Nonconvexities in the production of timber, biodiversity, and carbon sequestration

ARTICLE IN PRESS

Journal of Environmental Economics and Management 46 (2003) 251–268

Nonconvexities in the production of timber, biodiversity, and carbon sequestration Marco Boscoloa,
and Jeffrey R. Vincentb b

a Center for International Development, Harvard University, Cambridge, MA 02138, USA Graduate School of International Relations & Pacific Studies, University of California, San Diego, CA 92093, USA

Received 21 June 2001; revised 10 December 2001

Abstract Fixed logging costs and administrative constraints on logging regulations can create nonconvexities in forestry production sets that include timber and nontimber products. Managing forests to produce multiple values at a landscape level, through the aggregation of stands that are completely or partially specialized in the production of timber or nontimber products, can consequently be superior to management systems that treat all stands uniformly, even when all stands are identical. Both fixed costs and administrative constraints are empirically important sources of nonconvexity in tropical rainforests. The former is more important when the nontimber product is carbon sequestration, while the latter is more important when the nontimber product is biodiversity protection. Uniform management appears to be superior for the joint production of timber and carbon sequestration, while specialized management might often be superior for the joint production of timber and biodiversity, at least at low discount rates. r 2003 Elsevier Science (USA). All rights reserved. JEL classification: Q2; R3 Keywords: Forest management; Nonconvexity; Timber; Biodiversity; Carbon sequestration; Tropical rainforests

1. Introduction A long-running forestry policy debate centers on how to manage forests for multiple goods and services [10,22]. This debate is especially sharp in the context of tropical forests, which are not only a globally important timber source but are also the planet’s biologically most diverse


Corresponding author. Address: 16 Thayer Road, Belmont, MA 02478, USA. Tel.: +617-489-7231; fax: +617-4950527. E-mail address: marco [email protected] (M. Boscolo). 0095-0696/03/$ - see front matter r 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0095-0696(02)00034-7

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terrestrial ecosystems and a major storehouse of sequestered carbon. Although the need to consider multiple values in forestry decisions is widely recognized, the most efficient management approach for jointly producing timber and nontimber products is not clear. Consider a forest estate containing n individual management units, or stands. One approach would be to apply the same management regime over the entire estate, with each stand being managed in identical fashion to produce both timber and nontimber products. We call this uniform management. Another approach would be to differentiate the management regime and manage some stands more intensively (but not necessarily exclusively) for timber and others more intensively (again, not necessarily exclusively) for nontimber products. We call this specialized management. In contrast to uniform management, specialized management aims to produce multiple values at a landscape level, not at the level of each individual stand. Forest planners have long segregated timber production and environmental protection according to landscape characteristics. For example, logging is usually prohibited in upland forests that protect the headwaters of important waterways. Differences among forests are not the only justification for adopting a specialized management approach, however. This paper demonstrates that nonconvexities at the stand level can cause specialized management to be superior to uniform management even when all stands are identical. Expositions of multiple-use management in forest economics textbooks typically assume that production sets for timber and nontimber products are strictly convex, thus yielding familiar, outward-bowed production possibilities frontiers. However, several recent studies have presented evidence that forestry production sets are in fact nonconvex. Some have examined nonconvexities resulting from detrimental externalities that occur within individual stands [5,8,18],1 while others have demonstrated that nonconvexities can result from ecological interactions among stands [5,19–21].2 In this paper we draw attention to two new, and probably ubiquitous, sources of nonconvexity: fixed logging costs and administrative constraints on logging regulations. An example of the former is the cost of building roads and other logging infrastructure. By the latter we refer to the practical need to keep regulations simple if they are to be implemented and enforced by forestry agencies. An example is the use of simple harvesting rules that mandate the removal of all trees above a specified minimum diameter, even though the trees may belong to different species and serve quite different economic and ecological functions. The paper is organized as follows. We begin by using graphical methods to demonstrate how fixed costs and administrative constraints can create nonconvexities in forestry production sets. We then identify the conditions under which these nonconvexities can cause specialized management to be superior to uniform management. Next, we describe the simulation model that we used to explore the empirical magnitude of these nonconvexities. The model is based on an unusually large forestry data set from Peninsular Malaysia, and it predicts the impacts of different combinations of logging regulations on timber harvests, net income from harvested timber (stumpage value), and two nontimber values, carbon sequestration and biodiversity. We use the simulation results to construct two two-good forestry production sets, one for carbon and timber 1

See Baumol and Oates [1] for a general discussion of this source of nonconvexity. A third potential source of nonconvexity, which apparently has not been explored empirically, is a strong difference between the returns to management effort applied to timber production and forest protection [12,24,25]. 2

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and the other for biodiversity and timber. We find evidence of nonconvexities in both cases, but the relative importance of logging costs and administrative constraints as causes of nonconvexity differs between the two cases. Moreover, although uniform management is likely to be superior in the case of the carbon–timber production set, the relative superiority of the two management approaches is less clear for the biodiversity–timber production set.

