster than the existing ones. This means that they will be able to produce a greater amount of timber in their forests, but timber prices are, ceteris paribus, likely to be lower (than in the absence of the IRMs) in the future, as a result of the increase in production. The financial consequences of tree improvement, for the forest owners, depend on the relative magnitudes of the increase in timber yield and the decrease in prices. However, advances in tree improvement will increase the consumer surplus, because the increase in the productivity of forestland implies that the timber processing industry and other users of timber can purchase greater amounts of timber at lower prices.

When IRMs emerge, the anticipated changes in the productivity of forestland and in timber prices would probably lead to changes in silvicultural practices and changed rotation ages, both for existing stands and for stands to be established using the IRMs. This means that the relationship between timber supply and factors affecting the optimal harvest decisions may change. Under the assumption of rational behavior, forest owners will change their management decisions to increase their gains (or reduce their losses) resulting from the use of IRMs. If the market is perfect, it leads to a socially optimal allocation of the resources and the change in forest management behavior in response to the presence of IRMs would increase social welfare.

Figure 1 illustrates the changes in welfare at time t, when forest owners start to use IRMs at time 0. To keep the figure simple, we assume here that the timber demand and supply functions are both linear. Further, we pretend that the total surplus at time t is equal to the area between the demand curve and the supply curve.² The supply curve S^b(I^b, p) depicts the relationship between the optimal harvest level and timber price at time t, in the absence of IRMs, where I^b denotes the (mature) timber stock in the forests at time t. The supply curve S^b(Iⁿ, p) shows the amount of timber to be harvested at time t corresponding to different prices in the case where IRMs have been used, but there is no change in forest owners’ management behavior. Thus, the shift of the supply curve from S^b(I^b, p) to S^b(Iⁿ, p) is caused solely by the change in the growing stock of timber from I^b to Iⁿ. It does not involve any change in the supply function itself. Finally, the supply curve S^o(I^o, p) describes the relationship between the harvest and price at time t after the forest owners have changed their management behavior in response to the presence of IRMs. It gives the optimal harvest level corresponding to different prices at time t.

Figure 1. A graphical description of the welfare effects of tree improvement.

Figure 1 shows that the adoption of IRMs results in an increase in the welfare at time t by an amount equal to the area ABEF. This change in welfare can be decomposed into two parts: the direct effect (indicated by area ABCD), and the effect of changing management behavior (indicated by the area DCEF). The direct effect tells how much the total surplus would change, as a result of the adoption of IRMs, if forest owners manage their forests as they used to do (except that they use the IRMs when establishing new stands on harvested sites). The effect of changing management behavior refers to the additional change in welfare when forest owners adapt their management activities to the new biological and economic conditions resulting from the use of IRMs.

The magnitude of the effect of changing management behavior depends on the difference between the two supply curves S^b(Iⁿ, p) and S^o(I^o, p). If the use of IRMs does not induce any change in the relationship between the optimal harvest level and the factors influencing the optimal harvest decision, the supply curve S^b(Iⁿ, p) would be identical to S^o(I^o, p). Consequently, there would be no effect from changing management behavior. On the other hand, if the supply function changes significantly when IRMs are used, the effect of changing management behavior on welfare could be large.

It should be pointed out that the direct effect as well as the effect of changing management behavior varies with time. Figure 1 describes a situation where both types of effects are positive. It is possible that the emergence of IRMs causes the total surplus to increase at some points in time, but decrease at others. Thus, one cannot examine the welfare effects of tree improvement by examining the change in the total surplus (the sum of producer surplus, i.e., forest owners’ profits and consumer surplus) at a single point in time. Instead, one needs to examine the sum of properly discounted changes in total surplus at different points in time.

To assess the effect of changing management behavior on the welfare changes resulting from tree improvement, we need to know the “optimal” supply function both in the absence and in the presence of IRMs. We use the word “optimal” to emphasize that the supply function should describe the relationship between the optimal harvest level and its determinants.

Our task is to conduct counterfactual comparisons and this has shown to be very difficult, in particular if one bases the approach on relationships estimated using historical data. This insight was forcefully introduced in a paper by Robert Lucas in 1976 where he showed how policy based on parameters that are not policy invariant, that is, they change whenever the policy/experiment changes, could potentially be very misleading. An example would be a general equilibrium macroeconomic model where certain parameters, estimated from historical data, change whenever fiscal or monetary policy changes. This argument questioned the large-scale econometric models that lacked foundations in dynamic economic theory. Lucas suggested that, if we want to conduct a counterfactual experiment, we should model the “deep” parameters relating to underlying preferences, technology, and resource constraints.

