Keywords: Gum arabic; Deforestation; Abandonment/expansion; Real options; Sudan
1. Introduction
The gum belt in Sudan provides a natural buffer zonebetween the desert in the North and the more fertile agriculturallands in the South. Deforestation within the gum belt has lead toan increase in desert encroachment and threatens agriculturalproduction (IEED/IES, 1990; Keddeman, 1994; Olsson andArdö, 2002). Following the Sahel drought of the 1970s and1980s a southward shifts in the tapping of gum has beenreported (IIED/IES, 1990), as people moved from the morefragile environment in the northern parts of the gum belt to theless fragile and better environment of the south. Over the lastthree to four decades the land use practices have moved from arotation with long fallow periods (15–20 years) of gumcultivation interspersed with short period of cultivation (4–6 years) towards a more or less continuous cultivation (Olssonand Ardö, 2002). The low and highly volatile producer prices of
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
gum arabic over the previous decades have accelerated the gumdeforestation process (Barbier, 2000).
An important question is if it can be expected that theobserved deforestation of gum arabic will continue. Previousstudies on gum belt deforestation show contradictory resultswith regard to the profitability of gum production. Ahmed(2000) estimates the financial internal rate of return ofcultivating gum forest for 16 years to be around 15%. Barbier(2000) uses an economic analysis of six representative croppingsystems containing gum arabic to estimate the net present value.He finds that because of a decline in the real producer price ofgum arabic relative to other crops, the relative profitability ofgum arabic is lower than that of other crops except in areaswhere field crop damage occurs frequently. But he alsoconcludes that the inclusion of the environmental benefits ofgum arabic and the role of the gum belt in controllingdesertification means that its social profitability is much higherthan its private profitability.
The previous studies have assumed that gum arabicproduction directly competes with agriculture production forlabor. Agriculture production, however, mainly takes place
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during the rainy season while the harvesting of gum arabic takesplace during the dry season. Furthermore labor is oftenconsidered the most important constraint to agriculture fortraditional farmers in the gum belt area (Elmadih, 1992; El-Dukheri, 1997). As long as labor is relatively scarcer than land,comparing gum production in the dry season with agricultureproduction in the wet season can provide misleading results. Inthis study we analyze the incentives for abandoning gumproduction by comparing the benefits on the basis of theopportunity costs for labor in the various seasons.
The prices of gum arabic over the last few decades exhibitconsiderable fluctuation (Barbier, 2000; Elmqvist et al., 2005).The Discounted Cash Flow (DCF) technique used so far in theliterature to examine the profitability of gum cultivation doesnot consider the fluctuation in gum prices and the uncertaintyover gum return. DCF analysis assumes that either theinvestment opportunity is reversible or, if irreversible, is anow-or-never opportunity. As gum forests allow farmers tobenefit from the trees over a number of production periods theuncertainty over gum returns, the quasi-irreversible nature ofthe land allocation, and the flexibility in preserving, abandoningand adopting interact to generate a real option value for plantingadditional gum arabic trees and for abandoning gum arabicforests (Dixit and Pindyck, 1994). These real option values canbe substantial (Mithöfer et al., 2004) and ignoring them resultsin under estimation of abandonment and expansion costs. Thispaper contributes to the gum belt deforestation literature byanalyzing the incentives for abandoning and expanding gumproduction using a real option approach.
In summary, the two main objectives of this paper are toanalyze the economic incentives: first, for preserving theexisting gum forest to understand if in the near future furtherdeforestation of gum arabic can be expected and, second, forestablishing new plantations at farm level to assess whetherexpansion of gum forest by farmers can be expected in the nearfuture. More specifically we will answer the following researchquestions: first, how much do the opportunity costs of laborhave to rise to induce farmers to abandon their gum forest? Andsecond, how much do gum prices have to rise in order to inducean expansion of the area under gum forest by converting eitheragricultural or bare land to gum production?
The remainder of the paper is structured as follows.Section 2 presents the theoretical framework of the paper andintroduces the gum production and management system.Section 3 describes the model. Expected average annual net-benefits (annuities) from gum agroforest, gum forest andpermanent agriculture systems are introduced and comparedto identify critical conditions for continuation and expansionof gum arabic production. Section 4 presents the data baseand the parameters of the model. The expected annuities forthe different systems are calculated based on the dataobtained from a farm level survey. Uncertainty is consideredby using Monte Carlo simulation. Secondary time series dataare used for the estimation of the coefficients of the realoption model. Section 5 presents and discusses the results andcompares the expected annuities under uncertainty andirreversibility for the different systems with the critical
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
values for expansion. The conclusions are drawn in the lastsection.
2. Theoretical framework
From the perspective of private profit maximization,economic gain is a necessary but not a sufficient condition forpreserving or planting the gum trees. Expected returns from thetrees depend on the value of the services the trees provide.These in turn are determined by economic and biophysicalfactors such as costs, output prices and growth and yieldfunctions. As long as alternatives for allocating either land orlabor exist (e.g. off-farm income), preservation and plantationof gum arabic has an opportunity cost. Also, farmers do not facea now-or-never dichotomous choice of either abandoning thegum business or planting trees as they can postpone thedecision. Additionally, they face uncertainty and irreversibilityabout future benefits and costs. Taken together, flexibility,irreversibility, and uncertainty influences the optimal timing ofthe decision to abandon or expand the production of gum arabic.
2.1. The bush-fallow cycle of gum cultivation
For the purpose of exposition we will model the bush-fallowcycle of gum cultivation which prevails in west Sudan. Thebush-fallow cycle is an agroforestry system based on integratingannual crops with gum trees in a temporal sequence. There are,however, other ways in which gum arabic is cultivated orcombined with field crops by farmers throughout the gum belt.Other forms of gum cultivation are: the agroforestry systembased on a spatial mixture – where annual crops and gum areproduced from the same land unit simultaneously – and purestand gum forest used for the production of gum only. Based onour survey data 75% of the farmers mentioned to follow thebush-fallow cycle (agroforestry based on temporal sequence)either solely or together with a combination of spatialagroforestry or pure stand gum forest. About 30% of thefarmers mentioned to use spatial agroforestry either solely or incombination with the other two gums land use (Table A.1. in theAppendix shows the percentage of farmers practicing thedifferent gum cultivation systems).
