77257 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1: 105-31 The Tragedy of the Commons in Cote d'lvoire Agriculture: Empirical Evidence and Implications for Evaluating Trade Policies Ramon Lopez Expansion of cultivated land diminishes the extent of forestlands or reduces the length of fallow periods and, hence, reduces the amount of natural vegetation. The increase in land under cultivation has a direct output-increasing effect at the cost of reducing natural capital and agricultural productivity. The evidence for western Cote d'lvoire is consistent with, and provides an explanation for, the declining agricultural productiv- ity observed in Sub-Saharan Africa during the past few decades. This article uses a theoretical model to determine the level of land cultivation that maximizes village income, using data from Cote d'lvoire for 1985-87. An important part of the land is under common property, usually at the village level. The results show that farmers do not internalize even a small fraction of the external cost of bio- mass in their land allocation decisions. The lack of internalization of the social cost of the biomass resource leads to large income losses at the village level—as much as 14 percent of village income. These losses are many times larger than the usual estimates for conventional distortions. Natural vegetation represents an important factor of production in the context of traditional shifting cultivation. Overexploitation of this factor may cause sig- nificant loss of income among rural communities. Farmers in an area of western Cote d'lvoire have overexploited the natural resources (forests and natural veg- etation in fallows) through excessive cultivation of communal lands and, hence, the reduction of fallows and forest areas (Lopez 1993). Individual cultivators considered at most 30 percent—and, more likely, a negligible fraction—of the social cost of natural vegetation or biomass when deciding how much land to clear for cultivation. These social costs include the negative effects that the clear- ing of land by one farmer has on other farmers, through soil degradation, flood- ing, and sliding, the reduction of fallow and forest areas as well as the decline in natural soil fertility caused by a reduction in the fallow part of the cultivation cycle. Ramon Lopez is with the Department of Agricultural and Resource Economics at the University of Maryland. Financial support for this research was provided by the World Bank Research Committee, RPO 675-33. Research assistance was provided by Claudia Sepiilveda. The author would like to thank three anonymous referees for their helpful comments. © 1998 The International Bank for Reconstruction and Development / THE WORLD BANK 10S 106 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Rural communities have apparently failed to maintain a system of incentives and controls over individual cultivators that would induce a socially optimal allocation of land among forest, fallow, and cultivation and thus avoid the "trag- edy of the commons." These results give support to authors who have ques- tioned the effectiveness of indigenous forms of property in achieving a socially efficient allocation of natural resources (Perrings 1989; Sinn 1988; Lopez and Niklitschek 1991; Glantz 1977; and Allen 1985). In contrast, anthropologists, other social scientists, and several economists, most prominently Dasgupta and Maler (1990) and Larson and Bromley (1990), are of the opinion that commu- nities are able to develop controls on the use of common property resources to allow for their efficient exploitation. The evidence for western Cote d'lvoire is consistent with and provides an explanation for the declining agricultural productivity observed in Sub-Saharan Africa over the past few decades (FAO 1986 and ADB, ECA, and OAU 1984). Sev- eral studies have illustrated the connection between declining agricultural pro- ductivity and agricultural intensification, which, in turn, is associated with popu- lation growth and the fall in biomass. A process that Geertz (1963) calls "agriculture involution" is documented, for example, by Jones and Egli (1984) in areas of fast population growth in Burundi, Rwanda, and Zaire; by Ludwig (1968) for the Ukare Island in Lake Victoria; and by Lagemann (1977) for east- ern Nigeria. Niklitschek (1990) provides ample evidence of the close connection between rural population growth, expansion of area cultivated, reduction of fallows, and declining agricultural productivity in Sub-Saharan Africa. Do the results for western Cote d'lvoire hold for other tropical areas where farmers practice traditional agriculture in the context of communal lands with restricted access? Using data for all regions of Cote d'lvoire, this article provides further evidence on the efficiency of exploitation of common lands. Apart from providing results that are more representative for the country, this expanded data set also provides the degrees of freedom required for a substantially more disaggregated analysis. In particular, the analysis considers three agricultural outputs: tree crops (a capital-intensive output), cereals (land-intensive), and tu- bers and vegetables (labor-intensive). Using three outputs permits a much richer analysis of the effects of agricultural prices as well as certain economywide poli- cies than using an aggregate output. The article also evaluates agricultural price and trade policies in Cote d'lvoire. In particular, it looks at how price and trade liberalization affect agriculture, taking into account their effects on both natural resources (fallow reduction and deforestation) and conventional factors of production (labor, purchased inputs). Agricultural price and trade policies do not represent first-best solutions to even- tual overexploitation of natural biomass. However, institutional and sociopolitical limitations make it unlikely that poor developing countries will be able to imple- ment such policies effectively in the near future. Hence, in devising further price and trade policy reforms, analysts should verify whether such policies impose additional tradeoffs by magnifying the overexploitation of natural resources. Lopez 107 Section I provides background information regarding the role of natural veg- etation or biomass in agricultural production in tropical areas. Section II pre- sents the theoretical framework used in the analysis, while section III presents details about the empirical method. Section IV discusses the data and estimation techniques, and section V presents the results. Section VI discusses the implica- tions of agricultural price and other economywide policies. Section VII concludes. I. NATURAL VEGETATION AS A FACTOR OF AGRICULTURAL PRODUCTION A system of relatively long rotation between crop cultivation and fallows (shift- ing cultivation) is a dominant practice in Cote d'lvoire