Derissen S., Quaas M., (2013) Combining performance-based and action-based payments to provide...

8/10/2019 Derissen S., Quaas M., (2013) Combining performance-based and action-based payments to provide environment

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Analysis

Combining performance-based and action-based payments to provide environmentalgoods under uncertainty

Sandra Derissen , Martin F. Quaas

Department of Economics, University of Kiel, Germany

a b s t r a c ta r t i c l e i n f o

Article history:

Received 16 March 2012

Received in revised form 31 October 2012Accepted 3 November 2012Available online 27 November 2012

JEL classication:

Q28Q18H41

Keywords:

Conservation contractsPayments for ecosystem servicesPayments for environmental servicesBiodiversityUncertainty

Payments for environmental services (PES) are widely adopted to support the conservation of biodiversityand other environmental goods. Challenges that PES schemes have to tackle are (i) environmental uncertain-ty and (ii) information asymmetry between the provider of the service (typically a farmer) and the regulator.Environmental uncertainty calls for action-based payment schemes, because of the more favorable risk allo-cation if the farmer is risk-averse. Information asymmetry, on the other hand, calls for a performance-basedpayment, because of the more direct incentives for the farmer. Based on a principal-agent model, we studythe optimal combination of both, performance-based and action-based payments under conditions of envi-ronmental uncertainty and asymmetric information. We nd that for a risk-neutral regulator a combinationis optimal in the majority of cases and that the welfare gain of the combined scheme over a pure action-based(performance-based) payment increases with information asymmetry (environmental uncertainty). We fur-ther show that for a regulator who is risk-averse against uctuations in environmental goods provision theoptimal performance-based payment is lower than for a risk-neutral regulator. We quantitatively illustrateour ndings in a case study on the enhancement of the butter y Scarce Large Blue (Maculinea teleius) inLandau/Germany.

2012 Elsevier B.V. All rights reserved.

1. Introduction

The protection and enhancement of environmental assets are ob-jectives shared by many governments around the globe. Often theseassets depend on how farmers manage their private land, but asthey typically have characteristics of public goods, farmers have littleincentives to make socially optimal decisions (Bardsley and Burfund,2008). For this reason policy instruments such as payments for envi-ronmental or ecosystem services (PES) have been advocated to createincentives similar to those that would be provided by market prices, ifmarkets for environmental services would exist (e.g. Bulte et al.,2008; Corbera et al., 2007; Vatn, 2009).

Two types of payment schemes are used in practice: Action-basedpayments are bound to a predened action or measure, whereasperformance-based payments are directly bound to the outcome ofa desired ecosystem good or service.1

Performance-based payments have the advantage that they set thedirect incentive to provide ecosystem services efciently (Matzdorf,

2004; Zabel and Roe, 2009). A drawback of performance-based pay-ment schemes is that the risk of producing an ecosystem good comesat the expense of the farmer, since the quantity of environmental ser-vice also depends on external inuences beyond the farmer's control.If the farmer is risk-averse, and the regulator is risk-neutral, a pureperformance-based payment schemethus leads to an inefcient risk al-location.2 As a result, most existing schemes are action-based, althoughperformance-based payments are sometimes applied for the conserva-tion of an already given state or of existing biodiversity ( Hampicke,2001; Osterburg, 2006). Action-based payments may be a cost-effective alternative if there is a clear action that is required to providethe environmental good, known and observable by the regulator(Gibbons et al., 2011). If there is informational asymmetry betweenfarmer and regulator, however, a pure action-based payment is likelyto lead to an inefcient outcome.

In this paper, we consider payment schemes that combineperformance-based and action-based payments. We set up aprincipal-agent model to study what combination of both is optimalwhen there is both environmental uncertainty affecting the provisionof the environmental good and asymmetric information about how

Ecological Economics 85 (2013) 7784

Corresponding authorat: Department of Economics, Christian-Albrechts-Universityo fKiel, Wilhelm-Seelig-Platz 1, 24118 Kiel, Germany. Tel.: +49 431 880 5633.

E-mail address:[email protected](S. Derissen).1 Many labels for these payment schemes can be found within the literature. Other

common names for action-based payments are e.g. input- or measure-based payments,for performance-based payments the terms o utput-oriented, outcome- or result-basedpayments are also common.

2 An efciency improvement in the risk-allocation could be obtained by shifting riskfrom the risk-averse farmer to the risk-neutral regulator. One way of doing this (theone considered in this paper) is to combine a pure performance-based payment tosome extent with an action-based payment.

0921-8009/$ see front matter 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.ecolecon.2012.11.001

Contents lists available at SciVerse ScienceDirect

Ecological Economics

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productive a management action is for providing the environmentalgood.