Fig. 1 illustrates the bush-fallow cycle of gum cultivation.The cycle starts by coppicing old gum trees at 10 cm from theground surface. The land is then used for the cultivation of fieldcrops such as millet, sesame, groundnut, sorghum, watermelonand roselle (Hibiscus sabdariffa L.). The average duration offield crop cultivation is around 4–6 years. Once the land isabandoned and put under fallow the coppiced trees shoot up andregenerate. Gum harvest usually starts after the tree has re-grown for 5–6 years and continues up to 15–20 years. Whengum trees cease to produce they are coppiced again for cropcultivation and the cycle is repeated (Ballal, 2002). The finaltree stand is mainly the result of coppice regeneration, besidessome regeneration from seeds dispersed naturally and in fewcases from deliberate enrichment planting. During the period offield crop cultivation the coppiced shoots re-growth is removedto allow for the establishment and growth of agricultural crops.
or expanding gum arabic production in Sudan. Forest Policy and Economics
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The change in the soil fertility (which improves during gumfallow and declines during tillage) provides a motivation for theuse of the land rotation cycle in the bush-fallow system.
2.2. Gum forest management options
We consider two options: the option to abandon and theoption to expand gum production. The option to abandonimplies either temporary suspension of gum harvesting orswitching to a land use system of annual crops production. In thecase of temporary suspension farmers abandon gum productionbut can leave the land idle and allow the tree to re-grow, whereasswitching the land use system to agriculture requires either thecomplete removal or yearly coppicing of the tree.
Land in Sudan, however, is not a scarce resource, forinstance only 20% of the total cultivable land is exploited inKordofan region (El-Dukheri, 1997). Moreover gum produc-tion takes place during the dry season and does not competewith agricultural crops for labor but rather competes with jobopportunities during the dry season. One important trade-off toconsider therefore is between the income from gum harvestingwhich takes place during the dry season versus the incomefrom off-farm work during that same season. If farmers decideto continue the gum business they will receive a stochasticflow of benefits from gum harvesting during the dry season.Furthermore, if they follow the bush-fallow cycle they mayalso receive returns from agriculture crops during the first 4–6 years. More formally, we can say a gum farmer will continuecultivating gum trees down to a critical value of abandoning
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
below which stopping gum tree cultivation becomes econom-ically viable.
Similarly, the option of expanding will be exercised ifplanting of gum trees either as a forest or agroforest (includingproduction of annual crops during the first four years)generates a higher economic value than using the land andlabor for alternative purposes e.g. agriculture productionduring the rainy season and off-farm work during the dryseason.
In the following section we explain the economic model toanalyze incentives for abandoning gum forest production andincentives for expanding gum forest production in moredetail.
3. Model setting
Assume that a risk neutral farmer owns 1 ha of land whichis used for gum agroforestry. The farmer is deciding whetherto preserve this land use system or abandon the gumbusiness. One option is to neglect the land and let the treesre-grow. In this case abandoning gum arabic production doesnot entail any extra costs and includes the possibility to startcultivating gum trees again e.g. if the economic situationimproves such as by an increase in the price of gum. Theother option is to switch the land use to permanent agricultureand produce a portfolio of annual crops. But this optionwould only be applicable if land would be scarce. As this isnot very relevant in our case, we do not pursue furtheranalyzing this option.
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3.1. Benefits from gum arabic and agriculture
The normal bush-fallow rotation allows the farmer to obtainreturns from cultivating annual crops during the first four years ofthe rotation and returns from harvesting gum when the tree is sixyears and older. At the end of the life span (T ) the trees arecoppiced and start to rejuvenate. The total gross margin in presentvalue obtained from one rotation, TGMAGF1
1 of length T is:
TGMAGF1 ¼Z t¼4
t¼0RAd e
−ltdt þZ T
t¼4RGðtÞd e−ltdt þ Sd e−lt
� �
−Z t¼4
t¼0VCAd e
−ltdt þZ T
t¼4VCGðtÞd e−ltdt
� �
ð1Þwhere RA=PAYA is the gross revenue and VCA the variable costsfrom annual agricultural crops with PA, YA and VCA being theprice, yield and variable cost vectors, respectively. The grossrevenue of gum production is given by RG=PGYG(t) where PG isthe price per unit of gum, YG(t) the yield of gum and VCG thevariable cost vector of the gum crop. S is the net-benefit ofharvesting the timber, the stumpage value, at the end of therotation cycle T. Further, μ represents the private discount rate,equivalent to the ‘private rate of time preference’, and measureshow future benefits and costs are weighted relative to immediateones. The optimal rotation interval, T⁎, is obtained where themarginal benefit of the gum forest left growing for an additionalperiod equals themarginal opportunity cost of this choicewhich isa the maximum annuity (Tassone et al., 2004).2
Starting at time t=0 the total gross margin of the gumagroforestry over an infinite time horizon is given by
TGMAGF ¼ TGMAGF1
1−e−lT⁎: ð2Þ
Alternatively, the present value obtained from annual crops,TGMA1 over a rotation of length T⁎ is given by:
TGMA1 ¼ ðRA−VCAÞZ t¼T⁎
t¼0e−ltdt; ð3Þ
this gives over an infinite time horizon and constant grossmargin:
TGMA ¼ TGMA1
1−e−lT⁎: ð4Þ
The incremental total gross margin of abandoning the gumagroforestry system over an infinite time horizon TGMABG ismeasured as the incremental benefit of annual crops.3 This is the
1 AGF stands for Gum AgroForestry system and the subscript (1) on thepresent value terms indicates the number of rotation. Note that gum revenuemay occur from t=4, but its value in years 4–8 will be zero and gum harvestingstarts when revenue exceeds variable costs.2 To avoid notation clutter we do not differentiate further between an
agroforest and forest system.3 ABG refers to Abandoning Gum Agroforestry.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
difference between the present value of annual crops TGMA andthe present value of gum agroforestry TGMAGF:
TGMABG ¼ TGMA−TGMAGF: ð5Þ
3.2. Irreversibility
Dixit and Pindyck (1994) show that entry and exit underirreversibility, uncertainty and flexibility creates option valuesthat add additional costs to expanding an activity as well asadditional costs for abandoning an activity. As mentionedearlier if farmers want to abandon gum agroforestry and convertthe land to agriculture, they need to either uproot the gum tree orcoppice it every year. The costs of deforestation are denoted byDF. However, as land is not scarce resource in Sudan farmer canabandon gum production and leave the forest behind, weassume that there are no irreversible costs for abandoning gumarabic production as the land can just be left idle. That is DF isconsidered to be zero and there is no extra value of waiting toabandon the gum arabic production. Under this situation theabandonment condition for a gum arabic farmer will be met ifthe expected total gross margin from gum agroforestry turns outto be less than the opportunity costs of labor (OC),TGMAGFbOC.