2. Nonconvexities at the stand level Fig. 1 illustrates the link between convexity and uniform management for a forestry production set consisting of all technically feasible combinations of outputs of timber ðTÞ and a generic nontimber product ðNÞ: Suppose there are n identical stands, each with the production set shown in the figure. Furthermore, assume that the stand is the minimum spatial management unit, in the sense that the management regime cannot be varied within the stand. We will comment on the implications of this assumption later. Some aggregate combinations of T and N can be attained by either a uniform or a specialized approach. For example, the aggregate outputs nTC and nNC associated with managing each stand at any multiple-use point C on the line segment connecting points A and B could also be attained through a completely specialized strategy of managing an stands at the no-logging point A and ð1  aÞn stands at the no-protection point B; with a ¼ NC =NA ¼ 1  TC =TB : Due to the convexity of the production set, however, there are superior production points that only uniform management can achieve. For example, specialized management cannot achieve the aggregate output at points on the frontier like D; which matches point C’s output of T but offers a higher output of N; or point E; which matches point C’s output of N but exceeds its output of T: The remainder of this section explains how fixed logging costs and administrative constraints on logging regulations can make the production set for an individual stand nonconvex. The reason previous studies of forestry nonconvexities have neglected these common features of timber production is perhaps the studies’ analytical framework. Previous studies have tended to analyze nonconvexities in a Faustmann-style optimal rotation model. In its simplest form, this model ignores fixed logging costs, includes just one tree species and one age class, and involves just a single management decision, the age at which the entire stand is harvested (the rotation age). Although this model might describe plantation forest management adequately, it does not capture key aspects of tropical rainforest management, which is the setting of our analysis. The harvesting of tropical timber involves substantial fixed costs, and tropical forest management systems involve multiple decision variables. Similar complexities occur in temperate forests managed under uneven-aged regimes, so our findings are not necessarily unique to the tropics.3 2.1. Fixed logging costs Fixed costs that are associated with the production of one output but not another are a known cause of nonconvexity [14]. This situation is likely to occur in tropical forest management. Fixed 3

Studies of optimal harvest scheduling in uneven-aged temperate forests (e.g., [7,11]) have not, to our knowledge, considered the impact of nonconvexities.

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A

Nontimber Values

NA D

C

NC

E

B TC Timber Values

TB

Fig. 1. Multiple use with convex forest production set.

Nontimber Values

NA′

A A′

m′

m

B′

B

Timber Values

Fig. 2. Forest production set with fixed harvesting costs.

costs can account for nearly half of total logging costs in tropical forests and can run into the hundreds or even thousands of dollars per hectare, especially when roadbuilding is required [23]. In contrast, the costs of forest protection—other than timber-related opportunity costs, which are embodied in the tradeoffs in the production set—are mainly variable costs associated with monitoring and enforcement activities. They are typically low, on the order of barely a dollar per hectare [6]. Fig. 2 illustrates the impact of fixed logging costs on the forestry production set. In this figure and subsequent ones, production of timber is measured in monetary terms: it is the per-hectare stumpage value (resource rent) of harvested timber. Production of the nontimber good is measured in physical terms. In the absence of fixed logging costs, the production possibilities frontier is given by the dashed line m; which is the same as the frontier in Fig. 1. When fixed costs are present, the frontier shifts leftward by an amount equal to the fixed costs ð¼ the horizontal distance between B0 and B), to m0 :

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Due to the leftward shift, the frontier now intersects the N-axis at point A0 ; which is lower than A: The fixed costs drive stumpage value below zero for the small harvests associated with values of N greater than NA0 : The production set now consists of points along and within the new frontier m0 ; plus the original intercept A; which can still be attained by not logging the stand. This discontinuity makes the production set nonconvex. Certain types of logging regulations affect fixed costs and thus the degree of nonconvexity. For example, as a consequence of concerns about the sustainability of tropical timber production, many international forestry and conservation organizations advocate the adoption of reducedimpact logging (RIL) methods, which aim at reducing damage to unharvested trees, forest soils, and other environmental aspects of the forest. RIL entails such activities as detailed mapping of the area to be logged, careful planning and building of logging roads and skid trails, and replacing bulldozers with more specialized logging equipment. Putz and Pinard [17] estimated that the adoption of RIL in the east Malaysian state of Sabah would raise the fixed costs of logging by about $135/ha, which is an increase of nearly 20 percent compared to conventional logging ($800/ha). Because the adoption of RIL presumably affects N and perhaps T too, however, it shifts the frontier in a more complicated way than by a constant amount to the left.4 2.2. Administrative constraints on logging regulations Tropical rainforests are extremely complex ecological systems. A single hectare can contain hundreds of tree species of multiple ages and sizes. Timber management systems in these forests are frequently crude selective systems in which trees above a specified minimum diameter are harvested at regular time intervals, leaving smaller trees to grow to form the next harvest. Forest managers thus select at least two management variables, the harvest interval and the minimumdiameter cutting limit, not just one as in the Faustmann model. The harvest interval in selective systems is shorter than the age of harvested trees, and it is called the cutting cycle to distinguish it from the rotation age in the Faustmann model, which coincides with tree age. Forest managers sometimes differentiate cutting limits by species, but they seldom use more than two or three different limits in the same stand. Maximizing stumpage value while achieving a minimum level of nontimber benefits requires the application of harvesting rules that are more sophisticated than simple diameter-limit systems [2,7]. For example, only a portion of the trees in certain species groups and diameter classes might be harvested, rather than all the trees above the cutting limit and none of the ones below. Designing such sophisticated systems requires a great deal of silvicultural expertise, which is often lacking in tropical forestry departments. Even if the departments have the necessary technical expertise, they seldom have the capacity to monitor commercial logging operations closely. Under this constraint, cutting limits might be the best regulations that tropical forestry departments can actually implement. A similar observation can be made with respect to the cutting cycle. For example, the tendency to allow logging at regular intervals that are usually measured in even multiples of decades reflects a need for administrative simplicity.