We nd that the optimal payment typically will be a combination ofperformance-based and action-based payments (seeTable 1). A pureperformance-based payment is optimal for a risk-neutral regulator(the principal) only if either there is no environmental risk or if thefarmer (the agent) is risk-neutral. A pure action-based payment is opti-mal only if the regulator has full information about the marginal pro-ductivity of the actions for providing the environmental good. Theperformance-based fraction of the optimal payment increases with en-vironmental uncertainty, while the action-based fraction increaseswithinformation asymmetry. Thesendings are also reected in the welfaregains of the combined scheme over the pure performance-based oraction-based schemes: the welfare gain, measured as the payoff of a

risk-neutral regulator, of the optimally combined scheme over an opti-mally chosen, pure action-based (performance-based) payment in-creases with information asymmetry (environmental uncertainty).

The assumption of a risk-neutral regulator may be inappropriate, be-cause society's marginal willingness to pay for the environmental assetmay increaseif an environmentalasset becomes increasinglyscarce. Forthis reason we also consider a regulator who is risk-averse againstuc-tuations in environmental goods provision. As the argument for anaction-based payment scheme is the more favorable allocation of riskif the farmer is risk-averse but the regulator is risk-neutral, one mightexpect that the performance-based fraction of the optimal paymentmight be relatively higher when the regulator is risk-averse. We nd,however, that the optimal performance-based payment actually de-creases with the regulator's degree of risk aversion.

We apply our analysis to the case study on the enhancement of thebuttery Scarce Large Blue (Maculinea teleius) in Landau/Germany,based on data from the literature (Drechsler et al., 2007; Wtzold etal., 2008). Results indicate that the optimal combination of theperformance-based and action-based payments may lead to a welfaregain of several thousand euros per hectare.

2. Principal-Agent Model of Environmental Good Provision

Under Uncertainty

We consider a principal-agent setting where a regulator (the prin-cipal) offers a PES to a single, representative farmer (the agent), whochooses an action that contributes to the production of an environ-mental good. This means, we assume that all farmers share the

same characteristics with respect to preferences and production tech-nology.3 We thereby extend the approach ofZabel and Roe (2009),allowing for a combination of a performance-based payment withan action-based payment, and risk aversion on the regulator's side.

The temporal structure of the problem is that, rst, the principalannounces the payment scheme. Second, the agent decides onwhether or not he would like to participate in the program. If he par-ticipates, he receives (or pays) a base-payment. Third, the agentchooses his action, and fourth, nature adds stochastic disturbance. Fi-nally, the agent receives performance-based and action-based pay-ments from the principal, and society enjoys the environmental good.

The quantityy of the environmental good is produced according to

y x : 1

The provision of the environmental good can be increased by thefarmer's actionx with a constant marginal productivity . For exam-ple,xcan be thought of as the area of farmland set aside for biodiver-sity protection. We consider y to be the additional environmentalgoods provided, i.e. y is the (net) growth of the environmentalgood. This growth is also affected by a stochastic disturbance , cap-turing environmental noise, which is independent and identicallynormally distributed with zero mean and standard deviation .

4

Marginal productivity of the actionxis known to the farmer, butnot to the regulator. This information asymmetry arises, because thefarmer knows the peculiarities of his farmland while the regulatordoes not. The regulator only knows a prior probability distributionover . We assume that this is any probability distribution with amean and variance

2. The quantityx of the action exerted by thefarmer is common knowledge of both farmer and regulator.

Some important and restrictive assumptions about the productionof the environmental good are embodied in Eq. (1), which we shalldiscuss in the following.

(i) Taking asymmetry with regard to the observability of thefarmer's action into account has similar effects as the informa-tion asymmetry with regard to marginal productivity andcould be included in the model in a straightforward way. In ei-ther case the essential assumption is that the farmer may havemore information about his contribution to the provision of theenvironmental good than the regulator.

(ii) Assumingperfectinformation on on the farmer's side is rath-er strong. However, the crucial aspect of this assumption is thatthe farmer hasbetterinformation about what he is doing thanthe regulator. Assuming perfect information only simplies theanalysis. Environmental uncertainty, captured by in Eq.(1), isan aspect of incomplete information about the production ofyfaced by the farmer and the regulator to an equal extent.

(iii) As we are consideringa representative farmer, assumingproduc-tion of the environmental good according to Eq. (1)means thateither there are no external effects between farmers, or that allexternal effects are internalized, for example by a farmer's asso-ciation that negotiates about the PES contractwith the regulator.

