ANALYSIS
A dynamic approach to forest regimes in developing
economies
Shashi Kant *
Faculty of Forestry,Uni6ersity of Toronto,33Willcocks Street,Toronto,Ont.,Canada M5S3B3 Received 18 March 1999; received in revised form 27 July 1999; accepted 28 July 1999
Abstract
In the developing economies, optimal forest regimes should incorporate the socio-economic characteristics of the user groups. And, since socio-economic factors will change with time, optimal forest regimes will also follow a dynamic path. The two most important socio-economic factors are the heterogeneity of the user group with respect to forest management and the direct dependence of the user group on forest. Normally, the heterogeneity will increase and dependence will decrease with economic growth of user group. An optimal control model is used to integrate the dynamics of natural system such as joint product of forests and its growth function, and the dynamics of the two socio-economic factors — heterogeneity and dependence. The model demonstrates that the dynamics of optimal forest regimes will depend upon the change in natural factors, socio-economic factors, and on the interactions between natural and socio-economic factors. Hence, optimal forest management strategies would require a continuous refinement in forest management regimes, instead of static state regimes, as local communities in developing economies pass through different phases of economic growth. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Economic growth; Forest management; Institutions; Optimal control; Socio-economic factors
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1. Introduction
The existing forest resource regimes and tech-nology available determine forest resource use. A technological perspective has dominated economic discussions during the industrialisation era. How-ever, in the past decade the resource regime aspect of the institutional perspective has emerged strongly. As a result, the conventional view of the superiority of private or state regimes over
com-munity regimes has been challenged by a rich body of empirical evidence from around the world.1
This evidence points to the successful management of a wide variety of natural re-sources, including forests, as common or commu-nal property. Game theoretic models have also
1These include forests in India (Kant et al., 1991;
Poffen-berger and Singh 1991; Campbell, 1992), Kenya (Castro, 1995), Mexico (Alcorn, 1989), Nepal (Gilmour and Fisher, 1991); water in the Philippines (Cruz, 1989; Ostrom, 1990), and India (Wade, 1987); grazing lands in Botswana (Peters, 1987) and swamplands in Borneo (Vondal, 1987).
* Fax: +1-416-9783834.
E-mail address:shashi.kant@utoronto.ca (S. Kant)
been developed to explain the observed frequency of collective action in natural resource manage-ment (Runge, 1986; Ostrom et al., 1994; Baland and Platteau, 1996; Sethi and Somanathan, 1996). A large number of resource economists2 have attempted a comparison of different resource regimes while treating the system of ‘resource regime’ as a fixed input. Randall (1987, p. 159) argues that any one of the possible specifications of non-attenuated rights would lead to Pareto efficiency, but that the efficient solution would be different for each specification of rights. Thus, he limited himself to a consideration of the locally optimal outcome. Dahlman (1980, p. 138) argues the need to identify the exact relationship between production technology versus transaction costs. Cheung (1987) emphasises the importance of iden-tifying transaction costs and their determinants. Thus, though the importance of the relationship between production technology, resource regimes, and associated transaction costs has been recog-nised since the articles of Coase (1937) and Coase (1960), resource regimes have not been fully incor-porated into the economic production models of natural resources that are used to identify the most efficient regime using the full set of options, rang-ing from open access to private regime. An ade-quate production model — one which can identify a global maximum — must treat both physical inputs and resource regime as variables, and should account for variation in transaction costs. Kant (1996) and Kant et al. (1999) argue that the optimal regime for a given resource depends not only on the physical production (transforma-tion) efficiency with which the physical inputs are converted to physical outputs but also on the level of transaction costs (transaction efficiency). Hence, an adequate theory of forest resource use should incorporate the role of institutional struc-tures associated with different forest regimes and their associated transaction costs. The transaction cost of a forest regime will vary with the character-istics of the forest regime and the socio-economic
factors (SEFs) of the user group. The authors identified and defined the two SEFs, the user group’s heterogeneity with respect to forest management3and the degree of direct dependence of the user group on forests.4 They argue that
3User group heterogeneity with respect to forest
manage-ment: Members of the user group will often have somewhat different preferences regarding resource management, or as-sign different priorities to the various objectives of resource management, either because of differing personal interests in the resource or differing degrees of involvement in the social group. People think of themselves both as separate ‘individu-als’ and as ‘members of a social group’. In traditional societies, where people see themselves first as members of the group and only afterwards as independent individuals, an inherent spirit of co-operation is generally present even in the face of large economic differences and social stratification. This spirit is muted in modern industrial societies, where people are first and foremost ‘individuals’ and more truly homo-economicus. The heterogeneity of individual interests with respect to how a resource is managed reflects both economic differences (e.g. income level) and social and cultural traditions or norms; the extent to which ‘personal’ interest fully determines an individ-ual’s behaviour with respect to the resource depends on the degree of ‘community spirit’, hence, the level of heterogeneity (allowed to range between 0 and 1) will vary inversely with the degree of such ‘community spirit’ as well as with respect to economic differences. A hierarchy of the levels of heterogene-ity provides linkages between cultural, social and economic differences and resource management. The basic level consists of cultural, economic, ethical and social differences. Due to this basic heterogeneity, the members of the user group may have diverse preferences for timber and non-timber products and hence prefer different product mixes, and this could be termed second level heterogeneity. Diverse product preferences will result in different preferences for resource management regimes, which can be labelled third level heterogeneity. In summary, heterogeneity with respect to resource regime can be treated as a function of the product preference differences, which can in turn be treated as a function of cultural, eco-nomic, ethical, and social heterogeneity. The heterogeneity with respect to resource management is the inverse of full agreement on, and support for, the same resource management regime. (Kant, 1996; Kant et al., 1999).