The situation looks different if a farmer considers expandinggum arabic production. In this case farmers will face irreversibleafforestation costs, denoted by AF, and hence there are gainsfrom postponing planting of new trees. To model the uncertaintyof gum agroforestry revenue, we assume that the annualincremental benefits from agroforestry, denoted by4
RAGF ¼
R t¼4
t¼0RA:e−ltdtþ
R T
t¼4RGðtÞd e−ltdt
� �1−e−lT⁎
24
35−TGMA
el−1ð6Þ
follow a geometric Brownian motion of the form dRAGF=αR-AGFdt+σRAGFdz, with α being the drift rate, σ the variance rate,and dz a Wiener process. The assumption of geometricBrownian motion implies that the current value of the annualincremental benefit from gum agroforestry is known but futurevalues are log normally distributed with a variance that growslinearly with time i.e. RAGF is uncertain. Identification of thecorrect stochastic process the benefits follow (whether e.g.geometric Brownian motion or mean reverting) is difficult usingeconometric techniques to test the time series data. Dixit andPindyck (1994) pointed out that the results can be ambiguousand depend on the time frame used. They recommendedchoosing the stochastic process not based on testing stationarityassumption for time series data but on theoretical grounds. Froman empirical point of view the choice of the stochastic processmay be important if different processes lead to different resultsand policy recommendations. According to Hassett and Metcalf
4 For simplification we compare the revenue from gum agroforestry with thetotal gross margin from agriculture.
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(1995), however, the choice of stochastic process (geometricBrownian motion versus mean reversion) has no significanteffect on the results; hence the more tractable geometricBrownian motion process can be used without significant lossof realism.5
Following Dixit and Pindyck (1994, pp. 186–195) in solvingfor the critical incremental annual value of gum agroforestryR⁎AGF, where expanding the gum agroforestry system would bebeneficial, provides the following two non-linear equations foran optimal solution:
A1R⁎AGF
b1¼ B2R⁎AGF
b2þR⁎AGF=d−ðCAGF−SaÞ=l−AF ð7Þ
b1A1R⁎AGF
b1−1¼ b2B2R⁎AGF
b2−1þ1=d ð8Þ
where β1,26 is
b1;2 ¼12−ðl−dÞ=r2F ðl−rÞ=r2− 1
2
� �þ 2l=r2
� �1=2; ð9Þ
Here δ is the convenience yield and given by δ=μ−α.7 CAGF isthe sum of the weighted average cost of production of annualcrops and production of gum. Sa is the average annual timberbenefits based on STe
−μT for an infinite horizon.8 A1R⁎AGFβ1 is
the value of the option to plant new gum trees. This value needsto be matched by the value of planting gum arabic trees i.e. theright-hand-side of Eq. (7). R⁎AGF /δ− (CAGF−Sa) /μ indicates thetotal gross margin from gum arabic and AF the irreversibleplanting costs. B2R⁎AGF
β2 captures the value of future abandon-ing gum arabic production if prices drop but production can,however, restart without any additional irreversible costs. B2 isdefined as B2 ¼ ðCAGF−SaÞ1−b2
b1−b2b1l−b1−1d
� �(Dixit and Pindyck, 1994,
p. 189). Eq. (8) is another optimality condition, the so-calledsmooth pasting condition that needs to be met at the optimum.Solving Eqs. (7) and (8) for A1 gives the following equation:
As B2 is known Eq. (10) can be solved numerically to givethe critical incremental annual value of gum agroforestry RA
⁎GF
which can be compared with current values of the annualincremental benefits of gum agroforestry RAGF. This allows usto examine farmers' incentive to expand the gum business either
5 The main advantage of using geometric Brownian motion is that it leads totractable solutions and closed form expressions that can be readily analyzed(Dixit and Pindyck, 1994).6 β1 and β2 are the two roots of a second order homogenous equation as a
result of the solution for the real option value.7 We assume that δN0 implying μNα this assumption is made to ensure the
existence of an optimum otherwise waiting is always optimal.8 The gum arabic timber at the end of the rotation is mainly used as fuel wood
or for charcoal production. As the gain from fuel wood is relatively small, inour analysis we assume for simplification that the benefits equal the costs andset Sa=0.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
by converting idle land into gum agroforestry or by switchingthe land use system from annual crops to gum agroforestry.Computing the current values of RAGF requires calculating theaverage annuity of revenues and costs for the annual cropsportfolio, the gum agroforestry and for a pure stand gum forest.In the following section we will describe the data and thecalculation procedure in more detail.
4. Data and calculation
The data for undertaking the analysis of this paper weredrawn from a field survey that was conducted between Januaryand July 2003 in Kordofan region (West Sudan). Kordofan wasselected due to its long history of gum production. In additionthis area has been a major focus of the gum belt restockingactivities which were implemented after the Sahel drought bythe Sudanese government in collaboration with internationaldonor organizations. Kordofan region is administrativelydivided into three states: north, south and west Kordofan.First, 20 villages were purposefully chosen based on pastrestocking activities. In the absence of an official census and inorder to generate a sample of households, a household rosterwas compiled by asking each village headman to name all thehousehold heads under their authority. The household censusprovided the sampling frame within which we stratifiedhouseholds in each village into three categories: ‘adopters’(who are currently producing gum), ‘disadopters’ (who hadpreviously produced gum but who had discontinued the practicefor at least 3 years before the survey time), and ‘non-adopters’(who had not produced gum before). Then a 1-in-5 randomsample was drawn from each stratum in each village making atotal sample size of 377 households, during data processing,however, 9 were dropped out because of missing data andinconsistencies, leaving 368 households for which data wasavailable.9 For the purpose of this paper we only consider theadopters category (a sample of 228 households) as we areinterested in analyzing the economic incentives for preservationand expansion of gum forests by farmers who are alreadyplanting the gum trees either as agroforest or forest.