Our counterfactual experiment will use a slightly different approach based on an idea suggested by Gong (1994a, b) to handle “the Lucas critique.” Here we use a timber supply function to describe the forest owners’ management behavior and examine the impact of changing forest growth function on the supply function. The parameters of the supply function are determined by maximizing the total surplus conditional on a demand function. Parameters of the demand function are calibrated using previous econometric estimates of its position and its elasticity. The underlying resource constraints pertain to the state of the forest and its growth function. We determine the theoretically optimal timber supply function both in the absence and in the presence of new and better regeneration materials. These supply functions are then used to estimate the direct effect and the effect of changing management behavior on the total surplus following the introduction of new and better regeneration materials.

3. Methods 

3.1. Model

Conceptually, the timber supply function gives the optimal amount of timber harvest in each time period conditional on the current state of the forest and market conditions. This means that one can, in principle, identify the timber supply function based on the properties of the optimal harvest decisions. When considering a particular forest, the optimal harvest decision maximizes the value of a properly defined profit function that represents the preferences of the forest owner. Accordingly, the timber supply function for a forest estate could be determined by maximizing the forest owner's objective function (Gong [1994a, b]). In a perfectly competitive market, the time path of the aggregate supply of timber (the sum of optimal harvests from all forests in each time period) is characterized by maximization of the present value of the total surplus (Lyon and Sedjo [1983], Gong and Löfgren [2003]). Therefore, we determine the market supply function by maximizing the present value of the total surplus.

In this paper, we consider the case when the timber demand function is stochastic. We assume that all forest owners are risk neutral, and determine the market supply function by maximizing the expected present value (EPV) of the total surplus over time. Specially, we choose a functional form of the timber supply function S(X_t,  p_t; A) and determine the parameters A of the supply function by solving the following maximization problem

• (1)

• (2)

• (3)

• (4)

• (5)

• (6)

where E is the expectation operator; TS(A) is the present value of total surplus associated with supply function coefficients A; is the the aggregate supply of timber at time t; is the the amount of timber demanded at time t; p_t is the the market price of timber at time t; is the the inverse timber demand function at time t, the functional form of as well as the probability distributions of the random parameters (B_t) are assumed to be known; is the forest management and harvest costs as a function of the state of the forest and the harvest level; X_t is the the state of the forest at time t; X₀ is the the initial state of the forest; r is the discount rate; and is the the growth function of the forest.

Equation (4) is the market clearing condition. Equation (5) represents the dynamics of the forests. Equation (6) gives the initial state of the forests. Of course, the total harvest at each point in time cannot exceed the total growing stock of timber in the forests. This constraint is embedded in the supply function.

Except in some trivial cases, it is impossible to derive a closed form expression of the EPV of the total surplus given in equation (1). Solution of the above optimization problem will have to rely on numerical approximations of the objective function. In this case, stochastic variations in the total surplus originate from uncertainty in the coefficients of the timber demand function. Given a timber supply function, a simple way to estimate the EPV of the total surplus is to take the average of the present values of the total surplus associated with a large number of randomly drawn timber demand scenarios.

Let denote the coefficients of the demand function in years 1–T in scenario k, where is a random drawn from the distribution of B_t. A numerically tractable version of the optimization problem (1)–(6) can be formulated as

• (7)

• (8)

• (9)

• (10)

• (11)

• (12)

where N is the number of demand scenarios used to estimate the EPV of the total surplus; T is the time horizon within which the annual harvest of timber is determined using the supply function; and are the aggregate supply and demand of timber in year t in scenario k, respectively; is the market price of timber in year t in scenario k; is the state of the forest in year t in scenario k; and is the value of the forest in year T+1. To be specific, the term represents the sum of the discounted total surplus the forest will generate from year T+1 and onwards, that is

• 

By constructing a special rule of determining the harvest volumes Q_t for t=T+1 to infinity we will be able to estimate the value of the forest at time T+1. This is needed for estimating the EPV of the total surplus associated with a given timber supply function.

The optimization model (7)–(12) is used to determine the coefficients of the timber supply function both in the absence and in the presence of IRMs. In terms of the optimization model, the two cases differ from each other only in the growth function of the forests. Let G^b (X_t,  Q_t) and Gⁿ (X_t,  Q_t) denote the growth functions of the forests in the absence and in the presence of the IRMs, respectively. Then, by solving the optimization model (7)–(12) using the growth function G^b (X_t,  Q_t), we obtain the coefficients of the timber supply function and the EPV of the total surplus in the absence of IRMs. Denote this optimal solution by A^b and E[TS^b (A^b)]. Similarly, if the growth function G(X_t,  Q_t) in equation (11) is replaced by Gⁿ (X_t,  Q_t), then the optimal solution of problem (7)–(12) gives us the coefficients of the timber supply function and the EPV of the total surplus in the presence of IRMs. Denote this optimal solution by Aⁿ and E[TSⁿ (Aⁿ)].