4The degree of direct dependence of user groups on forests:
Everyone depends on forests in some way. Forests provide many values such as consumption, recreation, environmental, and spiritual. In developing economies, some tribal groups depend on forests, located close to their habitations, for their consumption items such as food, fuel, medicines, and even monetary income (from the sale of minor forest products) that are necessary for their subsistence. These groups have a one
2Including Krutilla and Fisher, 1975, pp. 19 – 38; Scott and
these two SEFs will be the main determinants of the transaction costs, the heterogeneity of the co-ordination cost and the direct dependence of the exclusion cost, of forest management in devel-oping economies, and suggested a mathematical formulation of the transaction function.5
Based
on the static analysis of the full production pro-cess, comprised of transformation and transaction functions, they found that for only a very small range of SEF values, particularly when the depen-dence of the user group on the resource is very low and heterogeneity very high, will one of a private or a state regime be optimal. In contrast, for a rather wide range of SEFs, some form of joint regime between state and community will be optimal.6
Baland and Platteau (1996) similarly argue that in selecting a form of resource regula-tion, a government is not confined to the spurious and simplistic ‘state versus community’ di-chotomy, but can choose among a rather wide range of intermediate options, which will be more or less effective depending on the strength of the collective action of basic user groups.
(group) to one (forest) direct dependence on the forest. In developed economies, most user groups depend on forests for derived items such as pulp and furniture, and these items may be available from any forest area. The derived items from one forest area may be available to many user groups, or one user group may get derived items from different forests. These groups also depend on forests for recreational values, but they again derive these values from different forest areas. Hence, in this case, there is a one (group) to many (forests) or many (groups) to one (forest) indirect dependence relationship be-tween the user group and the forest. In developed countries, some aboriginal groups have a one to one direct-dependence relationship with the forest. Similarly in developing economies, some groups may also have a one to many or many to one indirect-dependence relationship with the forests. Here, my interest is in the degree of the one to one direct dependence of the user group.
The degree of direct dependence is defined as the share of direct returns from forests in the total utility bundle. Its range is also defined as 0 to 1, and may be reasonably measured by the fraction of the user group’s gross local production con-tributed by the forest. The degree of direct dependence will depend on the substitutability of forest returns that, in turn, will depend upon the availability of substitutes and the capac-ity of the user group for substitution. The capaccapac-ity of the user group will depend on the composition of the utility bundle. In the case of the utility bundle being comprised of forest returns only, there is no possibility of substitution and hence, the degree of direct dependence will be very high and equal to one. The case of subsistence dependence of tribal communities will fall in this category because there are substitutes, but the user group is unable to acquire the substitutes because of their limited monetary income. In some cases, utility bundle may consist of returns from different sources including monetary income, but there may not be any substitute for forest returns such as spiritual values. In such cases, the degree of depen-dence will depend upon the share of spiritual values in the utility bundle. However, the share of spiritual values may not be quantified in monetary terms, but its share in the utility bundle can be determined by Participatory Rural Appraisal methods (Kant, 1996; Kant et al., 1999).