4

Certain RIL activities, like the use of directional felling techniques, also affect variable logging costs. They too shift the frontier, but not by a constant amount.

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Fig. 3. Forest production set with fixed costs and imperfect regulations.

The gap between hypothetical, ideal logging regulations and the simpler regulations that are actually implemented can be an additional source of nonconvexity. Fig. 3 shows how m and m0 are the production frontiers from Fig. 2. Assume that both frontiers reflect the application of ideal management systems. The infeasibility of these systems and the resultant reliance on minimumdiameter cutting limits causes m0 to shift downward for points other than the completely specialized timber production point B0 : All points on this new frontier, m00 ; other than B0 yield lower levels of N for any given level of T than do the corresponding points on m0 : The discontinuity along the N-axis is now greater than in Fig. 2—point A00 is farther from point A than is point A0 —and so is the nonconvexity.

3. Uniform vs. specialized management of multiple stands We are now in a position to explain how, and when, nonconvexities resulting from fixed logging costs and administrative constraints on logging regulations can make specialized management superior to uniform management when decisions pertain to more than one stand. Assume again that there are n identical stands, each with the production set shown in Fig. 3. F 00 is the point of tangency between the feasible production frontier m00 and the line segment originating at the complete protection point A: By managing an stands at point A and ð1  aÞn at point F 00 ; specialized management can achieve aggregate outputs equivalent to the amounts nNC 00 and nTC 00 ; nNC 00 ¼ anNA þ ð1  aÞnNF 00 ; nTC 00 ¼ ð1  aÞnTF 00 ; where NC 00 and TC 00 are the outputs associated with any point C 00 on the tangent.5 Uniform management cannot achieve these aggregate outputs, because points on m00 between A00 and F 00 lie 5

The second expression excludes TA ; which equals zero.

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below the tangent. For example, management of all the stands at point D00 can achieve the same output of timber ðnTD00 ¼ nTC 00 Þ but not as great an output of nontimber products ðnND00 onNC 00 Þ: To determine whether the nonconvexity matters from a management standpoint, we need to determine which approach, uniform management or specialized management, generates a higher welfare P level. Assume that the welfare function is UðN; TÞ; where N denotes aggregate nontimber outputP l Nl ; with l denoting a particular stand ðl ¼ 1; y; nÞ; and T denotes aggregate stumpage value l Tl : The inclusion of T in U can be interpreted as representing the consumption of goods purchased using income from timber harvests. Denote the ratio of marginal utilities at the welfareUT j

; and the absolute value of the slope of m00 at point F 00 by maximizing levels of N and T by U N N ;T dN dT jF 00 : Then there are four possible solutions: 1. Uniform (protection-only) management: all n stands are managed at point A: This corner UT j

p  dN solution results only if U dT jF 00 : N N ;T 2. Specialized management: an stands are managed at point A and ð1  aÞn stands are managed at UT j

¼ dN point F 00 ; with 0oao1: This solution results only if U dT jF 00 : N N ;T 3. Uniform (multiple-use) management: all n stands are managed at point F 00 or some other point UT dN on m00 between F 00 and B0 : This interior solution results only if dN dT jB0 4UN jN
;T
X  dT jF 00 : 4. Uniform (timber-only) management: all n stands are managed at point B0 : This corner solution is UT j

X  dN the opposite of the first solution, and it results if and only if U dT jB0 : N N ;T Note that the number of stands, n; does not appear in these conditions. This is because N and T involve linear combinations of the outputs of individual stands.6 UT In a partial-equilibrium setting, U j

equals a fixed price ratio, and this causes the solution to N N ;T UT j

¼ dN be indeterminant when U dT jF 00 : all points on the tangent, including the endpoints A and N N ;T 00 F ; yield the same welfare level. There is no welfare difference between uniform (protection-only), specialized, or uniform (multiple-use) management. In a general-equilibrium setting with convex indifference curves, however, it is possible for specialized management to be the unique welfaremaximizing solution. In other words, welfare in the second case ð¼ UðnNC 00 ; nTC 00 ÞÞ can then exceed welfare in both the first ð¼ UðnNA00 ; 0ÞÞ and third ð¼ UðnNF 00 ; nTF 00 ÞÞ cases.