Relating to Figure 1, the EPV of the total surplus in the absence of IRMs,E[TS^b (A^b)], corresponds to the area AOB. The EPV of the total surplus in the presence of IRMs,E[TSⁿ (Aⁿ)], corresponds to the area FOE. The difference between E[TSⁿ (Aⁿ)] and E[TS^b (A^b)] is, hence, the total welfare effect of using the IRMs.

We can decompose the total welfare effect into the direct effect and the effect of changing harvest behavior by estimating the EPV of the total surplus in the following situation: IRMs are used in forest regeneration, but the forest owners do not change their harvest behavior. The use of IRMs means that the dynamics of the forests should be described by the growth function Gⁿ (X_t,  Q_t). Because the forest owners do not change their harvest behavior, the timber supply function remains as S(X_t,  p_t; A^b). The EPV of the total surplus in this case, denoted by E[TSⁿ (A^b)], is estimated using the following set of equations:

• 

• 

• 

• 

• 

• 

The EPV of total surplus E[TSⁿ (A^b)] corresponds to the area DOC in Figure 1.

The direct effect of using IRMs on welfare is E[TSⁿ (A^b)] −E[TS^b (A^b)], and the effect of changing harvest behavior is E[TSⁿ (Aⁿ)] −E[TSⁿ (A^b)], which measures the result of an attempt to avoid the “Lucas critique.”

3.2. Model specification

This section describes in detail the specific version of model (7)–(12) we used in our numerical assessment of the effect of using IRMs. To make the presentation easier and less messy, we skip the demand scenario index k in all variables and parameters. Superscripts are still used, but for other purposes.

3.2.1. The state of the forests The total forest area covered in the analysis is 20 million ha (which includes all the productive forests in Sweden under the age of 120 years), divided into two soil productivity classes of approximately equal size (Table 1). All the initially existing forests are classified as “old forests.” The stands that will be established using the IRMs after an old stand has been harvested are referred to as “new forests.” It is assumed that the forests established using IRMs grow 40% faster (measured in terms of the maximum mean annual increment, MAI) than the existing ones with the same site productivity.

Table 1.  Total area and productivity of the forest land and regeneration costs.

	Old forests		New forests
Site productivity	Low	High	Low	High
MAI (m^3/ha/year)	3.5	5.5	4.9	7.7
MAI max age (years)	120	100	110	90
Regeneration cost (SEK/ha)	6500	8500	6600	8600
Total area (million ha)	10.522	9.524	0	0

As the new stands grow faster and provide larger timber yields than the old stands on similar land, they should be separated from the old ones in the model. The state of the forest in each time period is described by the age-distribution of each of the four types of stands (old stands on productive land, old stands on less productive land, new stands on productive land, and new stands on less productive land). For simplicity we call each type of stands a forest. The state of the ith forest is denoted by

• 

where (i= 1 … 4; t= 1 … T; a= 1 … M) is the total area of a-year-old stands in forest i in time period t, T is the simulation time horizon, and M is the maximum age of the stands.

For all the forests, the maximum stand age recognized in our analysis was 120 years and the lowest allowable harvest age was 60 years. The dynamics of the forest state were described using the age-class transition model (see, e.g., Johansson and Löfgren [1985], Chapter 6, Tahvonen and Kallio [2006]).

The initial age-class distributions of these forests are determined based on data from national forest inventory (Figure 2). In the numerical analysis, each time period consists of 1 year. When determining the initial state of the forests, we assume that the forest stands within each age-class are uniformly distributed among different ages within that age-class.

Figure 2. The age-class distribution of the existing forests.

Timber yields (m³/ha) in different stands were estimated using a modified version of the production function of Fridh and Nilsson (1980).

• (13)

where a is stand age, Yⁱ is the maximum MAI, and is the stand age at which the MAI reaches its maximum (Table 1). The term within the last pair of parentheses of yield function (13) is an age-dependent conversion factor, used to calculate the equivalent volume of timber of some standard grade corresponding to the growing timber stocks at different ages. The purpose of measuring timber yields in a standardized volume unit is to avoid the need for explicitly dealing with different assortments of timber.

3.2.2. Demand and supply functions In the numerical analysis we used a constant elasticity demand function. The inverse demand function in time period t is

• (14)

where and are stochastic coefficients. We assume that and for t= 1 … T are independent and identically distributed normal variables. Furthermore, in each time period t the two parameters and are independent. Based on the results of earlier empirical studies (Brännlund et al. [1985], Brännlund [1988]), we assume that the average price elasticity of timber demand is –0.6, which gives us the mean value of β². The mean value of β¹ was determined based on the mean value of β² and the annual total supply and price in recent years. The standard deviations of the two parameters were set to 10% of their mean values (Table 2).

