Efficient payments in a two-tiered REDD mechanism : theory and illustration from Sumatra

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Efficient payments in a two-tiered REDD mechanism : theory and illustration from Sumatra

Sophie Thoyer, Solenn Leplay, Philippe Delacote

To cite this version:

Sophie Thoyer, Solenn Leplay, Philippe Delacote. Efficient payments in a two-tiered REDD mecha-

nism : theory and illustration from Sumatra. 18. Annual Conference EAERE, European Association

of Environmental and Resource Economists (EAERE). INT., Jun 2011, Italy. 26 p. �hal-01000722�

Ecient payments in a two-tiered REDD mechanism:

theory and illustration from Sumatra

January 28, 2011

Abstract

This paper develops an analytical model of a REDD+ mechanism with an international payment tier and a national payment tier, and calibrates land users' opportunity cost curves based on data from Sumatra, Indonesia. We compare the avoided deforestation and cost- eciency of government purchases across two payment types (xed price and opportunity cost), and across two government types (benevolent and budget maximizing). Our pa- per shows that xed-price payments are likely to be more ecient than opportunity-cost compensation payments at low international carbon prices, when the government is benev- olent, or when variation in opportunity cost within land users is high relative to variation in opportunity cost across land users. Thus, a program which pays local communities or land users based on the value of the global climate service provided by avoided deforestation may not only distribute REDD revenue more equitably than an opportunity cost-based payment system, but may be more cost-ecient as well

Keywords: Payment for Environmental Services (PES); avoided deforestation; agricultural ex- pansion; policy simulation; Reduced Emissions from Deforestation and forest Degradation (REDD);

Sumatra, Indonesia.

1 Introduction

More than 150 million hectares of tropical forest were lost between 1990 and 2010 (FAO 2010).

Most of these forests were cleared for intensive commercial farming of soy, palm oil, cattle and

other crops, as well as for timber extraction and for small-scale subsistence farming (Allen et al., 1985; Barbier and Burgess, 1997; Morton et al, 2006; Rudel, 2007, Angelsen, 2009). Tropical deforestation represents roughly 15 to 17% of anthropogenic emissions of CO2 (Van der Werf et al., 2009; IPCC, 2007) and mitigating climate change by curbing deforestation in Southern countries is widely considered to be less costly than abating industrial emissions in Northern countries (Murray et al., 2009; Naucler and Enkvist, 2009). Carbon sequestration and storage by forests is acknowledged as a key global environmental service provided by forest-rich tropical countries. International negotiations are taking place under the United Nations Framework Convention on Climate Change (UNFCCC) for a Reduced Emissions from Deforestation and forest Degradation (REDD) mechanism in a post-2012 climate agreement, in which developed countries would provided nancial incentives for developing countries to maintain their tropical forests.¹ In this context, Payments for Environmental Services (PES) are being increasingly mobilized, in which conservation incentive payments are made to local land users conditional on the CO2 emission reductions associated with avoided deforestation. The underlying logic is simple: the providers of environmental services (ES) forego alternatives uses of land, and are compensated by the beneciaries of the services, be they national governments, private rms, or public organizations seeking the provision of public goods (Bond et al., 2009). A large spectrum of payment rules exists and has been tested under dierent programs (see Wunder 2009 for a review).

The emerging international REDD mechanism has been likened to a two-tiered international PES program (Angelsen and Wertz-Kanounniko, 2008; Angelsen, 2009). In an international tier, developed country governments pay developing country governments for a reduction in national deforestation emissions. In a domestic tier, developing country goverments pay land users for reductions in local deforestation emissions. International transactions are voluntary and conditional. Voluntariness implies that tropical countries need not bear the opportunity costs of conserving forests where more protable landuse options are preferred. Conditionality implies that under-compliance can be penalized by reducing planned international payments. Moreover, the REDD mechanism, by enabling tropical countries to access new nancial resources, makes

1The full concept of REDD+ also includes conservation, sustainable management of forests, and enhancement of forest carbon stocks. However, this paper focuses on reduced deforestation and leaves aside other elements of

an incentive-based approach to forest conservation more aordable: REDD income can be used by recipient governments to pay domestic land users for on-the-ground CO2 emission reductions through less deforestation and degradation activities.

Governments in tropical countries would need to determine the type of PES payment program they wish to implement at the local scale. Payments could either be based on the quantity of emission reductions provided by local suppliers (xed price payment type), or could be based on local suppliers' foregone economic surplus from conserving forest (opportunity cost payment type). Literature on payment designs for PES have commented that xed-price schemes retain a greater share producer surplus within local communities, and avoid complicated mechanisms for eliciting supplier willingness-to-accept (Börner et al, 2010, Gregersen et al, 2010). Such studies have typically assumed that an opportunity-cost compensation scheme would be more cost-ecient for government purchasers than a xed-price scheme, since purchasers would pay suppliers for less consumer surplus. However, a xed-price scheme has a commonly overlooked advantage which is not possible under an all-or-nothing opportunity cost contract: a xed- price scheme allows suppliers to self-identify low-cost areas for conservation, while maintaining productive land for agriculture.

