CONSERVATION CONTRACTSAND

POLITICAL REGIMES∗

Bård Harstad Torben Mideksa

University of OsloJune 2016

Abstract

This paper presents a new model of resource depletion, such as deforestation, disentangles

the effects of (de)centralization and state capacity, and derives the optimal conservation

contract. When districts are "strong" and in charge of extracting their own resources

to get revenues, conservation in one district benefits the others since the reduced supply

raises the sales price. A central authority would internalize this positive externality and

thus conserve more. When districts are instead "weak" in the sense that they find it

expensive to protect their resources and extraction is mainly illegal, conservation in one

district increases the price and thus the profit from illegally depleting the resource in the

other districts. The externality from conservation is then negative, and centralization

would lead to less conservation. These predictions can rationalize the puzzle that decen-

tralization has an effect on deforestation which differs starkly across countries. We also

derive the optimal conservation contract, and we explain when the principal benefits (or

loses) from contracting with the districts directly even when contracting with a central

authority would have led to more (or less) conservation.

Keywords: Deforestation, resource extraction, conservation, contracts, externalities, leakage,

crime displacement, state capacity, centralization, decentralization, climate change, REDD,

PES.∗We are grateful to the editor, three referees, audiences at Harvard University, UC Berkeley, Stanford GSB,

NYU, Brown University, London School of Economics, Warwick University, University of Zurich, ToulouseSchool of Economics, Paris Ecole Polytechnique, Norwegian School of Economics, the World Bank, UniversidadCarlos III, University of Copenhagen, University of Oslo, the 2015 Environmental Protection and SustainabilityForum in Bath, and the 2016 Rotterdam Political Economy Workshop. We are especially thankful to the com-ments of Arild Angelsen, Philippe Delacote, Jonas Hjort, Chuck Mason, Halvor Mehlum, Kalle Moene, NicolaPersico, Torsten Persson, Francois Salanie, Steve Shavell, Kathryn Spier, Jon Strand, and Ragnar Torvik.Judith Levy and Frank Azevedo assisted with the editing. Please contact us at bard.harstad@econ.uio.no andtorben.mideksa@econ.uio.no.

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1 Introduction

This paper presents a new model of conservation, shows how the political system interacts

with economic forces, and derives the contract preferred by a third party that benefits from

conservation. Payments for environmental services (PES) are important in many situations,

and the resource in our model could be fossil fuels or land use quite generally, but our analysis

is motivated in particular by deforestation in the tropics and the emergence of contracts on

reducing emissions from deforestation and forest degradation (REDD).1

Deforestation in the tropics is an immensely important problem. The cumulative effect of

deforestation amounts to about one quarter of anthropogenic greenhouse gas emissions, which

generate global warming (Edenhofer et al., 2014). The annual contribution from deforestation

to CO2 emissions is around ten percent (Stocker et al., 2013), and the percentage is even

higher for other greenhouse gases. Nevertheless, tropical forest loss has been increasing at an

average rate of 2101 km2 each year since 2000.2 In addition to the effect on global warming,

deforestation leads to huge losses in biodiversity. The negative externalities of deforestation

amount to $2-4.5 trillion a year, according to The Economist .

However, estimates suggest that deforestation could be halved at a cost of $21-35 billion

per year, or reduced by 20-30 percent at a price of $10/tCO2.3 Third parties are therefore

interested in conservation. With the help of donor countries (in particular, Norway, Germany,

and Japan), the World Bank and the United Nations are already offering financial incentives

to reduce deforestation in a number of countries. Conservation contracts are favored by

economists who view them as the natural Coasian solution (Alston and Andersson, 2011) and

they are also likely to be an important part of future climate change policies and treaties. Also

for other types of resources, such as fossil fuel reserves, a climate coalition’s optimal policy

may be to pay nonparticipants to conserve particular reserves (Harstad, 2012).

It is therefore essential to understand how conservation contracts should be designed. So

far, however, there is little theory that can guide real-world contract designers. A useful

theory must take several facts into account. First, the causes of deforestation are mixed:

while local governments sell logging concessions in some countries, other countries fight illegal

logging for timber or the burning of the forest for agriculture. Second, markets for timber

and agricultural products are integrated and conservation in one region can lead to increased

deforestation elsewhere: for conservation programs in the U.S. west, the leakage rate (i.e.,

1See Engel et al. (2008) for PES more generally. See Karsenty (2008) and Parker et al. (2009) for anexplanation of the difference between alternative concepts such as RED, REDD, and REDD+.

2Hansen et al. (2013). Harris et al. (2012) offer more precise estimates of deforestation between 2000 and2005. The overall message that tropical deforestation has been increasing remains robust.

3See Edenhofer et al. (2014) and Busch et al. (2012), respectively.

2

the increased deforestation elsewhere per unit conserved in the west) was 43 percent at the

regional level, 58 percent at the national level, and 84 percent at the continental level; for

the 1987—2006 conservation program in Vietnam, the leakage rate was 23 percent, mostly

due to increased logging in neighboring Cambodia and Laos.4 The presence of leakage is not

surprising: conservation reduces the supply of forest products, and the price thus increases. A

higher price increases deforestation (Kaimowitz and Angelsen, 1998) and the cost of protection

elsewhere (as in Ross, 2001).

The third fact is that the level of decentralization plays an important, but puzzling, role.

Specifically, Burgess et al. (2012: 1751) find that "as the number of jurisdictions within a

provincial wood market increases, deforestation rises and prices fall." On the other hand,

Somanathan et al. (2009: 4146) find that "forests in the Indian central Himalayas have been

conserved at least as well and possibly better under decentralized management and at much

lower cost."5 Similarly, Edmonds (2002) argues that while deforestation in Nepal accelerated

under national management after 1957, deforestation decreased by 14 percent after 1993 in

response to decentralization of forest management. The effect of decentralization is ambiguous

also when comparing many other countries, as we will document in Section 6.

Despite these differences, contracts tend to be targeted mainly at national governments.

Norway, for example, recently declined to contract with the region Madre de Dios in Peru and

stated that it would only contract at the national level.

These facts and puzzles raise a number of important questions. What determines whether

decentralization leads to more conservation (as in Himalayas) or more deforestation (as in

Indonesia)? Can the donor benefit from contracting with districts rather than with central

authority, and which kind of contract leads to the largest amount of conservation?

Our first contribution is to provide a tractable model that is consistent with the facts and

can address all the questions above. Our model actually combines two separate models: In

the first, logging is illegal and the districts find protection expensive. Any parcel of the forest

will be protected only if the expected penalty is larger than the profit one may gain when

extracting that unit. The profit is given by the harvest price, and the price is decreasing in

total supply. Therefore, by letting one part of the forest be unprotected, some timber will be

supplied to the market and the price will decline; this decline reduces the pressure (and thus

4The numbers for the U.S. are from Murray (2008) and Murray et al. (2004); Meyfroidt and Lambin (2009)provided the study of Vietnam. Other estimates complement these numbers: according to Gan and McCarl(2007), 75% of EU’s, 70% of that of Australia and New Zealand, and 46% of that of United States’reducedtimber harvest are replaced by increased logging in the tropics. Atmadja and Verchot (2012) summarize thefindings on forest conservation leakage: the estimates vary widely between 5% and 95%, but typical estimatesare around 40%.

5Antinori and Rausser (2007), Baland et al. (2010), and Chhatre and Agrawal (2008) present similarevidence to that of Somanathan et al. (2009).

3

the monitoring expenditures) on the fraction of the resource that is to be protected. Thus,

in this model, deforestation is driven by high protection costs. Since the districts are not

themselves in charge of resource extraction, and they are unable to benefit from the profit, we

believe this model fits the setting in which districts are "weak."

The other model we present is a quite standard Cournot game, where extraction is sales

driven: Here, each district benefits from the profit of its harvest, and decides on how much to

sell on the common market. The larger the total supply, the smaller the price. The districts

are themselves in charge of extraction and, since they benefit from the profit, we believe this

model fits the setting in which districts are "strong."

These two models are combined in the analysis of our model. If we, for example, raise the

parameter measuring protection cost, or lower the parameter measuring how much districts

benefit from the revenues, then our model becomes more similar to the first variant, that of

illegal logging and weak districts.

Our second contribution is to show that this model explains the puzzle why decentraliza-

tion has an effect on conservation that differs between countries. To see this, note that the

(pecuniary) externality from conservation is negative in the first model where districts are

weak: if one district conserves, supply decreases, the price increases, and thus the pressure

and monitoring cost increase in the neighboring districts. This negative externality would

had been taken into account by a central authority, so centralization would lead to less pro-

tection. When districts are strong, as in the second model, the externality is positive, since

the high price following conservation leads to larger profit in the other districts. A central

authority would then request the district to sell less in order to keep the price high, while

decentralization would reduce the fraction that is conserved.