Table 2.  Mean and standard deviation of the demand function coefficients.

Coefficient	Mean	Standard deviation
β^1	473,610.0	473,61.0
β^2	−1.67	0.167

Because of the large number of age-classes needed to describe the state of the forests, it is not practical to include directly the areas of different age classes as arguments in the supply function. In the supply function, the state of the forests in each time period t was described by one aggregate state variable—the total growing stock of timber in all the stands that have reached the lowest allowable harvest age. The supply function is modeled as

• (15)

where is a vector of coefficients to be optimized.

3.2.3. The harvest areas in different stands The demand and supply functions enable us to determine the total harvest volume and timber price in each time period corresponding to a given state of the forests. To determine the management and harvest costs, as well as the age-distributions of the forests in the next time period, we need to decide which forest stands should be harvested to obtain the market-clearing amount of timber. The decision on the stands to be harvested in each period is made based on estimates of the expected gain of delaying the harvest by 1 year. The expected gain from delaying the harvest of an a-year-old stand in forest i is defined as

• (16)

where p_t is the timber price in period t, C_h is the per cubic meter timber harvest cost, and Lⁱ is the expected value of bare land in forest i, which is determined using the long-run steady state expected timber price.³ In each period t, stands were selected for harvesting in the order of increasing expected gain from delaying the harvest. That is, one starts by harvesting the stands that have the lowest expected gain from delaying the harvest, then continue to harvest the stands that have the second lowest expected gain and so on until a specific amount of timber has been obtained. This rule of selecting the stands to harvest is, in principle, the same as the rule of harvesting in the order of decreasing age of the stands.

Let (i= 1 … 4; t= 1 … T; a= m … M) denote the area of the a-year-old stands in forest i to be harvested in time period t. The rule of prioritizing the stand for harvest implies that

• (17a)

where is the expected gain function. This condition simply means that any particular stand will be harvest only if all the other stands that have lower expected gains from delaying the harvest have been harvested. The harvest areas in different stands should also satisfy the following conditions:

• (17b)

• (17c)

Equation (17b) means that the total amount of timber harvested from the forests should equal the amount delivered to the market. Equation (17c) says that the harvest area in each stand cannot exceed the total area of the stand. The three conditions (17a)–(17c) enable us to determine the area to be harvested in each stand conditional on the state of the forests and the total amount of timber to be harvested.

3.2.4. Harvest and regeneration costs We assume that the harvested area is regenerated immediately, but ignore all other management activities. Thus the state of the forests in each time period has no direct effect on the management and harvest costs.⁴ The total harvest area in forest i in period t is

• 

The total regeneration area in each of the forests depends on whether IRMs are available. In the absence of IRMs, the area of the “new forests” is always zero and the harvested area in each of the “old forests” remains in the same “old forest.” The total regeneration area in each forest in period t is

• (18a)

In the presence of IRMs, we assume that all harvested areas will be regenerated with the new materials.⁵ This means that, after regeneration, the harvested area in each of the “old forests” moves to the corresponding “new forest.” The total regeneration area in each forest in period t would be

• (18b)

Given the total regeneration area in each forest, the management and harvest costs in period t are

• (19)

where is the per ha regeneration cost of forest i. The harvest cost is 95 SEK/m³, the per hectare regeneration costs for different site productivity classes and with different regeneration materials are given in Table 1.

3.2.5. End value In order to estimate the value of the forests remaining at the end of the simulation time horizon, we assumed that these forests would be converted to the long-run “optimal steady state” by keeping the periodic harvest area in each forest at a constant level. The long-run optimal steady state is defined conditional on the assumption that the forests will be managed according to the Faustmann rule. It is determined using the following conditions:

• (a) 
  The total area of each forest is equally distributed among stands in different ages from one to the optimal rotation age.
• (b) 
  Only the stands that have reached the optimal rotation age are harvested and regenerated in each period.

By keeping the harvest area in each forest at a constant level, the forests remaining at the end of time period T will be converted to the optimal steady state after one rotation. During the transition period, the expected consumer and producer surplus in each year are implicitly determined by the age-distributions of each forest. Thereafter, the expected consumer and producer surplus will remain constant.

The simulation time horizon was set to 200 years (T= 200). One hundred randomly generated demand scenarios were used in the optimization of the supply function coefficients (N= 100). A real interest rate of 3% was used throughout the analysis.