We argue in this paper that the choice of PES payments at domestic level is also inuenced by the government's strategy with respect to international REDD payments. A governments' choice of payment type depends on its relative preference for budget surplus (measured by international REDD income minus domestic PES payments) and for economic surplus generated by alternative land uses (e.g. agricultural prot).

The aim of this paper is to provide insights on the strategic decisions made by tropical countries, both in terms of avoided deforestation achieved and in terms of domestic PES programs adopted to reduce deforestation, when taking into account both international payments and domestic program expenditures. In section 2, a two-tiered model is developed and calibrated that simultaneously captures deforestation decisions made by individual land users within a country and policy choices made by the national government. Section 3 applies the theoretical results obtained to a case study in Sumatra, Indonesia. Section 4 concludes with a discussion of policy implications.

2 Agricultural expansion and policy options to reduce de- forestation: a two-tiered PES scheme

This section provides a static model of deforestation decisions by land users, which is then used to identify optimal PES policy options by Southern governments.

2.1 Agricultural expansion and deforestation in a business-as-usual scenario

We consider a continuous population of land users, called farmers, practicing agriculture in frontier forest land. Each farmerichooses how much forest to convert to agriculture each year.

Assuming risk-neutrality, this choice takes the form of a prot maximizing problem:

max

L Π_i= max

L λ_if(L(λ_i))−ω L(λ_i) (1) f is the agricultural revenue function of additional deforested land L(λi). The agricultural revenue function implicitly encompasses the output price and the cost of other (xed) inputs.

We assumef to be twice dierentiable and quasi concavef⁰ >0andf⁰⁰≤0. λiis an eciency factor characterizing each farmeri(λi>0). It encompasses the productivity of deforested land, which depends on its slope, elevation and soil quality (Kaimowitz and Angelsen, 1998), the farmer's technical capacity, distance costs and bargaining power. The farmers' eciency factors are distributed uniformly along λi ∈

λ;λ

. ω is the unit cost of land conversion. We assume, without loss of generality, that this cost is constant across land at the forest frontier.

In the business-as-usual scenario (BAU), i.e. without any policy incentive to reduce defor- estation, each farmer i chooses the level of deforestationL^BAU_i (λ_i) that maximizes his prot.

The rst-order condition is:

dΠi

dL = 0 ⇐⇒ λif⁰(L(λi))−ω= 0 ⇐⇒ f⁰(L(λi)) = ω

λi (2)

Sincef⁰ is strictly monotonically increasing,L^BAU_i (λi) = (f⁰)⁻¹

ω λ_i

.

L^BAU_i (λ)>0. Total deforestation at the national level isL^BAU_T withL^BAU_T =´λ

λ L^BAU_i (λ)dλ. In order to provide comparative statics and numerical simulations, we choose a quadratic expression off(Li): f(Li) = ^a₂L²_i +bLi+c, with a <0, andb, c >0. Thusf⁰(Li) = aLi+b and the lower the value ofa , the steeper the marginal revenue curve, which will prove to be a crucial element determining the relative budgetary eciency of the two PES schemes.

The BAU deforestation rate for farmer i is thus L^BAU_i (λi) = _aλ^ω

i − ^b_a, and his prot is Π^BAU_i (λi) = −_2aλ^ω2

i + c−_2a^b2

λi + ^bω_a . We restrict parameter values in order to limit our analysis to a population of farmers having strict positive values of BAU deforestation: L^BAU_i >

0⇒^ω

b < λ_i andΠ^BAU(λ_i)>0⇒ −_2aλi^ω2 + c−^b_2a²

λ_i>−^bω_a.

2.2 The REDD mechanism: a North-South payment to avoid defor- estation

Each tropical country that reduces its deforestation receives a REDD paymentT from developed countries, proportional to its avoided carbon emissions. For simplicity, we calculate the REDD transfer on the basis of avoided deforestation A, multiplied by a single proxy value for the quantity of carbon stored in each hectare of forest. Several methods for setting the national reference level (Busch et al, 2009) with respect to which avoided deforestation emissions are calculated are under negotiation (UNFCCC, 2009). We make the assumption in this paper that emission reductions are measured relative to a business-as-usual (BAU) deforestation level L^BAU_T =´λ

λ L^BAU_i (λ)dλ. This reference level is compared to the observed deforestation under the PES contract, L^P_T = ´λ

λ L^P_i (λ)dλ, where each farmer i deforests L^P_i (λi) under the PES contract. The North-South transfer isT, calculated as:

T =t A=t(L^BAU_T −L^P_T)

t is the international payment rate for savedCO₂emissions. It reects the value of avoided deforestation in terms of reduced emissions of carbon. t = P ×EF where P is either the international carbon price, xed by the market if forest carbon is introduced in the international carbon market, or an exogenous value negotiated between Northern and Southern countries; and

EF is the proxy carbon emissions factor, which converts deforestation into carbon emissions. In this paper, we do not consider dierences of carbon density within a country's forest. Rather, we assume for simplicity thatEF is the same across all forest types.

