77258 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1: 133-53 Economic Parameters of Deforestation Joachim von Amsberg In theory, economic instruments should overcome the market failures that lead to excessive deforestation. Secure property rights could h$ established and enforced to eliminate the open access problem. In practice, the size of the welfare loss that arises from market failures in the forest sector in the absence of such first-best policies is determined by the incentives, prices, and policies faced by those who make decisions about land use. In many cases, the effects of policies on deforestation are not straight- forward. For example, there are conflicting views on whether an increase in the price of logs leads to an increase or a decrease in deforestation. The effect of a change in the price of logs has particular relevance for the controversial debate about the effect on deforestation of a ban on log exports or other trade restrictions that lower the domes- tic price of logs. This article provides an analytical framework for determining the effects of changes in economic policies and parameters on deforestation. It models dynamic, profit- maximizing land-use choices and obtains unambiguous comparative static results by distinguishing between unmanaged and managed forests. The results suggest that mea- sures to reduce the producer price of logs could be a second-best policy to reduce the pressures on the frontiers of unmanaged forests and to protect biodiversity. Property rights to forests in frontier areas are rarely established or enforced. As a result of open access, deforestation (the conversion of forested lands to other uses) can be excessive. Even when property rights are established, forested lands provide external benefits that do not accrue to the owner, government forester, or other decisionmaker. These external benefits include stabilization of the re- gional and global climate, conservation of the soil, prevention of floods, preser- vation of biodiversity, and gathering of nontimber products by individuals who do not own the forest. These externalities can be another reason for excessive deforestation. In theory, economic instruments would overcome the market failures that lead to excessive deforestation. Secure property rights could be established and enforced to eliminate the open access problem. External benefits of forests could be internalized by taxes on deforestation or subsidies for the maintenance of forestlands equal in amount to the external benefits. Such first-best policies would Joachim von Amsberg is with the Brazil Country Management Unit, Latin America and the Caribbean Region, at the World Bank. The author would like to thank Ken Chomitz, Jeffrey Hammer, Muthukumara Mani, David Wheeler, and two anonymous referees for their helpful comments. This article is a summarized version of the World Bank Policy Research Working Paper 1350, "Economic Parameters of Deforestation." O 1998 The International Bank for Reconstruction and Development/THE WORLD BANK 133 134 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 lead individuals to make efficient land-use decisions through the operation of market forces. In practice, however, governments rarely use first-best polices such as Pigouvian taxes. Some externalities are international in nature (carbon sequestration and biodiversity conservation), and individual countries have no incentive to implement globally efficient policies. Other reasons for the absence of efficient policies are political (for example, the owners of forests have better representation than the beneficiaries of positive forest externalities). In addition, the establishment and enforcement of secure property rights are costly. In the absence of first-best policies, the size of the welfare loss that arises from market failures in the forest sector is determined by the incentives, prices, and policies faced by those who make decisions about land use. Economic param- eters, such as transportation costs, royalty structure, trade policy, foreign ex- change policy, and productivity changes in the forest sector as well as in agricul- ture, influence the patterns of deforestation through their effects on the incentives of those individuals making choices about land use. Therefore, two questions arise in the absence of first-best policies for forest management and land use. First, which policies should be avoided because they would increase the welfare loss arising from excessive deforestation? Second, which second-best policies can be implemented to reduce the welfare loss arising from excessive deforestation? In many cases, the effects of policies on deforestation are not straightforward. For example, there are conflicting views on whether an increase in log prices leads to an increase or a decrease in deforestation. In one view, lower log prices reduce logging profits and the incentives for logging and hence reduce deforesta- tion. In the opposing view, lower log prices reduce the profitability of forestry and hence encourage the conversion of forestlands to other uses such as agricul- ture (see Vincent 1990; Brandon and Ramankutty 1993; and Sharma and others 1994). The effect of changes in log prices has particular relevance for the contro- versial debate about the effect on deforestation of a ban on log exports or other trade restrictions that lower the domestic price of logs. This article is related to three strands of the theoretical literature. First, an extensive forestry literature builds on Faustmann (1968, originally published in 1849) and examines the effects of changes in various economic parameters on the optimal management of a forest (see Jackson 1980; Chang 1983; Nautiyal and Williams 1990; Hyde and Newman 1991; Thiele 1995; and Thiele and Wiebelt 1994). Most of these papers use comparative statics analysis to deter- mine the effect of changes in production costs, discount rate, and various taxes on the optimal rotation age and the optimal management intensity for a given forest. These models rarely consider possible changes in land use. Second, static land-use models have been used to analyze the optimal use of land at a given point in time. This work was pioneered by von Thiinen (1826), applied to for- estry by Ledyard and Moses (1974), and recently used by Chomitz and Gray (1996). Third, the effect on land use of changes in the price of logs has been explored in recent work that applies land-use models to deforestation problems (Deacon 1994; Deininger and Minten 1996; Southgate 1990; Kishor and von Amsberg 135 Constantino 1993; Hyde, Amacher, and Magrath 1993; and Barbier and Rauscher 1993). In addition, several authors have analyzed the empirical relationship be- tween economic parameters and deforestation (see Barbier and others 1995 and Cropper and Griffiths 1994). None of these works, however, has produced un- ambiguous results with regard to the directional impact on deforestation of ap- parently simple changes, such as a drop in the price of logs. This article provides an analytical framework for determining the effects of changes in economic policies and