5A resource regime typically has several economically
im-portant dimensions — comprehensiveness, exclusiveness, benefits conferred etc. each of which may vary across a spectrum. However, in the case of developing economies, the most important dimension is exclusiveness, and hence the focus is on this dimension only. Thus R is the continuous resource regime variable representing different level of
exclu-siveness, scaled for simplicity between 0 to 1 (but excluding the end points). On this scale, open access (no exclusion) is represented by a number near zero, and a private regime, which means full exclusion, by a number close to 1. Given the way the two costs — exclusion cost and co-ordination cost — are linked to forest regime, the most plausible simple assump-tion is that the transacassump-tion funcassump-tion is either monotonically increasing, monotonically decreasing, or has a single maxi-mum value somewhere in the domain ranging from open access to private regime. Such a transaction functionG(R) can be expressed by the mathematical form:
G(R)=dRa(1−R)b
The parameter ais the heterogeneity of the user group with respect to forest management, and b the degree of direct dependence on forests.dis a scaling factor that normalises the maximum value of the transaction function. Readers interested in more details of this function can refer to Kant, 1996; Kant et al., 1999.
6As mentioned in footnote 5 on the exclusion dimension,
Hence, the static analysis of the total produc-tion process of forests provides useful insights into the relationship between the socio-economic environment of the user groups and the globally optimal forest regimes in developing economies. However, communities are dynamic and their so-cio-economic environment changes over time, hence, optimal forest regimes will also have an evolutionary nature. Even though evolutionary economics have been gaining importance in the last decade, the evolutionary nature of resource, forest, regimes has been unable to attract the attention of either economists or forest managers. Evolutionary theories have been used to explain social conventions and norms (Axelord, 1986; Sudgen, 1986, 1989), law (Posner, 1980), property rights (Schotter, 1981; Barzel, 1989; Libecap, 1989; North, 1990), and various forms of social and economic organisations (Williamson, 1975; Nelson and Winter, 1982; Williamson, 1985). Bromley (1989) called these writings the ‘property right school’ of institutional change, and sum-marised other contemporary writings in two cate-gories: the ‘induced institutional innovation approach’ associated with Hans Binswanger, Ver-non Ruttan, and Yujiro Hayami, and the ‘North Theory’. The property rights school is based on transaction costs, the induced institutional inno-vation approach is based on the supply and de-mand theory of institutional innovations. North started with relative prices being a major source of institutional change (North and Thomas, 1973), and brought in many other factors such as technology, information, institutional inertia, and path dependence as sources of institutional change in his writings (North, 1990). However, all of these writings have been focused on explaining the existence of different institutions or explaining the institutional changes that have already oc-curred. Hence, these evolutionary approaches have been criticised for their limitations in sug-gesting policy measures for correcting the existing inefficiencies in institutional arrangements.
Another stream of economists, now known as ecological economists, make strong arguments to move away from implicit assumptions of neo-clas-sical economic analysis which eliminate the links between natural and socio-economic systems
be-cause, due to the strength of the real-word inter-actions among these components, failure to link them can cause severe misperceptions and policy failures (Costanza and Daly, 1987; Norgaard, 1989).
2. The dynamic nature of socio-economic factors
Communities are dynamic and their SEFs change with time. In the present era, as communi-ties pass through different phases of economic development, the two SEFs — heterogeneity and dependence — change. The nature of these changes is discussed herein.