2.3 National level PES programs

2.3.1 Southern government's optimal decisions to curb deforestation

The Southern country sets up a PES program to join the international REDD mechanism de- scribed above. We make the assumption that Southern countries have readied the infrastructure necessary to monitor emission reductions at the national level.² The Southern government may be of two types: a benevolent government maximizing social welfare (measured as total agri- cultural prot plus income from the international REDD payment), and a budget-maximizing government that maximizes the dierence between income from the international REDD pay- ment and payments made to farmers under PES schemes³. This budget-maximizing type can capture the features of a corrupt government, seeking to divert public money to the benet of a political elite, but it can also describe a government wishing to invest REDD income in other sec- tors (ie. for education, health, or infrastructure). All linear combinations of these two extreme types describe the range of governmental behaviors that could be observed. The government maximizes its utilityU, subject to a budget constraint that total PES payments cannot exceed REDD transfers:

max U = T +α(Π^BAU_T + Π^P_T) + (1−α) (−E) (3) s.t. T ≥E

2Monitoring emission reductions requires access to reliable data on deforestation and emission factors, which can be provided by satellite imagery, periodic on-site checks, and central database development (Angelsen, 2009).There is currently wide variability in the availability of these data in tropical countries, but many countries seeking to be eligible for REDD have joined a readiness phase of building monitoring, reporting and verication (MRV) capacities and strengthening institutions (Herold and Skutsch, 2009). In the 2009 Copenhagen accord and 2010 Cancun agreements, a number of developed countries promised to contribute nancially to fast-start funds to enable MRV of REDD.

3For simplication, we do not consider the potential positive feedback eects on the budget of tax revenue from agriculture.We also assume that governments do not take into account in their utility function the environmental degradation associated with deforestation.

whereΠ^P is the total agricultural prot, excluding PES received,⁴of all farmers participating in the national PES scheme, and Π^BAU is the total agricultural prot of all farmers who do not participate in the PES scheme and pursue their BAU agricultural activities. Ecorresponds to the payment from the Southern government to farmers participating to the PES.α= 1corresponds to a benevolent government;α= 0describes a budget-maximizing government.

Two PES programs may be implemented⁵: an opportunity cost compensation program⁶, and a xed-price program⁷

2.3.2 The opportunity cost compensation program

In the opportunity cost compensation program (OC), the government oers a payment to farm- ers equal to their foregone prot, if farmers agree to abate their level of deforestation to zero (L^P_i (λi) = 0if ijoins the program). In theory, farmers are expected to be indierent between participating in the program in exchange for the foregone prot, or pursuing their agricultural activities. We assume here that, if given the choice, farmers sign up and abate deforestation to zero. The government can thus select the farmers to whom to propose a PES contract, and will select those farmers with the lowest opportunity costs.

The government chooses the total level of avoided deforestation which maximizes its utility, subject to the budget constraint. Farmers are invited to join the program, starting with the lowest opportunity cost farmer, up to the marginal farmerλˆ, whose contribution to the program enables the government to achieve its chosen level of avoided deforestation. Farmerλˆis thus the last farmer joining the OC program. This farmer splits the population into two groups: those who participate,λ∈[λ,λ]ˆ, and stop deforestingL^P_i (λi) = 0 in exchange for an exact compensation of their opportunity costs, and those who do not participate,λ∈[ˆλ, λ], and continue to deforest as usualL^BAU_i (λ_i).

4PES payments to farmers are not included in accounting here because they are considered domestic transfers;

they are deducted from the public budget and added to farmers surplus. If we assume that PES have no transaction costs, then these payments are neutral in terms of total domestic welfare.

5These two programs align closely with the quasi-auction scenario and per-ton carbon payment modality described in Borner et al (2010)

6An example of such a scheme would be the Conservation Stewards Program of the NGO Conservation Inter- national (Niesten et al., 2010)

7This is the policy implemented by the Government of Costa Rica to reward avoided deforestation, called Pago por Servicios Ambiatales (Pagiola, 2008; Wunder, 2009; Ogonowski et al., 2009).

Under this program, the benevolent government's maximization problem is:

max

ˆλ^B

U = max

ˆλ^B

t ˆ ^ˆλ^B

λ

L^BAU_i (λ)dλ+ ˆ λ

λˆ^B

Π^BAU_i (L(λ))dλ (4) s.t. t

ˆ ^ˆλ^B λ

L^BAU(λ)dλ ≥ ˆ ^ˆλ^B

λ

Π^BAU_i (L(λ))dλ

Meanwhile, the budget-maximizing government's problem is:

max

λˆ^M

U = max

λˆ^M

t ˆ λ^ˆM

λ

L^BAU_i (λ)dλ− ˆ ^ˆλ^M

λ

Π^BAU_i (L(λ))dλ (5) s.t. t

ˆ ^ˆλ^M λ

L^BAU(λ)dλ ≥ ˆ λ^ˆM

λ

Π^BAU_i (L(λ))dλ

The two maximization problems are equivalent: increasingλˆhas exactly the opposite impact⁸ on´λ

λˆ Π^BAU_i (L(λ))dλas on´^ˆλ

λ Π^BAU_i (L(λ))dλ. Therefore, both types of government choose the same marginal agentλˆ = ˆλ^B = ˆλ^M. This agent has an average opportunity cost of avoided deforestation is equal tot,t= ^{Π(LBAU(ˆλ))}

L^BAU(ˆλ) . This result, which is only valid for the OC scheme, is understood as follows: the interests of the benevolent government (which maintains agricultural activity of high prot farmers) converge with the interests of the budget-maximizing government (which selects the lowest cost farmers to limit PES expenditures). Moreover, the budgetary constraint imposes that the minimum North-South payment rate t must be at least equal to the average opportunity cost of λ: in this case λ is the only farmer joining the scheme and tmin= ^Π(^LBAU(λ))

L^BAU(λ) . For more details, see Appendix 1.