as well as in most other countries in Sub-Saharan Africa where population levels are not yet too large. The fallow period plays the important role of replenishing the fertility of the land by allowing natural vegetation to grow. The natural vegetation is incorpo- rated into the soil as natural fertility (usually as ashes after burning) at the time of cultivation. Fallow periods that are too short lead to insufficient growth of natural vegetation and consequently to low soil fertility, soil instability because the vegetation does not have a sufficiently strong root system to protect it at the time of cultivation, and cultivated areas that are not protected against flooding and sliding. Thus, the vegetation that is allowed to grow in the fallow period is a form of capital that accumulates and is eventually used at the time of cultiva- tion. The closed forest areas (that is, those areas not yet disturbed by cultiva- tion) also play important roles not only as a reserve of land for eventual use but also as protection against soil erosion, watershed destruction, and flooding. Expansion of the cultivated land diminishes the forestlands or reduces the length of the fallow periods and, hence, reduces the natural vegetation. The tradeoff between cultivated land and forest/fallow is clear: an increase in land under cultivation has a direct output-increasing effect at the cost of reducing the natural capital, thus reducing agricultural productivity. An optimal fraction of the land should be cultivated in order to maximize social income. If the level of land cultivated is above or below the optimum, income is reduced. The land is under common property (farmers have exclusive rights on the land usually for as long as they cultivate it), usually at the village level (that typically encom- passes hundreds of families). In the absence of communal controls, individual cultivators are likely to overexploit the natural resource by cultivating too much. In deciding how much land to cultivate, farmers in this case likely consider only the private costs, ignoring contemporary and intertemporal effects on other cul- tivators. If communal controls are adequate, individuals would behave as if they fully accounted for both the private and social costs of clearing land. The em- pirical model tries to elucidate whether this happens. There are of course substitutes for natural vegetation as a factor of produc- tion. The use of fertilizers could replenish the fertility lost as a result of shorter fallow periods. The construction of drainage and other infrastructure could re- 108 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 place part of the protective role of natural vegetation. These substitutes, how- ever, are likely to be imperfect particularly in humid tropical soils where the benefits of fertilizers and other chemicals are much reduced (Sanchez 1976). Thus, the availability of substitutes may allow for a reduction in natural vegeta- tion, but elimination of the natural vegetation is unlikely to be optimal. Further, in the absence of community controls on the use of natural resources, individual cultivators will not be prone to use usually expensive substitute inputs for natu- ral vegetation (and thus increase land productivity) as long as forest or fallow communal lands are available for clearing. Consistent with this is the fact that only a very small fraction of the farmers located in areas where fallow lands and forest still exist use chemical fertilizers. n. THE THEORETICAL MODEL Equation 1 defines the net revenue function for farmer / who is assumed to take the stock of natural vegetation as given, (1) R ' W , e , p , * ' ) = max [py'-wlJ:F(yi,I>,Q,kl,xl) = O] y ' ,L' where p is a vector of output prices; w is a vector of input prices other than biomass, land, and capital; x1 is land cultivated by farmer /; 9 is the stock of village-level biomass per hectare; k! is capital; y is a vector of output quantities produced by farmer ;; L' is labor used by farmer /'; and F() is the set of produc- tion possibilities. The function R'() satisfies all the conditions of a variable profit function in p and w (Diewert 1973) and is assumed to be increasing and concave in 8, x*, and k'. The stock of biomass 6 per hectare can be defined as (2) e = Ti(i-x/x) where TJ is the (average) density of biomass per acre in the land that is not culti- N vated, x is the total land available, and x = £ x' is the total land under cultiva- ;»1 tion by the community or village (N is the number of cultivators in the village). Lopez (1993) has shown that the rate of extraction of biomass under shifting cultivation is proportional to the rate of land cultivation x/x. Thus, if y is the natural increase of biomass in the areas not under cultivation, change in bio- mass density in the uncultivated land is (3) T\ = y-r\Itx'/x. The level of land cultivation that maximizes the income of the village (rather than the income of individual cultivators independently) is obtained by Lopez 109 1 R1 (w;x',T](1- Z x'/x),p,k>) - ex N subjea to r\ = y - T| £ x'/x n(0) = no. where c is the private cost of land clearing per unit of land, r is the discount rate, t is time, and a dot over the variable name reflects a change over time. The optimization (expression 4) is a benchmark for comparing actual alloca- tions. The solution of expression 4 defines the allocation that is socially optimal from the community or village point of view. It maximizes the wealth of the community. The model does not assume this optimization; expression 4 is pro- vided only for the purpose of comparing its solution with the observed alloca- tions. The actual decentralized allocations by individual cultivators may not be consistent with expression 4, depending on the institutional conditions prevail- ing, the level of monitoring, and transaction costs. See, for example, Baland and Platteau (1996) for the nature of the games that could lead to efficient allocation of common resources through collective action and other forms of cooperation. In the steady state, the first-order conditions of expression 4 imply that (5) Ri(-) = c + ^ S ^ ( - ) + Ti«/3c, j = %...,N X i=l where Rk = and u = (l-x/x) £ ^r= is the shadow value of biomass dx' MT + X I x desity T). Equation 5 is the key benchmark for deriving the empirical methodol- ogy. It says that if cultivators choose socially optimal levels of land cultiva- tion, the marginal revenue of the last unit of land cleared for cultivation should equal the private cost of land clearing (c) plus the marginal revenues forgone N ( by all cultivators that one additional unit of land cleared causes now \r\ X R{ -1 I '=i ) and in the future (T| (ulx)) due to the fall in T| that increasing x* causes. The second right-hand term in equation 5 measures the forgone marginal income for all cultivators caused by reducing the area covered with natural vegetation given a level of biomass density (T|) per acre of noncultivated land. The third right- hand term in equation 5 captures the present value of all future forgone incomes due to the fall in r\ that will occur in the future as the rotation period is reduced as a consequence of increasing x1. 