A dynamic approach to forest regimes in developing economies

Ecological Economics 32 (2000) 287–300

ANALYSIS

A dynamic approach to forest regimes in developingeconomies

Shashi Kant *Faculty of Forestry, Uni6ersity of Toronto, 33 Willcocks Street, Toronto, Ont., Canada M5S 3B3

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 theuser groups. And, since socio-economic factors will change with time, optimal forest regimes will also follow adynamic path. The two most important socio-economic factors are the heterogeneity of the user group with respectto forest management and the direct dependence of the user group on forest. Normally, the heterogeneity will increaseand dependence will decrease with economic growth of user group. An optimal control model is used to integrate thedynamics of natural system such as joint product of forests and its growth function, and the dynamics of the twosocio-economic factors — heterogeneity and dependence. The model demonstrates that the dynamics of optimalforest regimes will depend upon the change in natural factors, socio-economic factors, and on the interactionsbetween natural and socio-economic factors. Hence, optimal forest management strategies would require a continuousrefinement in forest management regimes, instead of static state regimes, as local communities in developingeconomies 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. Atechnological perspective has dominated economicdiscussions during the industrialisation era. How-ever, in the past decade the resource regime aspectof the institutional perspective has emergedstrongly. As a result, the conventional view of thesuperiority of private or state regimes over com-

munity regimes has been challenged by a richbody of empirical evidence from around theworld.1 This evidence points to the successfulmanagement of a wide variety of natural re-sources, including forests, as common or commu-nal property. Game theoretic models have also

1 These 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: [email protected] (S. Kant)

0921-8009/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S 0921 -8009 (99 )00100 -7

S. Kant / Ecological Economics 32 (2000) 287–300288

been developed to explain the observed frequencyof collective action in natural resource manage-ment (Runge, 1986; Ostrom et al., 1994; Balandand Platteau, 1996; Sethi and Somanathan, 1996).A large number of resource economists2 haveattempted a comparison of different resourceregimes while treating the system of ‘resourceregime’ as a fixed input. Randall (1987, p. 159)argues that any one of the possible specificationsof non-attenuated rights would lead to Paretoefficiency, but that the efficient solution would bedifferent for each specification of rights. Thus, helimited himself to a consideration of the locallyoptimal outcome. Dahlman (1980, p. 138) arguesthe need to identify the exact relationship betweenproduction technology versus transaction costs.Cheung (1987) emphasises the importance of iden-tifying transaction costs and their determinants.Thus, though the importance of the relationshipbetween 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 ofnatural resources that are used to identify the mostefficient regime using the full set of options, rang-ing from open access to private regime. An ade-quate production model — one which can identifya global maximum — must treat both physicalinputs and resource regime as variables, andshould account for variation in transaction costs.

Kant (1996) and Kant et al. (1999) argue thatthe optimal regime for a given resource dependsnot only on the physical production (transforma-tion) efficiency with which the physical inputs areconverted to physical outputs but also on the levelof transaction costs (transaction efficiency).Hence, an adequate theory of forest resource useshould incorporate the role of institutional struc-tures associated with different forest regimes andtheir associated transaction costs. The transactioncost 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 authorsidentified and defined the two SEFs, the usergroup’s heterogeneity with respect to forestmanagement3 and the degree of direct dependenceof the user group on forests.4 They argue that

3 User group heterogeneity with respect to forest manage-ment: Members of the user group will often have somewhatdifferent preferences regarding resource management, or as-sign different priorities to the various objectives of resourcemanagement, either because of differing personal interests inthe resource or differing degrees of involvement in the socialgroup. 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 andonly afterwards as independent individuals, an inherent spiritof co-operation is generally present even in the face of largeeconomic differences and social stratification. This spirit ismuted in modern industrial societies, where people are firstand foremost ‘individuals’ and more truly homo-economicus.The heterogeneity of individual interests with respect to how aresource is managed reflects both economic differences (e.g.income level) and social and cultural traditions or norms; theextent to which ‘personal’ interest fully determines an individ-ual’s behaviour with respect to the resource depends on thedegree of ‘community spirit’, hence, the level of heterogeneity(allowed to range between 0 and 1) will vary inversely with thedegree of such ‘community spirit’ as well as with respect toeconomic differences. A hierarchy of the levels of heterogene-ity provides linkages between cultural, social and economicdifferences and resource management. The basic level consistsof cultural, economic, ethical and social differences. Due tothis basic heterogeneity, the members of the user group mayhave diverse preferences for timber and non-timber productsand hence prefer different product mixes, and this could betermed second level heterogeneity. Diverse product preferenceswill result in different preferences for resource managementregimes, which can be labelled third level heterogeneity. Insummary, heterogeneity with respect to resource regime can betreated 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 heterogeneitywith respect to resource management is the inverse of fullagreement on, and support for, the same resource managementregime. (Kant, 1996; Kant et al., 1999).