3.4. Solution methods

The optimization problem (7)–(12) was solved as an unconstrained minimization problem—we solved the problem by finding the values of the supply function coefficients A that minimize the negative of the EPV of total surplus. The constraints (8)–(12) were taken into account when determining the objective function values associated with different values of the supply function coefficients. Figure 3 describes the procedure for estimating the EPV of the total surplus associated with different values of the coefficients of the supply function. The solution method we used was a combination of gradient descent and Powell's method (Powell [1964]). Given an initial guess of the values of A, we used the gradient decent method to find an optimal solution with low precision, from where we continued the search for the optimal solution using Powell's method.

Figure 3. Estimation of the expected present value of total surplus.

When optimizing the values of the supply function coefficients, the EPV of total surplus was estimated using 100 demand scenarios, both in the absence and in the presence of IRMs. After the optimal values of the supply function coefficients have been determined for the respective cases, extended simulations using different sets of demand scenarios were carried out to estimate the EPV of the total surplus in different situations. The purpose of running the extended simulations was to reduce the random errors in the EPV estimates. Optimizations of the supply function coefficients as well as the simulations were implemented in Turbo Pascal.⁶

4. Results 

4.1. Timber supply function

It is well known that a nonlinear optimization problem may have multiple local optimal solutions. In an attempt to find the global optimal solution, we solved the optimization problem repeatedly using different starting points, both for the benchmark case and the case when IRMs are used in forest regeneration. Table 3 presents 10 optimal solutions in the benchmark case (when IRMs are not available), in the order of a decreasing objective function value. These solutions were obtained using the same set of timber demand scenarios, and hence the objective function values associated with different solutions are directly comparable. To be more certain about the relative performances of the different supply functions, we estimated the EPV of the total surplus associated with each of the supply functions in Table 3 using additional 10 different sets of timber demand scenarios, where each set consists of 1000 scenarios. The results for the first two supply functions are presented in Table 4. The last column in Table 4 shows the difference in the EPV of the total surplus between the first and the second solution presented in Table 3. The results in Table 4 show clearly that the first solution is superior to the second one.⁷ The simulations showed that the first solution led to significantly larger EPV than each of the other nine solutions. Therefore, we chose the first solution in Table 3 as the global optimum for the benchmark case. That is, the optimal market supply function in the absence of IRMs is

• (20)

Table 3.  Optimal values of the supply function coefficients and the expected present value of the total surplus (billion SEK) in the absence of regeneration materials.

Solution no.	α1	α2	α3	E[TS^b(α^b)]
1	−19.759881	1.975686	1.720915	22,475.4805
2	−0.733306	0.091132	0.774019	22,438.4648
3	0.214024	0.100281	0.602536	22,432.5384
4	0.394788	0.041671	0.643698	22,431.2745
5	0.399262	0.052216	0.629837	22,431.2237
6	0.589985	0.043376	0.608511	22,429.8152
7	0.613215	0.009356	0.648415	22,429.7295
8	0.616827	0.065843	0.575978	22,429.4367
9	0.652272	0.039568	0.602555	22,429.3543
10	0.677073	0.048903	0.586619	22,429.0750

Table 4.  Estimates of the expected present values of total surplus (billion SEK) associated with the first two solutions presented in Table 4. Each estimate is the average of 1000 random samples.

Simulation no.	Solution no. 1	Solution no. 2	Difference
1	22,440.3458	22,403.50	36.8456
2	22,483.4690	22,446.63	36.8342
3	22,480.0278	22,442.80	37.2307
4	22,491.9954	22,454.33	37.6694
5	22,480.3823	22,443.20	37.1823
6	22,486.3847	22,449.45	36.9347
7	22,446.8810	22,409.81	37.0710
8	22,490.5597	22,453.59	36.9697
9	22,471.9369	22,435.02	36.9169
10	22,483.7921	22,446.44	37.3521
Average	22,475.5775	22,438.48	37.1007

Following the same procedure, we obtained the optimal supply function in the presence of IRMs

• (21)

What may appear remarkable about the supply functions is that the inventory elasticity and the price elasticity are abnormally high. It should be emphasized that most of the solutions we obtained do have “normal” inventory and price elasticity (see Table 3 for the benchmark case). Yet, these solutions lead to a lower EPV of the total surplus, which implies that these supply functions do not provide better descriptions of the relationship between timber supply and the explanatory variables.

The inventory elasticity of timber supply depends partly on the definition of inventory and the assumption about the area of forestland. For example, a change in the mature timber stock would have a larger impact on supply than a change in the total timber inventory in the forest. One can also imagine that the effect of increasing timber stock caused by an increase in the share of older stands in a forest would be larger than when the timber stock increase is caused by an expansion of the forest area. Likewise, the price elasticity of timber supply may depend on the age-class distribution of the forests. In this study, we used the mature timber stock (timber inventory in stands which are older than 60 years) as an independent variable in the supply function. The total area of forestland was fixed, which, together with the ranking rule used to select the stands to harvest, imply that the mature timber stock changes only through the change in the area of the oldest stands in the forests. The initial mature timber stock is over 2000 million m³, which is about 20 times larger than the annual harvest volume. With this background, it is not surprising that the inventory elasticity of supply is very high. The existence of this enormous mature timber stock is also the reason why the price elasticity of timber supply is high. When there is a large amount of timber in old stands, a small increase in timber price would cause a considerable change in the harvest volume.