4. The forest simulation model We used a forest simulation model developed and refined in a series of studies by Boscolo et al. [2–4] to estimate the empirical magnitude of the nonconvexities discussed in the previous section. The model predicts timber and nontimber values associated with alternative assumptions about logging regulations: the cutting cycle, cutting limits for different species groups, and requirements to use RIL instead of conventional logging. In effect, it predicts the points in the production set in Fig. 3, both on m00 and within it. 6

Consider the case of specialized management, where U ¼ UðanNA þ ð1  aÞnNF 00 ; ð1  aÞnTF 00 Þ: Rearranging the UT F 00 j

¼ nNAnTnN ; which simplifies to the condition in the text. first-order condition for a yields U 00 N N ;T F

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We also solved the model by removing the constraints imposed by the diameter-limit cutting system—the requirement that all trees above a minimum diameter be harvested, and none below—and maximizing timber values for given levels of nontimber values. This enabled us to identify points on m0 and thus to distinguish nonconvexities due to administrative constraints from nonconvexities due to fixed costs. 4.1. Recruitment, growth, and mortality The core of the simulation model is a dynamic ecological model that predicts the growth of residual (unharvested) trees in a logged-over forest and the recruitment (regeneration) of new trees. It uses matrices of transition probabilities to predict recruitment, growth, and mortality in a representative hectare of tropical rainforest. It can be summarized as ytþ1 ¼ G½yt  ht  ð1  2=3oÞDht þ c;

ð1Þ

where yt ¼ ½yijt is an IJ  1 vector indicating the number of trees in species group i ð¼ 1; y; IÞ and diameter class j ð¼ 1; y; JÞ alive at time t; G is an IJ  IJ matrix of probabilities that a tree of species group i and diameter class j will grow into diameter class j þ 1 by the next period, ht ¼ ½hijt is an IJ  1 vector indicating the number of trees of species group i and diameter class j harvested at time t; o is a parameter related to logging technology (0 ¼ conventional logging, 1 ¼ RIL), D is an IJ  IJ matrix of logging damage parameters, and c is an IJ  1 vector of the expected number of new seedlings of species i that become established in the forest by the next period. The state of the forest at a given time thus depends on its state before harvest, the combined impact of harvest and damage on the number of trees that survive logging, the number of years since the last harvest, and the growth (and, implicitly and mortality) and recruitment parameters in G and c: Data on the initial structure of the forest ðt ¼ 0Þ and for estimating the growth and recruitment parameters came from a long-term forest research plot in Pasoh Forest Reserve in Negeri Sembilan, Peninsular Malaysia. The Pasoh plot is one of the most intensively inventoried forest research plots in the tropics [15]. It is a 50-ha plot in a virgin, never logged forest, and it is inventoried every 5 years to determine tree growth, mortality, and recruitment. It contains more than 300,000 individual trees of more than 800 species. These species are aggregated in the model into three groups: dipterocarps (species in the plant family Dipterocarpaceae, which includes the most important timber trees), other commercial species, and noncommercial species. Individual trees in each group are further aggregated into seven 10-cm diameter classes, which range from 10–20 cm to 70 þ cm: 4.2. Regulatory scenarios The model contains a single, representative logging company that is assumed to comply perfectly with given logging regulations.7 We simulated the company’s timber harvests and the 7

For an analysis of the discrepancy between compliant and unconstrained profit-maximizing behavior by logging companies and instruments for encouraging compliance, see Boscolo and Vincent [4].

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resulting impacts on timber and nontimber values over a 60-year period.8 We ran the model for all combinations of the following regulations: *

*

*

Cutting cycle (2)—we simulated two cutting cycles, 30 and 60 years: These are approximately the endpoints of the actual range applied in Peninsular Malaysia, with cycles at the lower end of the range being more common. The simulated logging company harvests the virgin forest at t ¼ 0 in both cases and the second-growth forest at either t ¼ 30 and 60 (the 30-year cycle) or just t ¼ 60 (the 60-year cycle). Logging technology (2)—we simulated the use of both conventional logging methods and RIL. The elements of the matrix D in Eq. (1) are the numbers of small trees (diameter ¼ 10–20 cm) of species i that are killed when a tree of size j is harvested using conventional logging methods. Conventional logging typically damages about half of the trees in this class [9]. We assumed that full implementation of RIL ðo ¼ 1Þ would reduce this damage by two-thirds. Cutting limits (36)—we allowed the minimum-diameter cutting limits to differ between dipterocarps and commercial nondipterocarps. We simulated all possible combinations of the following limits for these two groups: 30, 40, 50, 60, 70 cm; or no logging at all. This is a broader range of combinations than is actually implemented in Peninsular Malaysia, where cutting limits are typically on the order of 60 cm for dipterocarps and 50 cm for nondipterocarps.