4 The degree of direct dependence of user groups on forests:Everyone depends on forests in some way. Forests providemany values such as consumption, recreation, environmental,and spiritual. In developing economies, some tribal groupsdepend on forests, located close to their habitations, for theirconsumption items such as food, fuel, medicines, and evenmonetary income (from the sale of minor forest products) thatare necessary for their subsistence. These groups have a one

2 Including Krutilla and Fisher, 1975, pp. 19–38; Scott andJohnson, 1985; Bromley and Szarleta, 1986; Fortmann andJohn, 1988; Magrath, 1989; Pearse, 1990, pp. 173–93; Brom-ley, 1991; Luckert, 1992.

S. Kant / Ecological Economics 32 (2000) 287–300 289

these two SEFs will be the main determinants ofthe transaction costs, the heterogeneity of theco-ordination cost and the direct dependence ofthe exclusion cost, of forest management in devel-oping economies, and suggested a mathematicalformulation of the transaction function.5 Based

on the static analysis of the full production pro-cess, comprised of transformation and transactionfunctions, they found that for only a very smallrange of SEF values, particularly when the depen-dence of the user group on the resource is verylow and heterogeneity very high, will one of aprivate or a state regime be optimal. In contrast,for a rather wide range of SEFs, some form ofjoint regime between state and community will beoptimal.6 Baland and Platteau (1996) similarlyargue that in selecting a form of resource regula-tion, a government is not confined to the spuriousand simplistic ‘state versus community’ di-chotomy, but can choose among a rather widerange of intermediate options, which will be moreor less effective depending on the strength of thecollective action of basic user groups.

(group) to one (forest) direct dependence on the forest. Indeveloped economies, most user groups depend on forests forderived items such as pulp and furniture, and these items maybe available from any forest area. The derived items from oneforest area may be available to many user groups, or one usergroup may get derived items from different forests. Thesegroups also depend on forests for recreational values, but theyagain derive these values from different forest areas. Hence, inthis 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-dependencerelationship with the forest. Similarly in developing economies,some groups may also have a one to many or many to oneindirect-dependence relationship with the forests. Here, myinterest is in the degree of the one to one direct dependence ofthe user group.

The degree of direct dependence is defined as the share ofdirect returns from forests in the total utility bundle. Its rangeis also defined as 0 to 1, and may be reasonably measured bythe fraction of the user group’s gross local production con-tributed by the forest. The degree of direct dependence willdepend 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 capacity of the usergroup will depend on the composition of the utility bundle. Inthe case of the utility bundle being comprised of forest returnsonly, there is no possibility of substitution and hence, thedegree of direct dependence will be very high and equal to one.The case of subsistence dependence of tribal communities willfall in this category because there are substitutes, but the usergroup is unable to acquire the substitutes because of theirlimited monetary income. In some cases, utility bundle mayconsist of returns from different sources including monetaryincome, but there may not be any substitute for forest returnssuch as spiritual values. In such cases, the degree of depen-dence will depend upon the share of spiritual values in theutility bundle. However, the share of spiritual values may notbe quantified in monetary terms, but its share in the utilitybundle can be determined by Participatory Rural Appraisalmethods (Kant, 1996; Kant et al., 1999).

5 A resource regime typically has several economically im-portant dimensions — comprehensiveness, exclusiveness,benefits conferred etc. each of which may vary across aspectrum. However, in the case of developing economies, themost important dimension is exclusiveness, and hence thefocus is on this dimension only. Thus R is the continuousresource regime variable representing different level of exclu-

siveness, scaled for simplicity between 0 to 1 (but excluding theend points). On this scale, open access (no exclusion) isrepresented by a number near zero, and a private regime,which means full exclusion, by a number close to 1. Given theway the two costs — exclusion cost and co-ordination cost —are linked to forest regime, the most plausible simple assump-tion is that the transaction function is either monotonicallyincreasing, monotonically decreasing, or has a single maxi-mum value somewhere in the domain ranging from openaccess to private regime. Such a transaction function G(R) canbe expressed by the mathematical form:

G(R)=dRa(1−R)b

The parameter a is the heterogeneity of the user group withrespect to forest management, and b the degree of directdependence on forests. d is a scaling factor that normalises themaximum value of the transaction function. Readers interestedin more details of this function can refer to Kant, 1996; Kantet al., 1999.