2.1. The dynamic nature of heterogeneity
The presence of diversity in language, culture, religion and race, but strong ‘primordial attach-ments’ of kinship, race, language, religion and custom, are the features of many developing economies. Hence, these economies have cultural, social, and economic heterogeneity at the macro-level but a high degree of homogeneity at the micro or community level. Other features of these economies are the pooling of family resources to hedge economic uncertainties, the system of self-help to hedge other hazards and difficulties of life, and non-integration with market and market economies. The process of economic growth at-tempts to bring these economies within the fron-tiers of market. However, market arrangements reduce the need for compassion, patriotism, brotherly love and cultural solidarity as motivat-ing forces behind social improvement (Schwartz, 1987, p. 247), and favours social stratification and the dissolution of ethnic bonds and customs (Seeland, 1991). In the early stages of growth, the community moves from an agricultural to an industrial foundation, and machines and non-hu-man factors take the role of nature and hunon-hu-man factors which leads to impersonal relationships, competition, and absence of altruism. On conver-sion of subsistence farming to commercial farm-ing, members of rural communities leave for urban areas without their immediate family mem-bers, resulting in a disruption of existing social relationships and a decline in the quality of per-sonal existence. Hence, these new processes of economic growth lead to social and cultural het-erogeneity. In addition, the initial stages of urban-isation and industrialurban-isation may also intensify awareness of religious, racial, and cultural differ-ences, and thus produce social tensions (Adelman
and Morris, 1973, p. 31). An increase in agricul-tural productivity, due to commercial farming initiatives, tend to benefit the larger, more pro-gressive farmers disproportionately in both abso-lute and relative terms, and hence tend to increase income inequalities (Adelman and Morris, 1973, p. 18). Similarly, dualism, seen in the joint exis-tence of traditional sectors and rapidly growing exchange sectors, is accompanied by inter-sector differences in factor productivity and per capita income (Adelman and Morris, 1973, p. 20). The availability of new resources such as a physical infrastructure, opportunities for income genera-tion and socially-sancgenera-tioned access to valued jobs and administrative positions, creates conflicts of interest among various groups, and thus leads to social stratification. The new employment oppor-tunities created through the development process require specialised knowledge that is not equally distributed, and hence gives rise to social as well as economic heterogeneity. Thus, normally, within the development process first level hetero-geneity will increase. However, the rate of change of heterogeneity will depend upon the rate of economic growth of the community and the inter-nal inertia of the community against this change. Forest product preferences are dependent on the economic as well as the social and cultural condi-tions of a community. As communities pass through different stages of economic growth, product preferences of people move from unpro-cessed raw products, such as non-timber forest products, fuelwood, and poles for house construc-tion, to quality products such as furniture and paper products, and finally to outdoor recreation and environmental values. Hence, even in small traditional communities, differential impacts of economic growth will increase product preference heterogeneity.
different phases of economic growth. Hence, di-verse forest product preferences and preference for different management practices by the people in different economic groups will increase the diversity of forest management practices. Nor-mally, third level homogeneity of resource man-agement will depend upon the first and second levels of homogeneity. However, the third level of homogeneity may sometimes be imposed upon by external factors such as mutual dependencies over social, economic, or cultural heterogeneous groups. But, these are exceptions to general rules, and are not of direct concern to the present discussion.
2.2. Dynamic nature of the direct dependence on forests
Economists have discussed the role of natural resources in different stages of economic develop-ment. Rostow (1956) attributed the critical role of natural resources in the first and third stage of development. In the first stage (traditional soci-eties), natural resources offer a quick yield of increased productivity to new techniques and per-mit the application of innovations. In the takeoff (third) stage, foreign trade of natural resources contributes significantly to enhanced investment. Schultz (1961) observed that, at a particular time, the proportion of natural resources to all re-sources employed for income generation is greater in poor countries than in rich countries. The share of natural resources declines with economic growth due to improvements in the efficiency of resource use, substitution of natural resources by man-made resources, and the service sector taking a leading role over the manufacturing sector. Adler (1961) argued that in the earliest stages of organised society — ‘collectional’ economy of hunters and ‘pre-cultural’ nomads — economic activity was entirely dependent upon natural re-sources, and in each subsequent stage, dependence upon the resource-base of a particular location diminishes. A rise in the national or per capita income, an increased share of industrial produc-tion in GDP, urbanisaproduc-tion, a higher rate of liter-acy, increased nutritional awareness, and an improved information media are associated with
economic growth. The change in individual in-come transforms the composition of the utility bundle, and increased and diversified industrial production enhances the range of the substitute product. An inclusion of monetary income in the utility bundle of traditional, resource-dependent communities enhances the possibility of substitu-tion of forest products by man-made products. Nutritional awareness will encourage the substitu-tion of raw forest products by quality products with desired nutritional values, and an improved information media will extend the knowledge of substitute products. Urbanisation reduces the di-rect pressure of local populations on forests. Hence, economic growth will lead to a reduction in the direct dependence of such communities on forests. However, higher per capita consumption, including the consumption of pulp and paper and other wood products, and increased environmen-tal awareness and recreational values are associ-ated with economic growth. But these associassoci-ated phenomena will increase the one-to-many or many-to-one indirect-dependence on forests, and not the direct one-to-one dependence. Assuming that economic growth is a continuous process, the direct dependence of a forest-dependent commu-nity will decrease continuously. However, this rate of decrease may not be the same for all communi-ties in a country. The rate of decrease will depend on the rate of economic growth. However, eco-nomic growth may not have a direct relationship in some special cases such as a community’s de-pendence upon spiritual values. But, indirectly, the economic growth may reduce the spiritual values, and hence, may subsequently also decrease the direct dependence.