parameters on deforestation. The framework allows the systematic analysis and reconciliation of opposing views on the effect on deforestation of changes in the price of logs. A simple theoretical land-use model also provides results on the effects on deforestation of specific policy changes, such as the imposition of a ban on log exports. Section I outlines the modeling approach. Section II presents a formal model of the comparative statics of land use. Section HI discusses tentative policy implications. Section IV concludes with a discussion of extensions and further research. I. MODELING APPROACH This article analyzes the links between economic parameters and deforesta- tion through a theoretical model of profit-maximizing choice of land use. Fol- lowing von Thiinen's (1826) approach, it assumes that land is put to the use that maximizes the present value of profits to the decisionmaker. The analysis of land-use dynamics is based on a formal comparative statics model, similar to those in the traditional forestry literature. It differs from previous work by si- multaneously incorporating two elements that are critical for understanding deforestation processes: a distinction between different types of forests and the dynamic nature of land-use decisions involving forests. First, the analysis clearly distinguishes between managed and unmanaged for- ests. In unmanaged forests, net timber growth is zero because decaying timber offsets biological growth. Logging of such a mature forest can be modeled like the mining of a nonrenewable resource (see Lyon 1981). Unmanaged forests would include primary forests and mature second-growth forests. Managed for- ests, such as plantation forests, by contrast, are planted in order to be harvested at regular intervals. Even though the dichotomy of managed and unmanaged forests is somewhat extreme, the distinction not only simplifies the analysis but also clarifies the often opposite impact of a policy on managed and unmanaged forests. Moreover, the distinction is relevant from a policy perspective because unmanaged and managed forests provide different types of environmental exter- nalities. Unmanaged forests typically have higher value for the conservation of biodiversity, while managed forests (depending on the subsequent use of forest products) can provide greater benefit in terms of carbon sequestration. The second difference from previous work is the analysis of land-use changes in a dynamic context. A static analysis based on a comparison of returns to different land uses at one point in time can be misleading. The relevant question 136 THE WORLD BANK ECONOMIC REVIEW, VOL 12, NO. 1 is not only whether deforestation would occur on a given piece of land but also when it would occur. For example, the introduction of forest plantations could increase logging of unmanaged forests in the short run but slow down deforesta- tion in the long run when the plantation output reaches the market. The timing of excessive deforestation is important from a policy point of view because it determines the effectiveness of corrective policies that are taken at a specific point in time. Therefore, the analysis of policy impacts has to be based on the comparison between different land-use patterns through time. In a dynamic context, land-use decisions depend on not only current log prices but also the expectation about future prices. The analysis assumes certainty and rational expectations. Therefore, agents determine their profit-maximizing be- havior in the first period for all times in the future based on the expected path of log prices. In the absence of unanticipated shocks, there is no difference between the expected and realized price path and the expected and realized behavior. As a result of geographic conditions and anticipated changes in log prices, deforestation rates can increase or decrease over time without a change in policy. Because deforestation rates can change without policy changes, the relevant ques- tion for analyzing the effect of policy changes is not whether deforestation rates fall or rise after a change in policy occurs, but whether deforestation rates differ from what they would have been if the change in policy had not occurred. This comparison of the actual with the counterfactual scenario is the natural realm of theoretical modeling. The analysis models a policy change as an unanticipated shock that changes price expectations and, therefore, profit-maximizing behav- ior. The analysis focuses on the change in behavior that results from such unan- ticipated policy changes. II. A FORMAL MODEL OF DYNAMIC LAND USE This section contains a partial equilibrium model of profit-maximizing land use to determine dynamic land use as a function of an exogenous path of log prices over time. The model analyzes the timing of land-use changes for each specific parcel of land. It derives results for spatial land-use changes by combin- ing the changes in the timing of land-use changes for each class of land (land with the same locational characteristics). Initially, all land is covered with unmanaged forest. There is no profit to the owner of an unmanaged forest until it is converted. After converting the unmanaged forest, the owner puts the land to its profit-maximizing use, either as managed forest or as farm land. The decision to convert an unmanaged forest depends on the profit or loss at the time of conversion (value of logs—if sold— minus clearing or logging costs) and the profits from alternative land use after logging (farming or managed forest). In this model, the value of logs represents all forest products, including latex, fruits, nuts, and fuelwood. The model is equally applicable in cases where (a) the unmanaged forest is logged, the logs are sold, and the land is subsequently cultivated, (b) the unmanaged forest is logged, von Amsberg 137 but the land is left idle after logging, or (c) the removal of logs is not profitable, and the forest is simply cleared for subsequent farming or managed forestry. After the initial conversion of the unmanaged forest, the owner may switch between different alternative land uses. Of course, on some lands logging might not occur in finite time. The following diagram shows the sequence of possible land uses: Managed forest Unmanaged forest f ^ ^ I Farming where f is the time of converting unmanaged forest to managed forest or farm- ing, and f is the time of switching from managed forest to farming or from farming to managed forest. Equation 1 defines the present value of profit from profit-maximizing land use, IT", in land class / from the time of conversion of unmanaged forest to infinity. Superscript a refers to the profit-maximizing land use—either managed forest or farming—after logging the unmanaged forest. The land class is for a particular parcel of land and represents a generalization of von Thiinen-type distance from market, including other location-specific factors such as slope and fertility. (1) Uia(r,k)=]e-"nia(s,k)ds t" where k is a parameter that represents the effect of exogenous policy changes on the log price, n is profit in each period, and s is the