6 As mentioned in footnote 5 on the exclusion dimension,the resource regime varies from open access to private regime.In operational aspects, in the case of open access, there are norestrictions on the use of any output from forests. Under thecommunity regime, the user group is entitled to all the prod-ucts, but use is typically regulated in terms of harvesting timeand quantities to be harvested during a particular time. In thecase of a joint regime (between the state and community) inIndia, the user group and the state both get a share of timberproducts and of nationalized non-timber products, while non-nationalized non-timber products go to the user group. Undera state regime, the local community is totally excluded fromtimber and nationalized non-timber products, but not from theactual use of non-nationalized non-timber forest products.Under a private regime, the user group is excluded from allproducts.


Hence, the static analysis of the total produc-tion process of forests provides useful insightsinto the relationship between the socio-economicenvironment of the user groups and the globallyoptimal 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 anevolutionary nature. Even though evolutionaryeconomics have been gaining importance in thelast decade, the evolutionary nature of resource,forest, regimes has been unable to attract theattention of either economists or forest managers.Evolutionary theories have been used to explainsocial conventions and norms (Axelord, 1986;Sudgen, 1986, 1989), law (Posner, 1980), propertyrights (Schotter, 1981; Barzel, 1989; Libecap,1989; North, 1990), and various forms of socialand economic organisations (Williamson, 1975;Nelson and Winter, 1982; Williamson, 1985).Bromley (1989) called these writings the ‘propertyright school’ of institutional change, and sum-marised other contemporary writings in two cate-gories: the ‘induced institutional innovationapproach’ associated with Hans Binswanger, Ver-non Ruttan, and Yujiro Hayami, and the ‘NorthTheory’. The property rights school is based ontransaction costs, the induced institutional inno-vation approach is based on the supply and de-mand theory of institutional innovations. Northstarted with relative prices being a major sourceof institutional change (North and Thomas,1973), and brought in many other factors such astechnology, information, institutional inertia, andpath dependence as sources of institutionalchange in his writings (North, 1990). However, allof these writings have been focused on explainingthe existence of different institutions or explainingthe institutional changes that have already oc-curred. Hence, these evolutionary approacheshave been criticised for their limitations in sug-gesting policy measures for correcting the existinginefficiencies in institutional arrangements.

Another stream of economists, now known asecological economists, make strong arguments tomove away from implicit assumptions of neo-clas-sical economic analysis which eliminate the linksbetween natural and socio-economic systems be-

cause, due to the strength of the real-word inter-actions among these components, failure to linkthem can cause severe misperceptions and policyfailures (Costanza and Daly, 1987; Norgaard,1989).

In the case of forest resources, local communi-ties in developing economies during pre-colonialperiods were engaged in management practicesbased on their specific socio-economic environ-ment (Castro, 1995; Kant and Berry, 1999). Thecolonial administration undermined communalbonds, traditional authority, and indigenous man-agement systems, leading to the decline of com-munal controls that has been termed as thetragedy of invasions (Brightman, 1987). The gov-ernments of independent countries continued thesame exclusionary state regimes, mainly due topast practices and prescriptions from neo-classicaleconomic analysts and policy makers that arebased on the segregation of natural and socio-eco-nomic systems. In many cases, these state regimeshave become de-facto open access regimes, andare one of the main factors in global deforestationand forest degradation (Kant and Redantz, 1997).Hence, the challenge to resource economists andforest managers is to integrate the socio-economiccontext with the natural system, and to designand refine the forest regime arrangements as thesocio-economic context of the user group changes.

This paper is focused on dual objectives: tointegrate the dynamics of natural and social sys-tems, and to develop an evolutionary approach offorest regimes that can provide useful policy mea-sures to design and refine optimal forest regimeswithin varying socio-economic environments.Hence, the dynamic nature of the two socio-eco-nomic factors that are the pillars of our optimalforest regime theory are first discussed. Second,using the optimal control theory, the linkagesbetween natural factors, such as the compositeproduct of a forest and its growth function, andthe two SEFs are established in the context of thedynamics of an optimal forest regime. Next, theimpact of natural and socio-economic factors onthe dynamics of optimal regimes is discussed.Finally, some suggestions for designing optimalforest regimes in developing economies arepresented.