We consider a payment for the provision of the environmentalgood that is composed of a base paymentb, a payment for the action,a x, and of a payment for the performance, i.e. the provision of the en-vironmental good,p y,5

baxpy: 2

Because of environmental uncertainty,y may be negative. In sucha case the performance-based payment p ywill be negative as well,although typically the expectedperformance-based payment will bepositive. The base payment b is chosen such that the farmer neverthe-less has an incentive to participate in the PES scheme. Using the basepayment to meet the participation constraint is in line with the recentliterature on PES that has adopted this approach from labor econom-ics (Zabel and Roe, 2009).6

Table 1

Table showing the optimal PES scheme for a risk-neutral regulator.

Asymmetric informationbetween farmer and regulator

Both perfectlyinformed

Environmental risk Combination Action-basedNo environmental risk Performance-based Any

3 The question how to deal with heterogenous farmers (for example by designingadequate auction schemes such as, e.g., Latacz-Lohmann and Van der Hamsvoort,

1997) is beyond the scope of this paper.

4 Note that the net growth of the environmental good may be negative even with apositive effortx, due to environmental uncertainty.5 We restrict our analysis to linear combinations of the three payment parts here. An

analysis of more general payment structures is left for future research.6 One example for combined payment schemes can be found in Switzerland: Here

the schemes contain site-specic direct payments, similar to the base payment consid-ered here. Additional payments are bound to the condition that 7% of the farm area aremanaged in line with specic ecological standards, corresponding to the action-basedpayment considered here. Finally, the Swiss authority adds a performance-based pay-

ment when biodiversity is sufciently high.

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The participation constraint could also be met in other ways, for ex-ample by increasing the action-based component of the overall pay-ment to compensate for expected losses in the performance-basedcomponent, or by restricting the performance-based payment to benonnegative. These approaches will lead to lower welfare, however,either because they induce distortions in the payment structure (asfor the case of the adapted action-based payment), or because theexpected public expenditures associated with the PES scheme are un-

necessarily high (when performance-based payments are restricted tobe nonnegative). For these reasons, a negative base payment may wellbe part of the optimal payment scheme.

If the farmer participates in the program, his payoffYis given by

Y c

2x

2: 3

Here we usecto denote the cost parameter of the action, with lin-early increasing marginal costs. If the farmer does not participate,both payment and costs are zero, and thus the net payoff is zero.

The farmer maximizes expected utility. We assume a risk-aversefarmerwith preferences that exhibit constant absolute risk aversion(CARA):7

U E

expY ; 4

whereis the coefcient of constant absolute risk aversion andEde-notes the expectation with respect to environmental uncertainty .

As participation is voluntary, expected utility of participation inthe program must at least equal utility from not participating inthe program and receiving a zero net payoff for sure. With U(0)=exp(0)=1 denoting the reservation utility level of the farmer,the participation constraint is

Eexp Y 1: 5

The regulator receives a benet

v y y

2

y2

6

from the provision of the environmental good. The quadratic benetfunction (6) captures in a simple form that the regulator may beaverse against uncertainty in the provision of the environmentalgood, with being the regulator's coefcient of risk aversion. Thebenetv(y) is measured in monetary terms, such that the regulator'snet benet is given by v(y). This assumption may actually bequite restrictive. It presupposes that the environmental good desiredby the regulator is well-dened and that further its benet can bemeasuredin monetaryterms. For the case study, we use published re-sults from a contingent valuation study for this purpose. We makethis assumption here, as we are not interested in studying the effectsof ill-dened objectives.8 The quadratic benet function(6) impliesthat themarginalenvironmental benet is linear iny. As the marginal

environmental benet can be identied with the willingness to pay(WTP) for the provision of the environmental good, the specication(Eq.(6)) is in line with a common empirical specication of the WTPfor environmental goods.

The optimal payment scheme (a,b,p) is derived by solving the reg-ulator's optimization problem to maximize expected net benet

maxa;p;b

EEv y 7

subject to the constraints that the action x is chosen by the farmersuch as to maximize the farmer's expected utility and the participa-tion constraint (Eq.(5)).

3. Analytical Results: Optimal Combination of Performance-Based

and Action-Based Payments

The problem is solved backwards by rst considering the farmer's

optimization for given payment levels (b,a,p). Inserting Eqs.(1) and(2)into Eq.(4), the farmer's expected utility is

E exp b ap xpc

2x

2 h i

: 8

Taking the expectation over environmental uncertainty we obtain

U1

ln U b ap xc

2x

2

2p

2

2; 9

which is the certainty equivalent of the income lottery generated byparticipating in the PES with uncertain provision of the environmen-tal good.