4.2. Welfare effects

To obtain reliable estimates of the welfare effects of using IRMs, we re-estimated the EPV of the total surplus through an extended simulation based on 1000 demand scenarios in each of the three cases: the benchmark case, the case with the new forest growth function and the benchmark supply function, and the case with the new growth function and new supply function. For each the three cases, 20 replications of the extended simulation were conducted.

Table 5 presents the EPVs of producer surplus (forest management profits), consumer surplus, and the total surplus in the benchmark case. The huge EPVs of consumer surplus and total surplus are mainly the results of the iso-elastic demand function. One should keep in mind that it is the changes in the consumer surplus and in the total surplus that are important. The absolute values of the consumer surplus and the total surplus are not directly relevant.

Table 5.  The expected present values of producer surplus, consumer surplus, and total surplus in the absence of IRMs (unit: billion SEK).

Simulation no.	Producer surplus	Consumer surplus	Total surplus
1	623.73	21,816.61	22,440.35
2	626.51	21,856.96	22,483.45
3	627.85	21,852.18	22,480.03
4	628.72	21,863.28	22,492.00
5	626.43	21,853.95	22,480.38
6	626.57	21,859.81	22,486.38
7	624.24	21,822.65	22,446.88
8	627.12	21,863.44	22,490.56
9	625.81	21,846.13	22,471.94
10	627.31	21,856.48	22,483.79
11	629.26	21,883.17	22,512.43
12	623.78	21,818.19	22,441.97
13	627.61	21,850.39	22,478.00
14	627.60	21,859.93	22,487.54
15	631.29	21,890.95	22,522.24
16	624.20	21,823.23	22,447.43
17	626.57	21,845.96	22472.53
18	627.15	21,851.37	22,478.52
19	629.64	21,884.78	22,514.42
20	624.79	21,825.45	22,450.24
Mean	626.81	21,851.25	22,478.06

The EPV of forest management profits also appears to be very large. The actual profit from timber production in Sweden during 1987–2006 was, on average, 11.85 billion SEK per year (see Table 6). If we assume that the profit will remain at this level in the future, then with an interest rate of 3% the present value of all future profits would be 395 billion SEK, which is about 60% of the EPV shown in Table 5. In our analysis, we included timber harvest and regeneration costs, but ignored the costs of all other management activities such as forest road construction and maintenance, drainage, and precommercial thinning. The total cost of these activities is about 1.5 billion SEK per year. The present value of these costs is in the order of 50 billion SEK. Another simplification, which leads to overestimation of the EPV of future profits, is that we ignore thinning in our analysis. A considerable portion of the existing forests has been thinned before, and the growing stock of timber in the existing forests is lower than the estimate produced using the yield function (13). Compared with the data from national forest inventory (Swedish Forest Agency [2010]), the yield function (13) overestimates the initial mature timber stock in the existing forests by about 800 million m³. Very roughly, this means an overestimate of forest owners’ profits of 100 billion SEK. After these two biases are corrected, our estimate of the EPV of forest owners’ profits reduces to 476 billion SEK, which is 20% higher than the value estimated based on the actual profits.

Table 6.  Annual revenues, costs, and profits of timber production in Sweden during 1987–2006 (billion SEK at 2006 price level). Source: Statistical Yearbook of Forestry.

	Mean	Min	Max	Std
^aInclude construction and maintenance of forest roads, drainage, precommercial thinning, etc.
Gross revenue	23.47	18.75	28.76	2.66
Harvest cost	8.79	6.66	13.40	1.85
Regeneration cost	1.36	0.96	2.13	0.37
Other costs^a	1.47	0.97	2.17	0.38
Profit	11.85	8.81	16.86	1.91

When determining the aggregate timber supply function, we assumed that the timber market is perfectly competitive and ignored the impact of timber harvest on the non-timber benefits of the forests. Most forest owners in Sweden have multiple objectives and do not maximize solely the profits from timber production (Carlen [1990], Andersson and Gong [2010]). Moreover, the timber market in Sweden is not fully competitive on the demand side, which further reduces the profits of timber production (Brännlund et al. [1985], Brännlund [1988]). The EPV of the forest owners’ profits associated with the optimal supply function ought to be higher than the actual profits. There is no precise estimate of the potential increase in the timber production profits in Sweden that can be used to verify our results. However, it is not unrealistic that the present value of future profits can increase by 20% if the timber market is perfectly competitive, and the forest owners manage their forests to maximize the profits from timber production.