Furthermore, focus group discussions were also held in eachof the surveyed villages. Information regarding the minimumand maximum selling prices for the various crops, variableinputs required for the agricultural operations per unit of land,input costs and the cost of planting trees were generated fromthese village level focus group discussion. Using the farm levelquestionnaire we obtained information regarding the proportionof land allocated to each crop and the yield of the different cropsper unit of land. To calculate the gross margin of the annualcrops we constructed a portfolio of the three major cash crops inthe study area based on the average proportion of land allocatedto each, as found in the farm level survey. The portfolio includesa 50% share of sesame, a 20% share of groundnut and a 30%share of roselle.
9 The number of households interviewed from each state classified byadoption category is shown in Appendix A.2.
or expanding gum arabic production in Sudan. Forest Policy and Economics
Fig. 3. Schematic representation of the Monte Carlo simulation.
Table 1Expected annuities for agriculture, gum arabic agroforestry, and gum arabicforestry for 1 ha of land in SD a
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The farm level survey also included hypothetical questionsdesigned to measure the rate of time-preference, μ for thesurveyed farmers in the study area following Holden et al.(1998). Respondents were asked to show their preferences forcurrent values PVi versus future values FV to be obtained in ayear time. The rate of time-preference for individual i was thencomputed as li ¼ ln FV=PVið Þ. We use the maximum, mini-mum and mean computed farmers' real rate of time-preferenceas the discount rate in the different models. The summarystatistics of the survey results are given in Table A.3 andTable A.4 in the Appendix.
We estimated the age-yield function of gum trees using theHoerl function y= vgξekgu and following others such asHaworth and Vincent (1977), Wesseler (1997) and Mithöferet al. (2004). The functional form assumes that yield y in a givenyear depends on age g. It also includes a multiplicativedisturbance term u which implies that the distribution of yieldfor any given age is log normal. The coefficients v, ξ and k canbe estimated using ordinary least squares. Fig. 2 shows the age-yield function estimated using data from Pearce (1988).Production of gum starts when the tree is six years old; afterwhich a sigmoid growth portion follows up to the age of about14 years then production starts to decrease. The estimated age-yield function for a gum forest of 400 trees gives a maximumyield of 1400 kg of gum arabic per hectare at age 14.10
The average value of 1 ha of gum agroforestry VAGF for oneproduction cycle over an infinite time horizon is calculated fromthe results of a Monte Carlo simulation following Wesseler(1997). The Monte Carlo simulation approach adopted involvesmaking probability distribution assumptions for the parametersof the model. In our analysis we only considered uncertaintywith regard to gum prices, portfolio prices and farmers' rate oftime-preference. Gum prices are modeled as a triangular
10 Table A.5 in the Appendix shows the costs and benefits for using 1 ha ofland to produce the crop portfolio in SD. The costs and benefits for the cropportfolio are shown for one year. Calculations are given for the expected valuesfor the uncertain parameters: rate of time preference 0.33 and portfolio price166.05 SD. SD refers to Sudanese Dinar. 1 USD was equivalent to 250 SDduring the survey period. Table A.6 in the Appendix shows the costs andbenefits for 1 ha of gum forest with 400 trees in Sudanese Dinar (SD).Calculations are given for the expected values of the uncertain parameters: rateof time preference 0.30 and gum price 89.87 SD.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
distribution with minimum, maximum and modal farm gateprices of 65, 140 and 70 SD/kg for the 2002/03 season. Portfolioprices are assumed to follow a uniform distribution between 80and 200 SD/kg, which are the minimum and maximum pricesfarmers received based on the survey data. The private rate oftime-preference is also considered to be uniformly distributedbetween 0.19 and 0.53, which are the minimum and maximumfarmers' rate of time-preference obtained from the survey. Thena multiple simulation of the outcomes of the model aregenerated by randomly sampling the uncertain parameters.Using the Monte Carlo simulation results we then calculate theaverage annuity of revenues and costs from agriculture and froma pure stand of gum forest trees. Fig. 3 sketches the schematicrepresentation of the Monte Carlo simulation.
As mentioned before we assume that the annual incrementalrevenues from gum agroforestry RAGF follow a geometricBrownian motion. Unfortunately, only time series data forprices and amounts of gum arabic and other agricultural crops
Sources: Computations of total revenue and real prices are based on dataobtained from El Obeid Auction Market Bureau various annual reports.Computations of real floor price are based on data obtained from Gum ArabicCompany 27th annual meeting report (2000).a Portfolio is based on a weighted average of crops with weights of 0.5, 0.2
and 0.3 for sesame, groundnut and roselle, respectively.b Total revenue is calculated from the amount traded during one calendar
year weighted with the average real price of the calendar year.c Average real price of the calendar year.d Real floor price for gum arabic as published in the annual report of the Gum
Arabic Company (GAC) of Sudan.