time passed after conversion of the unmanaged forest at f. Superscript u refers to unmanaged forest, and r is the discount rate of the decisionmaker. Equation 2 defines the land expectation value, LEV, the present value of the sum of conversion profit and subsequent land-use profits. The model is based on an exogenous log price path. The model, thus, applies to a situation of perfectly elastic demand, that is, for log exports of a small country. For the log price path, the analysis assumes that p, > 0 and that (pttl pt) < r. (Here and throughout subscripts denote partial derivatives.) This assump- tion appears eminently reasonable given that (ptt I pt) < r is satisfied for any constant rate of price increase less than the discount rate, r. The assumption is also consistent with empirical observation and with the results from theoretical models of nonrenewable resource extraction (logs from unmanaged forests) with 138 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 increasing extraction costs and a renewable back-stop technology (logs from managed forests) that would make log prices rise at a declining rate. Market simulations support the price path assumptions (see section IV). The effect of policy interventions that would depress log prices is expressed in the form of a parameter k that enters the log price with the following character- istics: pk<0 and (p^ I pii) < r. An increase in k either reduces the level of the log price path or reduces the price at any time in some other form; however, an increase in k does not reduce the slope of the price path more than permitted by {ptklpk) < r- With profit functions increasing in log prices, the profit from both conversion and subsequent cultivation will decline with a drop in log prices, resulting in the following properties: n^ < 0, II jf < 0. The Remaining Untnanaged Forests How do changes in the log price path affect the area of unmanaged forests that will ultimately remain? The unmanaged forest will never be converted in any class of land in which the LEV is less than zero for any finite time of conver- sion. By contrast, all land will ultimately be converted in classes of land in which the LEV is greater than zero at least at some time. With these properties, LEV decreases, for all f, with a drop in the log price path, k. With a lower log price path, there is no land class in which unmanaged forest that is ultimately con- verted would not also have been converted with higher prices. However, some classes of land that would ultimately be converted under a higher log price path may not be converted at all under lower prices. Hence, the unmanaged forest area that will ultimately be converted is equal or less under a lower log price path. Up to this point, the model is general enough for the results to hold indepen- dent of the property rights regime and the specific production functions dis- cussed in the following sections. It also applies for a Faustman-type rotation model for managed forests in which forest intensity and rotation period are chosen to maximize the LEV. Conversion of Unmanaged Forests with Secure Property Rights The next step is to analyze how economic parameters affect land use during the time of transition from all-unmanaged forest to the final land use. To pro- vide stylized answers to this question, this section assumes very simple produc- tion functions. The analysis is carried out first for the case of secure property rights and then for the case of open access. Under secure property rights, conversion profits and profits from subsequent cultivation accrue to the owner or decisionmaker. Even under secure property rights, externalities occur in the form of nontimber benefits of the forests that do not accrue to the landowner, such as climatic and soil stabilization, biodiversity conservation, and nontimber forest products. The case of secure property rights is also applicable where logging decisions are made by a government that cares about logging revenues but ignores nontimber benefits of the forest. Such gov- von Amsberg 139 ernment behavior appears reasonable for a variety of reasons. In contrast to nontimber benefits, logging often generates government revenues from stump- age fees. Some nontimber benefits such as climate and soil stabilization will accrue in the future, possibly after the tenure of the current government. A con- centrated logging industry can generate lobbying pressure on the government more easily than the less-organized recipients of nontimber benefits can. Finally, some nontimber benefits may accrue as international externalities. Under secure property rights, the owner of each piece of unmanaged forest- land maximizes the LEV by choosing the optimal time for converting the unmanaged forest, the optimal subsequent land use, and possibly the optimal time for switching later from managed forest to farming or from farming to managed forest. For simplicity, the analysis uses Leontief (constant coefficient) technology for the production of logs. In real-life forestry, there is clearly some substitutability between timber land and effort. Different logging intensities and technologies can be observed in logging operations throughout the world. De- tailed analysis shows that the main result of this section—conversion of unmanaged forests proceeds less rapidly with lower log prices—continues to hold under very reasonable conditions even with variable logging effort (von Amsberg 1994). The two inputs to production are unmanaged forestland and logging effort (with effort representing all inputs other than land, for example labor and capital such as chainsaws). The profit from converting unmanaged forest is if"(t, k) = lmp(t, k) - c"*, where /*" is the quantity of logs that can be sold once at the time of converting (logging) one unit of land of unmanaged forests in land class i, and d" is the cost of converting one unit of land of unmanaged forest in land class i and transporting logs to the market. For simplicity it is assumed that a managed forest produces a constant timber crop. The model abstracts from the question of optimal effort and optimal rota- tion periods in the managed forest and focuses squarely on the question of land conversion. The profit from a managed forest is i&"(t, k) = e~rdtmp{t, k) - c™, where /"* is the quantity of logs that can be produced each period by cultivating one unit of land in land class i with managed forest, d™ is the cost each period of cultivating one unit of land in land class /" with managed forest and transporting logs to the market, and d is the fixed rotation period until the harvest of a managed forest. Land that is left idle after logging yields zero profits. Profits from farming are assumed to be independent of p, c", cm, and r. The profits from profit- maximizing land use after converting unmanaged forest are assumed to be nondeclining.1 With these assumptions, the following properties result: 7t^ > 0, 1. The assumption about nondeclining profits refers to the time of logging, t", and not to the time passed since land conversion, s. For simplicity, the model does not allow for profits to depend on s. Even though not shown formally, the basic intuition of this model would not change if profits were declining in t as long as the present value of future alternative land uses at the time of conversion would be nondeclining in f. With this extension, the basic results would carry through also in the cases of shifting or nutrient-mining agriculture where agricultural profits would typically decline in s (but not in t"). 