Ecological Economics 68 (2009) 2114–2121
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Ecological Economics
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e c o n
Analysis
Agri-environmental schemes: Adverse selection, information
structure and delegation
Joan Canton a,⁎, Stéphane De Cara b, Pierre-Alain Jayet b
a
b
University of Ottawa, Economics Department, 55, Laurier Avenue E, Room 10111, Ottawa, ON, Canada K1N 6N5
INRA, UMR “Économie Publique” INRA/AgroParisTech, Centre de Grignon, BP01, F-78850 Thiverval-Grignon, France
a r t i c l e
i n f o
Article history:
Received 10 September 2008
Received in revised form 5 January 2009
Accepted 9 February 2009
Available online 9 March 2009
Keywords:
Agri-environmental policies
Contracts
Adverse selection
Information structure
Delegation
a b s t r a c t
This work analyzes alternative designs of agri-environmental schemes and how different incentive
mechanisms impact on their overall efficiency. It focuses on spatial targeting and delegation in an
asymmetric information context. First, the optimal contract under adverse selection is modeled. This model
underlines the trade-off between information rents and allocative efficiency. The impact of spatial targeting
is then addressed. Disaggregated information structures increase the optimal efforts asked of the farmers. It
may also involve higher information rents and may reduce the net contributions of some farmers. Finally, the
consequences of delegating authority within the principal–agent relationship are investigated. The results
illustrate that spatial targeting and delegation, when combined, have asymmetric impacts on farmers'
payoffs.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
The balance of objectives of the Common Agricultural Policy (CAP)
has considerably shifted over the past two decades. The importance
of the support to farmers' income—although still a cornerstone of
the CAP—has been fading away through the successive reforms,
whereas rural development and environmental protection have been
increasingly emphasized. Agri-environmental schemes (AES) have
become the dominant instrument of EU agri-environmental policy
(Latacz-Lohmann and Hodge, 2003), with EU expenditure on agrienvironmental measures amounting to EUR 2.2 billion in 2005 and
agri-environmental contracts covering more than a quarter of the EU25 utilized agricultural area (European Commission, 2008). Through
AES contracts, farmers voluntarily commit themselves to adopting
practices that go beyond the minimal “Good Farming Practices”. In
return, they are entitled to payments meant to compensate incurred
costs and foregone income.
Asymmetric information often prevails in the design of agrienvironmental contracts. Opportunity costs associated with alternative practices depend on variables that are known to the farmer, but not
readily known to the regulator. Another important characteristic of
AES is that the scale at which they are designed, implemented and/or
monitored varies greatly. Some of the agri-environmental measures in
place in the EU are restricted to farmers located in narrowly-delineated
zones, whereas others are available to all farmers regardless of their
⁎ Corresponding author. Tel:. +1 613 562 5800x1750.
E-mail address: [email protected] (J. Canton).
0921-8009/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2009.02.007
geographic location. Likewise, implementation and monitoring may be
the responsibility of a national agency or delegated to subnational
authorities (Oréade-Brèche, 2005, p. 12).
Indeed, spatial dimensions and environmental performances are
not independent. In this respect, the trade-off between ‘wide-andshallow’ versus more targeted schemes provides a good illustration. In
recent years, there has been no clear trend favoring one type of
instrument over the other. The ‘Environmental Stewardship’ scheme,
introduced in the UK in 2005, is an example of the ‘wide-and-shallow’
approach. It has replaced the more targeted schemes that were in
place since the mid eighties (Dobbs and Pretty, 2008; DEFRA, 2008). In
the meantime in France, the introduction of ‘Contrats Agriculture
Durable’ marked the opposite trend toward more geographically
differentiated measures.
One possible explanation of the great diversity in geographic
coverage and scale of implementation of actual AES lies in the spatial
heterogeneity of environmental impacts. Spatial targeting of agrienvironmental measures may then be justified by cost-effectiveness
arguments (Wu and Babcock, 2001; Wünscher et al., 2008) and the
need to tailor AES to the specific conditions prevailing in a given area
(OECD, 2003). Another explanation may lie in the (dis)economies of
size characterizing the administrative and transaction costs involved
by agri-environmental schemes (Falconer et al., 2001).
In this paper, we explore a third possible determinant of the degree
of spatial differentiation prevailing in actual AES. We consider that
spatial targeting can be used by the regulator to reduce the effects of
asymmetric information. A direct consequence is that information and
spatial dimensions cannot be studied separately. This is a novel aspect
of this paper to tackle both dimensions together. Delegation of the
J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
implementation of AES to sub-national authorities can then be seen as
a means of improving the regulator's ex-ante information. This leads
us to address two interrelated questions in this paper: ‘How does a
more geographically disaggregated design affect asymmetric information and the overall efficiency of AES?’ and ‘What are the distributional effects of delegation?’