110 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Using the definition of u, the last two right-hand terms in equation 5 can be combined, and thus equation 5 can be rewritten as (6) R£() = <: + 1 1 / 3 t — X £;,(•), j=\. ..,N r + z i+\ N where z = X x'lx is the (endogenous) rate of depreciation of the stock of bio- <=i mass density T|. If individual cultivators make decisions completely independently and face no constraint from their communities, they would only consider I/Nth of the external effects (of the second right-hand term in equation 6) as part of the cost of increasing x1. In this case, a Nash equilibrium would arise as the solution of the N equations: (7) Ri() = c ^ Depending on the effectiveness of the village controls on individual cultivators' decisions, the equilibrium vector of x = (x1, x2, . . . , xN) will be given by equa- tion 6, or by equation 7, or an intermediate solution if controls exist but are imperfect. To model these intermediate outcomes empirically, I postulate a more general specification for equation 6 or equation 7: (8) where X is an efficiency parameter that could fluctuate between 1/N and 1, de- pending on the efficiency of the village controls. The closer to 1 is parameter k, the more efficient are the land allocation decisions. The specification of the model assumes a fixed stock of physical capital, k!. It may be argued that this is inconsistent with the dynamic nature of the model and, therefore, that a mechanism of capital accumulation needs to be incorpo- rated explicitly into the theoretical model. There are several ways of doing this. One possibility is to assume the extreme opposite of the assumption made so far, that capital is instantaneously adjusted to optimal levels instead of being fixed. In this case, it should be clear that the land allocation equation (equation 7 or 8) remains intact, except that the revenue function R'(-) would include the rental price of capital instead of the stock of capital. A less extreme possibility is that capital is neither fixed nor fully variable, but quasi-fixed. That is, a gradual process of capital accumulation takes place through time. To model this, there are several avenues depending on what source pre- vents an instantaneous adjustment of the capital stock. Appendix A presents a Lopez 111 growth model that explicitly incorporates the two state variables, the stock of biomass and the stock of capital. Except for the addition of the biomass state variable, the model is a conventional neoclassical growth model. That is, it as- sumes that the main reason for slow capital adjustment is the existence of a utility function that is strictly concave in consumption and that capital accumu- lation is financed entirely through the savings of the individuals. Appendix A shows that in the steady state the land allocation decision is still ruled by a specification analogous to equation 7. That is, at least in the steady state, the specification used is in a sense quite robust to the assumption used regarding fixity, quasi-fixity, or full variability of the capital variable. The empirical model is based on the assumption of a steady state. Dropping this assumption would change the specification of the land equation. The right- hand side of the land equation would be the same except that a new term involv- ing the change in biomass,9, would have to be added (Lopez 1993). If 9 < 0, the true shadow value of biomass is underestimated in a steady-state specification; if 9 > 0, the model would overestimate the shadow value of biomass (Lopez 1993). Because biomass decreases through time, the steady-state specification under- estimates the social value of biomass. That is, the social cost of expanding x exceeds the value assumed in equation 6. This implies that the steady-state assumption will provide a value for X that is larger than the true value of X. So the estimated X will be an upper bound of the true X if biomass declines through time. A potential limitation of the model is that it assumes that producers are risk neutral. Poor farmers tend to be risk averse and, hence, if cultivated land is risk- decreasing, farmers may behave as if the true marginal cost of cultivated land were less than the right-hand side of equation 8. It may be argued, then, that the model might estimate a X value below unity because a misspecification is associ- ated with ignoring risk rather than because institutions fail to assign land effi- ciently. However, two aspects considerably weaken this objection. First, the spe- cific variable that dictates the value of X is the shadow value of biomass for the community. If the omitted variable, risk level, causes a downward bias in X, the level of risk and the shadow value of biomass would be positively correlated. It is hardly plausible, however, to argue that the shadow value of biomass for a community is correlated with the level of risk or uncertainty prevailing in the community. Second, the empirical model in section III does not use actual values for the private costs of cultivating land, c. Instead it uses an estimate of the private cost coefficient that can change across villages (these are the village fixed effects). So, if the level of risk or uncertainty faced by the farmers varies more across villages (due to climatic and agroecological differences or to proximity to markets) than through time, as might be expected, its effect would be captured by the village fixed effects without biasing the estimates of X. Another potential problem of the model is that it ignores the existence of credit market imperfections. Some analysts have argued that imperfect capital markets and low incomes drive farmers to behave myopically. One way of con- sidering capital market imperfections is through the interest rate. Basu (1989), 112 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 for example, argues that most farmers in developing countries have access to the informal credit market, where the main mechanism of allocation is (usually high) interest rates rather than credit rationing. If farmers face credit constraints in the formal capital market, they have to rely on informal credit sources, where inter- est rates are much higher than interest rates in the formal market. Although the model obviously ignores credit market imperfections, it does not rely on the existence of perfect credit markets. In fact, it explicitly allows the discount rate to assume various values in the empirical estimation, within a wide range. The analysis does not use market interest rates as a proxy for r, but rather