Table 3Critical values for expanding gum arabic production for a selection of variousdrift (α) and variance (σ) rates for the geometric Brownian motion and usingdifferent discount rates (μ)
Minimum discountrate (μ=0.19)
Mean discountrate (μ=0.36)
Maximum discountrate (μ=0.53)
Drift and variance rate based on real total gum revenueCritical valuesGum agroforestry(RAGF
⁎)58,336 58,918 59,440
Gum forest(RGF
⁎)3747 4014 4269
Drift and variance rate based on real gum priceCritical valuesGum agroforestry(RAGF
⁎)48,204 48,775 49,215
Gum forest(RGF
⁎)1306 1497 1678
Drift and variance rate based on real floor price for gumCritical valuesGum agroforestry(RAGF
⁎)48,235 48,774 49,194
Gum forest(RGF
⁎)1678 1312 1497
Drift and variance rate based on real total revenue of the portfolioCritical valuesGum agroforestry(RAGF
⁎)53,418 54,085 54,643
Gum forest(RGF
⁎)2407 2660 2896
Drift and variance rate based on real price of the portfolioCritical valuesGum agroforestry(RAGF
⁎)49,556 50,237 50,764
Gum forest(RGF
⁎)1558 1780 1985
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traded at El Obeid Auction Market Bureau are available. Thisdoes not allow us to calculate a time series for RAGF. Instead, weestimate the drift and variance rates of gum agroforestry revenuesfrom the real prices and real total gross revenue time series dataof the crop portfolio and gum arabic. We then use the differentvariance and drift rates to calculate the critical R⁎AGF usingMicrosoft Excel following Campbell et al. (1997, Chapter 9).
5. Results and discussion
The results of the Monte Carlo simulation are presented inTable 1. The three columns show the expected annuities for using1 ha of land either for agriculture, for gum arabic agroforestry orpure stand of gum arabic trees. Table 2 shows the estimated driftand variance rates of gum arabic, the three major cash cropsconsidered in the portfolio, and the weighted average for theportfolio. The various drift and variance rates were calculatedusing two data sources for agricultural crops (prices and grossrevenues of crops traded at El Obeid auction) and three for gumarabic (prices and gross revenues of gum arabic traded at ElObeid auction and gum arabic floor price). The drift and variancerates are used to calculate the critical values for establishing gumarabic agroforest or a forest system.
Table 3 reports the critical incremental annual value of gumagroforestry R⁎AGF needed for switching land use either to gumarabic agroforest or forest system calculated using different driftrates, variance rates and discount rates μ (minimum, mean andmaximum). These values can be compared with the expectedannuities for gum agroforest reported in Table 1.
5.1. Abandoning gum arabic
The results in Table 1 show that agriculture currently pro-vides the highest expected economic benefits. The average
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
annual reversible net-benefits from agriculture are about 27%higher than from the gum arabic agroforestry and about 90%higher than from the gum arabic forests. We mentioned earlierthat gum arabic does not directly compete with agriculture butwith off-farm labor opportunities during the off-season. Theobserved cultivation of gum arabic can therefore be explainedby the non-overlapping labor requirement and under suchsituation farmers might abandon gum production while leavingthe forest land idle if they find better off-farm opportunities. Theeconomy studied here is traditional and stagnant with limitedoff-farm labor opportunities. Based on our results the forest willbe left behind when the critical value for the opportunity costsof labor is equal to the average revenues from gum arabic perunit of labor. For this to happen the average opportunity costs oflabor will have to increase by about nine to ten times (5270/555). Therefore, diversification of the economy and increasingoff-farm and non-agricultural employment in relatively largervillages in the gum belt zone can result in the abandonment ofthe gum forest and reduce the deforestation pressure. At thesame time it can have an adverse effect on gum production andthe Sudanese exports of gum arabic. As the increase in off-farm
or expanding gum arabic production in Sudan. Forest Policy and Economics
11 As a result of pressure and belief that the GAC monopolistic arrangementshould be de-regulated to allow free entry into the industry, the system hascurrently been partially liberalized and the export of semi-processed gum byprivate companies is now permitted by the Sudanese government.12 At the theoretical level the assumption of a trader paying the minimumadequate price if he could pay less is not realistic. Driven by profitmaximization motives traders will always attempt to pay a lower price.
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income has to be substantial, it can be expected that abandoningof gum arabic production may not happen in the near future.
It is worth mentioning here that labor has been priced in ourmodel as average costs over all farmers and not at marginalcosts of an individual farmer. Though our analysis and resultshere suggest low incentive for abandonment it is not necessarilythat no abandonment of gum production will happen as themarginal opportunity cost of labor for some farmers might behigher than the one we used in our analysis. Nevertheless, thecurrent situation of agricultural land abundance and laborscarcity prohibits the expansion of agricultural production bydeforesting gum arabic trees. Because of this, the conversion ofgum forests to agricultural production only becomes a problemif the population density in Sudan would increase and the laborconstraint is relaxed.
5.2. Expanding gum arabic production
The second research question in our analysis is when can weexpect farmers to expand the gum arabic forest? There are twooptions that we need to consider. The first option is convertingidle land with zero opportunity costs and the second to convertagricultural land into land for gum arabic production. Bothtypes of land can either be converted to an agroforestry system,including agricultural production during the initial years, or apure stand of gum trees without agricultural production.
5.2.1. Converting idle land to a gum arabic forestTable 3 shows the critical incremental annual values for gum
agroforestry R⁎AGF and gum forestry R⁎GF calculated based on aselection of drift rates, α, variance rates, σ, and using differentdiscount rates μ. The critical incremental annual values for gumagroforestry range from about 48,200 to 59,500 Sudanese Dinar(SD) per hectare, whereas the critical values for gum forestryrange from 1300 to 4200 SD per hectare. The currentincremental average annual benefits of gum arabic agroforestsand the forest system, as shown in Table 1, are 76,412 and 5270SD per hectare respectively. Since the opportunity cost of idleland is zero both values are above the calculated critical valuesreported in Table 3. Given this, we would expect farmers toexpand gum arabic production; however, this is not seen inpractice. Why is this not happening? There are two main factorsthat may explain the current situation. One factor is laboravailability. We mentioned earlier labor has been priced in ourmodel at average costs over all farmers and not at marginalcosts of an individual farmer, as marginal costs of labor perfarmer are difficult to observe. It is reasonable that themarginal opportunity cost of labor for some farmers might behigher than the reported average costs, so expansion of gumarabic may be limited by labor availability. A second factor isproperty rights. We have assumed that farmers will face noproblem in securing their access to the harvest of gum over aninfinite life-time of the forest. The current political instabilityin the country, however, may force families to abandon theirfarms and move to a different place. This most likely willdiscourage long-term investments such as the decision to planttrees.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
5.2.2. Converting agriculture land to a gum arabic forestThe current incremental average annual benefits for converting
agricultural land to a gum arabic forest or a gum arabic agroforestare about 5270–44,809=−39,539 or 76,412–44,809=31,603respectively. The difference between the two values can simplybe explained by the higher expected benefits from agricultureduring the first four years of the bush-fallow cycle. Both valuesare below the calculated critical values reported in Table 3.Currently, we can not expect farmers to convert permanentagricultural land to gum arabic forest or agroforest. If wecompare the incremental average annual benefits for a gumarabic agroforest system with the critical values reported inTable 3 we observe that the average annual benefits from thegum arabic agroforest have to increase by at least 53%. Thisis equivalent to an increase in the prices of gum arabic of atleast about 315% (48,204−31,603) / 5270. Even much higherprice increase is needed to induce a shift to gum arabic forests,i.e. the price for gum arabic has to increase by at least 775%.These results indicate that even if the constraints on thelabor market will be reduced and political uncertainty isresolved, conversion of agricultural land to gum arabic forestsis very unlikely to happen in the near future without anyadditional support to farmers in the form of improving theprice incentive.