The number of scenarios was therefore 144. The virgin forest was the initial condition for all scenarios. 4.3. Calculating timber and nontimber values The model predicts the number of trees in each species group and diameter class that are harvested or damaged at each harvest and the recovery of the forest between harvests. These results enabled us to calculate the stumpage value of harvested timber and the impacts of logging on nontimber values. We calculated the net present value of timber harvests under a given scenario by ( ) T X X t ð2Þ d ðPij  Cj Þhijt  FC  oFRIL : PVp ¼ t¼0

i;j

As mentioned above, T equals 60 years; and t has values of either 0, 30, and 60 years (the 30-yearcutting cycle) or 0 and 60 years (the 60-year cycle). hijt and o are defined as in Eq. (1). The new parameters are dt ; which is the discount factor ð1 þ rÞt ; Pij ; which is the market value of the logs in a tree of species group i and diameter class j; Cj ; which is the variable cost of felling a tree in diameter class j and transporting the logs it yields from the forest to the market; FC ; which is the fixed cost of conventional logging; and FRIL ; which is the additional fixed cost associated with full

8

We experimented with longer time horizons and found that the results were not significantly different from those for the 60-year simulation period. The reasons are two: the effect of discounting, and the large impact that the initial (year 0) harvest has on the present values of timber, carbon, and biodiversity.

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implementation of RIL ðo ¼ 1Þ: Boscolo and Vincent [4] describe the data sources for these parameters. Note that we ignored the possible impacts of RIL on variable logging costs. We ran the simulations for two values of the discount rate r; 2 and 10 percent. The former is the rate suggested by Weitzman [26] for periods 25–75 years from the present. It is also the modal rate from a survey of more than 2000 professional economists reported in a different study by Weitzman [27]. The 10-percent rate is typical of the rates used by international organizations when they evaluate natural resource projects. In addition to generating a good, i.e. timber, logging generates a ‘‘bad,’’ i.e. carbon emissions. Through harvest and damage, logging reduces yt and causes carbon stored in trees to be released into the atmosphere.9 After logging, the forest sequesters carbon through biomass accumulation as it recovers. The model records these changes as positive and negative emissions, respectively. We discounted the emissions to account for the different times when they occur. The present value of carbon emissions under a given scenario was thus

PVC ¼

T X t¼0

dt

X

kij f½hijt þ ð1  2=3oÞDhijt  ½yijt  yijt5 g;

ð3Þ

i;j

where kij is an element in k; an IJ  1 vector of coefficients that predict the amount of carbon stored in the above-ground and below-ground biomass of living trees. We drew the values of k from Boscolo et al. [3]. The coefficients are expressed in tons of carbon per tree, and so Eq. (3) yields a present value in physical terms, not monetary terms. The first expression in square brackets after kij in the equation gives emissions caused by logging, while the second expression gives carbon accumulation (negative emissions) from one period to the next. Because emissions occur in the years between harvests as well as during harvests, we measured carbon emissions at 5-year intervals: t ¼ 0; 5; 10; y; 60 years: Logging also affects the diversity of plant and animal species in the forest. As an operational definition of diversity, Boscolo and Vincent [4] constructed a ‘‘proximity to climax’’ index (PCI) that uses the structure of the virgin forest as a reference point. The index is defined as one minus the root mean squared deviation of basal area:10 vP ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u i;j ðyij0 BAj  yijt BAj Þ2 ; PCIt  1  u P t ðyij0 BAj Þ2

ð4Þ

i;j

where yij0 is the number of trees in species group i and diameter class j in the virgin forest, yijt is the corresponding number of trees in t years after the initial harvest in the virgin forest, and BAj is the basal area of a tree in diameter class j: PCI equals 1 if the logged-over forest has the same structure and composition as the virgin forest and 0 if it is devoid of trees. The implicit 9

We ignored long-term storage of harvested timber in finished wood products. This simplification has minor implications for the results [2]. 10 The basal area of a tree is the cross-sectional area of its trunk at a point 1:5 m above the forest floor (‘‘breast height’’).

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assumption is that biodiversity is correlated with forest structure and is highest in the virgin forest.11 As in the case of carbon, we developed a long-term summary measure by computing the present value of PCIt : PVD ¼

T X

dt PCIt ;

ð5Þ

t¼0

where t is again at 5-year intervals. In contrast to carbon, note that we are implicitly assuming that the value of biodiversity is related to its stock, not its change from period to period. The results from the 144 regulatory scenarios enabled us to construct two-good production sets by plotting PVC against Pp (the carbon–timber production set) and PVD against PVp (the biodiversity–timber production set). 4.4. Optimization scenarios As mentioned at the beginning of this section, we also solved the model for the unconstrained selection system—the number of trees harvested in each species group and diameter class (i.e. ht Þ—that maximized PVp ; subject to the constraint that PVC or PVD equaled a given value. The logging company was free to harvest any number of trees from zero to yijt in any species group i or diameter class j: We continued to restrict the choice of the cutting cycle and logging technology to the two discrete values (i.e. 30 vs. 60 years and conventional logging vs. RIL).12 For the 2-percent discount rate, we set PVC equal to five different values (10–50, by increments of 10) and PVD equal to eight different values (4.0–7.5, by increments of 0.5). For the 10-percent rate, the number of given values was seven for PVC (10–70, by increments of 10) and six for PVD (1.4–2.4, by increments of 0.2). This relatively small number of values was sufficient for generating a good sketch of m0 for both production sets and both discount rates. We conducted the optimization simulations using the software GAMS.