experi- ments with a broad range of values for r and considers the sensitivity of the estimates of X to changes in r. There is still a potential problem if the levels of r vary across farmers rather than being constant, as implicitly assumed in equation 8. The problem in this case could be that the omitted variable r; is correlated with the level of the shadow value of biomass, which is the variable that determines X. However, the shadow value of biomass is village-specific, not farmer-specific. Hence, village fixed ef- fects will control for the effect of the possible intervillage variations in the inter- est rate. The only remaining problem would be if the interest rate varies system- atically through time. III. THE EMPIRICAL MODEL The empirical model requires the specification of the normalized net revenue function, which is assumed to be identical for all farmers. The revenue function is normalized by the farm price of tree crops. Equation 9 is a normalized qua- dratic functional form for the revenue function: (9) R' =A0+ Axw + A2x' + A3Q + A4k' + Aspc + A6p0 + X An"2 + X An*i2 + X A^ + X A«V2 + X AssPc + Anwx' + Al3wQ + Auwk' + A15wpc + A16wp0 + Anx'Q + A24k'x' + A25x'pc + A16x'p0 + A^Qk' + A35Qpc + A36Qp0 + A45k'pc where R' = R'lq is the net revenue normalized by the price of tree crops (q); w = w/q; pc and pQ are the prices of cereals and other crops (tubers, vegetables), re- spectively, also normalized by q; H^ are household-specific characteristics; Vh are village characteristics; Ah A^, Bk, and yh are fixed parameters; and e'y is an error term assumed to be normally distributed with zero mean and finite vari- ance. The village characteristics also interact with the prices and wage rate. These interactive terms are omitted in equation 9. The well-known symmetry or red- Lopez 113 procity conditions that arise from the implicit optimization assumption in the context of well-behaved production technologies are imposed on equation 9. The symmetry conditions imply that A^ = A,, for all / * /. This considerably reduces the number of parameters to be estimated. Using equation 8, an explicit functional representation for farmer/'s demand for land to cultivate is (10) 22 ""22 -"22 "22 "22 "22 N [A 1TT ^ 3 + ^13w + A23Q + A34k' + A3spc + A36p0) + e° 22 T+ Z where e° is an additive disturbance assumed to satisfy the same properties as £*, and x = X*, is the total area cultivated in the village. The function R in equation i 9 is assumed to satisfy the usual regularity assumptions: it is convex in p and w; it is increasing and strictly concave in xJ, 0, and k'; and the marginal revenues of 9, k!y and x are increasing in the level of the other factors. These conditions imply that An, A33, and ^44 are all negative and that Au, A24, and A 34 are all positive. These conditions assure that cultivated land is decreasing in c and in- creasing in 6 and k'. Using Hotelling's lemma, the labor demand and output supply equations im- plicit in equation 9 are -L' = A, + Anw + Anx' + A139 + Auk' + Aupc + Aup0 + ef, (11) Q£ = A5 + Alsw + A2sx' + A35Q + A45k' + A55pc + A56p0 + e% 0£ = K + Al6w + A26x' + A36Q + A46k' + AS6pc + A66p0 + e°° where L' is labor demand by farmer /, and Q'c and Q^ are the supply of cereals and other crops, respectively. Equation 11 omits the household-specific charac- teristic effects and the village characteristic effects. The supply of perennial crops (or tree crops) is obtained by noting that Qj, = R' - wU - pcQ'c- poQo- Thus, (12) Qi, = A, + A2x] + A3Q + AAk> -/2Auw2 - Y2AssP2c -^A^pl 12 2 i2 + y2Anx + /2A33Q + y2A44k +lBkH>k + ZyhVh + ej. k h The system of equations 10 and 11 and either equation 9 or 12 is jointly estimated using a maximum likelihood procedure. The joint estimation of the system permits the identification of all the relevant coefficients. The X coefficient can be identified conditional on a fixed level of the discount rate r. The estima- tion strategy consists of estimating alternative values of A. for a plausible range of discount rates. Given the symmetry conditions (that is, Atj = A^), the coeffi- 114 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 cients inside the square brackets in equation 10 (A3 and Aa, i = 1 , . . . , 6) are all identified by the rest of the system or by the linear part of equation 10 itself. Hence, as T| and z are observed variables, X. can be exactly identified if r is also known. But since r is unknown, alternative fixed values are postulated for r. The value of X will, of course, vary directly with the postulated level of r. This re- flects the fart that any land allocation can be considered optimal if the discount rate is large enough. Thus values for X are estimated within a plausible range of r. The key question is how high the discount rate r would have to be to make the observed resource allocation socially efficient. The normalized quadratic is a flexible functional form, in the sense that it provides a second-order approximation to any functional form. This is one of the functional forms that Diewert (1973) proposes for revenue functions and has been frequently used in the literature (Binswanger and Evenson 1984 and Diewert and Morrison 1988). This form imposes little a priori restrictions on the matrix of elasticity of substitution and on the implicit production technolo- gies. Unlike other commonly used functional forms (such as Cobb-Douglas and Constant Elasticity of Substitution), the normalized quadratic allows for differ- ent elasticities of substitution, it does not impose separability, and it allows for nonhomotheticity.1 The function does impose the price homogeneity conditions that production theory predicts for input demand and output supply equations.2 IV. DATA AND ESTIMATION The data come from three sources—the Living Standards Survey (LSS) con- ducted annually in Cote d'lvoire between 1985 and 1988, remote sensing data based on satellite images of 20 villages scattered throughout the country for the years 1985 to 1988, and field visits to the villages. The total area covered by the remote sensing analysis is about 450,000 hectares. The LSS and remote sensing data sources were carefully matched for each of the villages and years consid- ered. The LSS information allows the creation of a panel data set for a sample of 16 farm households in each of the 20 villages for the 1985-87 period. The LSS data used in this article concern information on farm production, labor hired, household member's work on the farm, land cultivated, other inputs used by each of the farm households, as well as demographic characteristics. The analy- sis also uses village-level information such as the number of households per vil- lage. (See appendix B for data definitions.) The remote sensing data provided information about the total land under cultivation in the village, land under fallow per village, land under closed forests 1. Some of the flexible functional forms do impose quasi-homotheticity and certain separability conditions (see Lopez 1985). 