Using the rst-order conditions of utility maximization with re-

spect to x , we

nd that the farmer's optimal choice of action is (seeAppendix A)

x

(

ap

c if U0

0 if Ub 0:

10

Assuming that the farmer participates in the PES program (whichis the case if 0), the optimal action is increasing in bothaction-based and performance-based payments, and decreasing inthe cost parameter c, which is in line with intuition. For a givenperformance-based payment p, it is also increasing in the marginalproductivity of the action (cf.Appendix A).

Using the result of Eq.(10)in Eq.(1), we nd that the (uncertain)provision of the environmental good under payment scheme (b,a,p)

is given by

y

ap

c : 11

For a given marginal productivity of the farmer's action, and agiven payment scheme (b,a,p), the expected benet of environmentalgood provision (conditional on) thus is

Ev y

E ap

c

2

ap

c

2

ap

c

2

ap

c

2

2

2:

12

To obtain this result, we have used that the expected value ofiszero. Environmental uncertainty thus decreases the benet o f arisk-averse regulator, but this effect is independent of the paymentscheme. This means that, in the absence of asymmetric information,risk aversion on the regulator's side has no inuence on the optimalpayment scheme. Put differently, we have the following lemma(which we need to deriveResult 3):

Lemma 1. Environmental uncertainty does not directly affect the opti-

mal payment scheme for a risk-averse regulator.

Environmental uncertainty affects the optimal payment scheme in-directly, however, because the farmer is risk-averse, as we will showbelow.

To meet the participation constraint, the regulator has to set the

base paymentbsuch that reservation utility is reached. The certainty

7 We make this assumption to be able to solve the model analytically. It is in linewith most models of this type. More realistic is the case of decreasing absolute riskaversion (Gollier, 2001). A deeper exploration of this case is, again, left for futureresearch.8 Ill-dened objectives may favor action-based payments compared to performance-

payments (Zabel and Roe, 2009).

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equivalent of participating in the PES is obtained by using Eq. (10)inEq.(9). Equating this to the certainty equivalent of not participating,which is equivalent to an income of zero, we obtain the minimal basepaymentb of

b

2p

2

2

ap 2

2c : 13

With a risk-averse farmer, environmental uncertainty increasesthe base payment. As the performance-based payment p y may eitherbe positive (in case of favorable environmental conditions) or nega-tive (in case of very unfavorable environmental conditions), the effectofp on the based payment is ambiguous. The action-based payment a,by contrast, unambiguously decreases the base payment.

Overall, the base payment may well be negative, because theexpected value of action-based and performance-based payments ispositive. In such a case the regulator can use the base payment to re-duce expected public expenditures associated with the PES scheme.Such a negative base payment then means that a farmer will haveto make a payment to the regulator in order to benet from the par-ticipation in the PES scheme. Depending on the parameter constella-tion, in particular if environmental uncertainty is large and the farmeris very risk-averse, the base payment may of course also be positive.

In this case the participating farmer receives a paymentjust for agree-ing to participate in the PES program.

Using Eqs.(10), (11), and (13)in Eq.(2), the expected paymentcan be expressed as

E ap

2

2c

2p

2

2: 14

As the farmer is risk-averse, and the performance-based paymentis affected by environmental uncertainty, the optimal payment rate pdepends on environmental uncertainty. Using Eqs. (12), (13), and(14)in Eq.(7), and employingLemma 1, the regulator's optimizationproblem can be written as

maxa;p

E apc

2 ap

c

2 ap

2

2c

2p22

( ): 15

In Appendix B we show that the optimal action-based andperformance-based payments are

a

c

2 2

c

2

2

16a

p

2

1

c

2

2

16b

with

2c

2

c 22

2

22

c

2

2

2

2

c2

2

4

34

>0:

17

To analyze the optimal payment scheme, we rst focus on the caseof a risk-neutral regulator, assuming =0. In this case, the optimalpayments are given by the following, much simpler expressions.

a0

c

2

2c2

18a

p

0

2

2

c2

18b

The following result is obtained immediately.

Result 1. For a risk-neutral regulator (=0), the optimal PES schemeincludes both an action-based and a performance-based component,except for the following cases

If the farmer is risk-neutral (=0), or if there is no environmentaluncertainty (

2=0), the action-based component of the optimalpayment scheme is zero.

If there is no asymmetric information, 2=0, the performance-based component of the optimal payment scheme is zero.