Considering our quadratic specication of f, both benevolent and budget-maximizing gov- ernments adopt the same target group of participating farmers. The marginal agent splitting the farmers' population into two groups isˆλ:

ˆλ = b(ω+t) +√

t²b²+ 2acω²+ 4acωt b²−2ac

With values ofa,b, c,t,andω chosen such thatt²b²+ 2acω²+ 4acωt >0.

8under the assumption that theλs are uniformly distributed

2.3.3 The xed-price program

In the xed-price program (FP), the government oers a xed price K per unit of avoided deforestation supplied by the farmer. Each farmer i joining the program chooses a level of deforestation L^P_i (λ_i), in order to maximize his income R^P(λ_i). The government chooses the total deforestation level to maximize its utility, then sets the optimalK^∗per hectare of avoided deforestation corresponding to the desired total avoided deforestation.

The farmer's maximization program is:

max

L R^P = λif(L(λi))−ω L^P_i (λi) +K L^BAU_i (λi)−L^P_i (λi)

(6) s.t. L^BAU_i (λ_i)> L^P_i (λ_i) andR^P(λ_i)>Π^BAU_i (L_i)

and the rst-order condition is:

dR

dL = 0 ⇐⇒ f⁰(L^p(λi)) = ω+K

λi (7)

Since ^ω+K_λi ≥ _λ^ω

i and f⁰ is a decreasing function, L^P_i (λi) =f⁰⁻¹(^ω+K_λ

i )≤L^BAU(λi)always holds.

The benevolent government's maximization problem is:

max

K^B

U K^B

= max

K^B

t ˆ λ

λ

L^BAU_i (λ)−L^P_i λ, K^B dλ+

ˆ λ λ

Π^P_i λ, K^B

dλ (8) s.t. t ≥ K^B

while the budget-maximizing government's problem is:

max

K^M

U K^M

= max

K^M

t−K^M ˆ λ

λ

L^BAU_i (λ)−L^P_i λ, K^M

dλ (9)

s.t. t ≥ K^M

Total avoided deforestations and total PES budgets under optimalK^B∗andK^M∗are available in appendix 1. Note that we need to distinguish between 3 cases: case 1, in which all farmers

contract to partially reduce their deforestation; case 2, in which K^∗ is high enough to induce some farmers to stop deforestation altogether; and case 3, in whichK^∗is such that all farmers contract to abate to zero⁹.

With the quadratic specication, farmers maximize their income, choosing their level of deforestation L^P_i (λi) = _a¹

ω+K λ_i −b

. Avoided deforestation by farmeriis A=L^BAU_i −L^P_i =

−_aλ^K

i >0and farmer i's income increases from participating in the PES program: R^P_i −Π^BAU_i =

−_2aλ^K2

i > 0. Avoided deforestation increases as K increases and is greater for farmers with lower productivity (low λ_i) and or atter opportunity cost curves (low a). Moreover, there is a reinforcement eect: _∂λ^∂2_i^A_∂Kⁱ = _aλ¹2

i

< 0 ; When K increases, the gains in terms of avoided deforestation are lower for high productivity farmers with highλ_i.

The farmers' participation constraint imposes that they are better o when the FP program is introduced. Moreover, the net gain in income is larger for farmers with low productivity and for farmers whose marginal prot curves are atter: ^∂(RiP−Π_∂λi^{BAUi )}<0 and ^∂(RPi−Π_∂ai^{BAUi )}>0.

OptimalK^∗depends on the parameter values. In case 1, whenK^∗< λf⁰(0)−ω, the benevolent government redistributes the total amount of North-South REDD transfer through the xed- price scheme (K^∗=t); while the budget-maximizing government redistributes only half of the international REDD transfer K^∗=₂^t

. Cases 2 and 3 are more complicated and can only be calculated numerically (see Leplay et al, 2011).

2.3.4 Comparison of the two programs

Both the xed-price and the opportunity-cost compensation programs have contrasted advan- tages and drawbacks. It is straightforward that the FP program provides farmers with a positive net surplus since farmers are always paid more than their true opportunity costs. In contrast, in the OC program, farmers receive no extra surplus. From a poverty alleviation viewpoint, the FP program is more desirable than the OC program. From a budgetary eciency viewpoint, it might seem natural to suppose that the OC program would always perform better. But this is not always the case. When farmers that join the scheme have to reduce deforestation to zero, the last units of avoided deforestation may be unnecessarily costly, especially if the marginal opportunity cost curve of farmers is steep. Thus, considering the OC scheme versus the FP scheme implies

a trade o between including the most protable units of deforestation of agents deforesting the least in the OC scheme, and the least protable units of deforestation by all agents in the FP scheme. Which program is more ecient hinges upon a comparison of the overall opportunity costs across farmers, and the steepness of individual farmers' marginal prot curve. ¹⁰