2. Some of the implicit input demand and output supply equations are linear in the normalized prices, and one of the output supply functions is nonlinear in prices. As Diewert (1973) shows, this feature imposes no special peculiarities on the underlying production technology. Ldpez 115 per village, and average biomass density of the fallow land in each of the three years considered. Village biomass is estimated by multiplying the total land area under fallow by the biomass density index obtained from the remote sensing analysis. Also included is an estimate of biomass calculated in the same way for forest areas that have not been cultivated recently. Some of the regressions only use the fallow biomass, others use the sum of fallow and forest biomass, and still others use the two measures as separate variables. Preliminary regressions showed that the fallow biomass was the key to agricultural productivity and that includ- ing forest biomass added very little to the regressions. Therefore, the regressions reported in this article use only fallow biomass per hectare. The matching of the LSS household-level data and remote sensing village-level data provided a panel data set that combines individual household information with information on natural resource endowments at the village level. Field visits to the villages provided data concerning the agricultural area that is under the sphere of influence of each village, that is, the area that is considered "property" of the village group. Moreover, the field visits provided certain es- sential qualitative information on issues such as land allocation decisions, the state of the communal system, and the functioning of labor markets within the communities. Three main conclusions that emerged from the field visits are im- portant for the empirical analysis. First, shifting cultivation is the dominant prac- tice in all the villages considered. Second, the system of land allocation for culti- vation of the fallow areas is not transparent. In some villages, a village council is still quite important in determining the extent of land given to cultivation. In most villages, however, the decisions appear to be much more decentralized, with little input from the village chiefs. Additionally, in several areas an incipi- ent and spontaneous process of privatization is taking place, and one of the mechanisms for obtaining land rights is to cultivate the fallow lands continu- ously. In general, the assessment of people in the field is that the traditional system of land allocation is changing mainly because of the reduced power of the village leaders and the process of gradual privatization. Third, in most cases, an active and seemingly efficient labor market operates within the villages. Table 1 gives an overview of the land allocation information provided by the remote sensing analysis for Cote d'lvoire as a whole. Table 1 shows, even at the aggregate country level, a significant degree of change in land allocation over the three-year period from January 1985 to January 1988. In particular, a decrease in the forest area of almost 9 percent and an increase in the area cultivated of about 2.5 percent a year are quite remarkable. At the same time the fallow area shows a less conspicuous but significant downward trend. The village-level data that are actually used in the regression analysis exhibit an even greater variability through time than the aggregate data for the country. The remote sensing data also include a measure of the average biomass density per hectare in the fallow land. In order to make intervillage comparisons of fallow meaningful (a village may have a large fallow area but very little vegeta- tion density, and another may have a smaller area but much greater vegetation 116 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Table 1. Changes in Land Allocation in Cote d'lvoire, 1985 and 1988 (hectares) Percentage Land area 198S 1988 change Total area surveyed 447,132 447,132 0.0 Under closed forest 125,410 114,217 -8.9 Under fallow 172,391 169,585 -1.6 Cultivated 132,222 142,073 7.5 Source: EARTHSAT ( 1 9 9 1 ) . cover), the fallow area of each village is weighted by its corresponding average biomass density. Two alternative definitions of biomass are used in the empirical model. A narrow definition only includes average biomass per hectare in fallow lands. A broad definition includes all biomass in fallow lands as well as in forestlands (biomass is, in this case, normalized by the total fallow plus forest areas). The two measures turn out to be highly correlated, and the econometric results are only marginally different when either measure is used. Equations 9, 10, and 11 are estimated jointly as a system restricting the A, and A,j coefficient across equations using FIML (full information maximum like- lihood) estimators. Assuming that the variables N, w, 0, and la1 are not corre- lated with the error terms, the system is recursive (rather than simultaneous), a feature that greatly facilitates the estimation. Furthermore, a random effects model is used, allowing for a component of each error term that is common to a given year's observations corresponding to households located in the same village. That is, if ef;-f is the total residual in equation s for household / located in village ; at time t, assume that ef;( = p^, + Af;, where p^ is the common-to-the-village component and Asijt is the idiosyncratic component. E(p/OA,;,) = 0 is assumed for all k. The variance of the across-village estimated component (py,) is signifi- cantly larger than the variance of the idiosyncratic component in all three equa- tions. This means that imposing a single residual would give inconsistent esti- mates of the standard errors of the regression. Another important issue is the validity of the assumption that the residuals are uncorrelated with the exogenous variables. In particular, of most concern is the possibility that the biomass variable could be correlated with the error terms. This would, of course, lead to inconsistent estimates of the parameters. The endogenous variables (household revenue, cultivated area, labor demand, and the supply of the various crops) are explained by village-level variables as well as by household characteristics. A problem of simultaneity may arise if the village explanatory variables and the household dependent variables are correlated with important but unobserved variables. The key question concerns the source of variability of the village-level variables. A positive correlation between farm revenues or output and biomass may arise if some villages have greater biomass than others because they have better Lopez 117 soil and climate that allow the natural vegetation to grow faster. These better climatic and soil