This result shows that an optimal PES scheme should combineboth an action-based and a performance-based payment. The only ex-ceptions are extreme cases where either environmental uncertaintyplays no role or the regulator has perfect information about the pro-ductivity of the farmer's actions. Furthermore, the relative shares ofthe action-based and the performance-based component of the opti-mal PES scheme depends on environmental uncertainty and informa-tion asymmetry in a very intuitive way, as stated in the followingresult.

Result 2.

a) For a risk-neutral regulator (=0), the optimal action-based pay-ment increases and the optimal performance-based payment de-creases with the farmer's degree of risk aversion, , and withenvironmental uncertainty,.

b) For a risk-neutral regulator (=0), the optimal action-based pay-ment decreases and the optimal performance-based payment in-creases with the degree of asymmetric information, .

We now turn to the case of a risk-averse regulator, assuming> 0,and focus on the question how the optimal payment scheme com-pares to the case of a risk-neutral regulator. The optimal paymentscheme is much more complicated than in the case of a risk-neutralregulator. We show inAppendix Cthat the optimal action-based pay-ment depends in an ambiguous way on the degree of risk aversion.For low levels of risk aversion for both the regulator and the farmer,the optimal action-based payment increases with the regulator's de-gree of risk aversion. We nd that even for a risk-neutral farmer theoptimal action-based payment for a risk-averse regulator is positive,which is different from the case of a risk-neutral regulator. For veryhigh levels of risk aversion of regulator and farmer, however, the op-timal action-based payment will decrease again with the regulator'srisk aversion. The performance-based payment, by contrast, de-creases with the regulator's degree of risk aversion whenever it ispositive at all.

Result 3.

a) For a risk-averse regulator, the optimal action-based payment ispositive even when the farmer is risk-neutral.

b) The optimal performance-based payment decreases with the reg-ulator's degree of risk aversion,

p

b 0 for all p

>0: 19

The intuition behind this result is as follows. The farmer will choosehis action x in response to the payment according to Eq. (10). Anincrease in the action-based payment will increase the farmer's actionindependently of the marginal productivity, while an increase in theperformance-based payment will lead to a lower (higher) increasein the level of his action if marginal productivity is low (high). Rela-tive to the action-based payment, the performance-based payment

thus amplies the effect of the regulator's uncertainty on marginal



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productivity on the provision of the environmental good. The morerisk-averse the regulator, the relatively less attractive becomes theperformance-based payment compared to the action-based payment.9

In the extreme, the performance-based payment may even be-come negative. This is the case if

> c

22:

22

A second effect is that the presence of informational asymmetryand the associated risk premium make the payment for environmen-tal services overall less attractive for the risk-averse regulator. If thiseffect is sufciently strong which is the case for high environmentaluncertainty also the optimal action-based payment is lower for arisk-averse compared to a risk-neutral regulator.

As a nal step of the analysis we study how high is the welfaregain, measured by the regulator's objective function, for the com-bined payment scheme compared to either a pure action-based or apure performance-based payment scheme. The pure action-based,or performance-based, schemes are obtained by setting p0, ora0, in the regulator's optimization problem (Eq. (15)).

InAppendix Dwe derive the welfare levels for all three paymentschemes, assuming a risk-averse regulator. We nd that the com-

bined payment scheme outperforms the pure action-based schemeexcept for the case when the regulator has full information, i.e.

2=0.The combined scheme outperforms the pure performance-basedscheme except for the casewhen thereis no environmental uncertainty,2=0,andwhen the regulator is risk-neutral, =0. For a risk-averse

regulator, the pure performance-based scheme is worse than the com-bined scheme even in the absence of environmental uncertainty (seealsoResult 3).

For a risk-neutral regulator, the comparisons for the welfare levelsare as follows. The welfare gain of the combined payment schemeover the pure action-based scheme is given by

E v y E v y

p00

12c

4

2c2

; 21a

and the welfare gain of the combined payment scheme over the pureperformance-based scheme is given by

E v y E v y

a0

0

12c

c2

22c

2

2 2c2

:21b

Finally, the welfare difference between the pure performance-based PES scheme and the pure action-based one is given by

E v y a0E v y p00 12c

4

2

2c

2

2 2

c2

: 21c

Using these relationships, we obtain the following result:

Result 4. For a risk-neutral regulator (=0),

a) The welfare gain of the combined PES scheme over the pureaction-based scheme increases with information asymmetry

2

and decreases with both the farmer's degree of risk aversion and environmental uncertainty,

2.

b) The welfare gain of the combined PES scheme over the pureperformance-based scheme decreases with information asymme-try

2 and increases with both the farmer's degree of risk aversionand environmental uncertainty,

2.c) The pure performance-based PES scheme is better than the pure

action-based one if and only if

c2b

2 1

2

2 !: 22

Inequality(22)gives an explicit condition which instrument touse if only pure performance-based or action-based payments areavailable. As found inResult 2, the performance-based componentof the optimal payment tends to be low when the farmer's coefcientof risk-aversion,, and environmental uncertainty,are high, whilethe action-based component of the optimal payment tends to be lowwhen the degree of informational asymmetry is high. These effectsare also captured in condition (22). A high coefcient of risk-aversion thereby means that 1/is low relative to the cost parameterc, and a highinformational asymmetry means thatis high relativeto .