2. The dynamic nature of socio-economic factors

Communities are dynamic and their SEFschange with time. In the present era, as communi-ties pass through different phases of economicdevelopment, the two SEFs — heterogeneity anddependence — change. The nature of thesechanges 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 andcustom, are the features of many developingeconomies. Hence, these economies have cultural,social, and economic heterogeneity at the macro-level but a high degree of homogeneity at themicro or community level. Other features of theseeconomies are the pooling of family resources tohedge economic uncertainties, the system of self-help to hedge other hazards and difficulties of life,and non-integration with market and marketeconomies. The process of economic growth at-tempts to bring these economies within the fron-tiers of market. However, market arrangementsreduce 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 andthe dissolution of ethnic bonds and customs(Seeland, 1991). In the early stages of growth, thecommunity moves from an agricultural to anindustrial foundation, and machines and non-hu-man factors take the role of nature and humanfactors 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 forurban areas without their immediate family mem-bers, resulting in a disruption of existing socialrelationships and a decline in the quality of per-sonal existence. Hence, these new processes ofeconomic growth lead to social and cultural het-erogeneity. In addition, the initial stages of urban-isation and industrialisation may also intensifyawareness 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 farminginitiatives, tend to benefit the larger, more pro-gressive farmers disproportionately in both abso-lute and relative terms, and hence tend to increaseincome inequalities (Adelman and Morris, 1973,p. 18). Similarly, dualism, seen in the joint exis-tence of traditional sectors and rapidly growingexchange sectors, is accompanied by inter-sectordifferences in factor productivity and per capitaincome (Adelman and Morris, 1973, p. 20). Theavailability of new resources such as a physicalinfrastructure, opportunities for income genera-tion and socially-sanctioned access to valued jobsand administrative positions, creates conflicts ofinterest among various groups, and thus leads tosocial stratification. The new employment oppor-tunities created through the development processrequire specialised knowledge that is not equallydistributed, and hence gives rise to social as wellas economic heterogeneity. Thus, normally,within the development process first level hetero-geneity will increase. However, the rate of changeof heterogeneity will depend upon the rate ofeconomic growth of the community and the inter-nal inertia of the community against this change.Forest product preferences are dependent on theeconomic as well as the social and cultural condi-tions of a community. As communities passthrough different stages of economic growth,product preferences of people move from unpro-cessed raw products, such as non-timber forestproducts, fuelwood, and poles for house construc-tion, to quality products such as furniture andpaper products, and finally to outdoor recreationand environmental values. Hence, even in smalltraditional communities, differential impacts ofeconomic growth will increase product preferenceheterogeneity.

Forest management practices vary from tradi-tional management based on the concepts of sub-sistence, respect for nature, minimal timberharvesting, and intensive labour, to modern west-ern forest management practices that are based onprofit maximisation and modern technology, andare export-oriented and capital intensive. The in-tensity of these variables of forest managementpractices varies across communities that are under


different phases of economic growth. Hence, di-verse forest product preferences and preferencefor different management practices by the peoplein different economic groups will increase thediversity of forest management practices. Nor-mally, third level homogeneity of resource man-agement will depend upon the first and secondlevels of homogeneity. However, the third level ofhomogeneity may sometimes be imposed upon byexternal factors such as mutual dependencies oversocial, economic, or cultural heterogeneousgroups. But, these are exceptions to general rules,and are not of direct concern to the presentdiscussion.

2.2. Dynamic nature of the direct dependence onforests

Economists have discussed the role of naturalresources in different stages of economic develop-ment. Rostow (1956) attributed the critical role ofnatural resources in the first and third stage ofdevelopment. In the first stage (traditional soci-eties), natural resources offer a quick yield ofincreased productivity to new techniques and per-mit the application of innovations. In the takeoff(third) stage, foreign trade of natural resourcescontributes 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 greaterin poor countries than in rich countries. The shareof natural resources declines with economicgrowth due to improvements in the efficiency ofresource use, substitution of natural resources byman-made resources, and the service sector takinga leading role over the manufacturing sector.Adler (1961) argued that in the earliest stages oforganised society — ‘collectional’ economy ofhunters and ‘pre-cultural’ nomads — economicactivity was entirely dependent upon natural re-sources, and in each subsequent stage, dependenceupon the resource-base of a particular locationdiminishes. A rise in the national or per capitaincome, an increased share of industrial produc-tion in GDP, urbanisation, a higher rate of liter-acy, increased nutritional awareness, and animproved information media are associated with

economic growth. The change in individual in-come transforms the composition of the utilitybundle, and increased and diversified industrialproduction enhances the range of the substituteproduct. An inclusion of monetary income in theutility bundle of traditional, resource-dependentcommunities 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 productswith desired nutritional values, and an improvedinformation media will extend the knowledge ofsubstitute products. Urbanisation reduces the di-rect pressure of local populations on forests.Hence, economic growth will lead to a reductionin the direct dependence of such communities onforests. However, higher per capita consumption,including the consumption of pulp and paper andother wood products, and increased environmen-tal awareness and recreational values are associ-ated with economic growth. But these associatedphenomena will increase the one-to-many ormany-to-one indirect-dependence on forests, andnot the direct one-to-one dependence. Assumingthat economic growth is a continuous process, thedirect dependence of a forest-dependent commu-nity will decrease continuously. However, this rateof decrease may not be the same for all communi-ties in a country. The rate of decrease will dependon the rate of economic growth. However, eco-nomic growth may not have a direct relationshipin some special cases such as a community’s de-pendence upon spiritual values. But, indirectly,the economic growth may reduce the spiritualvalues, and hence, may subsequently also decreasethe direct dependence.