Consistent with these predictions, countries in which decentralization reduced deforestation

have been referred to as weak: in the Himalayas, "the Forest Department was poorly staffed and

thus unable to implement and enforce the national policies, and deforestation increased in the

1960s and 1970s" (Shyamsundar and Ghate, 2014: 85). In Indonesia, where decentralization

increased deforestation, deforestation is sales driven: "Deforestation in Indonesia is largely

driven by the expansion of profitable and legally sanctioned oil palm and timber plantations

and logging operations" (Busch et al., 2015: 1328).6

This empirical pattern is not limited to these regions. As we discuss in Section 6, the data

from a cross-section of countries are broadly consistent with our prediction: decentralization

reduces deforestation in countries with weak state capacity while increasing it in countries

6The literature on state capacity often refers to states in East Asia as strong; see the references in Acemogluet al. (2015).

4

with strong state capacity.

Given that our main positive prediction appears to be consistent with the evidence, it is

worthwhile to also present some normative conclusions from our analysis. Thus, our third

contribution is an analysis of the optimal conservation contract. The externalities discussed

above translate into contractual externalities when a principal or "donor" pays one district to

conserve. In line with the reasoning above, the externality on the other districts is negative

when districts are weak, but positive when districts are strong. The contractual externality

will be internalized by a central authority and it will influence the donor’s cost of achieving

conservation. When districts are weak, the externality is negative, a central authority will

be reluctant to accept, and the donor is better off signing the conservation contracts with

individual districts. When districts are strong, the externality is positive, a central authority

will internalize the benefit to the neighbors, and the donor achieves conservation at a lower

cost when contracting with central authorities. Given the interest in reducing expenses, the

donor may prefer decentralized contracts even in situations in which centralized contracts

would have led to more conservation– and vice versa.

After discussing our contribution to the literature, Section 3 presents our model of con-

servation and extraction, which we solve in Section 4. Conservation contracts are analyzed

in Section 5. In both Sections 4 and 5 we emphasize the effects of (de)centralization. The

concluding Section 6 presents some preliminary empirical findings: while a serious test must

await future research, the numbers we present do suggest that such an investigation may be

worth the effort. The Appendix provides all the proofs.

2 Contributions to the Literature

Our paper disentangles different aspects of the political regime, such as state capacity and the

level of decentralization, and we show how they interact with each other and with the economy

when determining the level of conservation. As discussed above, our model is consistent with

the evidence on leakage and our results may explain the puzzling effect of decentralization.

Our theory also contributes to the literature on the causes of deforestation. The literature has

identified such causes as optimal land use, income growth and demand for forest products,

corruption, costly enforcement, illegal logging, and other institutional weaknesses.7 Our first

7See, for optimal land-use models: Hartwick et al. (2001); income growth and demand for forest products:Foster and Rosenzweig (2003); corruption: Burgess et al. (2012); Amacher et al. (2012); Delacote (2011);Robinson and Lokina (2011); costly enforcement: Clarke et al. (1993); Dokken et al. (2014); illegal logging:Amacher et al. (2007); Clarke et al. (1993); Robinson et al. (2013); and for other institutional weaknesses:Angelsen (2001); Mendelsohn (1994). Kaimowitz and Angelsen (1998) and Angelsen and Kaimowitz (1999)provide a detailed review of the earlier literature regarding economic models of tropical deforestation.

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contribution to this literature is to provide a tractable workhorse model that can be used for

all these alternative drivers. When the levels of the parameters in our model are suitably

adjusted, it can be applied whether the deforestation driver is corruption, revenue generation

at the local level, or illegal logging by small farmers or by large corporations.

Our theoretical framework draws from, and ties together, the literatures on state capacity,

the resource curse, and crime displacement. The terminology "strong" vs. "weak" states

(or districts), is borrowed from the literature on state capacity (Acemoglu, 2005; Besley and

Persson, 2009, 2010, 2011), which refers to states as weak if they are unable to control the

economy, to support private markets, or to raise revenues.8 The role of institutions has

also been emphasized by the literature on the resource curse, which has found that a larger

resource stock is beneficial for a country with strong institutions, but not for a country with

weak institutions.9 We show that conservation contracts will aggravate the dependence on

institutions, since the contracts generate positive externalities when districts are strong, but

negative externalities when they are weak.

The papers cited above do not consider the interaction between districts. But estimates

of "leakage" can be quite high, as mentioned above, and scientists have pointed out the

importance of accounting for leakage when comparing various types of conservation contracts

(Busch et al., 2012).10 In our model, the leakage is related to shifts in market shares when

districts are strong, and to crime displacement when districts are weak and the extraction is

illegal. There is plenty of empirical support for crime displacement,11 but the literature has

largely ignored how the market facilitates crime displacement. To the best of our knowledge,

our model is the first to recognize that by letting a fraction of the resource be unprotected, the

supply (of the harvest) increases and the price declines, thereby reducing the pressure on and

the enforcement cost for the part that is to be conserved. This mechanism thus adds a new

perspective to the more general literatures on crime, enforcement, and inspection games.12

8While much of this literature endogenizes investments in state capacity and shows how such investmentsrelate to conflict and war (Gennaioli and Voth, 2015), we take state capacity as given and show how it willrelate to resource extraction and should relate to conservation contracts.

9See Brollo et al. (2013), Mehlum et al. (2006), Torvik (2009), Robinson et al. (2006), Robinson et al.(2014), or the survey by van der Ploeg (2011). The value of forests can be an important driver of the resourcecurse (Ross, 2001).10In contrast to the estimates in that paper, we analytically derive the optimal contract in a setting which

also allows for illegal logging and protection costs.11See Dell (2015) or Gonzalez-Navarro (2013) for recent evidence; for surveys, see the handbook chapters

by Johnson et al. (2012), Helsley (2004), or Epple and Nechyba (2004).12For overviews, see Polinsky and Shavell (2007) and Avenhaus et al. (2002). Eeckhout et al. (2010) and

Lando and Shavell (2004) also reach the conclusion that it may be optimal to monitor some places (or groups)intensively, and not at all elsewhere. The reason is, as in this paper, that enforcement must reach a certainlevel to have any effect. However, these papers do not take into account that abstaining from monitoring insome places causes monitoring costs to decline for the places where the law is to be enforced. This effect,which we emphasize, means that there is an interior solution for the amount of area that is to be protectedeven when there is no budget constraint or convex effort cost. Our mechanism also differs from that in Kremer

6

We also contribute to the literature on conservation contracts. We diverge from the growing

literature on how to design agreements for PES (Engel et al., 2008) or REDD (Kerr, 2013),

which tends to focus on textbook contract-theoretic problems such as moral hazard (Gjertsen

et al., 2016), private information (Chiroleu-Assouline et al., 2012; Mason, 2015; Mason and

Plantinga, 2013), or observability (Delacote and Simonet, 2013). Instead, the analysis in our

paper relates more to the literature on contracts in the presence of externalities. While the

general theory has been outlined by Segal (1999),13 our model endogenizes the sign and the

level of the externality, and our results are more detailed in characterizing the contract for the

particular case of resource extraction.14 More importantly, we go further than Segal (1999)

by searching for the principal’s optimal contracting partner (central vs. local governments),

which is an important issue for real-world conservation contracts.

3 A Theory of Conservation

This section presents a model of conservation and resource extraction in which there are

many districts and a common market for the harvest. The framework is general in that the

resource can be any kind of resource (for example, oil or land) but, to fix ideas, we refer to

the resource as forest. The harvest can be timber or agricultural products, and the districts

can be countries or villages.

To introduce our framework, we start by sequentially presenting two alternative models of

conservation before we combine them. In both cases there is a regional market with n ≥ 1

players, or districts, and xi is the extraction level in district i ∈ N = {1, ..., n}. The xi’s

are decided simultaneously and the aggregate harvest, x =∑

i∈N xi, is sold on the common

market. The larger x, the smaller the price p (x). Our results hold for a general price function,

as long as p′ (x) < 0. To get explicit (and additional) solutions, and to visualize the results,

we will frequently mention the case of a linear demand curve:

pL (x) = p− ax, (1)

where p and a are positive constants.

and Morcom (2000), where the regulator may want to increase the (potential) supply– not to reduce themonitoring cost, as here– but in order to reduce the incentive to poach and thus eliminate the bad equilibriumin a dynamic game with multiple equilibria (one of them being extinction and thus low supply).13Other important articles in this literature are Segal and Whinston (2003), who focus on privately observed

contracts; Gomes (2005), who studies multilateral contracts; and Genicot and Ray (2006), who allow agentsto coordinate (but not centralize), and show that the principal still manages to "split and rule."14For example, we show how the optimal reference level should generally differ from the business-as-usual

level, in contrast to the traditional presumption and advice (Busch et al., 2012).