140 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 0, Jt" < 0, (n-,/7^) < r, T?U = 0, (nft / nj) < r, 7t?> 0,7iT< 0, *?< 0,7t7< 0, and 0. (To simplify notation, superscript / is omitted from expressions that hold for all i.) Land use after the logging of unmanaged forest is determined by maximiz- ing profits by choice of land use over time (managed forest or farming). The optimal time of logging the unmanaged forest is determined by maximizing the present value of returns from logging and subsequent profit-maximizing cultivation (s is the integration variable, running from the time of logging, f, to infinity): (3) maxLEV = ertmnu(t",k)+ [e~"n'(syk)ds J r r subject to the condition that max LEV > 0 because logging would not take place within finite time if max LEV < 0. The first-order condition is: (4) LEV. = dt" where an asterisk denotes the LE V-maximizing conversion time. The intuition of this first-order condition is that at the optimal time of conversion, the rate of appreciation of logs in the unmanaged forest, due to the increasing log price, must equal the forgone returns from logging as well as alternative cultivation of the land. The effect of changes in the parameters on the optimal time of conversion, ***, is determined by solving the total derivatives of equation 4 with respect to k, cf, and r for (df"' / dk), (df' I dc"), and (df' I dr), respectively: dt" LEV^ _ r7t% + Jig — 71^ „ AU ~ _J p V ~ ^x __« _a w L£V (5) " -"--" nU+n "r—>0if»i"+it">0. dr -LEVtt nutt~r%ut-nat Hence, on any piece of land, a reduction in the log price path (an increase in k) delays the profit-maximizing logging time. An increase in the cost of logging also delays logging. If profits from logging are positive and greater than the reduction in profits from land cultivation with an increase in the discount rate, then an increase in the discount rate advances deforestation. von Amsberg 141 Conversion of Unmanaged Forests with Open Access Unmanaged forests typically involve frontier situations with poorly defined property rights and some form of open access. Angelsen (1996), Schneider (1995), Mendelsohn (1994), Mahar (1989), Anderson and Hill (1990), and Binswanger (1989) have modeled such situations of frontier land use and land races. In these models, property rights are granted only for colonists who invest resources (which typically means that they clear the land). Such a policy regime has been analyzed in the case of Brazil but is common in other countries as well. Mendelsohn (1994) shows that development (or conversion of unmanaged forest) will occur wher- ever the value of land is positive; however the rents of land with values above zero will be at least partially dissipated through the investments necessary to establish property rights. The following modification to the basic model ana- lyzes how changes in log prices affect unmanaged forest conversion under this particular policy regime. If access to the unmanaged forest is open and property rights are acquired by clearing and cultivating land, conversion does not take place at the profit- maximizing time but as soon as the sum of profit or loss from conversion and the present value of profits from subsequent cultivation rises to zero. All lands with positive conversion profits would already have been converted in the past. The condition that determines the time of conversion is thus: (6) LEV = nu(f\k) The comparative statics results can be formally derived, similar to the case of secure property rights. For the open access case, the algebra is tedious, but the results are rather obvious. Therefore, the formal derivation of the following comparative statics result is not shown here: Under open access, a drop in the log price path delays the logging time, as in the case of secure property rights. This is intuitively obvious by observing that LEV in equation 6 is increasing in f and decreasing in k (it? > 0 and 7rf S 0 by assumption, and 7rJ < 0 and JT| ^ 0 because profit functions are increasing in output price). Therefore, any increase in k has to be offset by an increase in t", or vice versa, in order for equation 6 to hold. The Switch between Managed Forests and Agriculture After unmanaged forest has been converted, the land will be put to the profit- maximizing use, which may be farming or managed forest. If there is a change in the relative profitability of these activities, there may be a later switch from one 142 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 to the other. If there is a switch, the optimal time of the switch from managed forest to agriculture [t°'), or from agriculture to managed forest, is determined by the condition of equal profits in both land uses: (8) 7t (t ) = K (t , k) where superscript f refers to farming. Solving the total derivative of equation 8 with respect to k, Ji{), then f' marks the time of optimal conversion from agriculture to managed forestry. With the assumptions on profit functions made above: dt"' n? dk nft - < (9) df' m _ *r dc dcm n{t - n' -nn? t m df At"" < TTm dr n[ - 7if 1 If, however, 7C7 < 7i( (in this case, f* marks the time of optimal conversion from managed forestry to agriculture), then all signs are reversed: (df'ldk) < 0, (dfVdc"1) < 0, and (df'/dr) < 0. These results simply show that the switch from farming to managed forests, if it occurs, is delayed by factors that reduce the profits from managed forests (a drop in the log price path, an increase in the cost of managed forests, or an increase in the discount rate). A switch from managed forests to farming, if it occurs, is advanced by the same factors. Land-Use Changes The analysis has produced unambiguous results on the timing of land conver- sion for any land class i. Because this analysis is valid for any land class, it implies results for aggregate land-use changes over time. A drop in the log price path delays the possible conversion of unmanaged forest to other uses (including managed forests), delays the possible switch from fanning to managed forest, and advances the possible switch from managed forest to farming, all for any land class /'. Therefore, at any time after the drop in the log price path, there will be more or equal land under unmanaged forests and less or equal land under managed forest than if the price drop had not occurred. The effect on the aggre- gate area of agriculture is ambiguous. A drop in the log price path reduces the conversion of unmanaged forests and, thus, retains a larger area of unmanaged forests. At the same time, how- ever, a lower log price path reduces the area under managed forests. Keeping in von Amsberg 143 mind the distinction between unmanaged and managed forests, the intuition of the main result is easily