5.2.3. Price policies to onvert agriculture land to a gum arabicforest
The farm gate price of gum arabic results from a complexcombination of domestic and international factors. The market-ing of gum arabic is controlled by the Gum Arabic Company(GAC), who has monopoly over raw gum exports from Sudanand also plays an important role in the local marketing of gumarabic.11 The GAC sets not only the export price for gum arabicbecause of its large market share but also announces and isassumed to supervise a fixed minimum price at the gum auctionmarkets as a mechanism to ensure that producers are adequatelyremunerated.12
One policy option for increasing the farm gate price is toincrease the export price level. Given the recent changes in theinternational gum market and the decline in Sudan marketshare (Macrae and Merlin, 2002), however, increasing the gumexport price is likely to be difficult to achieve. Even if anincrease in export price level is feasible it would be difficult tosustain; it is very likely that international demand will decreaseas a response to higher prices and further development of gummanufactured substitutes will be triggered. A high and abruptincrease in producer price may encourage over-tapping. Over-tapping and the concomitant death of the trees in the processtook place in the 1970s when the GAC increased the domestic
or expanding gum arabic production in Sudan. Forest Policy and Economics
9A.H. Rahim et al. / Forest Policy and Economics xx (2007) xxx–xxx
ARTICLE IN PRESS
market price considerably (by 300% in nominal terms in aperiod of 2 years—1973–1974 season) in an attempt tointroduce incentives for boosting gum production after theSahel drought (Larson and Bromley, 1991). Stabilization ofboth domestic and international market prices is thereforeimportant for sustaining the gum forest as well as Sudaneserevenue from gum export.
Another policy instrument that can give farmers long-termconfidence and the incentive necessary to induce treeplanting and investment is to adopt measures that willremove the distortions in the domestic pricing and marketingof gum. Two features of the domestic market prevent pro-ducers from receiving a higher remuneration for their pro-duction. These are high levels of profits margins and taxescharged by the GAC and the Sudanese government and thepredominance of informal money lending institutions at thevillage level.13
Regarding the former (excessive level of profit and taxationby the government) despite the fact that the GAC is undermajority private ownership (70% of the company share areowned by individuals and the gum producers association),over 20% of the FOB value of gum arabic currently ends up inthe public treasury via various types of taxes, fees and exportduties.14 The farm gate prices, depending on the extent towhich farmers are able to sell at the official announced prices,may be as low as 21% of the FOB value.15 Accordingly,improving the returns to producers could be feasible in casepolicy makers are willing to reduce the level of profits andtaxation that end up in the GAC or the public treasury. Nev-ertheless, the fact that the Sudanese gum market has been de-regulated to some extent might have some positive effect onproducers' future price levels.
Another feature that distorts the domestic gum market is thepredominance of informal credit institution i.e. the sheil system.It is assumed that gum producers sell their product at the localauction markets in order to receive the officially announcedminimum price. Most producers, however, are often preventedfrom selling their product at the auctions due to transportproblems. Only 6% of the interviewed farmers sold their gumat the auctions market, 86% sold their gum to the villagemerchants (who in most cases are the money lendersthemselves) and 64% mentioned that they sold their gum at aprice lower than the announced floor price. Formal credit
13 The informal money lending institution is known locally as the sheil systemwhereby village merchants or intermediate traders provide loans to farmers inanticipation of their harvest. Credit is paid in the form of consumer goods or incash. Because farmers who resort to the sheil system generally have lowbargaining power they sell their future harvest at lower prices than what theycould obtain if they sell their product directly to the merchants after harvest.14 This figure is calculated based on information provided by the GAC annualreports and it does not include GAC profit, which accounts for 9% of the FOBprice.15 In 2003 (survey period), the announced floor price was 3500 SD/kantar, andthe export FOB price was 1480 USD/MT. Using the prevailing exchange rateduring the period, which is one USD is equivalent to 250 SD and as one Kantaris equivalent to 45 kg, one can calculate that the floor price represents 21.02%of the FOB value. Macrae and Merlin (2002) report that producers in Sudan areestimated to receive one fifth of the final gum export price.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
facilities within the agricultural sector in Sudan are extendedonly to farmers who are able to provide a guarantee to thebank, mainly in the form of stored products and land titles(IEED/IES, 1990). Because small farmers are seldom able toprovide guarantees, they are greatly dependent on the sheilsystem. This dependency can act as a constraint and preventfarmers from receiving better prices for their gum harvest.Therefore, promoting a mechanism that will reduce the highcredit costs of the sheil system (e.g. extending formal credit togum farmers through cooperative schemes) can increase returnsfrom gum arabic production.
6. Conclusion
This paper focuses on the analysis of the economic incentivesfor abandoning or expanding gum arabic production in Sudanusing a real options approach. Conversions of land use systemfrom gum agroforestry (forest) to a continuous annual croppingsystem and vice versa imply a quasi-irreversible but flexiblenature of land allocation. In addition the benefits and opportunitycosts of such actions are uncertain, therefore, the decision todeforest or to plant gum trees generates an option value.