In a recent paper, Ferraro (2008) identifies three approaches to
reduce information rents: acquire information on observable attributes, offer landowners a menu of screening contracts, and allocate
contracts through procurement auctions. The first approach consists
in identifying observable attributes correlated with the unknown
variable. The other two approaches rely on direct revelation mechanisms. While Ferraro (2008) focuses on the latter approach, we study
the consequences of the combination of the first two.
Our contribution builds on three strands of the literature. First, the
implications of asymmetric information for the design of agricultural
and environmental policies have been extensively investigated
(Bourgeon et al., 1995; Fraser, 2004; Gren, 2004; Bontems and
Bourgeon, 2005). See for instance Chambers (2002) for a survey. In
contexts characterized by hidden information, scholars have studied
truthful direct revelation mechanisms and highlighted the trade-off
between information rents and social efficiency. We underline this
trade-off in the specific context of AES.
The second related strand of literature considers endogenous acquisition of ex-ante information. Lewis and Sappington (1991), Cremer
and Khalil (1992) and Cremer et al. (1998) study the welfare
implications if agents could acquire additional information before
contracting. In Nosal (2006), the principal can choose to acquire
additional information about the state of the world before he contracts
with an agent. To the best of our knowledge, our contribution is the first
to specifically model information acquisition by the principal through a
disaggregated information structure, with perfect knowledge from agents.
Third, we build on the extensive literature that has analyzed the
effects of delegation on the social costs of transfers (Melumad et al.,
1992; Poitevin, 2000; Faure-Grimaud and Martimort, 2001; Mookherjee
and Reichelstein, 2001). As delegation introduces an intermediate layer
in the principal–agent relationship, it is likely to affect the social costs of
transfers. We use results from this literature to address the trade-offs
between the costs and benefits of delegation on allocative efficiency. We
show in this context that delegation may have contrasted distributional
impacts.
We develop a framework that allows us to analyze a one-stage
screening situation where agents are offered a menu of contracts
involving an environmental effort and a transfer in a context of
asymmetric information. We consider the possibility of a finer information structure, which, as defined by Laffont and Tirole (1993, p. 123),
“corresponds to a finer partition of the set of states of nature”. In other
words, the regulator can segment the population of farmers and adapt
the menus of contracts offered to agents depending on their respective
position in the new partition. In order to disentangle the effects of
asymmetric information and delegation costs, we proceed in two steps.
We first assume that the regulator has access to the disaggregated
information structure at no cost. We then relax this assumption and
consider that finer information structure requires delegation, which
involves specific costs.
Our contribution is twofold. First, we show that under a disaggregated information structure the regulator can impose higher environmental efforts on all farmers. The impact on information rent is less
straightforward. Although a disaggregated information structure tends
to limit the potential for imitative behavior, the greater level of effort
involves larger transfers, which in turn tends to increase the information
rents. Depending on the relative strength of these two effects, the
information rent may increase for some farmers and it may reduce some
farmers' net contribution to the policy. Second, we stress the role of
delegation as a means of acquiring information. The conjunction of a
disaggregated information structure and delegation implies asymmetric
2115
consequences for spatial targeting. For the same cost of delegation, the
consequences are much more important in the areas with the most
efficient farmers. This calls for a better control from the principal over
the most sensitive areas.
The remainder of the article is organized as follows. Section 2 presents
the analytical model, from which optimal contracts are derived under
asymmetric (and exogenous) information. Section 3 focuses on the effect
of a disaggregated information structure and highlights the role of spatial
targeting as a means of improving the ex-ante regulator's information. Section 4 is devoted to the analysis of the asymmetric impact of
delegation on the efficiency of spatial targeting. Section 5 concludes.
2. Benchmark model under asymmetric information
Consider a set of heterogeneous farmers. Each farmer may have a
beneficial (or less damaging) impact on the environment if certain
changes in producing activities are undertaken, e.g. through the adoption
of environmentally friendly practices. The environmental benefit, B(a),
depends on the level of effort undertaken, a, which represents for
example the amount of land enrolled in the program. The cost incurred
̲ to
undertake the effort a is denoted by V(a,θ), where θ ∈ Θ =[θ̲;θ ] is a
parameter representing the farmer's private information (the farmer's
type). The cumulative distribution function G(θ), with density g(θ),
summarizes the existing heterogeneities in the conditions of production.
In the subsequent analysis, the following assumptions are made:
(1) B(.) is continuously differentiable and satisfies B′(a) N 0 and B″
(a)≤ 0;
(2) V(a,θ) is thrice differentiable, increasing in both arguments, and
it satisfies:
"
#
"
#
A2 V
A A2 V
A A2 V
ða; θÞN 0;
ða; θÞ z 0 and
ða; θÞ z 0 for all θ a Θ;
AaAθ
Aa AaAθ
Aθ AaAθ
(3)
GðθÞ
gðθÞ
is increasing in θ.