explained. The conflicting views about the effects of log price changes on deforestation arise from the dual nature of forestland as stor- age for logs and as an input to the production of logs. This article reconciles the two opposing views by analyzing the distinct impacts of changes in the price of logs on different types of forests, which are characterized by the difference in the importance of land as storage for logs or as an input to log production. A higher log price path increases the logging of unmanaged forests that are used to store logs but that are no longer productive. With a higher log price path, the logging of more remote, unmanaged forests with higher site-specific extraction costs becomes profitable, and the logging of unmanaged forests increases. By con- trast, managed forestlands are productive. A higher log price path increases the profitability of log production and results in more land being devoted to log production. Therefore a higher log price path leads to a smaller area of unmanaged forest and a larger area of managed forest. Figures 1 and 2 illustrate the translation of results for the timing of conver- sion of a specific land class to results for aggregate land use over time. The land- use graph in figure 1 shows different land classes on the vertical axis, with higher land classes representing increasingly unfavorable conditions for cultivation, for example increasing transport costs in a von Thiinen-type model. The horizontal axis represents time beginning with a situation in which all land is covered with unmanaged forest. In good locations (near the horizontal axis), agriculture is relatively more profitable than forestry. Conversion of unmanaged forest would begin at these most favorable locations and, as the price rises along the log price path, proceed to less favorable locations. At sufficiently high log prices, man- aged forestry becomes profitable as shown in the example in figure 1. Once the log price stabilizes, no further conversion of unmanaged forests occurs. Figure 2 illustrates the effect of a drop in the log price path (an increase in k). For each land class, the conversion of unmanaged forests—if it occurs—is de- layed (compared with the dark line that represents the base case), the switch from agriculture to managed forests—if it occurs—is delayed, and the switch from managed forestry to agriculture—if it occurs—is advanced. As a result of these changes in the timing of conversion of specific land classes, there are changes in aggregate land use at any specific time. An unanticipated drop in the log price path leads to an increase in the area under unmanaged forests and a reduction in the area under managed forest at any time after the shock. Table 1 summarizes the results of the analysis. It compares aggregate land use at any time after a hypothetical shock with a situation in which the shock would not have occurred. Additional results, not all analytically derived here, include the following (see von Amsberg 1994). • An increase in conversion (logging) costs for unmanaged forests (or a logging fee per unit of unmanaged forest) produces an increase in unmanaged forests and a decrease in managed forests and farming area. 144 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Figure 1. Log Price and Land Use in the Base Case Log price path Price • • - • • • . ' • — — • • • ) ' ' ' • « • « ^ — — — - - v- < ' . ."':. ;• • •'<, L ' • .>••. • A, .' • . • - . . . . - • • . ;. .., . ;^ L : • . 1 • ] • . • " . . : • 't " . i ' ' • • - • : •,/: 1 J - 1 1 1 1 1 i [ , 1 i i i i i i i i Time Land use Land class Time Agriculture ^ Managed forest | Unmanaged forest von Amsberg 14S Figure 2. Log Prices and Land Use in the Log-Price Drop Case -r-. Log price path . _ Price Time Base case Log-price drop case Land use Land class i i i i i i i I i i I I I i i I Time LJ Agriculture ^ Managed forest H Linmanaged forest Note. Black lines depict the base case land use for comparison. • . 'Wf. 146 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 • An increase in the decisionmakers' discount rate produces a reduction in unmanaged forest if logging is relatively profitable (see equation 5) and an increase in the area of unmanaged forest otherwise. • An increase in farming profits produces a reduction in the area of both unmanaged and managed forests and an increase in the area of farming. • A reforestation subsidy per unit of land produces a reduction in the areas of unmanaged forests and farming and an increase in the area of managed forests. in. POLICY IMPLICATIONS In a very simple land-use model, a drop in the log price path leads to a delay in the conversion of unmanaged forests in all land classes. The quantity of unmanaged forests that is ultimately preserved is the same or larger under a lower log price path. The area of managed forests is reduced under a lower log price path. Great care needs to be taken in applying the results of a simple theo- retical model directly to complex real-life policy situations. However, the main result of the basic model and its underlying basic intuition appear to be robust enough to suggest some implications for the policy debate on timber trade re- strictions, agricultural intensification, and changes in the cost of capital. Table 1. Policy Interventions and Changes in Land Area Used for Unmanaged Forest, Managed Forest, and Farming Policy intervention Unmanaged forest Managed forest Farming Drop in log price Increase Decrease Decrease at the unman- caused by log unit aged forest margin; tax or log export increase at the ban managed forest margin Increase in conver- Increase Decrease at the Decrease at the sion costs (logging unmanaged forest unmanaged forest tax per land unit) margin; no effect margin; no effect at at the agriculture the managed forest margin margin Increase in the Decrease if logging Uncertain effect if Increase if logging discount rate unmanaged forest logging unman- unmanaged forest is is relatively aged forest is relatively profitable; profitable; relatively profit- uncertain otherwise increase otherwise able; decrease otherwise Increase in fanning Decrease Decrease Increase profitability Reforestation sub- Decrease Increase Decrease sidy (per area unit) von Amsberg 147 Timber Trade Restrictions Many timber-exporting countries have imposed log export bans (LEBs) or high log export taxes (see Crossley 1993). LEBS were imposed primarily with the ob- jective of promoting domestic processing and the export of higher-valued sawnwood or manufactured goods. Even though LEBs were conceived as instru- ments for the protection of infant industry, they have implications for logging rates, and a lively debate centers on the environmental effects of LEBS (see Goodland and Daly 1994). LEBS, most other timber trade restrictions, as well as consumer boycotts in importing countries lower the price of logs in the export- ing country. Following a log export ban in Costa Rica, for example, domestic log prices have fallen to 20-60 percent of international price levels (Kishor and Constantino 1993). This article suggests a differentiated approach to analyzing whether lower