7

Weak districts. By "weak districts" we have in mind that many countries or regions do

not fully control the extraction of their resources, perhaps partly because of high monitoring

or protection costs. Extraction would then be "protection-cost driven" (or simply "protection-

driven"). In this setting, the price p is what an illegal logger earns when extracting a unit of

the forest. This profit must be compared with the expected penalty, θ, which one faces when

logging on that unit of the forest. The enforcement is preventive if and only if the expected

penalty is larger than the benefit:

θ ≥ p (x) . (2)

We let districts set their expected penalties in advance in order to discourage extraction. In

principle, the expected penalty can be increased by a larger fine or penalty, but there is a

limit to how much the fine can be increased in economies with limited liability. To raise the

expected penalty further, one must increase the monitoring probability, which is costly.15 We

let c > 0 denote the cost of increasing monitoring enough to increase the expected penalty

by one unit. Thus, if (2) holds, it will bind: there is no reason to monitor so much that (2)

holds with strict inequality. Further, if (2) does not hold, then θ = 0: if monitoring does not

prevent logging, there is no reason to monitor at all. These corner solutions imply that for

each unit of the forest, the district either protects the unit and ensures that (2) binds, or does

not protect at all, and that unit of the forest will be cut.

District i has a large forest or resource stock Xi, and it is allowed to monitor each unit

with a different intensity. Since the optimal monitoring intensity for each unit ensures that

the expected penalty is either p or 0, it follows that a part of the forest will be protected

and conserved, perhaps as a national park, while the remaining part will not be protected

and thus will eventually be cut. The model thus predicts that conservation policies will be

"place-based" (for example, restricted to geographically limited but protected national parks),

as seems to be the case in Indonesia, where "national and provincial governments zone areas

of forest land to be logged" (Busch et al., 2015: 1328 ). Since xi denotes the extraction

level in district i and θ = p (x) for the part (Xi − xi) that is conserved, district i’s payoff

is −cp (x) (Xi − xi) − vxi.16 Parameter v is the marginal opportunity value when losing the

forest. For example, v may represent the environmental benefits that the forest provides.

15If π is the probability of being caught, while w is the largest possible penalty (for example, the wealth ofan illegal logger), then monitoring requires π ≥ p (x) /w.16To be precise, let Si be i’s forest stock of size Xi, and let θs be the expected penalty when logging unit

s ∈ Si. If the forest units are divisible then i’s payoff is

ui = −c∫Si

θsds− v∫Si

1sds,

where 1s = 1 if θs < p (x) but 1s = 0 if θs ≥ p (x). Since there will be a corner solution for the optimal θs, uican be written as −cp (x) (Xi − xi)− vxi.

8

Strong districts. While our protection-driven model for weak districts is new, we will

also consider the more standard "sales-driven" setting which is appropriate when districts are

"strong." In this case, we assume that the districts control their resource management, and

they decide on the xi’s directly and benefit from the profit generated. In the simplest version

of this model, a district i’s payoff can be written as bpxi − vxi, where b measures the benefit

of profit. As before, p = p (x) is the price for the harvest and v is the value of the forest (v

can alternatively be the cost of extraction).

The combined model. More generally, district imay benefit from the part of the resource

extracted and sold, xi, while simultaneously finding it expensive to protect the remaining part,

Xi−xi. When the arguments above are combined, and we define x−i ≡∑

j∈N\i xj, the utility

of district i becomes:

ui (xi, x−i) = bp (x)xi − cp (x) (Xi − xi)− vxi. (3)

With this combined model, the distinction between "strong" and "weak" districts is no

longer binary. Thus, we will often refer to districts as being (relatively) weak, and extraction

as protection-driven, if parameter b is small while c is large, so that the model resembles our

first variant, presented above. Similarly, we will refer to districts as being (relatively) strong,

and extraction as sales-driven, if parameter b is large while c is small. This terminology is

consistent with that in the literature on state capacity, discussed in the Introduction.

Remark 1: Alternative interpretations and generalizations. There are several

alternative interpretations of the combined model such as it is summarized in (3). For example,

even if all extraction is illegal, parameter b may reflect the probability that the government

in a district captures the profit from the illegal loggers, even in the areas where the forest is

not protected.17 Note also that we may write the utility function as

ui (xi, x−i) = bp (x)xi + (v − cp (x)) (Xi − xi) ,

if ui (xi, x−i) ≡ ui (xi, x−i) + vXi, to recognize that the value v can be interpreted as a benefit

from the part that is conserved. Since we take Xi as being exogenous, this distinction will not

matter for the analysis.

The model is simple and can easily be generalized in several ways. For example, we allow

17As another interpretation, if district i decides to extract xsi units for sale in order to raise revenues, suchextraction may require infrastructure and roads, which in turn may also lead to illegal logging in the amountαxsi , where α > 0 measures the amount of illegal logging when the government logs. Such a complementarityis documented by de Sá et al. (2015). Total extraction is then xi = (1 + α)xsi even though the fraction of thetotal profit, captured by the government in district i, is only b ≡ 1/ (1 + α). The larger the fraction of illegallogging, the smaller b is. Whatever is not cut must be protected, just as before.

9

for heterogeneous vi’s in the Appendix, and district-specific parameters b and c in our working

paper.18 One can also allow the districts (or the donor, introduced in Section 5) to take into

account some of the consumer surplus: this generalization will merely make the analysis messier

without altering the conclusions qualitatively. Since tropical timber and agricultural products

are exported, in reality, it is reasonable that districts will not take consumer surplus into

account.

Furthermore, note that we have linked the districts by assuming that the harvest is sold

at a common downstream market, but we could equally well assume that districts hire labor

or need inputs from a common upstream market. To see this, suppose that the price of the

harvest is fixed at p, and consider the wage cost of the labor needed to extract. If the labor

supply curve is linear in total supply, and loggers are mobile across districts, then we may

write the wage as w + ax, where w is a constant and a > 0 is the slope of the labor supply

curve. Defining p ≡ p + w, we can write this model as (1)—(3). It is thus equivalent to the

model described above with linear price.

Remark 2: Nonpecuniary externalities. If a district cares about the other districts’

extraction level directly, then these concerns may interact with the effect through p in arbitrary

and complex ways. It is beyond the scope of this paper investigate these effects in detail.

However, note that, if the price is linear, we can easily allow for cross-externalities such that

district i loses v−i when the other districts extract. To see that our model already captures

this case, suppose that i’s true payoff is:

ui = bpL (x)xi − cpL (x)(Xi − xi

)− vixi − v−i

∑j∈N\i

xj.

We can then write the payoff as (3) if we simply define ui ≡ ui+pv−i/a while vi ≡ vi− v−i and

Xi ≡ Xi− v−i/ca. Thus, a larger cross-externality can be captured by considering a reduction

in vi and Xi in the model described above. Although we now simplify by assuming that the

vi’s are homogenous, heterogeneous vi’s are permitted in the Appendix.

4 Conservation and Political Regimes

Using the combined model above, in which resource extraction can be sales-driven or protection-

driven, this section discusses the equilibrium amount of extraction and conservation and in-

18Harstad and Mideksa (2015). The additional insight does not justify the added complexity, however, sincewhen two heterogeneous districts centralize authority, the result would be a corner solution on xi in at leastone district. These corner solutions are not worth to emphasize, in our view, since they are unlikely to berobust to other changes in the model.

10

vestigates the effect of political centralization. These results are interesting in themselves,

they can explain empirical irregularities, and they are necessary to describe before we analyze

conservation contracts in the next section.

4.1 Equilibrium Conservation

Each district i ∈ N decides on xi, taking as given the other districts’extraction level, x−i =

{xj}j∈N\i and x−i =∑

j∈N\i xj. It is easy to see that extraction levels are strategic substitutes,

so that i prefers to extract less if other districts are expected to extract more. This property

holds in both variants of our model: In the protection-driven model of weak districts, a large

xj lowers p (x) and thus the protection cost when i decides on how much to conserve. In a

sales-driven model of strong districts, a large xj lowers the price and therefore the marginal

profit i gets from extraction.

To ensure that the solution for the xi’s are interior, we will throughout the paper assume

that the Xi’s and the aggregate stock X ≡∑

i∈N Xi are suffi ciently large. If Xi were small,

we would typically get a corner solution where i extracts zero or everything. Such corner

solutions are not worth our attention here, since they are unlikely to be robust or survive

under more general functional forms.

Proposition 1.

(i) If c or Xi increases, or v decreases, then xi increases, x increases, and p decreases.

Furthermore, xj decreases in Xi, j 6= i. In the unique equilibrium, the equilibrium xi’s are

implicitly given by xi = x0i , where:

x0i =c

b+ cXi +

(b+ c) p (x0)− v−p′ (x0) (b+ c)

∈ [0, Xi] and (4)

x0 =c

b+ cX + n

(b+ c) p (x0)− v−p′ (x0) (b+ c)

(5)

if each stock is suffi ciently large and the second-order condition is satisfied:

Xi ≥ max

{(b+ c) p (x0)− v−p′ (x0) b ,

v − (b+ c) p (x0)

−p′ (x0) c

}; (6)

(−p′

(x0))2

>p′′ (x0) [(b+ c) p (x0)− v]

2 (b+ c).

11

(ii) With pL (x), the second-order condition is satisfied and (4)-(6) can be written as:

x0i =bp− v

ab (n+ 1)+ c

v + ab [(n+ 1)Xi −X]

ab (b+ c) (n+ 1), and

x0 =nbp− nvab (n+ 1)

+ cnv + abX

ab (b+ c) (n+ 1), if

Xi ≥ max

{(b+ c) p− caX − v

ab (n+ 1),−(b+ c) p− caX − v

ac (n+ 1)

}, ∀i ∈ N .