characteristics would lead to higher agricultural productivity in the villages that have more biomass. Thus any positive correlation between out- put and biomass could be spurious. In order to deal with this issue, village- specific characteristics (including soil and climate) are controlled for using vil- lage dummy variables. Using village effects should control for unobserved variables such as climate and soil quality as well as for other village characteristics such as infrastructure and distance to markets. Thus, the use of village dummies is likely to eliminate the influence of such variables from the coefficients associated with the other explanatory variables. The use of village-specific dummies (rather than house- hold dummies) is an adequate procedure because the biomass variable used is also defined at the village level. This procedure is possible because the analysis uses panel data for three years for all the relevant variables. A remaining problem, however, is that the variation of biomass through time in a village may be associated with changes in weather. Agricultural productiv- ity is also likely to be associated with fluctuations in weather, and, hence, a spurious correlation between biomass and agricultural productivity may arise. The extent of the biases induced in the coefficient of biomass will depend on the importance of the fluctuations in weather. Other estimates (not reported here) are obtained using instrumental variables for the various terms involving the biomass variable. These include average family size as well as two regional dummy variables. The results, particularly the sign and statistical significance of the co- efficients, do not change with the instrumental variable procedures. These vari- ables are not likely to be correlated with the weather variable but are good instruments, in the sense that they explain a high proportion of the changes in biomass. There are large differences in agroecological conditions across the main re- gions in the country (West Forest, East Forest, and Savanna). In particular, the inland Savanna has a different pattern of production than the tropical forest belt in the west and in the east. Thus, using different village intercepts in the estimation of the revenue function may not be enough to capture all the pro- duction and ecological differences across the three regions. This would call for allowing the slope coefficients to vary across regions as well. Unfortunately, given the large number of coefficients of the revenue function, this is not fea- sible. However, using a more restricted approach with one aggregate output variable, Lopez (1993) estimates a similar revenue function for the western region of Cote d'lvoire, which has enough village observations to estimate the revenue function. The effect of biomass on gross revenues is indeed higher in the west than in the country as a whole, but the differences are not great. For the west, the estimates for the contribution of biomass are 0.18-0.20, only slightly larger than those for the country as a whole. The contribution of land to gross revenues is slightly larger in the forest region (with an elasticity of about 0.41 compared with 0.38 in the analysis for the whole country), but the 318 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 contribution of labor is significantly smaller in the west (about 0.10 compared with 0.18 for the whole country). V. THE RESULTS Table 2 shows the FIML estimates of the system of equations 9, 10, and 11. The estimates were obtained assuming a discount rate of 0.2. Several other esti- mates were obtained by specifying different discount rates. In general, the re- sults are robust to the changes in the assumed discount rate, and only the X coefficient changes numerical values, but without altering its sign and degree of statistical significance. In table 2 the estimates in the first and second columns, respectively, were obtained with and without using village dummies. The estimates are mostly (but not completely) consistent with the properties of the revenue function postu- lated by the optimization model, hi particular, the revenue function estimated is monotonically increasing in land cultivated, biomass, and capital as well as in the output prices and is monotonically decreasing in the wage rate. The normal- ized revenue function estimated is not, however, convex in prices. Although the An and A66 coefficients have the expected signs, the fact that A5S is negative implies a violation of the convexity property (although this coefficient is not statistically significantly different from 0). The revenue function estimated is also strictly concave in land cultivated, biomass, and capital, implying that the marginal revenue functions are downward-sloping as expected. The most important finding concerns the resource efficiency parameter X. As can be seen in table 2, the parameter X is positive but not statistically different from 0 in either of the estimates presented. The model was also estimated as- suming even higher discount rates (up to r = 0.6), and the X parameter is never statistically significant.3 This result implies that farmers do not internalize even a small fraction of the external cost of biomass in their land allocation decisions.4 Thus, farmers are cultivating too much land to maximize the village income. Or, equivalently, given the tradeoffs between land cultivated and the stock of biomass, the village wealth can be increased by reducing the amount of land cultivated and, conse- quently, allowing for more natural biomass. Moreover, the income loss associ- ated with this inefficiency is quite large. Several reasons might explain why such a clear inefficiency occurs in a situation where village farmers exploit the biomass resource in an essentially 3. In the L6pez (1993) study, a statistically significant X was found for the west of Cote d'lvoire at least under certain specifications; the highest X found was about 0.3. 