In order to quantify these effects, we apply our analysis to the caseof buttery protection.

4. Quantitative Application: Optimal Payment Scheme for

Buttery Protection

We base our quantitative application on published ecological-economic studies on the conservation of the Scarce Large Blue(M. teleius) in the region of Landau, Germany (Drechsler et al.,2007; Wtzold et al., 2008). Within European nature conservation,butteries of the Maculineagenus are considered as important ag-ship species (Dierks and Fischer, 2009; Thomas and Settele, 2004)and have suffered substantial population declines with local extinc-tions in recent years (Wynhoff, 1998). M. teleiusis therefore consid-ered as a threatened species in Europe (Swaay and Warren, 1999).

The buttery is characterized by a complex life cycle whereby theearly instars of this speciesrst feed on the blossoms ofSanguisorbaofcinalis (Great Burnet). Late instars are carried by ants (e.g. Myrmicarubra) into their nests where the larvae actively prey on ant brood.Especially the blooming ofS. ofcinalisand therefore the egg deposi-tion and stage of development of the early instars ofM. teleius aredetermined by the mowing regime (Dierks and Fischer, 2009). Con-servation measures for different mowing regimes have been appliedfor the enlargement and enhancement ofM. teleius.

Before turning to the application of our model, we would like toemphasize the limitations with regard to the direct applicability ofour analysis for the conservation of Scarce Large Blue in the Landauregion. To obtain effective conservation, many farmers have to be in-cluded in the protection scheme, and external effects of management

arise due to metapopulation dynamics (Drechsler et al., 2007). Thus,the assumption of a single, representative farmer is a strong abstrac-tion from reality. It should therefore be kept in mind that furthersophistication of payment schemes may be needed to actually imple-ment the optimal conservation scheme for buttery conservation inLandau. Given these caveats, the quantitative results derived in thefollowing still give some feeling how large the potential welfaregains of combining performance-based and action-based paymentscould be.

Environmental benety is measured in monetaryterms. Wtzold etal. (2008,Table 1) provide modelingresultsof how manybutteries canbe conserved by applying conservation measures (alternative mowingregimes) to a certain area of farmland. Specically, the authors considerthree projects that correspond to 4, 16, and 64 ha on which conserva-

tion measures are applied. The results of a Contingent Valuation study

9 This result depends on the assumption that the informational asymmetry betweenthe farmer and the regulator is with regard to the marginal productivity of the action,

but that there is no hidden action.

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published inWtzold et al. (2008, Table 3), indicate societal conserva-tion benets of approximately 260, 297, and 426 thousand euros forthe three projects. Taking the number of hectares with conservationmeasures as the farmer's actionx, a simple OLS regression shows thatthe expected marginal productivity of applying conservation measuresis 2:74 thousand euros per hectare.10 According toDrechsler et al.(2007, page 183), the coefcient of variation of marginal productivityis about = 0:25. Hence,

2=0.47.Wtzold et al. (2008) use a linear cost function with constant mar-

ginal costs of 0.123 thousand euros per hectare. However, Fig. 7b inDrechsler et al. (2007)suggests that it is equally plausible to assumean overall convex cost function. A quadratic cost function with costparameter c=0.015 [1000 euros/ha] gives the best t for the rangeof hectares (4, 16 and 64) considered byWtzold et al. (2008), as-suming log-normal errors.

We assume a coefcient of relative risk aversion for farmers of=0.74, which is consistent with experimental evidence for WesternEuropeans (Andersen et al., 2008). The mean income for Germanfarmers in 2011 was 24.6 thousand euros per year. This leads to an es-timate for the degree of absolute risk aversion of about =0.74/24.6= 0.03/ thousand euros.