Thus, the two SEFs, the heterogeneity of com-munity and the direct dependence upon forests,will change over time; and their rates of changewill depend upon the rate of the economic growthprocess, as well as some social and cultural at-tributes of communities. Hence, one of the maintasks of forest managers in developing economiesis to design forest regimes in such a way that theyremain optimal with respect to the evolving socio-economic environment. In the next section, thedynamic nature of these two SEFs is incorporatedinto a model that helps to explain the dynamicnature of optimal forest regimes.


3. Optimal control model of dynamics of forestregimes

Many authors have used optimal control theoryfor 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 atraditional production function, which includesonly the transformation function. The concept ofthe transaction function, and hence, resourceregime, is missing from these models. An optimalcontrol model of the full forest production pro-cess, which is described by the non-separable7

(across time) transformation and transactionfunctions, is developed in this section, and thedynamic path of optimal resource regime for agiven forest and user group environment isexamined.

I assume, for simplicity and clarity of analysis,a composite forest product which comprises alltimber and non-timber products, with a net valueper unit area, at time t, of V(t). The timber isremoved on a rotation period, whereas NTFPsare removed continuously. Hence, V(t) representsthe sum of the net value of standing timber attime t and the net value of all NTFPs removedand available to be removed up until time t. AsV(t) is the net value, all costs, such as regenera-tion, harvesting and land rent, except the cost of aresource regime (the transaction cost), are ac-counted for in this formulation of V(t). The costof the resource regime Pr(R) will be treated sepa-rately. It is also assumed that there are only two

production factors: time8 and the resource regime.It is further assumed that, in the absence of theeffect of the resource regime, the rate of change ofvalue is represented by the logistic function: (dV/dt)=mV [1− (V/Va)]= f(V(t)), where m is thepositive 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 transactionand transformation functions, resource regime ar-rangements (the transaction function) will affectthe growth rate of forests as well as the net valueof the composite product available to the legalright holder. As per the definition of the transac-tion function, the net value available to the legalright holder will be the product of the natural netvalue V(t) times the transaction functionG(R(t), t). It is also assumed that the effectivegrowth rate9 will also be the product of the natu-ral growth rate times the transaction function. Inthis context, policy makers or forest managers willlikely design and modify forest regimes in such away that the legal right holder can maximise thenet returns from forests. Hence, the policy makeror 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, inwhich V(t) is the state variable, and R(t), which isbounded within 0+ and 1−, is the control vari-

7 Renewable resources such as forests grow and regenerateover economically relevant periods of time. The growth ofthese resources depends upon the existing growing stock,which is clearly affected by resource regime arrangements.Hence, the transformation and transaction functions worksimultaneously, or are non-separable. Non-renewable re-sources are formed by geological processes that typically takemillions of years, thus for practical purposes, these can betreated as having a fixed stock. In such cases, transformationand transaction functions can be treated as separable. How-ever, even in the case of non-renewable resources, the quantityretrievable for use is related to the transformation process.Hence, in the broader perspective of the transformation pro-cess, the transaction and transformation functions will benon-separable even in the case of a non-renewable resource.

8 In the case of forest resources, the period of production islengthy, and ‘time’ itself acts as a factor of production (Nau-tiyal, 1988, p. 335). Hence, it is common practice to haveforest production models in terms of time.

9 The natural growth rate means the growth rate attainableby the forest in the complete absence of any interference. But,as formulated, the resource regime arrangement may alter thetotal existing volume (growing stock) which will also alter thegrowth rate, resulting in the effective growth rate instead ofnatural growth rate.


able. This optimal control problem can besolved by a standard method. The current valueHamiltonian of this optimal control problemcan 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 statevariable V(t), and is also known as the shadowprice of the state variable. In the case of thecurrent value Hamiltonian, l(t) gives the currentmarginal value of the state variable at time t. Ialso assumed that the objective function and thefunction which is describing the law of motionof the state variable ( f(V(t))G(R(t)) are con-cave, hence the necessary first order conditionsof the optimal control problem will also be thesufficient 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 todenote the partial derivative with respect to avariable given in subscript. Hence, Eq. (2) gives:

l= (PrR−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-statevariable. The equation can be written as:

((l/(t)(1/l)+ fVG+G/l=r. (4a)

Eq. (3) gives the shadow price of the state vari-able, and is equal to the marginal net value perunit of available growth due to marginal changein 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), thesecond term gives the value available from thegrowth of the state variable, and the third term

gives the relative available value from one unitof the state variable with respect to the shadowprice. The right hand side gives the psychic costdue to time preference. A common understand-ing of the nature of forest growth ( f6 beingquite high in the early and middle stages of aforest, 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 optimalpath. However, even though the value is mar-ginally decreasing, the forest is not cut becausethe value of available growth is greater than thevalue obtained by cutting the forest (Donnellyand 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)= [(PrR−VGR)/lGR ]G (6)

The co-state variable equation (Eq. (4)) and thelaw of motion equation (Eq. (6)) give the mo-tion of the co-state and state variables, respec-tively. The standard practice is to study thepaths of the state variable and co-state variableor the path of the state variable and controlvariable. Hence, one option is to analyse theoptimal path of the state and co-state variables.However, even though these two first order dif-ferential equations (Eqs. (4) and (6)) are au-tonomous (time does not appear explicitly), bothequations contain the control variable (R(t)) insome form. Hence, the analysis of the motion ofthe state and co-state variables, with the help ofa phase diagram of these two equations in thepresent form, is not feasible. In addition, themain aim of this paper is to integrate naturaland social systems, and to study the impact ofthese systems on the evolution of optimal re-source regimes. Hence, I focus upon developingan equation of the dynamics of an optimal re-source regime that can aid in evaluating the im-pact of the dynamics of natural and socialfactors upon the dynamics of forest regimes.


On differentiating Eq. (3) with respect to t, andsubstituting the value of l, and ((l/(t) in Eq. (4)and further substituting the value of ((V/(t) fromEq. (5), the following is achieved:

−PrR f((GR/(t)

= (PrR−VGR)GR [ ft+ f(r− fVG)] (7)

Since, G(R(t))=d(t)R(t)a(t)(1−R(t))b(t), andGR=G [(a/R)− (b/(1−R))].

When GR is 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), Iget

h2((R/(t)

= [h1{(VGR−PrR)/Pr

R}{r+ ( ft/f )− f6G}]

− (1/d)((d/(t)h1+ ((a/(t)[−h1 ln(R)−1/R ]

+ ((b/(t)[{1/(1−R)}−h1 ln(1−R)] (9)

where h1={(a/R)− (b/(1−R))}.

and h2= [h12− (a/R2)+ (b/(1−R)2)].

Eq. (9) gives the rate of change of the optimalresource regime. The solution to two non-lineardifferential equations of motion (Eqs. (6) and (9)),subject to the initial conditions, which will pre-scribe the initial values of the two SEFs (a and b),the scaling factor (d), the state variable, and thetransversality10 conditions, will give the uniqueoptimal path of the state variable V(t) and thecontrol variable R(t). However, as stated earlier,the main objective of this paper is not to find aunique path for given initial and transversalityconditions, but rather to develop an understand-ing of the interactions between natural and social

systems, and their impact on the dynamic path ofoptimal forest regimes. Hence, I examine Eq. (9),and evaluate the role of natural and socio-eco-nomic factors in the dynamic path of optimalresource 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 regimewill depend upon neither the natural factors, northe social factors, but rather upon both of thefactors as well as upon their interactions.11

As stated earlier, the resource regime (R) repre-sents the degree of exclusion of the local usergroup and varies from 0 to 1. Hence, a positiverate of change of resource regime means moreexclusion or a shift towards a private regime, anda negative rate of change means a move towardsless exclusion or a community regime. As per Eq.(9), four terms contribute to the rate of change offorest regimes. The first term comprises the statevariable V(t), growth function ( f ), transactionfunction and transaction costs, and one term eachrepresents the contribution of the rate of changeof the scalar function, the heterogeneity of the

10 Normally, the forest manager’s main tasks are to developa management plan for a fixed period or to find out anoptimal rotation and develop a management plan for thisrotation period. In the first case, the time horizon is fixed, and,normally, there is no limit on the terminal value of the statevariable V(T). Hence, the terminal condition is that V(T)remains free. This terminal condition gives l(T)=0 as atransversality condition. The latter case of determining theoptimal rotation is the free terminal-time problem, in which Tis not specified in advance. In this case, the maximum principleincludes the transversality condition that the Hamiltonian, attime T, (H(T)), is equal to zero. Depending upon the objectiveof the forest manager, both of these two transversality condi-tions with initial boundary conditions can be used to deter-mine the unique optimal path of state and control variables.