Quite intuitively, a district extracts more if conservation is costly (i.e., if c is large). Fur-

thermore, a district i extracts more if its own resource stock is large, since a larger xi reduces

p (x) and thus the protection cost for the (large) remaining amount. Since, similarly, j ∈ N\i

extracts less when Xj is large, the level of xi decreases in Xj as xi and xj are strategic sub-

stitutes: when p (x) is small, it is both less profitable for i to sell, and less expensive for i to

protect its resource. For both reasons, district i conserves more when Xj is large, for j 6= i.

Part (ii) also shows that, with pL (x), aggregate extraction x is larger if demand is large

(p/a large). In this case, understanding parameter b’s ambiguous effect is straightforward. In

the expressions for x0i and x0, the first terms on the right-hand sides refer to the equilibrium

Cournot levels (as if c = 0): these terms increase in the benefit of profit, b. The second terms

show the additional extraction level due to costly enforcement. The larger c is, the larger

these terms are, and extracting more than the Cournot level becomes optimal even though

this reduces revenues. When b increases, revenues become more important and thus the second

term is smaller. In sum, x increases in b if and only if protection is inexpensive:

∂x

∂b> 0 if and only if c <

nv

aX. (7)

4.2 Conservation and (De)Centralization

In this section we study the effect of (de)centralization on conservation and emphasize how

this effect depends on state capacity, as captured by parameters b and c. If a set of districts

centralizes authority, we will assume that the forest stocks are pooled and that the extraction

rates are set to maximize the sum of the merging districts’ payoffs. Thus, the aggregate

resource stock X remains unchanged, while the number of relevant governments n declines.

To isolate this effect, we assume b and c remain the same after centralization. Any changes in

b and c could be added to the effects we isolate.

Note that there are important (pecuniary) externalities in this economy. If j ∈ N con-

serves, the price increases and this increase affects every districts’payoffs. The externality

12

can be positive or negative. Since i ∈ N\j maximizes (3), the envelope theorem gives:

∂ui (xi, x−i)

∂ (−xj)= −p′ (x) [(b+ c)xi − cXi] . (8)

If b or xi is large, it is important for i that the price be high, and then i benefits when j

conserves. If, instead, c and Xi are large, it is more important to reduce the cost of protection

and thus the pressure on the resource. Thus, when districts are weak, one district loses when

its neighbors conserve more.

When i maximizes ui by deciding on xi, xi is given by (4) and, combined with (8), we get

the equilibrium level of externality:

e ≡∂ui(x0i , x

0−i)

∂ (−x−i)= (b+ c) p

(x0)− v ⇒

e =(b+ c) p− acX − v

n+ 1when p (x) = pL (x) .

This last equation shows that, when p (x) is linear, the equilibrium externality e increases

in b and decreases in c, even when we take into account how the choice of xi is influenced

by these parameters. Furthermore, e is then decreasing in the aggregate stock, X, and not

only in Xi. All these claims continue to hold if p (x) is nonlinear, as is stated in the following

proposition (and proven in the Appendix):

Proposition 2.

(i) The equilibrium externality from conservation, e, decreases in X and increases in b. Fur-

ther, e is smaller if the districts are weak and c is large, as long as:19

(−p′

(x0))2

>−nep′′ (x0) / (b+ c)

−p′ (x0) (X − x0) /p (x0)− 1and X > x+

p (x)

−p′ (x). (9)

(ii) Small districts extract smaller fractions of their resources if and only if districts are weak.

For Xi < Xj, we havex0iXi

<x0jXj

⇔ e < 0.

(iii) If authority is decentralized (and n is larger), more is conserved if and only if districts

are weak:∂x0

∂n< 0⇔ e < 0.

19The first condition in (9) is satisfied if either e or p′′(x0)is relatively close to zero (as for pL (x)). The

second condition requires that the demand curve be so steep at x0 that a linear approximation would have ledto a negative price if the entire stock X were sold on the market: with pL (x), it reduces to p− aX < 0.

13

(iv) With pL (x), we get the explicit solutions

x0iXi

−x0jXj

=

(1

Xi

− 1

Xj

)e

a (b+ c)and

∂x0

∂n=

e

a (b+ c) (n+ 1).

Part (ii) suggests that the sign of e is also important for district i’s strategy. If e > 0,

district i prefers a high price, and thus i has an incentive to keep the price high by strategically

conserving more. If e < 0, district i has an incentive to extract more to reduce the price, and

thus the pressure. These strategic incentives are particularly important for a large district

that influences the price more by a given change in xi/Xi. The theory thus predicts that

while large districts conserve a larger fraction of their resources in a sales-driven model where

districts are strong, they conserve a smaller fraction when districts are weak and extraction

is protection-driven.

Part (iii) follows as the natural next step in this line of reasoning. If multiple districts merge

and centralize authority, the merged unit will be larger and it ought to increase conservation

if and only if e > 0. The result holds whether it is only a couple of districts that centralize

authority to a common central authority, or whether all the n districts centralize power to a

single government. Intuitively, members of the merged unit will internalize the externalities

on each other and thus conserve more if and only if conservation is beneficial to the partners.

With strong districts and a sales-driven model, it is well known from Cournot games that

if the number of sellers increases, so does the aggregate quantity supplied, while the price

declines. It is comforting to know that Proposition 2(iii) confirms this intuition. With weak

districts and protection-driven extraction, however, districts conserve less when they take into

account the fact that the pressure on the resource weakens as a consequence. In this case, the

result is reversed, and centralization reduces the amount of conservation.

As mentioned in the Introduction, we present some empirical support for Proposition 2 in

the concluding section. This empirical support lends some credibility to our theory, which is

comforting before we evaluate conservation contracts in the next section.

5 Conservation Contracts

In this section we study contracts between the districts and a principal or a "donor" D. We

assume that D’s utility is uD (x) = −d (x), where d′ (x) > 0 measures the marginal damage D

faces from the districts’extraction. A particularly simple case, which we at times will revert

14

to, is to assume that the damage function is linear and given by dL (x) = dx.20

We further assume that every i ∈ D ∪ N has a payoff that is linear and additive in the

transfer i receives, τ i ∈ <. By budget balance, τD = −∑

i∈N τ i. Before the districts simul-

taneously choose the xi’s, D can unilaterally offer transfers (in a take-it-or-leave-it fashion)

that are contingent on the entire vector of extraction levels. That is, let D commit to transfer

functions τ i (x) for every i ∈ M , where M is the set of districts that D can contract with.

Even if D would like to contract with all n districts, doing so may be unfeasible for exogenous

(or political) reasons. When D is not contracting with districts in N\M , it faces the problem

of "leakage": by paying i ∈ M to conserve, p (x) increases, and nonparticipants in N\M will

extract more. In fact, by summing every xi for i ∈ N\M , as given by (4), we get an equation

where x is implicitly defined as an increasing function of xM =∑

i∈M xi, which we may write

as x (xM).21

Since everyone can calculate the response of the other districts, it suffi ces for D to suggest

a carefully chosen vector x∗M = {x∗i }i∈M and pay i if and only if xi = x∗i . Another simple

contract is the linear version. This is the contract actually observed in reality, as when Norway

offers REDD contracts to the partnering countries, and it should thus be of particular interest.

In this case, D commits to pay i ∈M an amount that is linear in i’s choice of xi:

τ i = max {0, (xi − xi) ti} .

Here, xi is the "baseline" or "reference" level for district i’s deforestation level. The contract,

which consists of the pair (ti, xi), implies that district i receives ti dollars for every unit by

which actual extraction xi is reduced relative to the baseline level xi. If xi ≥ xi, no payment

takes place. The contract is valid for country i regardless of what the other districts decide to

do. When discussing linear contracts, we will assume that a district cannot commit to decline

payments in the future.22

20A general concave function d (x) can also account for the consumer surplus, which is ax2/2 under pL (x).However, when we simplify to dL (x), we ignore the possibility that the donor may value the consumer surplus.This assumption is not very restrictive, in our view: after all, the donor should not be regarded as a benevolentplanner, but rather as an NGO or a single country offering REDD contracts, such as Norway.21The function is

x (xM ) = xM +c

b+ cXN\M +

(b+ c) p (x (xM ))− v−p′ (x (xM )) (b+ c)

and it is easy to check that x′ (xM ) ∈ (0, 1) when the second-order condition holds. With pL (x), we get:

x (xM ) = xM +(n−m) (b+ c) (p− axM ) + acX − (n−m) v

a (b+ c) (n−m+ 1)⇒ x′ (xM ) =

1

n−m+ 1∈ (0, 1) .

22This assumption is not very restrictive: In the previous version of the paper, when contracts had to belinear, we allowed districts to commit to decline any future payments. This condition resulted in a "participa-tion constraint" that, in some situations, became harder to satisfy than the "incentive constraints," discussedbelow. Since the results were otherwise qualitatively similar, and since it may be questionable whether dis-

15

Although we impose the limited-liability assumption that τ i cannot be strictly negative,

it may, in reality, be possible for D to penalize a district if it extracts more than what D has

requested. For example, some tropical countries may receive development aid and this aid can

be witheld. In the following, we do allow for this, and we let fi ≥ 0 measure how much D can

credibly withhold or punish if i does not conserve as requested.