3. Optimal control model of dynamics of forest regimes
Many authors have used optimal control theory for modelling forest stands (Anderson, 1975; Clark, 1976, pp. 263 – 269; Sethi and Thompson, 1981, pp. 287 – 294; Synder and Bhattacharyya, 1990); however, these models are based on a traditional production function, which includes only the transformation function. The concept of the transaction function, and hence, resource regime, is missing from these models. An optimal control model of the full forest production pro-cess, which is described by the non-separable7 (across time) transformation and transaction functions, is developed in this section, and the dynamic path of optimal resource regime for a given forest and user group environment is examined.
I assume, for simplicity and clarity of analysis, a composite forest product which comprises all timber and non-timber products, with a net value per unit area, at time t, of V(t). The timber is removed on a rotation period, whereas NTFPs are removed continuously. Hence,V(t) represents the sum of the net value of standing timber at time t and the net value of all NTFPs removed and available to be removed up until time t. As
V(t) is the net value, all costs, such as regenera-tion, harvesting and land rent, except the cost of a resource regime (the transaction cost), are ac-counted for in this formulation of V(t). The cost of the resource regimePr(R) will be treated sepa-rately. It is also assumed that there are only two
production factors: time8and the resource regime. It is further assumed that, in the absence of the effect of the resource regime, the rate of change of value is represented by the logistic function: (dV/
dt)=mV[1−(V/Va)]=f(V(t)), where m is the positive growth parameter and Va is the asymp-totic value of V, and f(V(t)) is the growth func-tion of the value of the composite product.
Due to the non-separable nature of transaction and transformation functions, resource regime ar-rangements (the transaction function) will affect the growth rate of forests as well as the net value of the composite product available to the legal right holder. As per the definition of the transac-tion functransac-tion, the net value available to the legal right holder will be the product of the natural net value V(t) times the transaction function
G(R(t),t). It is also assumed that the effective growth rate9will also be the product of the natu-ral growth rate times the transaction function. In this context, policy makers or forest managers will likely design and modify forest regimes in such a way that the legal right holder can maximise the net returns from forests. Hence, the policy maker or forest manager’s problem is to maximise:
&
0 T[V(t)G(R(t),t)−Pr(R)]exp(−rt) dt subject to (dV/dt)=f[V(t)]G[R(t),t], where f[V(t)]=mV(t)[1−(V(t)/Va)],
G(R(t),t)=d(t)Ra(t)(1−R)b(t) and V(0)=V0
.
This is a standard optimal control problem, in whichV(t) is the state variable, andR(t), which is bounded within 0+ and 1−, is the control vari-7Renewable resources such as forests grow and regenerate
over economically relevant periods of time. The growth of these resources depends upon the existing growing stock, which is clearly affected by resource regime arrangements. Hence, the transformation and transaction functions work simultaneously, or are non-separable. Non-renewable re-sources are formed by geological processes that typically take millions of years, thus for practical purposes, these can be treated as having a fixed stock. In such cases, transformation and transaction functions can be treated as separable. How-ever, even in the case of non-renewable resources, the quantity retrievable for use is related to the transformation process. Hence, in the broader perspective of the transformation pro-cess, the transaction and transformation functions will be non-separable even in the case of a non-renewable resource.
8In the case of forest resources, the period of production is
lengthy, and ‘time’ itself acts as a factor of production (Nau-tiyal, 1988, p. 335). Hence, it is common practice to have forest production models in terms of time.
9The natural growth rate means the growth rate attainable
able. This optimal control problem can be solved by a standard method. The current value Hamiltonian of this optimal control problem can be written as:
H=[V(t)G(R(t),t)−Pr (R(t))]
+l(t)f(V(t))G(R(t),t) (1)
where l(t) is known as the co-state variable, which is the marginal valuation of the state variable V(t), and is also known as the shadow price of the state variable. In the case of the current value Hamiltonian, l(t) gives the current marginal value of the state variable at time t. I also assumed that the objective function and the function which is describing the law of motion of the state variable (f(V(t))G(R(t)) are con-cave, hence the necessary first order conditions of the optimal control problem will also be the sufficient conditions (Lambert, 1985, p. 175). First order conditions are given next.