5. Results 5.1. Production set with carbon and timber Fig. 4 shows the combinations of PVC and PVp resulting from the 144 regulatory scenarios (the hollow circles and diamonds) and the five optimization scenarios (the solid squares) for the 2percent discount rate. Circles and diamonds denote scenarios involving conventional logging and RIL, respectively. All of the optimization solutions involved RIL. The PVC -axis is inverted, because carbon emissions are a bad. PVC is minimized (carbon sequestration is maximized) at the origin, where no logging and thus no emissions occur. PVp is 11

The inclusion of basal area causes PCIt to weight larger trees more heavily. The rationale is that these ‘‘old-growth’’ trees play an especially important role in maintaining biodiversity. 12 In an exploratory analysis, we found that increased flexibility in the cutting cycle (for example, allowing cycles shorter than 30 years) did not have a significant impact on the shape of the frontier for the optimization scenarios.

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-$1,000

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

0 A

PVC (tons/ha)

20

40

60

80

100 Optimization

No logging

Conventional logging

RIL

Fig. 4. Carbon and timber production set ðr ¼ 2%Þ:

maximized at the lower right point in the production set. The management regime at that point is to harvest all commercial trees, both dipterocarps and nondipterocarps, above 30 cm on a 60-year cutting cycle using conventional logging. It yields PVp ¼ $4744 and PVC ¼ 84:8 tons: Achieving points above and to the left of this one—reducing carbon emissions by sacrificing timber values— involves shifting to RIL and adopting progressively higher cutting limits. Simply shifting to RIL without changing the cutting cycle or the cutting limits reduces PVC by more than a third, to 52:5 tons; and barely reduces PVp ; to $4646: PVp is negative for 14 of the regulatory scenarios, which indicates the presence of nonconvexities like those depicted in Figs. 2 and 3. The nonconvexity due to fixed costs is given by the difference between the origin, which corresponds to point A in Fig. 3, and the intercept of the optimization frontier, which corresponds to point A0 : Using ordinary least squares to fit a parabola to the five optimization points yields an intercept of 9:1 tons per ha:13 Hence, fixed costs do indeed create a nonconvexity. The intercept is equivalent to about 11 percent of the maximum value of PVC ; 86:2 tons: Administrative constraints are a weaker source of nonconvexity. As can be observed, the points for the optimization scenarios are barely superior to the points on the frontier of the regulatory scenarios. The intercept of the regulatory frontier can be approximated by the highest point from the regulatory scenarios that is on or near the carbon axis. That is the point with PVC ¼ 11:5 tons and PVp ¼ $37:50: The difference between the points corresponding to A0 and A00 ð¼ 11:5  9:1Þ is only about a quarter of the difference between the points corresponding to A and A0 ð¼ 9:1  0Þ: 13

The equation for the parabola is PVC ¼ 9:05 þ 0:000245  PVp þ 0:00000184  PVp2 ; with an R2 of 0.998. All coefficients are significantly different from 0 at the 1-percent level.

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8.0

7.0

PVD (index)

6.0

5.0

4.0

-$2,000

-$1,000

3.0 $0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

PVT ($/ha) Optimization

No logging

Conventional logging

RIL

Fig. 5. Biodiversity and timber production set ðr ¼ 2%Þ:

The line segment from the origin is tangent to the regulatory frontier at the point with PVC ¼ 31:8 tons and PVp ¼ US$3148:14 Compared to the PVp -maximizing point, this point has the same cutting cycle (60 years) but much higher cutting limits (50 cm for dipterocarps, 70 cm for commercial nondipterocarps) and involves RIL instead of conventional logging. The slope at this point is 0:0101 tons of carbon per US$. The inverse of this amount, US$99 per ton of carbon, UT ) above which specialized management is determines the threshold carbon price (the inverse of U N superior. Economic models of climate change commonly yield much lower values for the optimal price of carbon emissions. For example, the cooperative equilibrium in the RICE model by Nordhaus and Yang [16] yields a value of US$6.19 per ton in 2000, which rises to barely US$30 in 2100. Uniform management is thus superior to specialized management at these projected carbon prices. Raising the discount rate to 10 percent changes the scale of the production set—PVp decreases and PVC increases for a given regulatory combination, because stumpage values at 30 and 60 years and the negative carbon emissions that occur after logging are discounted more heavily— but not its basic shape. The nonconvexity due to fixed costs remains larger than the nonconvexity due to administrative constraints. Logging regulations at the tangency point are virtually the same—only the cutting limit for dipterocarps changes, from 50 to 40 cm—but the slope at this point is now steeper: 0.0155 tons per dollar. The minimum carbon price for specialized management to be superior to uniform management is thus lower, $64 per ton. This is still far 14

We identified the tangency point by: (i) calculating the slopes of all the line segments from the origin to points with positive values of both PVC and PVp ; and (ii) selecting the point with the smallest slope (in absolute value terms).