5.1 The Equilibrium Conservation Contracts

The objective of D is to maximize

−d (x (xM))−∑i∈M

τ i (x) , (10)

subject to the requirement that x must be implementable and thus the vector of equilibrium

extraction given the contracts {τ i (x)}i∈M . Note that if D implements x∗ by some {τ i (x)}i∈M ,

it can also implement x∗ by reducing all payments to zero (and penalizing i with fi) unless

x = x∗. D only has to make sure that every district i’s incentive constraint holds:

ui(x∗i , x

∗−i)

+ τ i (x∗) ≥ max

xiui(xi, x

∗−i)− fi. (ICi)

The right-hand side measures i’s best outside option, that is, the utility i can obtain by

freely choosing xi under the assumption that the other districts will continue to extract their

equilibrium quantities.23

To further reduce the amount of transfers to be paid, D would prefer to replace τ i (x)

by some τ i (x) − εi as long as (ICi) holds. As a result, every (ICi) will bind in equilibrium.

Substituting the binding (ICi)’s into (10), D’s problem is to maximize:

−d (x (xM)) +∑i∈M

ui (xi, x−i)−∑i∈M

maxxi

ui (xi, x−i) +∑i∈M

fi. (11)

The problem is particularly simple if there is only one district, M = N = i. Then, D

tricts in reality are able to commit to decline future payments, we here simplify the analysis by not allowingthe districts to commit in this way. With non-linear contracts, it is in any case straightforward to relax theparticipation constraint, since D can design contracts such that if one district rejects the offer, then it will bein the interest of the other districts to select xi’s at levels that would harm the district rejecting the contract.23This is the natural outside option as long as the xi’s are chosen simultaneously. Note that even if the

xi’s were gradually increasing over time, the xi’s would effectively be chosen simultaneously if it were diffi cultfor districts to observe the extraction levels at every point in time, before the contracting period has ended.However, if the model were dynamic and extraction levels immediately observable by the neighbors, then itmight be easier for a district, j ∈ N , to detect a deviation by another district i ∈ N\j. In this situation, itmay be simpler for D to reduce i’s temptation to deviate, since the contract with j may motivate j to choosea level of xj that penalizes i when i is on a track to deviate. A satisfactory analysis of this situation requiresanother model than the one we investigate here.

16

maximizes the sum of payoffs, −d (xi) + ui (xi), and implements the first best. When i = N ,

the first-best xi is given by (4) if just v is replaced by v+d′ (xi); so it follows that the first best

is implemented by a linear contract if just ti = d′ (x∗i ), and if xi is so large that (ICi) holds.

By reducing xi until (ICi) binds, D extracts the entire surplus even with linear contracts, and

linear contracts are then suffi cient.

The Appendix proves that linear contracts are suffi cient even when there are multiple

districts and D contracts with any number m ≡ |M | ∈ {1, ..., n} of them.

Proposition 3.

(i) Linear contracts are suffi cient: D’s preferred linear contract gives the same outcome and

payoffs as D’s preferred general contract does.

(ii) With pL (x) and dL (x), the contract with every i ∈M can be written as:

τ ∗i =d2

a (b+ c) (n+ 1)2− fi, and

x∗i =(b+ c) p+ ca [(n+ 1)Xi −X]− v − 2d (n+ 1−m) / (n+ 1)

a (b+ c) (n+ 1), implying

x∗ =n (b+ c) p+ caX − nv − 2md/ (n+ 1)

a (b+ c) (n+ 1).

The equivalent linear contract is:

t∗i =2d

n+ 1, and

x∗i = x0i +4m− 3 (n+ 1)

4a (b+ c) (n+ 1)t∗i − fi/t∗i .

Linear contracts are suffi cient since there is a deterministic and one-to-one relationship

between the xi’s and the ti’s, and since D must, in any case, ensure that transfers to i be so

large that i cannot achieve a higher payoffby selecting any other xi, when i takes x−i as given.

Of course, linear contracts would not suffi ce in more general environments with uncertainty

or non-concave utility functions, for example.

Part (ii) of Proposition 3 shows that we can get explicit solutions for the contract and the

equilibrium outcome if p (x) and d (x) are linear. Naturally, x∗ and the x∗i’s decrease in d, while

the transfers must increase. In this case, the linear contracts are particularly simple and both

t∗i and x∗i are linear in d. Since the leakage rate increases in n, t

∗i decreases in n, and t

∗i < d

if n > 1. It is comforting to note that the subsidy rate t∗i is robust and remains unchanged if

the parameters of the model either change or are unobservable to D. This robustness may be

one reason for why the linear contract is popular in reality.24 Note also that the fi’s do not24However, while the equilibrium choices of ti’s are independent of a, b, and c, the baseline level xi should

17

affect the equilibrium allocation of the x∗i’s; they only reduce the transfer which D has to pay.

The baseline xi will be set such that (ICi) binds and i is exactly indifferent between choosing

x∗i and ignoring the contract. If m = n = 1 and fi = 0, we have x∗i < x0i . This inequality

implies that i should not get paid as soon as i extracts marginally less that i would have done

in the absence of any contract, since, with such a contract, i would have been strictly better

off with than without the contract. If m is large, however, D is paying so many districts to

conserve, and the equilibrium price is so high, that the districts are much more tempted to

extract than they were without any contracts. In this case, D must increase the baseline to

motivate the districts to conserve. These results disprove the typical presumption that the

reference level should equal the business-as-usual level.25

Even though each district is indifferent between extracting x∗i and ignoring the contract

by extracting more, there is no equilibrium where i actually extracts more, since in that case,

D would have preferred to improve the terms of the contract. Further, there is no alternative

equilibrium where multiple districts ignore the contract by extracting more simultaneously.

The equilibrium is unique because the extraction levels are strategic substitutes, as we noted

in Section 4: a larger x−i reduces i’s temptation to extract more than x∗i .

5.2 Conservation Contracts and (De)Centralization

This subsection investigates how the equilibrium conservation level and D’s payoff depend on

the level of decentralization and the extent to which districts are weak or strong, such as these

are reflected by the (pecuniary) externality. The analysis is interesting not only because the

comparative static is important, but also because it is important to know how the political

system influences D’s preferences. In some cases, the donor may be able to decide whether it

wants to contract with a set of districts independently, or whether it instead wants to contract

with their common central government.26

Consider a subset L ⊆ M containing ∆ + 1 ≡ |L| districts. If these districts centralize

authority, then m, and n all decrease by the same number, ∆. We assume that such a

change does not influence the forest areas over which D can contract. Hence, D contracts with

vary with these parameters if D wants to ensure that the expenditures be minimized. Nevertheless, it is wellknown that simple, linear contracts may be optimal in dynamic settings with stochastic shocks being realizedover time (Holmstrom and Milgrom, 1987).25See, for example, Busch et al. (2012) or Angelsen (2008). The latter contribution also discusses why the

baseline level may be smaller than the business-as-usual (or historical) deforestation level, since a smallerbaseline reduces the amount that needs to be paid.26If a central government is already active and regulating local governments, it can always undo D’s offers to

the districts; decentralized contracts would then not be an option for D. If the central government is absent orpassive, however, D may evaluate whether it should contract with the districts or instead propose a contractto the union of some districts. The latter option may require that central authorities be activated or created.

18

m −∆ governments after the change, while the number of districts without a contract stays

unchanged at n−m.27

Note that centralization does not alter effi ciency, measured as the sum of payoffs. In fact,

the sum of payoffs is only a function of the aggregate, x, not of the distribution:

uD (x) +∑i∈N

ui (xi, x−i) = bp (x)x− cp (x) (X − x)− vx− d (x) .

Thus, in the first best, neither x nor the xi’s are altered after centralization. However, D

designs the contract to maximize (11) and not the sum of payoffs. An important difference

is that D benefits when i’s outside option is worsened, since D can reduce the transfers

accordingly. District i’s outside option is not a function of i’s own contractual x∗i , but of the

other districts’x∗j’s. The effect of xj on ui is exactly the (pecuniary) externality, discussed

in Section 3.2, and the externality is given by (8) for any given xi. At the outside option,

when district i maximizes ui(xi, x

∗−i), taking as given x∗−i, then i’s best choice is xi

(x∗−i)

=

arg maxxi ui(xi, x

∗−i), which is a decreasing function of x∗−i. In fact, xi

(x∗−i)is implicitly

defined by (4) when one takes into account that x = xi +x∗−i. Given the function xi(x∗−i), we

can define

ei(x∗−i)≡∂ui(xi(x∗−i), x∗−i

)∂ (−x−i)

= (b+ c) p(xi(x∗−i)

+ x∗−i)− v.