The biases should not have any significant impact on the estimated effect of IRMs on the EPV of forest owners’ profits, as the other management costs and thinning were ignored in both the absence and presence of IRMs.

Table 7 presents the EPV of the total surplus associated with different supply functions, in the presence of IRMs. Column C1 gives the estimates of the EPV of the total surplus when IRMs are used but the forest owners do not change their harvest behavior. The figures in Column C2 are the differences between the EPV estimates in column C1 and the corresponding estimates in the benchmark case (shown in the last column of Table 5), that is, the direct effect on welfare of IRMs. Column C3 presents the estimates of the EPV of the total surplus when IRMs are used and the forest owners change their harvest behavior accordingly. The resulting changes in the EPV of the total surplus (column C4) are, therefore, estimates of the total welfare effect of IRMs. The last column of Table 7 shows the effect of changing harvest behavior.

Table 7.  The expected present values of the total surplus in the presence of IRMs, estimated using different supply functions (unit: billion SEK).

Simulation no.	Benchmark supply function		Optimal supply function		Effect of changing harvest behavior C4-C2
	ETS C1	Change C2	ETS C3	Change C4
1	22,467.78	27.43	22,473.94	33.60	6.17
2	22,510.82	27.35	22,516.96	33.49	6.14
3	22,507.44	27.41	22,513.60	33.57	6.16
4	22,519.50	27.50	22,525.74	33.74	6.24
5	22,507.70	27.32	22,513.86	33.48	6.16
6	22,513.92	27.53	22,520.05	33.66	6.13
7	22,474.24	27.36	22,480.48	33.60	6.24
8	22,517.91	27.35	22,524.08	33.52	6.17
9	22,499.25	27.31	22,505.40	33.46	6.15
10	22,511.14	27.35	22,517.39	33.60	6.24
11	22,539.87	27.44	22,546.10	33.67	6.23
12	22,469.40	27.43	22,475.56	33.59	6.16
13	22,505.44	27.43	22,511.69	33.69	6.26
14	22,514.89	27.35	22,521.14	33.60	6.25
15	22,549.66	27.42	22,555.89	33.65	6.23
16	22,474.79	27.36	22,481.03	33.60	6.24
17	22,499.92	27.40	22,506.18	33.65	6.25
18	22,506.01	27.49	22,512.25	33.73	6.24
19	22,541.88	27.46	22,548.13	33.71	6.25
20	22,477.69	27.45	22,483.85	33.61	6.16
Average	22,505.46	27.41	22,511.67	33.61	6.20

From Table 7, we see that the direct effect of using IRMs on the EPV of the total surplus is 27.41 billion SEK, and the total effect is 33.61 billion SEK. Accordingly, the effect of changing harvest behavior is 6.2 billion SEK, or about 18% of the total effect.

Table 8 summarizes the effects of IRMs on the EPVs of forest owners’ profits and consumer surplus. The results show that access to IRMs causes the profits of timber production to decrease and the consumer surplus to increase. Once IRMs become available, they will be applied on large scales. This is simply the result of the force of competitive markets. As long as no single forest owner can influence the price of timber, it is better for the forest owner to use IRMs irrespective of whether the other forest owners use them or not. Widespread application of IRMs would cause timber supply to increase and timber price to decrease. If the price elasticity of timber demand is sufficiently large, the price effect would outweigh the effect of increasing the harvest on the forest owners’ profits.

Table 8.  The expected present values of producer surplus and consumer surplus in the presence of IRMs (unit: billion SEK).

	Producer surplus	Change^a	Consumer surplus	Change^a
^aCompared with the case where IRMs are not available.
Benchmark supply function	596.72	−30.10	21,908.75	57.50
Optimal supply function	583.35	−43.45	21,928.31	77.06

In a competitive market, forest owners behave as price takers. From the point of view of an individual forest owner, using the IRM would increase future timber yield but would not affect the evolvement of timber prices. In other words, for each forest owner, the access to IRMs implies that the value of forest land and, hence the opportunity cost of keeping the existing stands growing, increases. Therefore, the presence of IRMs would cause a forest owner to harvest the existing stands at lower ages. Simulations using the benchmark supply function do not capture this response by the forest owners, and therefore do not provide us with an estimate of the full welfare effect of IRMs.