11 However, this result is an outcome of the non-separablenature of the transaction and transformation functions which,I believe, represents the real growth process of renewableresources such as forests. In the case of separable transactionand transformation functions, the change in optimal resourceregime will be independent of natural factors and dependentupon the socio-economic factors only.


user group, and the dependence of the user group,respectively. The actual contribution of each termwill depend upon the initial conditions, and theaggregate rate of change of the resource regimewill depend upon the relative contribution of eachterm. However, an understanding of the maincontributors of each term will provide a broadframework to policy makers and forest managersin designing and modifying forest regimes as perthe requirements of change in natural and socialsystems. The impacts of natural and socio-eco-nomic factors on the rate of change of resourceregime are discussed next.

3.4. Natural and socio-economic factors and thedynamics of optimal forest regimes

Natural factors influence the path of the opti-mal resource regime through marginal relativereturn (VGR−Pr

R)/PrR} and relative growth (r+

( ft/f )− f6G). The marginal relative return is therelative rate of change of net benefit to the cost ofthe resource regime due to a marginal change inthe resource regime. Thus, if the change in the netbenefit, due to a change in resource regime, ishigher as compared to the resource regime cost,the rate of change of the resource regime will behigher. In neo-classical economic analysis, thecontribution of this term will be independent ofthe socio-economic conditions of the user group.However, in my formulation, even the contribu-tion of this term will depend upon socio-economicfactors because the value of the compositeproduct (V) and the transaction cost (Pr) aresensitive to socio-economic factors. The compo-nents of the composite product may change withtime depending upon the socio-economic condi-tions and preferences of the group. For example,in the early stages of economic development, thelocal people are dependent upon forests for theirlivelihood and V will include timber, as well asmany non-timber forest products which may nothave market value. With economic development,many non-timber forest products may not bevaluable to the user group anymore, and hencewill be excluded from V. Thus, when V includesmany high value products, and its value is veryhigh, the rate of change of the resource regime

will be highly sensitive to the values of V. Asmentioned throughout this paper, the transactioncost is mainly dependent upon the two socio-eco-nomic factors. Hence, as user groups pass on tothe next economic growth phase, the exclusioncost may be reduced due to a reduction in depen-dence, but co-ordination cost may increase due toan increase in heterogeneity. Thus, the overallimpact of the relative marginal valuation term willdepend upon the relative changes in V and trans-action costs. If the change in value is higher thanthe change in transaction costs due to a marginalincrease in exclusion, the resource regime shouldbe modified towards more exclusion (private). Ifthe change in values is less than the change intransaction 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-dependentcommunities, smaller changes in the forest regimein opposing directions than that of economicallyexpected may cause high economic and welfarelosses. At the same time, larger marginal costs ofthe resource regime will logically lead to smallerchanges in the resource regime. If there is highcost of change in the resource regime, it will notbe optimal to change it. The relative growth term(r+ ( ft/f )− f6G) implies that the higher rate oftime preference and the higher rate of change ofthe growth function with respect to time will leadto a higher rate of change of the optimal resourceregime, 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 regimesas compared to slower growing forests. However,the growth function, f, represents the growth ofV. The terms, ft and f6 will depend upon thecomposition of V, and hence upon the socio-eco-nomic factors of the user group. The dynamics ofthe rate of time preference, and hence its impactupon the dynamics of optimal forest regimes, is acontroversial issue. Strict neo-classical economistsare unwilling to deviate from equating the rate oftime preference to the real market rate of returnon man-made capital investments. Ecologicaleconomists are of the view that man-made capitaland natural capital are not substitutes (Costanza


and Daly, 1992), and thus, I subscribe to the viewthat the real rate of interest is not the correctmeasure of the rate of time preference for naturalcapital. Kant (1999) demonstrates that traditionalforest-dependent communities normally have alower rate of time preference for forest resourcesas compared to industrialised communities.12

Hence, the impact of the rate of time preferencewill also vary with the socio-economic environ-ment of the user group. The rate of change of theoptimal forest regime will be lower in the case oftraditional communities, who have a lower rate oftime preference, as compared to economically de-veloped communities.