4. According to the theoretical specification, the smallest possible value of X is 1/N rather than 0. Because the number of households in most villages is very large, fluctuating between 742 and 1,320 with a mean of 937, the lower bound of X is very close to 0, at about 0.001. Lopez 119 Table 2. Estimation Results for the Revenue Function, Cote d'lvoire, 1985-87 Using village Without using village Variable dummy variables dummy variables Constant -2.52 -2.97 (-2.85) (-3.44) Agricultural wage, w -1.09 -1.08 (-6.09) (-6.02) Land cultivated by farmer /', x< -1.39 -1.31 (-1.71) (-1.60) Stock of village biomass, 9 1.40 1.36 (7.75) (8.24) Capital owned by farmer /', kl 2.34 2.31 (4.54) (4.49) Price of cereals, pc 0.95 0.82 (2.18) (1.88) Price of other crops, po 0.02 -0.05 (0.05) (-0.11) Agricultural wage squared, w1 0.11 0.11 (2.05) (1.95) Land cultivated by farmer / squared, (x1)2 -1.22 -1.26 (-15.82) (-16.48) Stock of village biomass squared, 02 -0.20 -0.19 (-7.52) (-7.97) Capital owned by farmer / squared, (it')2 -0.33 -0.33 (-1.38) (-1.37) Price of cereals squared, (pc)2 -0.38 -0.47 (-1.24) (-1.53) Price of other crops squared, (po)2 0.38 0.38 (0.97) (0.95) Interaction with agricultural wage Land cultivated by farmer /, wx1 0.00 -0.008 (0.00) (-0.08) Stock of village biomass, wQ -0.003 -0.0022 (-0.33) (-0.28) Capital owned by farmer /, wk! -0.10 -0.10 (-2.90) (-2.77) Price of cereals, wpc -0.30 -0.30 (-3.30) (-3.30) Price of other crops, wpo -0.18 -0.20 (-1.83) (-1.87) Interaction with land cultivated by farmer j Stock of village biomass, x'S 0.04 0.05 (1.23) (1.37) Capital owned by fanner /, k'x1 -0.66 -0.67 (-10.44) (-10.54) Price of cereals, x>pc 0.81 0.84 (3.55) (3.61) Price of other crops, xipo 0.69 0.72 (2.56) (2.64) (Table continues on the following page.) 120 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 Table 2. (continued) Using village Without using village Variable dummy variables dummy variables Interaction with stock of village biomass Capital owned by farmer /', 6k1 0.03 0.04 (1.06) (1.08) Price of cereals, Qpc -0.15 -0.14 (-7.23) (-6.91) Price of other crops, Qpo -0.06 -0.05 (-3.72) (-3.33) Interaction with capital oumed by farmer j Price of cereals, k'pc 0.36 0.36 (4.12) (4.11) Price of other crops, k'po 0.15 0.15 (1.78) (1.69) Interaction between price of cereals and 0.67 0.65 price of other crops (2.81) (2.71) Biomass efficiency parameter, X 0.03 0.008 (0.30) (0.07) Private cost of land clearing, c 1.39 1.55 (2.13) (2.46) Dummy year 1986 -1.92 -2.57 (-3.19) (-5.47) Dummy year 1987 -1.79 -2.33 (-2.00) (-4.05) Number of observations 458 458 Note: Full information maximum likelihood was used to estimate the model (equations 9, 10, and 11 in the text), assuming a discount rate of 0.2. Five household demographic characteristics were included in the regressions: age of household head, education of household head, number of children, number of female adult members, and distance to health care facilities, f-statistics are in parentheses. Source: Author's calculations. closed-access form. The monitoring and other transaction costs involved in the implementation and design of institutional mechanisms to exploit the resource efficiently might be very large, particularly given the high popula- tion density prevailing in most villages. This may prevent the development of such mechanisms. Another explanation could be that most farm communi- ties may operate at subsistence levels and, thus, cannot afford investing in the resource by reducing the cultivated area. Equivalently, the true discount rate that communities use is even higher than the 60 percent annual rate used as an upper bound in the estimation. It could be that their true discount rate is almost infinity. The analysis shows, however, that the way in which farm- ers respond to price incentives does not seem to be consistent with the sub- sistence story. The significance of the coefficients associated with biomass (the A3j coeffi- cients) and the net positive effect of biomass on total revenues when evaluated at the data points show the importance of biomass as a factor of production. Using Ldpez 121 equation 9, the effect of biomass on total revenues is r)1wR fl (13) - ^ = [A3 + A33Q + Anw + A23x + A3'(O) = ki, / = 1,... where U(-) is an increasing and strictly concave utility function of the village households, y1 is consumption of household/', r is the discount rate, t is time, k! is capital, R' is revenue of farmer /, w is input prices other than biomass, land, and capital, x! is land cultivated by farmer /', r\ is the average density of biomass per acre in the land that is not cultivated, x is total land available, 8 is the (con- stant) rate of depreciation of the capital stock, c is the private cost of clearing the land, f|is the change in T|, k is the change in k, y is the natural increase of biomass in the areas not under cultivation, x' is the total land under cultivation by farmer /, and k'o is the initial level of capital of farmer /'. The first-order conditions of this problem are (ii) R|=C i £ (iii) e = (r + 5 - R i ) e j =\ . ..,N (iv) Li = (r + Ix73c)u-elR' 3 (l-X;t73c) (v) A-l, parts i and ii where e is the shadow value of the stock of capital, (l is the shadow value of biomass, a dot over a variable indicates rate of change, and subscripts indicate partial derivatives. It is important to note that for £ to be identical for all house- holds, it is necessary to assume that R'A is identical for all households. That is, assume that in equation A-2 the production technology is identical for all farm- ers and that they face the same prices w (conditions that are sufficient to assure that x1 is equal for all farmers) and start with identical capital stocks. This is equivalent to postulating the model using a representative consumer/producer fiction, as is usually done. Equation A-2, part ii, dictates the land allocation decisions in the short run. It is analogous to the short-run land allocation derived from equation 4 in the text, with the only exception being that now the shadow value of capital (or marginal utility of consumption), £, appears. Equation A-2, part ii, indicates that the so- cial cost of expanding the cultivated area should be weighted by the marginal utility of consumption. That is, if £ is large—that is, households are poor in the sense that their consumption is low, in which case U'(y") is high—the social cost of expanding the area cultivated (and, hence, of depleting biomass) is less than if Ldpez 127 households have a higher consumption level and consequently a lower IT(-) and e. This implies that, ceteris paribus, as a way of financing their capital buildup, capital-poor societies tend to deplete biomass more intensively than richer soci- eties. Thus, this model, unlike the one in the text, allows for a mechanism by which poverty may lead to greater resource degradation beyond the discount rate and the direct production substitution effects associated with capital or other factors. Compared with the model in the text, the steady state model has the same land allocation decision, but in addition it has an equilibrium equation for the optimal capital stock. It thus makes it possible to determine simultaneously the long-run equilibrium values of x and k, ^() c+ 5 Z R i ( ) ; 1,...,N Nx l + z/=i (ii) R'A(-) = r + S j= \...,N N (iii) 'Zx'/x=y/r\ where the functions R{(-), R^-), and R{(-) are evaluated at the steady-state equi- librium values of x', k\ and T|* derived from the solution of equation A-3. The land allocation equation (A-3, part i) is analogous to equation 7 in the text, ex- cept that it needs to be evaluated at k* instead of at k. For the empirical model, however, apart from being more difficult to imple- ment, it is not clear that using this specification (equation A-3), which