To illustrate this trade-o, consider a simple case of a society with only two farmersj andk (see gure 1, cases 1 and 2), who dier both in their total opportunity costs and marginal prot curves. In case 1, agents deforest roughly the same area and the slopes of their marginal prot curves are steep. In case 2, agents' marginal prot curves are atter than in case 1, andj⁰ and k⁰ do not deforest the same amount of land. In case 1, as the marginal prot curves are steeper than in case 2, for an equivalent amount of total opportunity costs, agents deforest less in case 1 than in case 2 so opportunity costs per hectare is higher in case 1 than in case 2. We assume that the government selects lower-cost agents j in case 1 and j⁰ in case 2 for participation to the OC program. Under this hypothesis, in case 1 (case 2), avoided deforestation area is OD (O'D') and total budget expenses are OMD (O'M'D'). Now consider that the government implements a xed-price program with an arbitrary xed-price of K in case 1, andK⁰ in case 2. Under this program, in case 1 (case 2) avoided deforestation is AD+EH (A'D'+E'H') and total budget expenses are ABCD+EFGH (A'B'C'D'+E'F'G'H'). We see graphically that in case 1 the FP program performs better in terms of avoided deforestation and it costs less than the OC program, while we observe the contrary in case 2. The OC program has a more ecient outcome than the FP program in case 2, and vice-versa in case 1. Overall, this simple example shows that we can expect the FP program to be more ecient for a government purchase - i.e.

to perform better in terms of avoided deforestation at lower cost - than the OC scheme, when the marginal benet curves are steeper. FP is more ecient when costs are more variable within suppliers, while OC is more ecient when costs are more variable across suppliers.

The structure of information, monitoring and control costs is also expected to dier across the two schemes. An OC program imposing abatment to zero is easier to control than an OC program where each land user is assigned a specic deforestation abatement level (table 1). On

10Of course, the ideal scheme from the perspective of a government buyer interested in cost-eciency would be an OC program in which the regulator can impose both the purchase price and the individual deforestation abatement to each farmer. Such OC program would surpass both the xed-price program and the opportunity- cost program in cost-eciency and there would be no interest in contrasting the two schemes. But such a scheme wouldunrealisticallyrequire perfect information on farmers' entire marginal abatement cost curves.

Figure 1: Comparison of the FP and OC programs with two agents

B K

A N

M

C

O

F

D E

G

H FP>OC

Avoided deforestation: OD < AD+EH PES budget expenses: OMD > ABCD + FGEH Agent j

Agent k Marginal profit of

deforestation

L

FP < OC

Avoided deforestation: O’D’ > A’D’+E’H’

PES budget expenses: O’M’D < A’B’C’D’+F’G’E’H’

K’ B’

A’

N’

M’

C’

O’

F’

D’ E’

G’

H’

Agent j’

Agent k’

Marginal Profit of deforestation

L Case 1 : Relatively steep marginal opportunity Case 2: Relatively at marginal opportunity

cost curves: FP more ecient than OC cost curves: OC more ecient than FP Table 1: Required information for each scheme

Information type OC program FP program

on total opportunity cost necessary not necessary on BAU deforestation level necessary necessary on individual deforestation level under PES not necessary necessary

on marginal opportunity costs not necessary not necessary

the other hand, it requires that information be available on individual opportunity costs to help the regulator select farmers to whom an OC contract is proposed. In contrast, under the FP program, the government does not need precise information on the opportunity costs structure of land users, but does need to establish a thorough monitoring and control system to measure individual deforestation and calculate compensation payments. Overall, both PES programs will include so-called transaction costs but thir nature dier. In the rest of the paper, we overlook those costs which are not easily measured to concentrate on eciency and eectiveness indicators.

In order to illustrate the dierent types of policy responses we can obtain, we choose two contrast two sets of parameters, presented in Table 2.

The two sets of parameters (simulations 1 and 2) lead to roughly equivalent total deforestation

Parameter a b c ω λ λ Π(λ) Π(λ) L^BAU_{T L}^Π(λ)BAU T

Π(λ) L^BAU_T

Simulation 1 -53 53 57 30 30 900 2 475 75 000 868 2 500 75 000

Simulation 2 -5 160 15 400 3 35 260 78 000 827 49 2 620

Table 2: Parameter values in the two simulations

under the BAU scenario. High prot farmers are also quite similar in the two simulations. The main dierence is that simulation 1 describes much steeper marginal prot curves. Moreover, the population in simulation 1 is more heterogenous in terms of opportunity costs than the population of simulation 2. The agricultural productivity factor is multiplied by 30 between the least productive and the most productive farmer in simulation 1; it is only multiplied by 12 in simulation 2.

We calculate total avoided deforestation and total utility of Southern governments, under the two schemes, for the benevolent government and for the budget maximizing government¹¹. Figures 2 to 5 present these results.

To analyze numerical results, we focus on two policy issues:

1) What is the preferred PES scheme of the benevolent government and of the budget- maximizing government, for a given level of international transfert?