Since we have no information on the degree of environmental un-certainty, we vary the standard deviation of environmental noise, .Furthermore, we also vary the regulator's coefcient of risk aversionto obtain an insight of how this parameter inuences the quantitativeresults. These are shown in Fig. 1. The left-hand panel in this gureshows the optimal performance-based payment, and the right-handside the optimal action-based payment as functions of environmentalstochasticity . In line with Result 2, the optimal performance-basedpayment decreases, and the action-based payment increases, withenvironmental uncertainty. With a risk-averse regulator (>0), the ef-

fect corresponds to Result 4: with increasing risk aversion, theperformance-based fraction of the combined scheme becomes less at-tractive for the regulator. The optimal action-based fraction is evenhigher than the performance-based fraction under circumstances withlow environmental stochasticity and increases slightly with increasingwhile the performance-based fraction decreases respectively.

Turningto a risk-neutral regulator again we quantifythe overall wel-fare gains of the different payment schemes for the case of the protec-tion of the Scarce Large Blue (M. teleius) in Landau. The results showninFig. 2 correspond to the theoretical ndings of Result 5: for lowenvironmental uncertainty the pure performance-based PES may dosubstantially better than the pure action-based PES, while for high envi-ronmental uncertainty, the pure action-based PES would be preferred.However, the combined payment scheme leads always to a higherwelfare than either the pure action-based or the pure performance-based scheme. The welfare gain of the combined payment over thepure action-based PES decreases with environmental uncertainty. Fur-thermore, the welfare gain of the combined scheme over the pureperformance-based PES is zero in the absence of environmental uncer-tainty, in which case the pure performance-based payment is optimal,as shown inResult 1, but is positive when environmental uncertaintymatters. Overall the welfare gain of the combined scheme over thepure schemes may sum up to several thousand euros per hectare.

5. Conclusion

In the ongoing discussion on new policy instruments for the provi-sion of environmentalgoods such as PES, performance-based payments

10 The estimated equation isy1=y0+ i x+, which results in the estimatesy0=250.8(standard error 2.9) and=2.74 (standard error 0.075), with an R2=0.999. Allowingfory0>0 we assume that there might be some willingness to pay also when x =0, andusey =y1y0as a measure for the additional environmental good provided. Thus weinterpret the results of the contingent valuation study differently than Wtzold et al.

(2008),who assume that the estimated willingness to pay must be zero for x =0.

=0.0010

= 0.0005

= 0.0001

= 0.0000

performance-basedpayment

0 0.50 0.1 0.51 0.2 0.52 0.3

1

0.8

0.6

0.4

0.2

0 = 0.0010

= 0.0005

= 0.0001

= 0.0000

action-basedpayment

[1000e/ha]

0 0.50 0.1 0.51 0.2 0.52 0.3

2.5

2

1.5

1

0.5

0

Fig. 1. Optimal performance and action-based payments for protection of the Scarce Large Blue (M. teleius) in Landau, Germany. The model is calibrated using datafromDrechsler etal. (2007)andWtzold et al. (2008).

welfare gain of pure performance-based over pure action-based PES

welfare gain of combined PES over pure action-based PES

welfare gain of combined PES over pure performance-based PES

welfaregain[1000euros/ha]

0 0.50 0.1 0.51 0.2 0.52 0.3

12

10

8

6

4

2

0

-2

Fig. 2. Welfare gains of combined payment scheme over pure performance-based orpure action-based payment schemes, and of pure performance-based payment schemeover pure action-based payment scheme for a risk-neutral regulator (=0) aiming to

protect the Scarce Large Blue (M. teleius) in Landau, Germany. Data as inFig. 1.

http://-/?-http://-/?-http://-/?-http://-/?-


7/8

gain signicant support. In contrast to action-based payment schemes,which are bound to a predened action or measure, performance-based payments are directly bound to the outcome of the desired envi-ronmental good. Even though in the literature performance-basedpayments occur as the preferred concept in many ways, examples ofaction-based payments still predominate in practical application. Al-though it is acknowledged that an action-based payment scheme isnot optimal under information asymmetry, a performance-based pay-

ment schememay not be the preferred optioneither if theperformanceis risky. Therefore, in this paper we have studied how both types ofpayment schemes could be optimally combined, because typicallyboth information asymmetry and environmental uncertainty matterin a real-world context.

Based on a principal-agent model we have shown that an exclu-sively performance-based payment is optimal only if there is no envi-ronmental uncertainty or if both the farmer and the regulator arerisk-neutral. An exclusively action-based payment is optimal only,if the regulator has full information about the productivity of theaction i.e. if there is no information asymmetry. In every other casea combination of performance-based and action-based payments(with different weighting) may increase welfare. Accordingly, thewelfare gain of the combined scheme over the pure action-basedscheme increases with information asymmetry, while the welfaregain of the combined scheme over the pure performance-basedscheme increases with environmental uncertainty.