imposes a certain structure on the level of k, is necessarily superior to a specification based on equation 7 in the text, which does not impose any specific mechanism for the derivation of k. A more eclectic empirical approach is simply to instrumentalize variable k. APPENDIX B. DATA Part of the data used in this article comes from the Living Standards Survey (LSS) conducted in Cote d'lvoire. About 50 percent of the sample is reinterviewed every year. These data provide information on demographic, labor, and produc- tion characteristics as well as the time allocation of households. The data used correspond to the period 1985-87. Statistics on agricultural land and biomass density at the village level were provided by a special study done for this project by EARTHSAT (1991) based on satellite images of 20 villages in the western region of Cote d'lvoire for the years 1985, 1986, and 1988. These statistics were incorporated into the LSS panel data. Matching the LSS and EARTHSAT data gives a panel data set of household 128 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 observations that combine the usual individual characteristics of the households with information on biomass density and area at the village level. Detection of Biomass Change Based on Remote Sensing Data Land was first classified into five categories: forestlands (areas with large and highly dense trees that do not appear to have been cultivated for at least 50 years), low-impact agriculture or bush fallow, high-impact agriculture (includ- ing sites of active agriculture or recently fallowed fields with negligible regenera- tion), human settlement areas (including villages and areas of construction), and other lands (including unproductive lands with little or no soil). The 1985 and 1986 imagery was geometrically corrected to fit the image space of the 1988 imagery, allowing comparative evaluations of the same areas over time. A principal components analysis was carried out on all imagery to normalize the data and to isolate radiometric anomalies. A statistical evaluation was carried out to determine the mean digital number value for each land-cover category, as represented by the principal component vectors from the various dates of imagery. Pixel counts were then carried out to determine the quantity of change in each of the five categories of land. The pixels were then converted to hectares (the pixel size was 28.5 square meters). From this information, it was possible to determine the change in area for each of the five categories of land over time for each of the village areas. The digital numbers of band four were divided by those of band three to pro- duce a vegetation density index for the forest and low-impact agriculture areas for each of the study units. The total biomass value in fallow was defined as the vegetation density index times the areas under low-impact agriculture and that of the forest area as the forest vegetation index times the areas under forest. Thus, an index of total biomass in each land category was obtained for each village area. Variable Definitions and Summary Statistics Table B-l provides the means and standard deviations for some of the most important variables. All the figures are in 1985 CFA francs. The deflator used was the African Food Price Index with base 1985 = 100. Table B-l. Means and Standard Deviations of Selected Variables Used in the Regressions for Cote d'lvoire, 1985-88 Variable Mean Standard deviation Net revenue per household (1985 CFA francs) 668,990 647,200 Land cultivated per household (hectares) 7.2 4.23 Biomass per hectare of fallow (index number) 6.50 3.56 Total days of work per household per year 1,428 867 Real wage rate (1985 CFA francs per hour) 450 216 Number of agricultural tools or implements per household 12.3 11.6 Source: Author's calculations. Lopez 129 The variables used as well as their definitions are presented below, where i denotes the index for household / = 1, . . . , n, and / denotes the village. (i) R4 ^ S\t + PHZ4 + S 4 + HCjt + HPl -w'ut +LHI-W* HA, LHMAj, -wHPJLHMP/ f C (ii) w^ S bfw'F + bmw>M + bcw^ where bM^c = ™ ^ ' lb = (iii) w'HP = CFuJf + CuwjM + Ccwjc, where C M > f , c = ^ ^ P ^ XC = 1 (IV) w> s aMw'F + aHAw'HA + aHMPw'HP, where aM = jj^aHMP = LL <*HA LHMA (v) LL'; = LH\ + LHMAj + LHMP/ (vi)e' sri'a-z') R,' = Real revenue of farmer / in village j SJ = Real total sales t o the market of farmer ;' in village j PHL', = Real value of payments in kind t o hired labor by farmer i in village = Real value of seeds kept by farmer i in village / HQ = Real value of home consumption of farmer i in village ; HP'j = Real value of home production or transformation of farmer / in village; LH\ - Number of days hired by farmer i in village / during the last 12 months LHMA] = Number of days worked in the field by members of the household i in village /' during the last 12 months tJp = Agricultural real wage per day earned by a female in village / idJu = Agricultural real wage earned per day by a male in village j Wg = Agricultural real wage earned per day by a child in village /' irfHA = Average agricultural real wage earned per day by a member of a household working in his o r her o w n field in village / uJHP - Average agricultural real wage earned per d a y by a member of a household working in the transformation of agricultural products in village /' uJ = Average real wage earned by a member of the household working in his or her own field o r in the transformation of his o r her agricultural products o r by a worker hired by farmer i in village / 130 THE WORLD BANK ECONOMIC REVIEW, VOL. 12, NO. 1 LL/ = Total number of days worked in the field or in home production by members of household i plus days hired by farmer / in village j & = Total biomass in village;', normalized by its total land area f\' = Average biomass density per acre of land under fallow in village; (from EARTHSAT) X' = Total land cultivated in village / (from EARTHSAT) X = Total agricultural land (cultivated plus fallow) in village / in hectares (from EARTHSAT) z! = Fraction of cultivated land to agricultural land in village / y = Marginal biomass density xl = Land cultivated by farmer i in village /' in hectares )-i = Average land cultivated in village / in hectares n N1 = Number of farms in village j Ei = Years of education of the head of household i in village / l\ = Number of family members in household i of village j TJ = Number of tree crops in farm i of village j E = Minimum value of Ej in the sample = 0 L = Minimum value of L,' in the sample k^ = The sum of the agricultural tools and implements used by household i in village j T = Minimum value of T\ in the sample = 0 r = Time discount rate REFERENCES The word "processed" describes informally reproduced works that may not be com- monly available through library systems. 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