Here, ei(x∗−i)is the externality on district i’s outside option when other districts are requested

to conserve one more unit. If every ei(x∗−i)is positive (negative), it is quite intuitive that

D will conserve too little (much) relative to the xi’s that maximize the payoffs of the con-

tracting partners, uD (x) +∑

i∈M ui (xi, x−i). Part (i) of the following proposition confirms

this intuition. Furthermore, parts (ii) and (iii) state that, if L ⊂M centralizes authority and

ei(x∗−i)< 0∀i ∈ M , x increases while D’s payoff decreases. In this situation, D would prefer

to contract with individual districts in L in a decentralized way.

Proposition 4.

(i) If D contracts with n = m = 1 , the outcome is first best. If n ≥ m > 1, D conserves too

little (much), relative to maximizing∑

i∈D∪M ui, if ei(x∗−i)> (<) 0∀i ∈M.

(ii) Centralization increases equilibrium x∗ if ei(x∗−i)< 0∀i ∈M .

(iii) Centralization decreases D’s equilibrium payoff if ei(x∗−i)< 0∀i ∈M .

(iv) With pL (x) and dL (x), centralization increases x if and only if (12) holds, and decreases

27In Harstad and Mideksa (2015), we also consider (de)centralization among the districts without a contract.

19

D’s payoff if and only if (13) holds:

e

d≤ 2

n+ 1

(1− m

n+ 1− m−∆

n−∆ + 1

), (12)

e

d≤ 1

n+ 1

(1− m

n+ 1− m−∆

n−∆ + 1

), where (13)

e ≡ (b+ c) p− acX − vn+ 1

, as before.

Parts (ii) and (iii) state suffi cient conditions for when centralization increases x and de-

creases D’s payoff, but these conditions are stronger than necessary. The exact conditions that

are both necessary and suffi cient can easily be derived when p (x) and d (x) are linear, as in

part (iv) of the proposition.

To first understand the effect on x, note that there are multiple ways in which centralization

influences x. The first effect is the one emphasized in Section 4: a central authority internalizes

the externalities and thus it lowers x if e > 0 and raises x if e < 0. This is the only effect

if d ≈ 0, and then (12) boils down to e ≤ 0.28 Another effect is that when d > 0 and D

contracts with m districts, then when L ⊂ M centralizes, D is effectively contracting with

a smaller fraction of the total districts than before centralization took place (the fraction

is reduced from m/n to (m−∆) / (n−∆)). The smaller fraction makes the contracts less

effective and the amount of leakage (in that the nonparticipants extract more) increases. This

effect dominates whenm is small, and then e > 0 is not suffi cient for centralization to decrease

x. For this reason, the requirement on e decreases in m. Condition (12) is illustrated as the

green/steepest line in Figure 1.

To understand the effect on D’s payoff, note that the two ways in which centralization

affects x will also work in influencing D’s payoff. In addition, D would like to save money.

A central authority internalizes the externality, so if the externality is positive (negative), D

achieves conservation with less (more) transfers under centralization than under decentraliza-

tion. For this reason, the threshold for e determining when centralization increases D’s payoff

is closer to zero than the threshold determining when centralization reduces x. Condition (13)

is illustrated as the blue/flatter line in Figure 1.

This difference between (12) and (13) means that when m is small and e/d is large, D may

prefer centralized contracts even in situations in which such contracts lead to less conservation

(region I in Figure 1). If m is large and e/d is small (region II), D prefers to contract

directly with the districts to reduce its expenses, even when centralization would have led to

28When D offers contracts and pays to reduce x, the effective externality increases and e > 0 is suffi cient butno longer necessary for centralization to reduce x. This observation explains why condition (12) is strongerthan e < 0 when m is large.

20

Figure 1: Centralization increases conservation above the green/steepest line, and D’s payoffabove the blue/flattest line. In region I (II), D prefers (de)centralized contracts to reducetransfers, even if this reduces conservation in equilibrium.

more conservation. In these areas, D is preferring the socially ineffi cient institution, because

the equilibrium extraction level is larger than the socially optimal level everywhere above

the red/increasing dotted line. Below the dotted line, D conserves too much in equilibrium

compared to the optimum, since D does not internalize the negative contractual externalities.

Here, D prefers decentralized contracts even if centralized contracts would have resulted in a

higher aggregate utility (as well as more extraction).29

Given that we know the equilibrium levels of transfers and conservation, it is easy to

29Two conditions are interesting for a welfare analysis. First, we can compare x∗ in Proposition 3 to thefirst-best level (which we find by setting m = n = 1 in the same equation). This comparison gives that x∗ islarger than the first-best level if and only if

e/d > −[(n+ 1)

2 − 4m]/ (n+ 1)

(n2 − 1

).

Second, since we have explicit equations for x∗, we can calculate aggregate utility as a function of n andm. If centralization increases x, then centralization increases aggregate utility if and only if (the condition isreversed if centralization decreases x):

(n−∆)n− 1

(n+ 1−∆)e < −d

[1− 2

(m

(n+ 1)2 +

m−∆

(n+ 1−∆)2

)],

If L = M , so that ∆ = m − 1, then each of these two conditions specifies a threshold for e which increasesin m and meets the green/steepest line in Figure 1 at m = n, as is illustrated. It is then optimal withdecentralized contracts to the left of both curves (i.e, to the left of both the steepest and the dotted line) butwith a centralized contract to the right of them. As noted already, full centralization leads to the sociallyoptimal outcome when m = n.

21

calculate D’s payoff when p (x) and d (x) are linear:

−dx−∑i∈M

τ i = −dnp (b+ c) + acX − nv − dm/ (n+ 1)

a (b+ c) (n+ 1)+∑i∈M

fi.

This expression for D’s payoff reveals D’s preferences for changing m and n, but also for

several other changes. First, given n, D is clearly better off with a large m: thus, D would

prefer to contract with as many districts as is politically feasible. Also, D benefits if the

demand for the harvest (measured by p) is low. This benefit could motivate D to support

a boycott against the harvested products. Finally, note that D’s payoff increases in v and

decreases in c, but the effect of b is ambiguous. This ambiguity is related to the discussion at

the end of Section 4 (and equation (7)), where we noted that x increases in b if c < nv/aX.

This increase is harmful for D. In addition, a larger b makes it more expensive to persuade

the districts to reduce the xi’s: thus, the condition for when D is harmed by a larger b is

weaker than (7) and given by c < nv/aX + dm/aX (n+ 1). In other words, D benefits from

strengthening state capacity insofar as such strengthening means that the protection cost (c)

is reduced or that districts’conservation valuation (v) is increased, but not necessarily when

the districts will be able to capture a larger fraction (b) of the harvest revenues. In fact, the

larger the the districts’conservation value v, or the smaller their protection cost c, the smaller

is the likelihood that D benefits from a large b.30

6 Conclusions, Predictions, and Preliminary Findings

This paper presents a novel, tractable model of conservation. We allow for many districts

and recognize that since extracting some of the resource increases the harvest supply, the

price declines and so does the monitoring cost for the part that is to be conserved. The

externality from one district’s conservation to others can be positive or negative, depending

on state capacities and the resource stock’s size. The model can be used to study various

types of resources and alternative drivers of extractions, but it is motivated in particular by

deforestation in the tropics.

The analysis has both a positive and a normative part. Our equilibrium characterization is

stated as several testable predictions. Most importantly, the theory predicts that decentraliz-

ing authority will increase conservation when districts are weak but will increase deforestation

30The previous version of this paper also analyzed districts’incentives for and benefits from merging witheach other, and how these incentives change when D is present and can design conservation contracts. Wethen showed that D’s presence may lead to either decentralization or centralization, and, in both cases, thisinstitutional change will always reduce conservation as well as D’s payoff. In some situations, the isolated effectof this change may outweigh the beneficial effect of D’s contract. If so, D’s presence leads to less conservation.

22

when districts are strong. Our analysis of optimal conservation contracts shows that a donor

benefits from contracting with the districts if the districts are weak, sometimes even in sit-

uations where centralized contracts would have resulted in more conservation. The analysis

of optimal contracts should be interpreted more normatively, in our view, since there are still

too few conservation contracts observed in reality, and since there are many reasons for why

these may not be optimally designed. However, the appeal of our normative analysis is clearly

strengthened if our positive predictions are consistent with the evidence.

Although large-scale institutional changes such as decentralization are not frequent, several

scholars have used clever empirical techniques to establish the relationship between deforesta-

tion and decentralization. Somanathan et al. (2009) estimate the effect of decentralization of

control of forests in the Indian central Himalayas on forest conservation and its costs. Burgess

et al. (2012) take advantage of the fact that Indonesia had embarked on decentralization

process for a decade: using the differential timing of decentralization in different regions, they

estimate the effect on deforestation of raising the number of district. As discussed in the Intro-

duction, while decentralization has resulted in more deforestation in Indonesia, the opposite

has happened in the Himalayas.

To supplement these studies with data from many countries, we present a cross-country

evidence. Although a serious empirical test would require access to better data, we estimate a

simple regression model using the forest-cover data from the World Development Indicators,

indicators of state’s protection capacity from Besley and Persson (2011), and decentralization

measures from Treisman (2008).31 State Capacity data is a dummy variable that takes value

of 1 if state capacity is in the top 25 percentile and zero if in the bottom 25 percentile.32 The

preliminary result is33:

Deforestation = 0.0969(1.21)

− 0.2052(−0.78)

StateCap.− 0.0054(−0.30)

Decentr. + 0.0335(0.48)

Interaction.