3.1. Optimality condition
((H/(R)=V((G/(R)−(Pr/(R+lf((G/(R)=0. (2)
In the remaining text, the subscript is used to denote the partial derivative with respect to a variable given in subscript. Hence, Eq. (2) gives:
l=(Pr
R−VGR)/fGR. (3)
3.2. Co-state 6ariable (l) condition
((l/(t)=rl−((H/(V)=rl−G−lfVG. (4)
This equation gives the motion of the co-state variable. The equation can be written as:
((l/(t)(1/l)+f
VG+G/l=r. (4a)
Eq. (3) gives the shadow price of the state vari-able, and is equal to the marginal net value per unit of available growth due to marginal change in the resource regime. Eq. (4a) gives the mo-tion of the shadow price. The first term in Eq. (4a) gives the relative rate of change of the mar-ginal valuation (the shadow price) of V(t), the second term gives the value available from the growth of the state variable, and the third term
gives the relative available value from one unit of the state variable with respect to the shadow price. The right hand side gives the psychic cost due to time preference. A common understand-ing of the nature of forest growth (f6 being
quite high in the early and middle stages of a forest, as compared to r, indicates that the rela-tive marginal value of the stand V(t) will de-crease at a decreasing rate along the optimal path. However, even though the value is mar-ginally decreasing, the forest is not cut because the value of available growth is greater than the value obtained by cutting the forest (Donnelly and Betters, 1991).
3.3. Law of motion
((V/(t)=fG=mV[1−(V/Va)]dRa(1−R)b. (5) On substituting the value of the growth function (f) from Eq. (2),
((V/(t)=[(Pr
On differentiating Eq. (3) with respect tot, and substituting the value ofl, and ((l/(t) in Eq. (4)
and further substituting the value of ((V/(t) from
Eq. (5), the following is achieved:
−Pr
Rf((GR/(t)
=(Pr
R−VGR)GR[ft+f(r−fVG)] (7) Since, G(R(t))=d(t)R(t)a(t)(1
−R(t))b(t), and
GR=G[(a/R)−(b/(1−R))].
WhenGRis differentiated with respect to time, the following is achieved:
((GR/(t)(1/G)=[{(a/R)−(b/(1−R))}2
−(a/R2
)
+(b/(1−R)2
)]((R/(t)
+[{(a/R)−(b/(1−R))}
×{(1/d)((d/(t)+((a/(t)ln(R)
+((b/(t)ln(1−R)}]
+[((a/(t)(1/R)
−((b/(t)(1/(1−R)]. (8)
On substituting the value of ((GR/(t) in Eq. (7), I
get
h2((R/(t)
=[h1{(VGR−PrR)/PR}{r r+(ft/f)−f6G}]
−(1/d)((d/(t)h1+((a/(t)[−h1ln(R)−1/R]
+((b/(t)[{1/(1−R)}−h1ln(1−R)] (9)
whereh1={(a/R)−(b/(1−R))}. andh2=[h1
2
−(a/R2)
+(b/(1−R)2)].
Eq. (9) gives the rate of change of the optimal resource regime. The solution to two non-linear differential equations of motion (Eqs. (6) and (9)), subject to the initial conditions, which will pre-scribe the initial values of the two SEFs (aandb), the scaling factor (d), the state variable, and the transversality10 conditions, will give the unique optimal path of the state variable V(t) and the control variable R(t). However, as stated earlier, the main objective of this paper is not to find a unique path for given initial and transversality conditions, but rather to develop an understand-ing of the interactions between natural and social
systems, and their impact on the dynamic path of optimal forest regimes. Hence, I examine Eq. (9), and evaluate the role of natural and socio-eco-nomic factors in the dynamic path of optimal resource regimes.
In brief, Eq. (9) can be written as:
((R/(t)
=function (V,f,Pr,r,(d/(t,(a/(t,(b/(t). Hence, the change in the optimal resource regime will depend upon neither the natural factors, nor the social factors, but rather upon both of the factors as well as upon their interactions.11
As stated earlier, the resource regime (R) repre-sents the degree of exclusion of the local user group and varies from 0 to 1. Hence, a positive rate of change of resource regime means more exclusion or a shift towards a private regime, and a negative rate of change means a move towards less exclusion or a community regime. As per Eq. (9), four terms contribute to the rate of change of forest regimes. The first term comprises the state variable V(t), growth function (f), transaction function and transaction costs, and one term each represents the contribution of the rate of change of the scalar function, the heterogeneity of the
10Normally, the forest manager’s main tasks are to develop
a management plan for a fixed period or to find out an optimal rotation and develop a management plan for this rotation period. In the first case, the time horizon is fixed, and, normally, there is no limit on the terminal value of the state variable V(T). Hence, the terminal condition is that V(T) remains free. This terminal condition gives l(T)=0 as a transversality condition. The latter case of determining the optimal rotation is the free terminal-time problem, in whichT
is not specified in advance. In this case, the maximum principle includes the transversality condition that the Hamiltonian, at timeT, (H(T)), is equal to zero. Depending upon the objective of the forest manager, both of these two transversality condi-tions with initial boundary condicondi-tions can be used to deter-mine the unique optimal path of state and control variables.