With a risk-averse regulator the situation changes as follows. Theregulator is not directly affected through environmental uncertainty,but indirectly through the farmer's choice of action, since the farmerchooses his actions considering environmental uncertainty. Under in-formation asymmetry a performance-based payment would amplifythe effect of the regulator's uncertainty about the action's productiv-ity compared to the action-based payment. Thus, for a risk-averseregulator, the performance-based payment tends to pay out less fa-vorable compared to the action-based payment.

Our quantitative application to the case study of buttery conser-vation indicates that the welfare gain of the combined scheme overthe pure action-based or performance-based schemes may be sub-

stantial, reaching several thousand euros per hectare.

Acknowledgments

We thank Stefan Baumgrtner, Uwe Latacz-Lohmann, and FrankWtzold for their helpful discussion and comments. The study wassupported nancially with a PhD scholarship from the Heinrich-BllStiftung and by the German Federal Ministry of Education and Re-search under grant 01UN0607.

Appendix A. Farmer's Optimal Choice of Action

The rst-order condition of maximizing Eq.(9)with respect toxis

ap cx 0: A:23

Rearranging leads to Eq.(10).Assuming that the farmer participates in the PES program, the

comparative statics of the farmer's optimal action with respect to a ,p,c, and are obtained as follows

x

a

1c> 0 A:24

x

p

c

>0 A:25

x

c

ap

c2 b0 A:26

x

p

c> 0: A:27

Appendix B. Optimal Payment Scheme

Taking expectation over according to the regulator's assumeddistribution with mean and variance

2, the optimization problemcan be written as

maxa;p

(ap

2

2

c

2

a2

2

2

2ap 3 32

p

2 4

622 34

c2

a

2 2app

2 2

p2

2

2c

2p

2

2

):

B:28

After few steps of simplication, the rst-order conditions withrespect toa and p can be written as

c a

p

a

2

2

p

2

32

0 B:29

2

2

c 1p

a

c p

2

a

3 32

p

4

622 34

c2

0:

B:30

Solving fora andp, we obtain

a

2c32c

3

2

c 2

22 4c

4 3

26c2 c

2 2ght

2

B:31a

p

c2 c

2

2

c

2

22 4c

4 3

26c2 c

2 2ht

2

: B:31b

The denominator of these expressions is

c 2

22 4c

4 3

26c2 c 2 2

2

c2 2c2 42

2 4c4 3

26c2 c 2 2

2

c2 2c2

c 22

2 22

c 2 2

2

22

4 34

:

B:32

Simplifying and dividing by c2 leads to Eq. (17). Plugging into

Eqs.(B.31a)and(B.31b), we obtain Eqs.(16a)and(16b).



8/8

Appendix C. Proof of Result 3

Differentiating Eq.(16b)with respect to yields

p

2

2

"

1c

2

2

2c

2

c

2

2

2

22

c 2

2

2

!

2

c2

2

4

34

!

1c 22

1c 22 2 22

c 2 2

2

2

c2

2

4

34

!#

2

c2

2

2

2c

2

2

c2

2

4

34

!" #

22

2

22

c

2

2

2

2c

2

4

34

#

2

c2

"3

2

2

22

2c

2

2 2

c

2

2

c

2

4

34

#:

C:33

Differentiating Eq.(16b)with respect to yields

a

c2

"22 2

2c

2

c 22

2 22

c 2

2

2

2

c2

2

4

34

c

2 2

c

2

2

2

2

2

22

c

2

2

2

2c

2

4

34

!#

c2

"2

2

2

2c

2

2

c2

2

4

34

!

c2 2

2

2

22

c

2

2

2

2c

2

4

34

c2 2

2

4 1

2

c2

4 3

4

!"

c2 44c 2 2

2 2c 2

4 34

:

C:34

Appendix D. Proof of Result 4

Using Eqs.(16a)and(16b)in the regulator's objective functionthat is given in Eq.(B.28), we obtain after few steps of rearrangement

E v y

12c

2

2

2

c

2

4

4

c

2

2

2 2

c2

2 22

2

c22

4 34

c2 1

c2

2 2

:D:35

for the combined PES.It is straightforward to verify that the optimal pure action-based

payment would be

ap0

1 c

2 2

: D:36

Using this, together withp0, in the regulator's objective functionyields a welfare level of

E v y p0

12c

2

1 c

2 2

D:37

for the pure action-based PES. Finally, the optimal pure performance-based payment would be

pp0

2

2

2 2

c

4 622 3

4

c2

: D:38

With this, the welfare level is

E v y

a0

12c

2

2

2

2 2c

4 622 3

4

c2

D:39

for the pure performance-based PES.

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