We show that agriculture currently provides higher expectedeconomic benefits than the gum agroforestry (forestry) system.However, in Sudan land is not scarce but labor is a relativelyscarce factor. Gum arabic is produced during the dry season anddoes not compete with other agricultural crops for labor demand.Because of the aforementioned reasons farmers might abandongum production, leave the tree on the land and pursue off-farmincome. Our results show that an increase of about nine to tentimes on the average opportunity costs of labor would be neededin order for farmers to abandon gum arabic production, neglect thegum forests and start working off-farm.
As for the decision on the expansion of gum forest weanalyzed two options: converting idle land into gum forest andconverting agricultural land into gum forest. Results show thatthe incremental average annual benefits of gum agroforestry orforestry systems are above the critical values for converting idleland to a gum arabic forest. This suggests that farmer's wouldexpand gum forest. However, this is not observed, and wesuggest two explanations for the observed non-conversion ofidle land into gum forest: scarcity of labor and insecure propertyrights caused by political instability in the country whichdiscourage long-term investments.
Furthermore, the current incremental average annualbenefits for converting agricultural land into a gum arabicagroforestry (forestry) system are below the calculatedthreshold values needed for the investment. Results suggestthat an increase in the prices of gum arabic respectively ofabout 315% and 775% is needed to induce a shift in land usesystem from continuous agricultural production to gumagroforestry or forestry land use systems respectively. Thisspecific result suggests that even if the constraints on the labormarket are reduced and the political uncertainty is resolvedconversion of agricultural land into gum arabic forests isunlikely to happen in the near future without an increase in thegum price.
or expanding gum arabic production in Sudan. Forest Policy and Economics
80 170 NA NA Groundnut 50 125 NA NA Roselle 100 300 NA NA Portfolio 80 200 NA NA Gum2 65 140 NA NA
Rate of time-preference3
Present value equivalent in SD(N=92)
5886
8270 7144.18 754.95
Rate of time-preference (N=92)
0.19 0.53 0.34 0.11
Source: Based on survey data (2003).1 The farm gate prices represent the average maximum price at which
farmers sell their crops early in the season and the average minimum price atwhich farmers sell their crops late in the season. Data on prices are based on theinterview of key informants at the village level. The average minimum andmaximum price are calculated from the values reported by the 20 surveyedvillages.
2 The modal price for gum (the most common selling price for gum amongthe surveyed villages based on key informants' interview) is 70 SD/kg.
3 To measure the rate of time-preference farmers were asked thefollowing question: if you have the choice between an amount of moneytoday (PV) and 10,000 SD (FV) to be received in one year with certainty,how large will the amount to be received today (PV) have to be for you toprefer it instead of the FV in one year?. The response rate to the hypotheticalquestions for measuring the rate of time-preference among the adopterscategory is 40%, therefore the sample size included in the above statistics is92 respondents.
Table A.4Labor requirements for crop production per hectare of land in hours and thecost of labor man-days in SD
1
Agriculturaloperation/crop
Labor hours required per operation for 1 ha ofthe crop
Laborcost(SD/man-days)
Sesame
Groundnut Roselle Portfolio Gumarabic
Land clearanceandpreparation
32
32 32 32 NA 400
Seeding andplanting
28
56 21 32 NA 300
First weeding
63 84 63 67 NA 300 Second weeding 24 49 21 28 NA 300 Early harvesting 98 84 70 87 NA 1000 Late harvesting 63 77 56 64 NA 1000
11A.H. Rahim et al. / Forest Policy and Economics xx (2007) xxx–xxx
ARTICLE IN PRESS
(continued)Table A.4 (continued )
31 40 0.1
69 61 22 32 0 54 1.5
0.2
.118
554
Agricultural
operation/crop
Please cite this a(2007), doi:10.1
Labor hours required per operation for 1 ha ofthe crop
0 4 91 00 00 00 089
58.1
rticle as: Rahim, A.H. et al. Economic incentives016/j.forpol.2007.02.002
Laborcost(SD/man-days)
Sesame
Groundnut Roselle Portfolio
0 0 .2 7 6 2 2 4 .9 .2 8 4
Gumarabic
293
400
40.34
0134
912082
8
2200
23200
30
05400
52.6
1
3.2
118087.8
15458.39
5
Other laborrequirements(post-harvestcleaning, seedseparation…Etc.)
18
28 14 19 NA 400
7 1
Gum tapping NA NA NA NA 52 300
6 58 0 0 0 84.
8.2
Gum collection NA NA NA NA 77 300
28 400
0.4
184
165
220
320
0 540
3.4
6.9
180
545
Total laborrequired(hours/ha)
326
410 277 328 129
…
5 31 0 0 0 7 0
Source: Based on survey data (2003).1 Data are based on the interview of key informants at the village level.
One labor man-day is equal to 7 working hours.
910
400
400
0.25
0.5
99220
8873
197
2200
220
3200
320
00
5400
540
504
387
324
102
324
135
108
439
Table A.5Costs and benefits for 1 ha of crop portfolios
Annual crops portfolio
Portfolio yield (kg/ha)
fo
760
… Portfolio revenue (SD/ha/year) 86,249
cost.