2) If Northern countries had to select REDD countries, which ones would they choose? We simply assume here that Northern countries select Southern countries that would provide the highest levels of avoided deforestation. Do the preferences of Northern countries coincide with policy choices made by Southern countries?

We note that in simulation 2, the values of K are close to t for the benevolent state and to ₂^t for the budget-maximizing state. In contrast, in simulation 1, the values of K move away respectively from t and ₂^t. We note that for the highest values of t, the xed-price of the benevolent state is inferior to the xed-price in maximizing the cost-eciency of payments by the budget-maximizing state.

ˆ In Simulation 1, for both types of governments, the FP program is prefered to the OC program, for all levels of carbon price. It provides the highest utility to the Southern government and the highest total deforestation. Northern countries would prefer benevolent

11Under the OC scheme, the results in terms of avoided deforestation and budget expenses per unit of avoided deforestation are similar for the two types of governments, because they choose the same marginal farmer.

Utility

t

Benevolent state under FP scheme Benevolent state under OC scheme Budget maximizing state under FP scheme Budget maximizing state under OC scheme

Avoided deforestation

t Benevolent state under FP scheme Budget maximizing state under FP scheme

Benevolent and budget maximizing states under OC scheme

Figure 2: Simulation 1 Figure 3: Simulation 1

Government utility as a function of t Avoided deforestation as a function of t

Utility

t Benevolent state under FP scheme Budget maximizing state under FP scheme benevolent state under OC scheme Budget maximizing under OC scheme

t2 t1

Avoided deforestation

t Benevolent state under fixed price scheme

Budget maximizing state under FP scheme

Benevolent and budget maximizing states under OC scheme

t1 t2

Figure 4: Simulation 2 Figure 5: Simulation 2

Government utility as a function of t Avoided deforestation as a function of t

Table 3: Outcomes in simulation 2

Choice t < t1 t1< t < t2 t > t2

of benevolent government FP program FP program indierent

of BM government OC program OC program OC program

of Northern countries Benevolent state BM state BM or benevolent state under FP program under OC program under OC program

governments..

ˆ Simulation 2 presents a more contrasted picture. For levels of t < t₂, the benevolent gov- ernment prefers the FP program to the OC program; fort > t2, the benevolent government becomes indierent between the two programs. The budget-maximizing government, on the other hand, increasingly prefers the OC program ast increases. For t < t1, Northern countries would select a benevolent government with a FP program. For t > t1, they will prefer any type of government adopting an OC program. This indicates that for val- ues of t between t1 and t2, Northern countries will select in priority budget-maximizing governments because for this samet range, benevolent states prefer FP pprograms.

3 Illustrative case study: Sumatra

The model described above is now calibrated based on marginal abatement cost curves from districts in the northern region of the island of Sumatra in Indonesia. Indonesia's greenhouse gas emissions ranked at the fourth-highest in the world in 2005 (CAIT, 2010). Over 70% of these emissions were due to conversion of natural forests and the associated burning and draining of peat lands (CAIT, 2010). Conversion is driven largely by production of lucrative export crops such as palm oil and coee, with extractive logging often oering a source of up-front nance for agricultural conversion. The island of Sumatra alone lost about 30% of this forest cover between 1985 and 1997 (FWI/GFW, 2002) and 9% of its forest cover between 2000 and 2005 (Hansen et al., 2008) .

However, Indonesia is involved in the REDD process and is advancing toward national REDD readiness. In 2007, Indonesia created the Indonesian Forest-Climate Alliance (IFCA), supported by several bilateral donors (for example GTZ, DFID, AusAID), and the World Bank has sup-

ported a national framework for long-term REDD implementation (Murdiyarso, in Angelsen ed., 2009) The Government of Indonesia recently signed a landmark $1 billion Letter of Intent with the Government of Norway to ready the institutions necessary for REDD in Indonesia. Dier- ent tools are currently being tried in Indonesia to implement REDD: protected areas (FFI and Carbon Conservation, 2007), concession purchases, and PES programs (Madeira, 2009). A num- ber of studies have examined REDD+ scenarios in the Indonesian context (Gaveau et al., 2009;

Venter et al., 2009; Koh and Ghazoul, 2010) but to our knowledge ours is the rst to examine the implications of alternative payment rules in PES programs.

3.1 Description of the data

Our study area comprises 3 provinces divided into 37 districts in the island of Sumatra, covering 121,561 km2. Forests are mainly threatened by the expansion of oil palm plantations, both by large companies in lowland areas and by smallholder farmers in upland areas (Gaveau et al, 2009). Our objective is to compare the BAU deforestation level from 1990-2000 with a scenario where various types of PES schemes would be implemented.

Data on forest cover observed for the years 1990 and 2000 was obtained from 30×30 m resolution by Landsat imagery (Hansen 2008), aggregated to the 900×900 m level using a 50% forest cover threshold. Between 1990 and 2000, the observed forest cover loss was 867 900 hectares (corresponding to an average annual deforestation rate of 1.3%).

The inuence of deforestation driver variables on forest cover was modelled using a logit regression comparing the probability of each cell¹² to be deforested against explanatory vari- ables including biophysical suitability for palm oil production (Conservation International, un- published), forest biomass (Ruesch and Gibbs, 2008), slope, and elevation (Jarvis et al, 2008).