Figure 4 presents the expected annual supply of timber both in the absence and in the presence of IRMs, over a time period of 200 years. Figure 5 presents the expected timber prices corresponding to the time paths of supply presented in Figure 4. These two figures are helpful in understanding the difference between the direct effect and the total effect of using IRMs on the EPV of the total surplus. When simulated using the benchmark supply function, the presence of IRMs has no effect on the expected timber supply and the price during the first 60 years, and causes the timber supply to increase and the price to decrease thereafter. The reason is that, without considering the change in harvest behavior, IRMs would affect the supply and the price only through the impact on the mature timber stock. The mature timber stock is not affected by the use of IRMs before the first stands regenerated using the IRMs have reached a mature age. Simulation results using the optimal supply function, in which the change in the harvest behavior is embedded, show that the timber supply would increase and the price decrease immediately after IRMs become available. As a result, the mature timber stock in the initially existing forests is depleted at a faster rate in the presence of IRMs, which has a negative effect on future supply. As time passes, the effect on timber supply of the decrease in the mature timber stock becomes greater and would eventually outweigh the positive effect of the change in harvest behavior. When the stands regenerated using the IRMs have reached a mature age, the mature timber stock starts to increase and so does the aggregate supply of timber.

Figure 4. Expected timber supply in the absence and in the presence of IRMs.

Figure 5. Expected timber price in the absence and in the presence of IRMs.

5. Summary, discussion and conclusions

This paper presents a “noneconometric approach” to determining timber supply function coefficients, and demonstrates how this approach can be applied to assess the welfare impact and the effect on the harvest behavior of using IRMs in forestry. This approach differs from the econometric method in that the supply function parameters are optimized conditional on the technological and policy context, which makes it possible to identify the effect of technological and/or policy changes on the supply function coefficients. The main results of the tree improvement case study are: (i) the presence of IRMs has considerable impacts on the aggregate timber supply function, (ii) the use of IRMs leads to a significant increase in the EPV of the total surplus, and (iii) a large proportion of the welfare gain from the use of IRMs results from the change in management behavior.

The focus of this paper is the new approach to conducting counterfactual comparisons in economics. The assessment of the impacts of tree improvements is performed for the purpose of demonstrating the application of the approach. For this reason, we made several oversimplifying assumptions in the case study. One of such simplification is the assumption that the use of IRMs is not associated with any biological risks. Because the growth effect of IRMs is known with certainty, when IRMs are available, they will be applied on large scales. In a competitive market, none of the forest owners alone can influence the price of timber. It is therefore better for each forest owner to use the IRMs, irrespective of whether other forest owners use them or not. Widespread application of the IRMs would cause the supply curve to shifts downwards to the right, which in turn would cause the price of timber to decrease. Depending on the price elasticity of timber demand, the negative effect of decreasing price on profit may outweigh the positive effect of increasing yield. Thus, the use of IRMs could result in reduction in forest owners’ profits from timber production, as our result shows. An obvious extension of this study would be to explicitly model the biological risks associated with the use of IRMs. Such risks might have important impacts of the speed of adoption of the IRMs and on future timber yields.

In this paper, we determined directly the coefficients of a log-linear aggregate timber supply function, assuming that both the functional form and the coefficients of the supply function are constant over time. An alternative strategy would be to derive the aggregate timber supply function based on the supply function(s) of one or several representative forest owner(s). With this alternative strategy one can model in more detail the preferences of different forest owners (e.g., to allow for risk-aversion and different valuations of non-timber goods). The presence of IRMs may lead to changes not only in the coefficients but also in the functional form of the supply function. Thus, although log-linear model is a commonly adopted functional form in econometric studies of timber supply, it may be worthwhile testing other functional forms of the supply function.

Another major simplification relates to the demand function. We assumed that the expected demand is constant over time and the demand functions in successive years are uncorrelated. However, we do not have any empirical evidence to support either of these assumptions. Furthermore, it is possible that the emergence of IRMs could stimulate the demand for timber (biomass). Technically, it is fairly easy to include a time trend in the demand function and serial correlation in timber demand. Such modifications of the model could have significant effects on the numerical results.

Despite the many simplifications, we can draw a conclusion from the results of this study an analysis that neglects the changes in management behavior could lead to significant underestimates of the welfare effect of IRMs. This conclusion can be extended to other counterfactual policy analysis.

ENDNOTES

• 1

  See Dutrow (1974) for a review of the earlier studies.

• 2

  This is incorrect in the context of multiple-period natural resource management problems.

• 3

  The expected timber price associated with the long-run steady state of the forests.

• 4

  The state of the forests affects the management and harvest costs indirectly through its impact on the total harvest volume and on the harvest area in each forest.

• 5

  It is perhaps more likely that only part of the harvested area in each forest will be regenerated with the new materials, at least in the early phase after the new materials are introduced.

• 6

  The program is available from the authors upon request.

• 7

  A simple t-test would show that the difference in the EPV between the two solutions is statistically significant.