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above the forecasts from the RICE model. Hence, uniform management appears to be the superior approach for producing optimal amounts of carbon sequestration and timber at both discount rates. 5.2. Production set with biodiversity and timber Fig. 5 shows the production set for PVD and PVp : The nonconvexity due to fixed costs is negligible: the parabola fitted to the optimization points yields an intercept of 7.57 on the diversity axis,15 which is not significantly different from the value of PVD in the no-logging scenario, 7.62. On the other hand, and in contrast to Fig. 4, the nonconvexity due to administrative constraints is sizable. There is a marked gap between the points from the optimization scenarios and the points from the regulatory scenarios. The intercept on the frontier of the points from the regulatory scenarios is approximately 6.64,16 which is 12 percent below the intercept on the optimization frontier. The nonconvexity due to administrative constraints is exacerbated by the heterogeneity of the forest. Notice that the points from the regulatory scenarios are in two distinct clusters, one to the left of PVp D$500=ha and the other to the right of PVp D$1200=ha: The points in the two clusters do not merge in a convex manner: the frontier of the left cluster has a slope of approximately 0:0011; while the frontier on the left end of the right cluster has a less steep slope of approximately 0:0002: This indenting of the regulatory frontier reflects a difference in the timber value of dipterocarps and nondipterocarps. Scenarios in the right cluster include the harvesting of dipterocarps, while scenarios in the left cluster do not. Harvesting a nondipterocarp tree of a given diameter has approximately the same impact on PVD as does harvesting a dipterocarp of the same diameter, but it reduces PVp by a smaller amount because nondipterocarps are less valuable. Hence, PVD falls off more rapidly for a given increase in PVp in the left cluster than in the right cluster. If all the trees were the same size and had the same price, as in a Faustmann model, then this nonconvexity would not occur. The optimization scenarios involve complex selection systems that are unlikely to be implementable given administrative constraints in Malaysia. To illustrate this point, Table 1 shows the details for hij0 at the point with PVD ¼ 7: It omits information on trees below the minimum commercial diameter ð30 cmÞ and trees of noncommercial species. The harvest is partial in eight of the ten species/diameter categories, with the harvest intensity varying greatly across categories, from a low of 1 percent for nondipterocarps in the 50–60 cm diameter class to a high of 50 percent for nondipterocarps in the 70þ cm class. This harvest pattern is obviously much more complicated than the one associated with minimum-diameter cutting limits, where either all trees are harvested (if they are above the cutting limits) or none are harvested (if they are below the limits). The pattern is similarly complicated for the other optimization points. As an aside, we note that one can interpret the results in Table 1 as indicating the consequences of relaxing the assumption that the stand is the minimum management unit. For example, if trees of different species and diameter classes are evenly distributed within the stand (not a realistic 15

The estimated equation is PVD ¼ 7:57  0:000488  PVp  0:0000000615  PVp2 ; with an R2 not different from 1 at 3 digits. All coefficients are significantly different from 0 at the 1-percent level. 16 The value of PVp at this point is $37:50:

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Table 1 Cutting regime that maximizes PVp subject to PVD ¼ 7 (2% discount rate) Diameter (cm)

Dipterocarps

Commercial nondipterocarps

No. trees/ha

30–40 40–50 50–60 60–70 70+

% Harvested

Before logging

After logging

5.40 3.90 3.60 2.50 5.90

5.40 3.60 3.60 1.99 5.24

0 8 0 20 11

No. trees/ha

% Harvested

Before logging

After logging

8.90 4.60 3.10 1.70 1.60

8.22 3.73 3.07 0.97 0.80

8 19 1 43 50

assumption, but an acceptable one for making the present point), then we can interpret the results as representing a differentiation of the stand-level management regime such that nondipterocarps above 70 cm are harvested in only 50% of the stand, nondipterocarps in the 60–70 cm class are harvested in only 43% of the stand, etc. This indicates that the existence of the nonconvexity due to administrative constraints is linked to the assumed indivisibility of the stand. This interpretation is not inconsistent with our main message, however: applying the same management regime within a stand is one way that forestry departments cope with administrative constraints. Although the optimization points are probably unattainable in practice, application of the same, simple cutting limits in all forests—i.e., uniform management—is not the only alternative. The existence of the nonconvexity shown in Fig. 5 suggests that specialized management could be superior. The point of tangency is the point with PVD ¼ 4:08 and PVp ¼ $4511: Logging is nearly as intensive as is possible at this point: the cutting limit is 40 cm for dipterocarps and 30 cm for commercial nondipterocarps, and the cutting cycle is 60 years; the only environmental concession is that RIL is the selected logging technology. The line segment from the no-logging point to this point lies above all the points from the regulatory scenarios except a few in the lower right corner. This strongly suggests that specialized management is superior. The absolute value of the slope of the tangent is 0.000785 diversity units per dollar, which implies a threshold biodiversity price of $1274 per unit. No previous study has estimated the welfare tradeoffs between timber and biodiversity when biodiversity is defined by an index like PVD : We can, however, crudely calculate this tradeoff by using information in a survey paper by Lampietti and Dixon [13]. To our knowledge, that paper presents the most comprehensive effort—in effect, an informal meta-analysis—to quantify the monetary value of nontimber benefits provided by forests in developing countries. Lampietti and Dixon estimated that the median value of the annual flow of such benefits, excluding carbon sequestration, is $112 per hectare. This translates to a present value of $3893 per hectare for a 2-percent discount rate and a 60-year time period. If we assume that biodiversity is an essential input for the production of these benefits and that the reduction of biodiversity from PVD ¼ 7:62 in the virgin forest to PVD ¼ 4:08 at the heavily logged tangency point wipes out these benefits, then the implicit price is $1100 ð¼ $3893=ð7:62  4:08ÞÞ: This is less than the threshold value, but not by much. Given that Lampietti and Dixon report a median value, nearly half of the forest sites covered by the studies