11However, this result is an outcome of the non-separable
user group, and the dependence of the user group, respectively. The actual contribution of each term will depend upon the initial conditions, and the aggregate rate of change of the resource regime will depend upon the relative contribution of each term. However, an understanding of the main contributors of each term will provide a broad framework to policy makers and forest managers in designing and modifying forest regimes as per the requirements of change in natural and social systems. The impacts of natural and socio-eco-nomic factors on the rate of change of resource regime are discussed next.
3.4. Natural and socio-economic factors and the dynamics of optimal forest regimes
Natural factors influence the path of the opti-mal resource regime through marginal relative return (VGR−P
r R)/P
r
R} and relative growth (r+ (ft/f)−f6G). The marginal relative return is the
relative rate of change of net benefit to the cost of the resource regime due to a marginal change in the resource regime. Thus, if the change in the net benefit, due to a change in resource regime, is higher as compared to the resource regime cost, the rate of change of the resource regime will be higher. In neo-classical economic analysis, the contribution of this term will be independent of the socio-economic conditions of the user group. However, in my formulation, even the contribu-tion of this term will depend upon socio-economic factors because the value of the composite product (V) and the transaction cost (Pr) are sensitive to socio-economic factors. The compo-nents of the composite product may change with time depending upon the socio-economic condi-tions and preferences of the group. For example, in the early stages of economic development, the local people are dependent upon forests for their livelihood and V will include timber, as well as many non-timber forest products which may not have market value. With economic development, many non-timber forest products may not be valuable to the user group anymore, and hence will be excluded from V. Thus, when V includes many high value products, and its value is very high, the rate of change of the resource regime
will be highly sensitive to the values of V. As mentioned throughout this paper, the transaction cost is mainly dependent upon the two socio-eco-nomic factors. Hence, as user groups pass on to the next economic growth phase, the exclusion cost may be reduced due to a reduction in depen-dence, but co-ordination cost may increase due to an increase in heterogeneity. Thus, the overall impact of the relative marginal valuation term will depend upon the relative changes in Vand trans-action costs. If the change in value is higher than the change in transaction costs due to a marginal increase in exclusion, the resource regime should be modified towards more exclusion (private). If the change in values is less than the change in transaction cost due to marginal increase in exclu-sion, the resource regime should be modified to-wards less exclusion (community). In other words, in less developed and highly forest-dependent communities, smaller changes in the forest regime in opposing directions than that of economically expected may cause high economic and welfare losses. At the same time, larger marginal costs of the resource regime will logically lead to smaller changes in the resource regime. If there is high cost of change in the resource regime, it will not be optimal to change it. The relative growth term (r+(ft/f)−f6G) implies that the higher rate of
time preference and the higher rate of change of the growth function with respect to time will lead to a higher rate of change of the optimal resource regime, and the effect of the rate of growth func-tion with respect to time and volume are in oppo-site direction. Hence, fast growing forests (high (ft/f)) will require rapid changes in forest regimes as compared to slower growing forests. However, the growth function, f, represents the growth of
V. The terms, ft and f6 will depend upon the
and Daly, 1992), and thus, I subscribe to the view that the real rate of interest is not the correct measure of the rate of time preference for natural capital. Kant (1999) demonstrates that traditional forest-dependent communities normally have a lower rate of time preference for forest resources as compared to industrialised communities.12 Hence, the impact of the rate of time preference will also vary with the socio-economic environ-ment of the user group. The rate of change of the optimal forest regime will be lower in the case of traditional communities, who have a lower rate of time preference, as compared to economically de-veloped communities.