log prices increase or decrease deforestation. A lower log price path would tend to reduce the logging of unmanaged forests but, at the same time, would also tend to reduce the area of managed forests. At any time, there would be more unmanaged forest and less managed forest than otherwise.2 This result is consis- tent with earlier findings that lower domestic log prices encourage wasteful log- ging and processing techniques (Repetto and Gillis 1988). In contrast to Repetto and Gillis (1988), however, this article suggests that the reduced logging inten- sity resulting from a lower log price path would go along with reduced logging (and larger remaining areas) of unmanaged forests and reduced areas of man- aged forests. Policies other than LEBs that reduce log prices include import restrictions by log-importing countries and consumer boycotts of tropical timber. Such policies would tend to reduce the pressure for logging unmanaged forests and therefore assist the conservation of biodiversity and other external benefits associated with unmanaged forests. The same measures would lead to reduced incentives for managed forestry and a decline in the area devoted to managed forests. Thus these policies have positive effects on the external benefits associated with unmanaged (old-growth) forests and negative effects on the external benefits associated with managed (plantation) forests. Because the effect on the com- bined area of managed and unmanaged forests is ambiguous, no statement can be made about the effect on external benefits that are associated with both types of forests. However, FAO (1992) estimated that 82 percent of the tropical forest area logged between 1981 and 1990 was in previously unlogged (unmanaged) forests. This figure would suggest the relative importance of the positive effect of lower log prices on unmanaged forest conservation compared with the nega- tive effect of reduced managed forests. 2. If protection is declining over time or the domestic processing industry gains some efficiency over time, the price depressing effect of an LEB would decline over time. The effect is thus well represented by the model, with an increase in k with pk < 0 and (p^l pk) < r. 248 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 The positive effect of LEBs on unmanaged forests should not be misinterpreted as an endorsement or a recommendation for LEBs. First, the effects of real-life LEBs include political economy effects that are not captured by the simple model presented here. Second, due to reduced logging and processing efficiency and increased logging wastes, LEBs and other trade restrictions are clearly inferior to first-best policies (for example, a charge for the conversion of forestland equal to the external benefits of unmanaged forests). Even in the context of the simple model presented in this article, LEBs can be justified as second-best policy instru- ments only if first-best instruments are impossible to implement and if the ben- efits of reduced logging outweigh the efficiency costs imposed on the economy as a result of the price distortions from trade restrictions. In policy terms, re- moving LEBs in the absence of efficient first-best policies for protecting forests will increase the pressure on unmanaged forests. Other Policies Policymakers sometimes claim that agricultural intensification programs as well as forest plantation projects reduce the pressures to convert unmanaged forests. Within the conceptual framework presented here, agricultural improve- ments, such as increased yields from improved seed varieties or improved farm- ing practices, would reduce pressures on forests only if they reduce the potential profitability of agriculture on currently forested lands. This would occur only if the demand for the agricultural product is very inelastic (for example, in the case of subsistence agriculture). Agricultural improvements would then reduce the prices of agricultural outputs and, thus, the profitability of agriculture. In this case, the same quantity of agricultural output would be produced on a smaller area of land, and pressures for deforestation would be reduced (for the subsis- tence case, see Angelsen 1996). By contrast, if demand for the agricultural product is elastic (for example, in the case of an export crop), agricultural improvements would increase the po- tential profitability of agriculture on currently forested lands. The area of agri- culture would expand at the expense of managed and unmanaged forests, and agricultural progress would unambiguously increase deforestation. If agricul- tural intensification does not change the potential profitability of agriculture on currently forested lands (for example, because irrigation systems are installed in currently cultivated areas only), there would be no effect on forestry. Several other policies increase producer prices and, thus, lead to increased productivity of land use in either agriculture or managed forestry. In the case of export goods, devaluation of the national currency increases the profitability of agriculture, managed forestry, and logging of unmanaged forests. Devaluation therefore contributes to increased conversion of unmanaged forests. Road building increases the producer prices paid to farmers and foresters, particularly in more remote and, therefore, often unmanaged forest areas. Road building is particu- larly harmful to the conservation of unmanaged forests, increasing the profit- ability not only of alternative cultivation but also of logging itself (see also Chomitz von Amsberg 149 and Gray 1996). Although higher producer prices reduce logging waste, they also go along with more logging of unmanaged forests. Measures that reduce decisionmakers' discount rates include improved access to credit and more secure tenure. Lower discount rates unambiguously increase the area of managed forests because they reduce the cost of waiting for trees to mature. The effect on unmanaged forests at the agricultural margin depends on the profitability of logging. If logging is profitable by itself (logs are typically sold in the market), a lower discount rate slows the logging of unmanaged for- ests because it reduces the opportunity cost of leaving the timber standing in the forest. If logging is not profitable by itself (logs typically are not sold but are burnt), land clearing is an investment that has costs (labor, equipment) and is made for obtaining the benefits of alternative land use. A lower discount rate stimulates this investment and advances the logging of unmanaged forests. The latter situation is reported for parts of the Brazilian Amazon (see Schneider 1993). Empirical evidence that the availability of credit advances deforestation is also provided by Ozorio de AJameida and Campari (1995), Barbier and Burgess (1996), Pfaff (1997), and Andersen (1997). At the frontier between unmanaged and managed forests, a lower discount rate can also lead to increased conversion if the higher returns to plantation forestry outweigh the reduction in opportu- nity costs of the standing unmanaged forests. Kishor and Constantino (1993) makes