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they survey would be expected to exceed the threshold. Hence, specialized management is often likely to be superior to uniform management for the production of biodiversity and timber. The relative importance of the two sources of nonconvexity changes when the discount rate is 10 percent. The nonconvexity due to administrative constraints is still present, but it is now slightly smaller than the nonconvexity due to fixed costs. Points on the tangent dominate even more of the frontier for the regulatory scenarios, as the cutting limit for dipterocarps falls to 30 cm at the tangency point. Yet, the heavier discounting of the flow of nontimber benefits makes specialized management less likely to be superior. The absolute value of the slope of the tangent is now 0.000317 diversity units per dollar, which implies a threshold biodiversity value of $3158 per unit. The price based on the Lampietti and Dixon study is now much lower than this value, only $827.

6. Discussion and conclusions Our results indicate that both fixed logging costs and administrative constraints on logging regulations are empirically important sources of nonconvexity in forestry production sets. The relative importance of the two varies, with fixed costs being relatively more important in the carbon–timber production set and, at least at a 2-percent discount rate, administrative constraints being relatively more important in the biodiversity–timber production set. The combined effect of the two sources is stronger in the biodiversity–timber production set: that production set is more nonconvex. Consequently, more of the multiple-use points on the regulatory frontier for that production set are inferior to the specialized management alternatives. Regarding the relative superiority of uniform and specialized management, we obtained an unambiguous result for the carbon–timber production set: uniform management is the superior approach at forecast optimal carbon prices for both discount rates. Reducing the intensity of logging in all stands is more efficient than setting aside some stands as carbon reserves where logging is prohibited, while simultaneously allowing logging in the remainder. In the case of the biodiversity–timber production set, a crude estimate of the price of biodiversity suggested that specialized management might be superior in many (though not most) tropical forests at a 2percent discount rate but few forests at a 10-percent discount rate. Some limitations of our analysis should be noted. One is that we limited the analysis to twogood production sets. Of course, the same forest that sequesters carbon also harbors biodiversity (and provides other nontimber benefits as well, e.g. hydrological functions). The question naturally arises as to the nature of nonconvexities when all three goods are considered together. The graphical methods we employed prevented us from addressing this question directly. Given that carbon sequestration and biodiversity protection are complementary activities, however— both are maximized when logging is prohibited and minimized when logging is most intensive— we expect the three-good production set to be even more nonconvex. This would tend to favor specialized use. Another limitation is that we focused on just fixed costs and administrative constraints as sources of nonconvexity. As our comments in the introduction indicated, these are not the only potential sources of nonconvexity. In particular, we ignored spatial interactions. Our forest growth model is not spatially explicit, and our measures of timber and nontimber values are

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independent of the location of individual trees and forest stands. Incorporating these nonconvexities into the analysis would also tend to favor specialized management, although we cannot predict whether it would reverse any of our results. The nonconvexities that we did consider will be smaller in forests where fixed costs are lower and the capacity to implement sophisticated forest management systems is greater. The fixed costs of logging in second-growth forests, where useable roads might already exist, could be significantly lower than the fixed costs in virgin forests. We ignored this potential reduction in fixed costs for the simulated harvests at years 30 and 60, because well-constructed and wellmaintained forest roads tend to be the exception in tropical countries. Implementing complex selection systems like the one shown in Table 1 might sometimes be more feasible when forests are under the control of local communities that have a good knowledge of individual tree species (and perhaps individual trees) and a low opportunity cost of labor. We focused instead on an institutional setting that consists of a government forestry department that prescribes logging regulations and a commercial logging company that harvests the timber, which is the situation in Peninsular Malaysia and most other timber-rich tropical nations. Our results suggest that replacing selection systems based on minimum-diameter cutting limits with more sophisticated forest management systems, either by strengthening forestry departments or devolving management responsibility onto local communities, would expand production possibilities more for biodiversity protection than for carbon sequestration.

Acknowledgments We are grateful to Randall Bluffstone and Stuart Davies, and two anonymous referees for useful suggestions and comments on earlier drafts. We thank the Forest Research Institute Malaysia and P.S. Ashton, S.P. Hubbell, J.E. Klahn, K.M. Kochummen, J.V. LaFrankie, N. Manokaran, and E.S. Quah for providing the biological data. This work was prepared with partial support from the Smithsonian Tropical Research Institute’s Center for Tropical Forest Science, the AVINA Foundation, the Center for International Development at Harvard University, and the Harvard Institute for International Development.

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