Despite the imperfections in the measurements of decentralization and state capacity as

well as lack of suffi cient statistical power due to a small number of observations, the evidence

from the cross-section of countries is qualitatively consistent with the findings of the previous

31Note that measures of state capacity and decentralization are economy-wide indicators and are not specificto forest protection/management. Thus, these indicators are approximate measures to the variables in thetheory.32The qualitative prediction of the model is robust to classifying weak-strong state capacity on the basis of

below or above one standard deviation from the mean as well as on the basis of bottom—top 20 percentile ofstate capacity.33Both the state capacity and the decentralization data are from mid-1990s, and deforestation is here

measured as net percentage decrease in forest cover between 1995 and 2005. We have 59 observations andt-values are in parenthesis. The superscripts *, **, and *** indicate statistical significance at at 10%, 5%, and1% significance levels, respectively.

23

literature (as described in the Introduction) and the main prediction of our model. That

is, deforestation is negatively correlated with degree of decentralization in weak states, i.e.,

-0.0054, where State Capacity takes the value of 0; whereas it is negatively correlated in

strong states, i.e. 0.0335 - 0.0054, where State Capacity takes the value of 1. Unfortunately,

we are not aware of larger data sets available on enforcement costs (rather than on state

capacity more generally) or decentralization of forest management authority (rather than

on decentralization, more generally). Nevertheless, these preliminary findings are, in our

view, suffi ciently interesting that they ought to motivate more serious investigations in future

research.

24

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7 Appendix: Proofs

Proof of Proposition 1. The proofs allow for heterogeneous vi’s, so ui (xi, x−i) = (b+ c) p (x)xi−cp (x)Xi − vixi.(i) The derivative of ui (xi, x−i)with respect to (w.r.t.) xi is:

(b+ c) (p′ (x)xi + p (x))− cp′ (x)Xi − vi. (14)

Thus, i extracts nothing if the derivative is negative even when xi = 0, which requires:

(b+ c) p (x)− cp′ (x)Xi − vi ≤ 0⇒ Xi ≤vi − (b+ c) p (x)

−p′ (x) c,

while i extracts everything if the derivative is positive also when xi = Xi:

(b+ c) (p′ (x)Xi + p (x))− cp′ (x)Xi − vi ≥ 0⇒ Xi ≤(b+ c) p (x)− vi−p′ (x) b

.

28

To ensure that xi ∈ (0, Xi), we must thus assume that each stock is suffi ciently large:

Xi > max

{vi − (b+ c) p (x)

−p′ (x) c,(b+ c) p (x)− vi−p′ (x) b

}.

Furthermore, note that the second-order condition (s.o.c.) is satisfied when:

(b+ c) (p′′ (x)xi + 2p′ (x))− cp′′ (x)Xi < 0⇒

−p′ (x) >p′′ (x) [(b+ c)xi − cXi]

2 (b+ c)=p′′ (x) [(b+ c) p (x)− vi] / (−p′ (x))

2⇒

(−p′ (x))2>p′′ (x) [(b+ c) p (x)− vi]

2 (b+ c), (15)

where we used (4). Assuming that s.o.c. is satisfied, (14) decreases in xi. Since the first-ordercondition (f.o.c.) is that (14) equals zero,

xi =(b+ c) p (x)− cp′ (x)Xi − vi

−p′ (x) (b+ c)=

c

b+ cXi +

(b+ c) p (x)− vi−p′ (x) (b+ c)

⇒ (16)

x =c

b+ cX +

n (b+ c) p (x)−∑

i∈N vi

−p′ (x) (b+ c).

We can see that if c or Xi increases, or vi > 0 decreases, x must increase and p (x) decrease.For similar reasons, xi increases.(ii) With pL (x) = p− ax, it is straightforward to solve for the xi’s to get Proposition 1(ii). ‖

Proof of Proposition 2.(i) With the envelope theorem, when

ui = maxxi

(b+ c) p (x)xi − cp (x)Xi − vixi ⇒∂ui

∂ (−xj)= −p′ (x) [(b+ c)xi − cXi] .

Since the f.o.c. can be written as

(b+ c) p (x)− vi = −p′ (x) [xi (b+ c)− cXi] , (17)

the externality is here on both sides of this inequality. To see the effect of b, aggregate (17)over the i’s to get:

(b+ c) p (x)−∑i∈N

vi/n = −p′ (x) [x (b+ c)− cX] /n. (18)

Now the (average) externality (e) is on both sides of the inequality, and every ∂ui/∂ (−xj)will change exactly as e if the vi’s are hold constant. Note that the l.h.s. of (18) decreases inx, while the r.h.s. increases in x if:

−p′′ (x) [x (b+ c)− cX]− p′ (x) (b+ c) > 0⇒−p′ (x) (b+ c) > p′′ (x) [x (b+ c)− cX] = p′′ (x) [ne/ (−p′ (x))]⇒

(−p′ (x))2> p′′ (x) en/ (b+ c) . (19)

Clearly, if X increases, the r.h.s. of (18) shifts down, x increases, and e and ∂ui/∂ (−xj)decreases. If b increases, both sides/curves in (18) shift up. This implies that (b+ c) p (x)increases and every ∂ui/∂ (−xj) increases. To see the effect of a larger c, note that both thel.h.s. and the r.h.s. of (18), as functions of x, shift to the right. If the horisontal shift in thel.h.s. is smaller than the horisontal shift in the r.h.s., then e and ∂ui/∂ (−xj) must decrease.

29

To see when this is indeed the case, keep the l.h.s. of (18) constant and differentiate w.r.t. cand x to get:

dx

dc lhs=

p (x)

−p′ (x) (b+ c).

To measure the horisontal shift in the r.h.s. of (18), keep the r.h.s. constant and differentiatew.r.t. c and x to get:

dx

dc rhs=

−p′ (x) [X − x]

−p′ (x) (b+ c)− p′′ (x) [x (b+ c)− cX],

where the denominator is positive under (19). By comparison, dxdc lhs

< dxdc rhs

if:

p (x) [−p′ (x) (b+ c)− p′′ (x) [x (b+ c)− cX]] < −p′ (x) (X − x) [−p′ (x) (b+ c)]⇒p′′ (x) p (x) [c (X − x)− bx] < −p′ (x) (b+ c) [−p′ (x) (X − x)− p (x)]⇒

p′′ (x) p (x)

(− ne

−p′ (x)

)< −p′ (x) (b+ c) [−p′ (x) (X − x)− p (x)]⇒

−p′′ (x) en < (−p′ (x))2

[−p′ (x) (X − x)

p (x)− 1

](b+ c)⇒

(−p′ (x))2>

−p′′ (x) en/ (b+ c)

−p′ (x) (X − x) /p (x)− 1.

The last step is valid and the denominator is positive under (9). Hence, the condition issatisfied if p′′ (x) or e are relatively close to zero; this was also suffi cient for the s.o.c. inProposition 1 to hold.(ii) If we divide both sides of (16) by Xi, we get:

xiXi

=c

b+ c+

1

Xi

(b+ c) p (x)− vi(b+ c) (−p′ (x))

⇒ xiXi

− xjXj

=

(1

Xi

− 1

Xj

)(b+ c) p (x)− v(b+ c) (−p′ (x))

if vi = vj = v.

(iii) The proof follows, for example, when we summarize the xi’s as given by (4) and substitutein for e: the l.h.s. must increase in x faster than the r.h.s. does for (15) to hold; and x musttherefore increase in n if and only if (b+ c) p (x)− v > 0 when vi = vj = v.(iv) The proof follows straightforwardly when substituting in for pL (x). ‖

Proof of Proposition 3.(i) If the contract is linear, i’s payoff is

ui (xi, x−i) + max {0, ti (xi − xi)} = (b+ c) p (x)xi − cp (x)Xi − vixi + max {0, ti (xi − xi)} ,(20)

so, when xi < xi, the f.o.c. w.r.t. xi is given by (16) where vi is replaced by vi + ti:

xi =(b+ c) p (x)− cp′ (x)Xi − vi − ti

−p′ (x) (b+ c). (21)

The s.o.c. is locally satisfied under the same condition (15) as before.To see that linear contracts suffi ce, note, first, that for x = {xi}i∈N to be implemented by

a contract, xi must be a best response to x−i for every i ∈ N\M . Then, given x and any xi,i ∈M , one can solve (21) for ti to find the subsidy rate which makes xi optimal for i. Hence,if {xi}i∈N is implementable, it is implementable by linear contracts.However, the s.o.c. may not hold globally because max {0, ti (xi − xi)} is kinked (and

convex) at xi = xi. Thus, (21) is a best response for i if and only if the corresponding payoff(20) is larger than what i can achieve by choosing any other xi > xi. The incentive constraint

30

is:

ui (xi, x−i) + max {0, ti (xi − xi)} ≥ maxxi

ui (xi, x−i)− fi ⇒

max {0, ti (xi − xi)} ≥ maxxi

ui (xi, x−i)− ui (xi, x−i)− fi.