this point in a static context. IV. EXTENSIONS AND FURTHER RESEARCH This article suggests a new conceptual approach to the analysis of economic determinants of forestland use. However, the model has limitations that reduce its direct applicability to policymaking situations. One limitation of the model is the assumption of an exogenous log price path and, hence, the assumption that log output does not influence log prices, von Amsberg (1994) contains a simulation model with the same structure underly- ing the model, but with an endogenous log price path. The simulation model determines the profit-maximizing land use and profit-maximizing forestry effort for a finite number of land classes (representing lands with differing transporta- tion costs) for a finite number of time periods assuming that all land is covered with unmanaged forests in the first period. The analysis compares the supply of logs that results from these land-use choices with the demand for logs for the same price at different levels of demand elasticity. The model is rerun until a log price path is found at which the log market clears in all periods. This simulation model allows analysis of dynamic land use in a situation in which log prices respond to supply. Such a situation would be expected, for example, for a local fuelwood market or for a large log-exporting country. The simulations also illustrate the theoretical results of the basic model and could be used together with location-specific data to estimate deforestation effects em- pirically in specific real-life policy situations. In all simulations, the resulting 150 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 equilibrium price path for logs shows the characteristic of declining rates of increase, consistent with the assumptions of the basic model with exogenous log prices. The simulations produce seven major results that are consistent with the theoretical results derived here. First, a tax on log sales (simulated by having the market clear for consumer prices that are equal to producer prices plus tax) leads to a reduction in the producer price compared to the base case. Consistent with the results of the analysis with the basic model, the reduced producer price path leads to a reduc- tion in logging of unmanaged forests and a decrease in the area with managed forests. The area with unmanaged forests increases, while the area with man- aged forests decreases. Agriculture contracts at the margin with unmanaged for- ests and expands at the margin with managed forests. Figure 2 shows the results of this simulation and the comparison with the base case. Second, a charge levied per area of unmanaged forests logged (like a Pigouvian tax for the reduction of external benefits from the standing natural forest) leads to a reduction in logging of unmanaged forests. This reduction in logging leads to a reduction in managed forests at the extensive margin. Log prices are some- what higher than in the base case, and the margin between agriculture and man- aged forests shifts in favor of managed forests. Third, a reduction in transportation costs (for example, as the result of road improvements) leads to increased pressure on the frontier and an expansion of agriculture and managed forest at the expense of unmanaged forests. The effect of road building on the log price path and logging intensity is ambiguous be- cause the reduction in transportation unit costs and the increase in distance due to increased logging operate in opposite directions. Fourth, an increase in agricultural productivity for a product with infinitely elastic demand (for example, exports of a cash crop from a small country) lead to an increase in agricultural area. The resulting increase in the log price path shifts the area of managed forests into the area of unmanaged forests, which decline. At the other extreme, an increase in agricultural productivity for a prod- uct with inelastic demand (for example, a pure subsistence crop) leads to a de- cline in the agricultural area, a fall in log prices, and a reduction in the logging of unmanaged forests. Fifth, if demand for logs is highly elastic (the case of small timber-exporting countries), an increase in the productivity of managed forestry creates additional pressures to convert unmanaged forests. However, if demand for logs is inelastic (for example, where timber supplies fuelwood for the local market), increased supply of logs from plantations reduces the price of logs and, thus, reduces the pressure to convert unmanaged forests. As in the case of agriculture, demand for logs in a real-life situation is neither fully elastic nor fully inelastic. The resulting net effect from the introduction of plantations is ambiguous and depends on case-specific demand elasticities. In certain cases, the increase in productivity of managed forests increases the logging of unmanaged forests in the short run because of the additional demand for managed forestland. In the long run, von Amsberg 151 however, as production from managed forests enters the market, logging of unmanaged forests is reduced. In the theoretical case of total absence of man- aged forestry, logs are a nonrenewable resource with increasing extraction costs. In this case, the price path shows an increasing rate of price increase. Sixth, an increase in the decisionmaker's discount rate (for example, as a result of a reduced time horizon or more uncertain tenure) leads to an expansion of agriculture into managed forest areas because log prices are lower and the returns to forestry are better than the returns to agriculture due to the longer growth period for trees. However, logging of unmanaged forests increases only slightly if timber rents at the margin of unmanaged forests are relatively low or even negative. In these cases, clearing land is an investment that is less profitable with a higher discount rate. Increasing security of tenure alone does not drasti- cally reduce deforestation. Seventh, open access to the unmanaged forests drastically advances logging. In the long run, however, the remaining unmanaged forest area is the same with open access and secure property rights because in both cases all lands with posi- tive conversion profits are ultimately logged. Under open access, the log price is initially lower (because of excessive supply from still abundant forests), later higher (because excessive logging leads to higher transportation costs), and fi- nally equal to the case of secure property rights. Important additional research in three areas would strengthen the analysis. First, many of the parameter values that are used in the simulations could be estimated empirically for specific locations, as is done for a related model for the case of Belize by Chomitz and Gray (1996). This would allow quantitative pre- dictions to be derived for specific policy interventions. Second, a model of a forest as a stock of homogenous timber is clearly unrealistic. In particular, unmanaged forests consist of a variety of tree species with highly different eco- nomic values. Even though some of the qualitative effects of this heterogeneity of timber are captured in the production function for logs employed in this ar- ticle, a modeling approach closer to the physical realities of a natural forest would be desirable but would require additional empirical work. Finally, impor- tant economies of scale in land use, both internal (for example, lumpy invest- ments necessary for forestry and agriculture) and external (for example, mini- mum area for biodiversity conservation), are not addressed in the current model. REFERENCES The word "processed" describes informally reproduced works that may not be com- monly available through library systems. Andersen, Lykke. 