In addition to these impacts of socio-economic factors through interactions with natural factors, the socio-economic factors also independently contribute to the rate of change of optimal forest regimes. As the transaction function is defined in terms of heterogeneity and dependence, it is natu-ral that the optimal resource regime will vary with the variation in these two socio-economic factors. The change in optimal resource regime is directly proportional to the rate of change in heterogene-ity and dependence. However, the increase in heterogeneity will drive the optimal resource regime towards a private regime, while an increase in dependence will drive towards a community regime. The scaling factor (d), which normalises the achievable maximum value of the transaction function, and the maximum value can be different under different socio-economic environments. Therefore, the two socio-economic factors will also affect the optimal resource regime through the scaling factor. This analysis demonstrates that socio-economic factors are critical to the optimal-ity of the total production process of forest re-sources, and that non-inclusion of the socio-economic environment, and its interaction
with natural factors, will result in economic inefficiencies.
The continuous rate of change in the resource regime may be questionable from the practical aspects of designing forest regimes. It is under-stood that to make continuous changes in the resource regime is not feasible, and this is the main reason why a specific solution to the two motion equations has not been attempted in this paper. However, the broad outcome of the model — the optimal resource regime arrangements not remaining stationary and changing over time ac-cording to changes in socio-economic factors — is very critical for efficient forest management decisions, and can be used by forest managers to improve the efficiency of forest management. Forest managers should include SEFs in their set of management variables, and necessary amend-ments should be made to the resource regime either to increase or decrease the exclusion of local communities as and when required due to changes in socio-economic factors.
4. Final comments
The dynamic model of forest regimes has demonstrated that socio-economic factors are in-terrelated with natural and biological factors in affecting the value and growth of renewable re-sources like forests, and these factors together affect resource regimes and other institutional structures. Hence, socio-economic factors can and should be incorporated in economic and forest planning processes, and planning and policy deci-sions neglecting the interactions between the natu-ral system and the social system will be inefficient. The dependence of optimal forest regimes upon socio-economic factors also indicates that uniform solutions, as advocated either by supporters of privatisation or total government control, will not be optimal in all socio-economic environments, and local or community-based management will also provide an ‘efficient’ management regime in many socio-economic environments of developing economies. The realisation of the sensitivity of optimal forest regimes to the socio-economic envi-ronment also demands the decentralisation of 12Kant (1999) demonstrates that the common
forest planning and management decisions. The decentralisation will help local forest managers in designing and modifying forest resource regimes according to local socio-economic environments and natural factors of the local forests. The non-inclusion of SEFs will lead to slow de-facto con-version of exclusionary regimes, such as state and private regimes, to open access regimes and confl-ict between local communities and forest man-agers. Such processes will not only be detrimental to efficiency and sustainability, but would also be responsible for a high rate of deforestation and resource degradation.
The analysis also indicates that the choice of forest managers is not limited to three discrete resource regimes. Hence the amendment in the existing resource regime does not mean change from community control to state control or na-tionalisation to privatisation. Once an optimal resource regime, according to the local socio-eco-nomic and natural factors, is implemented, it will require only marginal adjustments in resource regime arrangement to match the changes in so-cio-economic and natural factors. These adjust-ments will be in the terms of degree of exclusion of communities and hence the role of communi-ties and the state in forest management. For example, if certain communities start losing its control over community-based forest management practices due to increased heterogeneity and re-duced dependence on forests, forest managers should help in designing forest regimes based on greater role of state and a smaller role of communities.
Finally, the two necessary conditions for effi-cient forest use are: firstly, choosing an appropri-ate technology, and secondly, choosing an appropriate forest regime. Choosing an appropri-ate resource regime is critical to under-developed and developing economies. The economies of these countries need strategies that will lead to over-achievement if they are to catch up with the developed world. Hence, they require policies which build upon intangible sources of growth. The choice of an appropriate resource regime is one such source. In the early stages of economic growth, natural resources play a very prominent role in economic growth. Hence, an
understand-ing of optimal resource regimes, their linkages with socio-economic factors, and the dynamics of these optimal regimes and SEFs, can play a criti-cal role in economic growth of developing economies.
Acknowledgements
I would like to thank Albert Berry, G. Helleiner, Jagdish Nautiyal, D. Nowlan, D. Put-tock, and three reviewers for their insightful and useful comments. The manner in which their com-ments have been interpreted is entirely my respon-sibility. I would like to express my special thanks to one of the reviewers who provided deep in-sights about the paper’s implications. Research Funds from the Social Sciences and Humanities Research Council of Canada (Grant No. 410990343) and the Natural Sciences and Engi-neering Council of Canada (Grant No. 203032-98 RGPIN) are also greatly acknowledged.
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