In addition to these impacts of socio-economicfactors through interactions with natural factors,the socio-economic factors also independentlycontribute to the rate of change of optimal forestregimes. As the transaction function is defined interms of heterogeneity and dependence, it is natu-ral that the optimal resource regime will vary withthe variation in these two socio-economic factors.The change in optimal resource regime is directlyproportional to the rate of change in heterogene-ity and dependence. However, the increase inheterogeneity will drive the optimal resourceregime towards a private regime, while an increasein dependence will drive towards a communityregime. The scaling factor (d), which normalisesthe achievable maximum value of the transactionfunction, and the maximum value can be differentunder different socio-economic environments.Therefore, the two socio-economic factors willalso affect the optimal resource regime throughthe scaling factor. This analysis demonstrates thatsocio-economic factors are critical to the optimal-ity of the total production process of forest re-sources, and that non-inclusion of thesocio-economic environment, and its interaction

with natural factors, will result in economicinefficiencies.

The continuous rate of change in the resourceregime may be questionable from the practicalaspects of designing forest regimes. It is under-stood that to make continuous changes in theresource regime is not feasible, and this is themain reason why a specific solution to the twomotion equations has not been attempted in thispaper. However, the broad outcome of the model— the optimal resource regime arrangements notremaining stationary and changing over time ac-cording to changes in socio-economic factors —is very critical for efficient forest managementdecisions, and can be used by forest managers toimprove the efficiency of forest management.Forest managers should include SEFs in their setof management variables, and necessary amend-ments should be made to the resource regimeeither to increase or decrease the exclusion oflocal communities as and when required due tochanges in socio-economic factors.

4. Final comments

The dynamic model of forest regimes hasdemonstrated that socio-economic factors are in-terrelated with natural and biological factors inaffecting the value and growth of renewable re-sources like forests, and these factors togetheraffect resource regimes and other institutionalstructures. Hence, socio-economic factors can andshould be incorporated in economic and forestplanning 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 uponsocio-economic factors also indicates that uniformsolutions, as advocated either by supporters ofprivatisation or total government control, will notbe optimal in all socio-economic environments,and local or community-based management willalso provide an ‘efficient’ management regime inmany socio-economic environments of developingeconomies. The realisation of the sensitivity ofoptimal forest regimes to the socio-economic envi-ronment also demands the decentralisation of

12 Kant (1999) demonstrates that the common understand-ing of neo-classical economists that poor people have a highrate of time preference does not withstand the contextual testof forest use by traditional communities. An examination ofthe nature of forest returns and their role in economic andother necessities, specific risk attributes of forest returns, andpersonal factors in the context of forest use indicates a lowerrate of time preference for forest returns among traditionalcommunities compared to that of industrialized communities.


forest planning and management decisions. Thedecentralisation will help local forest managers indesigning and modifying forest resource regimesaccording to local socio-economic environmentsand 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 andprivate regimes, to open access regimes and confl-ict between local communities and forest man-agers. Such processes will not only be detrimentalto efficiency and sustainability, but would also beresponsible for a high rate of deforestation andresource degradation.

The analysis also indicates that the choice offorest managers is not limited to three discreteresource regimes. Hence the amendment in theexisting resource regime does not mean changefrom community control to state control or na-tionalisation to privatisation. Once an optimalresource regime, according to the local socio-eco-nomic and natural factors, is implemented, it willrequire only marginal adjustments in resourceregime arrangement to match the changes in so-cio-economic and natural factors. These adjust-ments will be in the terms of degree of exclusionof communities and hence the role of communi-ties and the state in forest management. Forexample, if certain communities start losing itscontrol over community-based forest managementpractices due to increased heterogeneity and re-duced dependence on forests, forest managersshould help in designing forest regimes based ongreater role of state and a smaller role ofcommunities.

Finally, the two necessary conditions for effi-cient forest use are: firstly, choosing an appropri-ate technology, and secondly, choosing anappropriate forest regime. Choosing an appropri-ate resource regime is critical to under-developedand developing economies. The economies ofthese countries need strategies that will lead toover-achievement if they are to catch up with thedeveloped world. Hence, they require policieswhich build upon intangible sources of growth.The choice of an appropriate resource regime isone such source. In the early stages of economicgrowth, natural resources play a very prominentrole in economic growth. Hence, an understand-

ing of optimal resource regimes, their linkageswith socio-economic factors, and the dynamics ofthese optimal regimes and SEFs, can play a criti-cal role in economic growth of developingeconomies.

Acknowledgements

I would like to thank Albert Berry, G.Helleiner, Jagdish Nautiyal, D. Nowlan, D. Put-tock, and three reviewers for their insightful anduseful comments. The manner in which their com-ments have been interpreted is entirely my respon-sibility. I would like to express my special thanksto one of the reviewers who provided deep in-sights about the paper’s implications. ResearchFunds from the Social Sciences and HumanitiesResearch Council of Canada (Grant No.410990343) and the Natural Sciences and Engi-neering Council of Canada (Grant No. 203032-98RGPIN) are also greatly acknowledged.

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A dynamic approach to forest regimes in developing economies

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