1997. "Modeling of the Relationship between Government Policy, Economic Growth, and Deforestation in the Brazilian Amazon." Working Paper 2. Department of Economics, University of Aarhus, Denmark. Processed. Anderson, Terry L., and Peter Hill. 1990. "The Race for Property Rights." Journal of Law and Economics 33:177-97. 152 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Angelsen, Arild. 1996. "Deforestation: Population or Market Driven? Different Ap- proaches in Modeling of Agricultural Expansion." Working Paper 9. Chr. Michelsen Institute, Bergen, Norway. Processed. Barbier, Edward B., N. Bockstael, J. C. Burgess, and I. Strand. 1995. "The Linkages between Timber Trade and Tropical Deforestation—Indonesia." World Economy 18(3):411-42. Barbier, Edward B., and Joanne C. Burgess. 1996. "Economic Analysis of Deforestation in Mexico." Environment and Development Economics l(2):203-39. Barbier, Edward B., and Michael Rauscher. 1993. "Trade, Tropical Deforestation, and Policy Interventions." Environmental and Resource Economics 4:75-90. Binswanger, Hans. 1989. "Brazilian Policies That Encourage Deforestation in the Ama- zon." Environment Department Working Paper No. 16. World Bank, Washington, D.C. Processed. Brandon, Carter, and Ramesh Ramankutty. 1993. Toward an Environmental Strategy for Asia. World Bank Discussion Paper 224. Washington, D.C: World Bank. Chang, Sun Joseph. 1983. "Rotation Age, Management Intensity, and the Economic Factors of Timber Production: Do Changes in Stumpage Price, Interest Rate, Regen- eration Cost, and Forest Taxation Matter?" Forest Science 26(2):267-77. Chomitz, Kenneth M., and David A. Gray. 1996. "Roads, Land Use, and Deforestation: A Spatial Model Applied to Belize." The World Bank Economic Review 10(Septem- ber):487-512. Cropper, Maureen, and Charles Griffiths. 1994. "The Interaction of Population Growth and Environmental Quality." American Economic Review 85:250-54. Crossley, Rachel. 1993. "Log Export Bans: Are They Economically and Environmen- tally Beneficial?" Agriculture Department, World Bank, Washington, D.C. Processed. Deacon, Robert T. 1994. "Deforestation and the Rule of the Law in a Cross-Section of Countries." Land Economics 70(4):414-30. Deininger, Klaus, and Bart Minten. 1996. "Poverty, Policies, and Deforestation: The Case of Mexico." Policy Research Department, World Bank, Washington, D.C. Processed. FAO (Food and Agriculture Organization of the United Nations). 1992. Forest Resources Assessment 1990: Tropical Countries. Rome. Faustmann, Martin. 1968. "Calculation of the Value Which Forestland and Immature Stands Posses for Forestry." In M. Gane, ed., Martin Faustmann and the Evolution of Dis- counted Cash Flow, pp. 27-55. Commonwealth Forestry Institute Paper 42. Reprinted from an article originally published in 1849. Oxford: Commonwealth Forestry Institute. Goodland, Robert, and Herman Daly. 1994. "If Tropical Timber Export Bans Are So Perverse, Why Are There So Many?" Environment Department, World Bank, Wash- ington, D.C. Processed. Hyde, William F., Gregory S. Amacher, and William Magrath. 1993. "Deforestation, Scarce Forest Resources, and Forestland Use: Theory, Empirical Evidence, and Policy Implications." Rural Development Department, World Bank, Washington, D.C. Pro- cessed. Hyde, William F., and David H. Newman. 1991. Forest Economics and Policy Analysis: An Overview. World Bank Discussion Paper 134. Washington, D.C: World Bank. Jackson, David H. 1980. The Microeconomics of the Timber Industry. Boulder, Colo.: Westview Press. von Amsberg 153 Kishor, Nalin M., and Luis F. Constantino. 1993. "Forest Management and Competing Land Uses: An Economic Analysis for Costa Rica." LATEN Dissemination Note 7. Latin America and the Caribbean Technical Department, World Bank, Washington, D.C. Processed. Ledyard, John, and Leon N. Moses. 1974. "Dynamics and Land Use: The Case of For- estry." In R. E. Grieson, ed., Public and Utility Economics. Lexington: Heath- Lexington. Lyon, Kenneth S. 1981. "Mining of the Forest and the Time Path of the Price of Tim- ber." journal of Environmental Economics and Management 89(4):330—44. Mahar, Dennis J. 1989. Government Policies and Deforestation in Brazil's Amazon Region. Washington, D.C: World Bank. Mendelsohn, Robert. 1994. "Property Rights and Tropical Deforestation." Oxford Eco- nomic Paper 46:750-56. Nautiyal, J. C , and Jeremy S. Williams. 1990. "Response of Optimal Stand Rotation and Management Intensity to One-Time Changes in Stumpage Price, Management Cost, and Discount Rate." Forest Science 36(2):212-23. Ozorio de Alameida, Anna Luiza, and Joao S. Campari. 1995. Sustainable Settlement in the Brazilian Amazon. New York: Oxford University Press. Pfaff, Alexander S. 1997. "What Drives Deforestation in the Brazilian Amazon? Evi- dence from Satellite and Socioeconomic Data." Policy Research Working Paper 1772. Policy Research Department, World Bank, Washington, D.C. Processed. Repetto, Robert, and Malcolm Gillis, eds. 1988. Public Policies and the Misuse of Forest Resources. Cambridge, U.K.: Cambridge University Press. Schneider, Robert R. 1993. "Land Abandonment, Property Rights, and Agricultural Sustainability in the Amazon." LATEN Dissemination Note 3. Latin America and the Caribbean Technical Department, World Bank, Washington, D.C. Processed. . 1995. Government and the Economy on the Amazon Frontier. World Bank Environment Paper 11. Washington, D.C: World Bank. Sharma, Narendra P., Simon Rietbergen, Claude R. Heimo, and Jyoti Patel. 1994. A Strategy for the Forest Sector in Sub-Saharan Africa. World Bank Technical Paper 251. Washington, D.C: World Bank. Southgate, Douglas. 1990. "The Causes of Land Degradation along Spontaneously Ex- panding Agricultural Frontiers in the Third World." Land Economics 66(l):93-101. Thiele, Rainer. 1995. "Conserving Tropical Rain Forests in Indonesia: A Quantitative Assessment of Alternative Policies." Journal of Agricultural Economics 46(2):187- 200. Thiele, Rainer, and Manfred Wiebelt. 1994. "Policies to Reduce Tropical Deforestation and Degradation: A Computable General Equilibrium Analysis for Cameroon." Quar- terly journal of International Agriculture 33(2):162-78. Vincent, Jeffrey R. 1990. "Don't Boycott Tropical Timber." journal of Forestry 88(4):56. von Amsberg, Joachim. 1994. "Economic Parameters of Deforestation." Policy Research Working Paper 1350. Policy Research Department, World Bank, Washington, D.C. Processed. von Thiinen, Johann Heinrich. 1826. The Isolated State. New York: Pergamon Press.