Predicted output variables from the regression were used to calculate an eective opportunity cost, representing the minimum payment per hectare necessary for a land user to choose to conserve forest rather than convert to oil palm for each cell. We use this value as a proxy for the prot obtained by deforestation. Details on the econometric model, the construction of the opportunity costs, the calibration and the validation are developed in (Leplay, 2011).

Data on above- and below- ground forest biomass was obtained from Tier I IPCC estimates

(Ruesch and Gibbs, 2008) enabling us to estimate density of forest carbon stored in each cell.

Average carbon density across the study region was 172 tC/ha. Estimated greenhouse gas emis- sions from deforestation in the study region between 1990 and 2000 amounted to 54.7 million tCO2/year. Using the estimated eective opportunity costs of each cell, we estimated that the total opportunity cost of stopping deforestation entirely would have been 2.33 billion US$ over ten years, or $4.25 per ton of CO2emitted

3.2 Simulations

While our analytical model is developed at the farmer level, we conduct simulations at the district level, because we have data on opportunity cost variability both within and across districts.

Reductions in deforestation achieved under alternative PES policy scenarios in Sumatra are thus modeled as if each district represented the aggregated decisions of all farmers living in the district.

In our simulation, the marginal opportunity cost curve of a district was built by ordering from the highest to the lowest value the estimated opportunity costs of every cell located in the district.

Districts were then ranked from the lowest average opportunity cost district (equivalent to our λ farmer in the section 2 model) to the highest (equivalent to farmer λ). The distribution of average district opportunity costs is not continuous but it is close to a uniform distribution as shown on gure 6.

In our model, the Indonesian government receives a transfer T from the international com- munity proportional to total avoided deforestation across the 37 districts: T =t×A. t is the international payment rate for avoided carbon emissions: t=P×CD×3.67where P is a price for carbon and CD is the average carbon density of Sumatra forests ((172 tC/ha), and 3.67 is the conversion ratio between tCO2 and tC. We conduct simulations under two hypotheses of governmental behaviour: either the government seeks to maximize the sum of international transfers and agricultural prots from forest conversion (benevolent government)); or it max- imizes the net budget revenue of avoided deforestation (budget-maximizing government). We vary the carbon price to simulate changes in utility and avoided deforestation under the dierent schemes.

ˆ Under the OC scheme, we assume that the government chooses the deforestation level that

0 50 100 150 200 250 300 350 400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Figure 6 : Distribution of average opportunity costs per hectare of deforested land per year and per district

maximizes its utility and then selects the districts (equivalent to our farmers in the model) with the lowest average agricultural prot when the scheme is proposed. In the previous section, we demonstrated that the marginal agent h is dened such thatt = ^Π_L^BAUh_BAU

h . All districts with an average opportunity cost per hectare of deforested areas per year lower thanhchoose to participate in the OC program. They are exactly compensated and stop deforestation altogether. All other districts choose the BAU rate of deforestation.

ˆ Under the FP program, the government oers a price K for each 81 hectares of avoided deforestation. Each district may choose to join the program and choose the cells in which to abate deforestation. Cells where the opportunity cost of avoided deforestation is greater than K are deforested; cells where the opportunity cost of avoided deforestation is lower than K remain forested and receive a compensation K. To facilitate the simulation, we assume thatK=t∗81for the benevolent government, and thatK=₂^t∗81for the budget maximizing government (following the theoretical results of table 3, case 1).

Our theoretically-dened budget-maximizing government would prefer a FP program under

$0

$1

$2

$3

$4

$5

$6

0 2 4 6 8 10 12

Utility (USD)Milliards

Carbon price (USD/tonCO2)

Benevolent state under the FP scheme Budget maximizing state under the FP scheme Benevolent state under OC scheme Budget maximizing state under OC scheme

0 1 2 3 4 5 6 7 8 9 10

0 2 4 6 8 10 12

Avoided deforestation (hectares)x 100000

Carbon price (USD/tCO2)

Benevolent state under the FP scheme Budget maximizing state under the FP scheme Benevolent and budget maximizing states under OC scheme

Figure 7: Governments' utility as a function Figure 8: Avoided deforestation as a function of international carbon price of international carbon price

illustrative carbon prices (above 4-5 US$/tCO2) (gure 8, table 4 and table 5). On the other hand, a benevolent government would prefer a xed-price scheme under all carbon prices, although the dierence between the two programs is eroded for high carbon prices. (gure 7, table 4 and 5).

We observe in gure 8, tables 4 and 5, that all deforestation is abated under an OC scheme for an illustrative carbon price of 6 USD$/tonCO2. The FP scheme is more ecient in terms of avoided deforestation than the OC scheme, for low illustrative carbon prices (below 4-5 US$/tonCO2) while for high illustrative carbon prices (above 4-5 US$/tonCO2), the OC scheme is more ecient.