Clearly, D prefers to reduce every xi until this condition binds. By substituting the corre-sponding equation into D’s payoff, −d (x)−

∑i∈M max {0, ti (xi − xi)}, we get that D’s payoff

is exactly the same as for general contracts:

−d (x) +∑i∈M

ui (xi, x−i)−∑i∈M

maxxi

ui (xi, x−i) +∑i∈M

fi. (22)

Hence, linear contracts are suffi cient and they leads to the same quantities of extractions andtransfers (and thus payoff to D).(ii) Consider first linear contracts. Given the linear pL (x), we can rewrite (21) by solving forxi as a function of x−i to get:

xi =p− ax−i

2a+caXi − vi − ti

2a (b+ c). (23)

It follows that i’s optimal response to x−i if i decided to ignore the contract (by not collectingti) is:

xIi =p− ax−i

2a+caXi − vi2a (b+ c)

= xi +ti

2a (b+ c),

where the price would be lowered from p = p− ax to:

pI = p− ti2 (b+ c)

.

Thus, if ui (xi, x−i) = (b+ c) p (x)xi − cp (x)Xi − vixi is i’s payoff, minus i’s transfer, when iacts according to the contract, then i’s payoff from deviating can be written as:

ui(xIi , x−i

)=

[(b+ c) pI − v

]xIi − pIcXi

=

[(b+ c)

(p− ti

2 (b+ c)

)− v](

xi +ti

2a (b+ c)

)−(p− ti

2 (b+ c)

)cXi

= ui (xi, x−i) +

[(b+ c)

(p− ti

2 (b+ c)

)− v]

ti2a (b+ c)

− ti2xi +

cXiti2 (b+ c)

= ui (xi, x−i) +t2i

4a (b+ c). (24)

Thus, the transfer τ i = ti (xi − xi) plus fi must be at least t2i /4a (b+ c) for this deviation tobe unattractive to i. When this (ICi) binds, it becomes:

ti (xi − xi) = ui(xIi , x−i

)− ui (x)− fi =

t2i4a (b+ c)

⇒ xi = xi +ti

4a (b+ c)− fi/ti. (25)

Given the linear pL (x), we can sum over the xi’s from (21) and write:

x =n (b+ c) p+ caX −

∑i∈N (vi + ti)

a (b+ c) (n+ 1). (26)

31

Thus, D maximizes

−dx−∑i∈M

τ i = −d[n (b+ c) p+ caX −

∑i∈N vi −

∑i∈M ti

a (b+ c) (n+ 1)

]−∑i∈M

t2i4a (b+ c)

.

For each ti, i ∈ M , the first-order condition becomes ti = 2d/ (n+ 1). The second-ordercondition trivially holds, so the contracts are symmetric and equal for every i ∈ M . Giventhis ti, we can substitute ti into (26) to get x, substitute into (23) to get xi, into (25) to findxi, and derive the total transfer from τ i = ti (xi − xi). ‖

Proof of Proposition 4.(i) Since D maximizes (22), D chooses x∗i > arg maxxi −d (x (xM)) +

∑i∈M ui (xi, x (xM)− xi)

if∂

∂xi

∑j∈M\i

maxxi

ui(xi, x

∗−i)

=∑j∈M\i

ej(x∗−j)< 0.

Thus, if N\i is empty, xi is first best. It is then straightforward to derive the first-best x∗i(which maximizes ui − d (x)) and see that it equals (21) if ti = d′ (x∗).(ii) When D contracts with the districts in M independently and determines xM = {xi}i∈M ,every i ∈ N\M chooses xi to maximize ui (xi, x−i). It is easy to show that xi will then bea function of xM ≡

∑j∈M xj, and x ≡

∑j∈N xj can be written as some increasing function

x = x (xM). D’s payoff is then∑

i∈M fi plus:

vdD (xM) = −d (x (xM)) +∑i∈M

ui (xi, x−i)−∑i∈M

maxxi

ui(xi, x

∗−i).

Let x∗M ≡ arg max{xi}i∈M vdD (xM).

If, instead, the set L ⊆ M centralizes authority, the payoff sum for L is uL =∑

i∈L ui,which is the same as under decentralization, given x. Note also that L’s sum of payoffs is nota function of the distribution {xi}i∈L, as long as the sum xL ≡

∑i∈L xi is the same. However,

L’s outside option is now different, and D’s payoff becomes∑

i∈M fi plus:

vcD (xM) = −d (x (xM)) +∑i∈M

ui (xi, x−i)−∑i∈M\L

maxxi

ui(xi, x

∗−i)−max

xL

∑i∈L

ui (xL, x−L)⇒

vcD (xM)− vdcD (xM) =∑i∈L

maxxi

ui(xi, x

∗−i)−max

xL

∑i∈L

ui (xL, x−L) . (27)

The proof is completed by showing that if ei(x∗−i)< 0∀i ∈ M , then ∂vcD (x∗M) /∂xj >

∂vdD (x∗M) /∂xj ∀j ∈ M , since, in this case, D benefits from increasing the xi’s under central-ization compared to x∗M . Thus, we henceforth assume that ei

(x∗−i)< 0∀i ∈M .

First, suppose j ∈ L. Since xj does not enter the last term in (27), we get, when takingthe derivative of (27):

∂[vcD (x∗M)− vdD (x∗M)

]∂xi

=∂

∂xi

∑i∈L\i

maxxi

ui(xi, x

∗−i)

= −∑i∈L\i

ei(x∗−i)> 0.

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Next, suppose j ∈M\L. When we take the derivative of (27), we get:

∂[vcD (x∗M)− vdD (x∗M)

]∂xj

=∂

∂xj

[∑i∈L

maxxi

ui(xi, x

∗−i)−max

xL

∑i∈L

ui (xL, x−L)

]=

∑i∈L

p′ (x) [(b+ c) xi (x−i)− cXi]− p′ (x) [(b+ c) xL (x−L)− cXL]

=∑i∈L−p′ (x) (b+ c)

(xL (x−L)−

∑i∈L

xi (x−i)

), (28)

where we used (8). If ei (x−i) = ∂ui(xi (x−i) , x

∗−i)/∂ (−xj) < 0, then ei (x−i) < 0 also when

other districts in L extract more: this follows because ei (x−i) = (b+ c) p (xi (x−i) + x−i) −vi decreases in every xj. Consequently, ∂ui (xi (x−i) , x−i) /∂ (−xj) < 0∀i ∈ M also atx =

{{xi (x−i)}i∈L ,x∗−L

}, since xj (x−j) > x∗j . Because the externality from conservation

on the other districts are then negative, L increases total payoffs by increasing xL. Hence,xL (x−L) >

∑i∈L xi (x−i), and the r.h.s. of (28) is positive. This, in turn, implies that

∂vcD (x∗M) /∂xj > ∂vdcD (x∗M) /∂xj, which concludes the proof.(iii) Suppose ei

(x∗−i)< 0∀i ∈M , and consider D’s optimal contract under centralization, xcM

and the associated x, xc.When xL (x−L) is L’s best outside option, it is obvious that:

maxxL

∑i∈L

ui(xL, x

c−L)≥∑i∈L

ui

({xj(xc−j)}

j∈L , xc−L

). (29)

Furthermore, since ei(x∗−i)< 0∀i ∈ M , and ei

(x∗−i)decreases in xj, we must also have that

∂ui

({xj(xc−j)}

j∈L , xc−L

)/∂xj > 0, and each term ui

({xj(xc−j)}

j∈L , xc−L

)on the r.h.s. of

(29) is reduced when xj is lowered from xj(xc−j)to xcj. Thus, the r.h.s. of (29) is larger

than∑

i∈L ui(xi(xc−i), xc−i

)=∑

i∈L maxxi ui(xi, x

c−i). Consequently, the sum of L’s outside

option is larger under centralization (i.e., the l.h.s. of (29)) than under decentralization, soD’s payoff is larger under decentralization than centralization even if D sticked to xcM afterdecentralization: vcD (xcM) < vdD (xcM). Of course, D does better by instead selecting x∗M , so Dis clearly better offunder decentralization than under centralization when ei

(x∗−i)< 0∀i ∈M .

(iv) By substituting ti = 2d/ (n+ 1) into (26), we can see how x depends on m and n:

x =n (b+ c) p+ caX −

∑i∈N vi

a (b+ c) (n+ 1)− d 2m

a (b+ c) (n+ 1)2. (30)

If we replace n and m with n−∆ and m−∆, we find x under centralization. A comparisonconcludes the proof.With x and τ i, we can easily write D’s payoff as a function of m and n:

−d(n (b+ c) p+ caX −

∑i∈N vi

a (b+ c) (n+ 1)− d 2m

a (b+ c) (n+ 1)2

)− md2

a (b+ c) (n+ 1)2+∑i∈L

fi

Recognizing the similarlity to (30), we immediately get that D’s payoff is lower after central-ization if and only if (13) holds. ‖

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