Portfolio cost
00 .02
⁎ able
Portfolio seed cost (SD/ha/year) 1000
7 4 0 8 0 0 0 0 0 0 0 0 0 0
vari
Land clearance cost (SD/ha/year) 1900
ds
Seeding cost (SD/ha/year) 1400
3 cee
First weeding cost (SD/ha/year) 2800
6 400
0.00
1 0 0 0 0 0 0 0 0 0 0 eex
Second weeding cost (SD/ha/year) 1200
enu
Harvesting cost (SD/ha/year) 22,000
rev
Cost of coppicing the shoot (SD/ha/year) 1000
… en
Portfolio labor cost (SD/ha/year) 30,300
wh
Portfolio other variable costs (SD/ha/year)
1000
tarts
Total portfolio cost (SD/ha/year)
62,600
2 400
0 0 0 0 0 0 0 0 0 0 0 0 gs
Annuity agriculture Benefits 126,194
stin
Annuity agriculture costs 62,600
arve
Annuity agriculture net-benefit 63,594
TableA.6
Costsandbenefitsfor1ha
ofgum
forestwith
400trees
Year
01
Gum
forest
Planted
trees/ha
0400
Gum
yield(kg/tree)
00
Gum
Yield
(kg/ha)
00
Gum
revenuein
SD/ha/year
00
Gum
productio
ncosts
Labor
tappingcost(SD/ha/year)
00
Labor
collectioncost(SD/ha/year)
00
Costforrejuvenatin
gthetrees(SD/ha/year)
00
Totalcost(SD/ha/year)
00
Totalcostdiscounted
(SD/ha/year)
00
Gum
revenue—
totalcost(gross
marginfrom
gum
forest)
00
Discountedgrossmarginfrom
thegum
forest(SD)
00
Accum
ulated
discounted
grossmarginfrom
gum
forest(SD)
00
Annuity
gum
forest(SD)
00
Maxim
umannuity
gum
forest(SD)
5458
NPV
gum
forest(SD)
18088
Annualdiscounted
costforgum
forest(SD)
2166
Average
annual
discounted
costforgum
forest(SD)
654
Optim
allifespan
29
Source:
Based
onsurvey
data
(2003).
⁎ Notethat
thereisyieldin
year
6and7,
butthevalueof
therevenueiszero
asgum
h
Source: Based on survey data (2003).
References
Ahmed, M., E., 2000. The socio-economic role of Acacia senegal in sustainabledevelopment of rural areas in the gum belt of Sudan. Unpublished PhDthesis. Technische Universität Dreseden, Germany.
Ballal, M., E., 2002. Causes of variability in gum arabic yield fromAcacia Senegalas related to some environmental and managerial factors. PhD thesis—Facultyof Forestry, University of Khartoum-Sudan.
Barbier, E.B., 2000. The economic linkages between rural poverty and landdegradation: some evidence from Africa. Agriculture, Ecosystems &Environment 82, 355–370.
Campbell, J.Y., Lo, A.W., MacKinlay, A.C., 1997. The Econometrics ofFinancial Markets. Princeton University Press, Princeton, NJ.
Dixit, A., Pindyck, R.S., 1994. Investment under Uncertainty. PrincetonUniversity Press, Princeton, NJ.
El-Dukheri, I. A., 1997. Past changes and future prospects of traditional rain-fedfarming in north Kordofan state. Unpublished PhD thesis München,Technische Universitat München-Germany.
Elmadih, M.A., 1992. Target MOTAD analysis of risk-income trade off, dry landfarming in the Nuba mountains region of Western Sudan. Unpublished M.Scthesis, Department of Agricultural Economics, Washington State University.
r abandoning or expanding gum arabic production in Sudan. Forest Policy and Economics
12 A.H. Rahim et al. / Forest Policy and Economics xx (2007) xxx–xxx
ARTICLE IN PRESS
Elmqvist, B., Olsson, L., Elamin, E.M., Warren, A., 2005. A traditionalagroforestry system under threat: an analysis of the gum Arabic market andcultivation in the Sudan. Agroforestry Systems 64, 211–218.
El Obeid Auction Market Bureau. Annual statistics on agricultural crops trade1960–2001 in Arabic. Ministry of Agriculture and Natural Resources,Kordofan, Sudan.
Hassett, K.A., Metcalf, G.E., 1995. Investment under alternative returnassumption: comparing random walk and mean reversion. Journal ofEconomic Dynamics & Control 19, 1471–1488.
Haworth, J.M., Vincent, P.J., 1977. Medium Term Forecasting of Orchard FruitProduction in the EEC: Methods and Analysis. European CommunitiesCommission, Brussels, Belgium.
Holden, S.T., Shiferaw, B., Wik, M., 1998. Poverty, market imperfections andtime preferences of relevance for environmental policy. Environment andDevelopment Economics 3, 105–130.
IEED and IES, 1990. Gum arabic rehabilitation in the republic of the Sudan:stage 1 report volume 2. Main report and recommendations for action.Khartoum, International Institute for Environment and Development(IEED), London, England and Institute of Environmental Studies (IES),University of Khartoum, Sudan.
Please cite this article as: Rahim, A.H. et al. Economic incentives for abandoning(2007), doi:10.1016/j.forpol.2007.02.002
Keddeman, W., 1994. Restocking of the gum belt for desertification control inKordofan, Phase III. Report of the evaluation mission (UNSO/SUD/89/X05). Netherlands Economic Institute, Agricultural and Rural DevelopmentDepartment, Rotterdam.
Larson, B.A., Bromley, D.W., 1991. Natural resource prices, export policies anddeforestation: the case of Sudan. World Development 19 (10), 1289–1297.
Macrae, J., Merlin, G., 2002. The Prospects and Constraints of Development ofGum Arabic in Sub-Saharan Africa. World Bank, Washington, D.C.
Mithöfer, D., Wesseler, J., Waibel, H., 2004. R&D and private investment: howto conserve indigenous fruit biodiversity of Southern Africa. PaperPresented at the 14th Annual Meeting of the European Association ofEnvironmental and Resource Economists, Budapest, Hungary.
Olsson, L., Ardö, J., 2002. Soil carbon sequestration in the degraded semi-aridagro ecosystems-perils and potentials. Ambio 31, 471–477.
Pearce, D.W., 1988. Natural resource management and anti-desertificationpolicy in the Sahel–Sudan zone: a case of gum arabic. GeoJournal 17 (3),349–355.
Tassone, V., Wesseler, J., Nesci, F.S., 2004. Diverging incentives for afforestationfrom carbon sequestration—an economic analysis of the EU afforestationprogramme in the south of Italy. Forest Policy and Economics 6 (6), 567–578.
Wesseler, J., 1997. Die Ökonomik der Einführung von Obstkulturen in derCordillera Central von Nordluzon, Philippinen. Shaker-Verlag, Aachen.
or expanding gum arabic production in Sudan. Forest Policy and Economics