4 Conclusion

Designing an ecient international scheme to reduce deforestation is a key challenge in interna- tional post-2012 climate change negotiations. As an international REDD+ mechanism emerges, forest countries are readying policy frameworks to eectively reduce deforestation. PES pro- grams, in which national governments pay local actors for their forests' climate services, and in

Table 4: Results for a carbon price equal to 3 US$/tonCO₂

Type of government Benevolent BM Benevolent BM

Type of PES scheme OC Fixed-price

Deforestation without REDD (ha/10 years) 867 900

Deforestation with REDD/PES (ha/10 years) 777 600 558 700 703 700 Avoided deforestation (ha/10 years) 90 300 309 200 164 200 Budget expenditures for PES scheme (million US$/10 years) 113 585 155

North-South REDD transfer (million US$/10 years) 171 585 310

Net budget surplus (million US$/10 years) 58 0 155

Government's utility (million US$/10 years) 2 386 58 2 636 155

Table 5: Results for a carbon price equal to 7 US$/tonCO2

Type of government Benevolent BM Benevolent BM

Type of PES scheme OC Fixed-price

Deforestation without REDD (ha/10 years) 867 900

Deforestation with REDD/PES (ha/10 years) 0 180 000 485 500

Avoided deforestation (ha/10 years) 867 900 687 900 382 400 Budget expenditure for PES (million US$/10 years) 2 328 3 036.5 844 North-South REDD transfer (million US$/10 years) 3 831 3 036.5 1 688

Net budget surplus (million US$/10 years) 1 503 0 844

Government's utility (million US$/10 years) 3 831 1 503 4 014 844

turn receive international payments through a REDD mechanism, are expected to be a mainstay in these policy frameworks. Forest countries face a choice whether to structure payments in national PES programs to be based on the climate services provided by land users' forests, or on land users' estimated opportunity costs.

In this paper we have developed and calibrated an analytical model of a REDD+ mechanism with an international payment tier and a national payment tier, to compare the avoided defor- estation and cost-eciency of government purchases across the two payment typesxed price and opportunity cost. Our model is simple and does not consider important issues of REDD implementation, including transaction and monitoring costs and property right issues (Gaveau et al, 2009). Nevertheless we provide the interesting insight that a xed-price payment program can be more ecient than an opportunity-cost payment program at low international carbon prices, when the government is benevolent, or when variation in opportunity cost within land users is high relative to variation in opportunity cost across land users. Thus, a PES program which pays land users based on the value of the climate service provided by avoided deforestation

may not only distribute REDD revenue more equitably than an opportunity cost-based payment system, but may be more cost-ecient as well.

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APPENDIX 1

Benevolent government Budget Maximizing government Opportunity Cost Program

Avoided deforestationA ´λ^ˆB

λ L^BAU(λ)dλ ´λ^ˆM

λ L^BAU(λ)dλ Level of deforestationL ´λ

ˆλ^BL^BAU(λ)dλ ´λ

ˆλ^ML^BAU(λ)dλ Budget expensesE ´λ^ˆB

λ Π^BAU(L)dλ ´λ^ˆM

λ Π^BAU(L)dλ

Agricultural ProtΠ ´λ

ˆλ^BΠ L^BAU

dλ ´λ

ˆλ^MΠ L^BAU dλ

Farmers' revenueR ´λ

λ Π^BAU(L)dλ ´λ

λ Π^BAU(L)dλ

Government utilityU t A+ Π t A−E

Fixed-price Program Case 1: K^∗< λf⁰(0)−ω Avoided deforestationA ´λ

λ L^BAU λ, K₁^B

−L^p λ, K₁^B

dλ ´λ

λ L^BAU λ, K₁^M

−L^p λ, K₁^M dλ Level of deforestationL ´λ

λ L^P λ, K₁^B

dλ ´λ

λ L^P λ, K₁^M dλ

Budget expensesE K₁^BA^{B,F P}₁ K₁^MA^{M,F P}₁

Agricultural ProtΠ ´λ

λ Π L^P λ, K₁^B

dλ ´λ

λ Π L^P λ, K₁^M dλ

Farmers' revenueR K₁^BA+ Π K₁^MA+ Π

Government utilityU t A+ Π t A−E

Case 2: λf⁰(0)−ω≤K^∗≤¯λf⁰(0)−ω Avoided deforestationA ´λ

λ L^BAU(λ)dλ−´λ

λ^B₀ L^P λ;K₂^B

dλ ´λ

λ L^BAU(λ)dλ−´λ

λ^M₀ L^P λ;K₂^M dλ Level of deforestationL ´λ

λ^B₀ L^p λ, K₂^B

dλ ´λ

λ^M₀ L^p λ, K₂^M dλ

Budget expensesE K₂^BA K₂^MA

Agricultural ProtΠ ´λ

λ^B₀ Π L^P λ, K₂^B

dλ ´λ

λ^M₀ Π L^P λ, K₂^M dλ

Farmers' revenueR K₂^BA+ Π K₂^MA+ Π

Government utilityU t A+ Π t A−E

Case 3: K^∗= ¯λf⁰(0)−ω Avoided deforestationA ´λ

λ L^BAU(λ)dλ ´λ

λ L^BAU(λ)dλ

Level of deforestationL 0 0

Budget expensesE K₃A K A

Agricultural ProtΠ E E

Farmers' revenueR 0 0

Government utilityU t A t A−E