The environmental benefit is assumed to be increasing and concave
with respect to the effort.1 Costs are assumed to be monotonously
increasing with respect to both the effort and the type index. For the
same level of effort a, farmers characterized by a lower θ face lower costs.
The first part of assumption 2 ensures that the standard “single-crossing”
property is fulfilled. This assumption implies that the indifference curves
of any two different types only cross once and that agents with a lower θ
are willing to receive less for a given increase in a than agents with higher
θ (Salanié, 2005). The remaining parts of assumption 2 ensure that the
problem is concave. Assumption 3 is also common in adverse selection
models. For most unimodal distributions, the hazard rate, as defined in
Laffont and Martimort (2002), is monotone increasing with respect to θ
(see Bagnoli and Bergstrom, 2005, for a comprehensive discussion of the
properties of such distributions). This condition ensures that the
incentive distortions are increasing with the agent's type.
As is often the case in asymmetric information problems, we assume
that the regulator—hereafter referred to as the principal—knows
the
̲
overall distribution of farmers' types, i.e. knows θ̲, θ , and g(θ), which are
common knowledge. Individual opportunity costs remain private information, and are therefore unknown to the principal prior to contracting.
Note that, in our setting, the only source of heterogeneity among
farmers lies in the costs of undertaking effort a, as the environmental
benefit for the same level of effort is equal across farmers. This
assumption is admittedly restrictive for at least two reasons. First, it
might not be possible to summarize the heterogeneity among farmers
into one single parameter. Second, environmental benefits may also be a
source of heterogeneity among farmers. Nevertheless, this simplifying
assumption will prove useful in obtaining tractable results. Taking into
1
Two sufficient continuity conditions ensure that all farmers contract: B′(0) = + ∞
and lima → 0B′(a)a = 0 (Laffont and Martimort, 2002).
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J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
account the multidimensional nature of heterogeneity among farmers
would require a fairly involved analysis. Depending on the degree of
correlation among the sources of heterogeneity, it also might result in
bunching equilibria and/or some agents being excluded at the optimum
(Salanié, 2005, pp. 78–82). Accounting for environmental benefits that
vary with agents' type would require additional assumptions2 without
changing fundamentally the nature of the results. As we focus on the
impact of targeting on asymmetric information, such an assumption
would impose unnecessary complexity.
Direct revelation mechanisms are first examined. The principal
proposes to farmers a payment schedule consisting of a transfer t(.)
and a level of effort a(.), which both depend on the type reported by
each farmer. By reporting a type θ ̃—possibly different from the true
θ—each farmer thus chooses the corresponding level of effort a(θ ̃)
and transfer t(θ ̃). The principal chooses a(.) and t(.) in order to
maximize the difference between total (expected) environmental
benefit and total (expected) transfers:3
Z
θ̄
W=
θ
¯
½BðaðθÞÞ − t ðθÞg ðθÞdθ
ð1Þ
The choice of the payment schedule is subject to participation and
incentive compatibility constraints:
t ðθÞ − V ðaðθÞ; θÞz 0 for all θaΘ
ð2Þ
t ðθÞ − V ðaðθÞ; θÞz t θ̃ − V a θ̃ ; θ for all θaΘ
ð3Þ
Inequality (2) ensures that each farmer is at least as well off when
signing the contract as when not signing. For the sake of simplicity, the
reservation utility is assumed to be the same across farmers and is
normalized to zero.4 Inequality (3) prevents imitative behavior on the
part of the farmers, and therefore ensures a truthful direct revelation
mechanism.
The information rent—denoted by R(θ)—is defined as the difference
between the payments made to farmers and their true cost,5 that is:
RðθÞ = t ðθÞ − V ðaðθÞ; θÞ
ð4Þ
Using Eq. (4), the program of the principal can be rewritten as
follows (see Appendix A.1):
Z
max
a;R
θ
¯
θ̄
½BðaðθÞÞ − V ðaðθÞ; θÞ − RðθÞg ðθÞdθ
ð5Þ
subject to
:
AV
ðaðθÞ; θÞ for all θaΘ
RðθÞ = −
Aθ
ð6Þ
:
aðθÞV 0 for all θaΘ
ð7Þ
R θ̄ = 0
ð8Þ
With increasing costs with respect to the type index, Eq. (6) implies
that the information rent is decreasing with respect to θ. The lower is θ,
2
In particular, with respect to the concavity of the problem. See the impact of a
marginal benefit that would depend on θ in Eq. (A.19).
3
The objective function is different from that of a welfare-maximizing regulator
here. It rather pertains to that of an environmental agency seeking to maximize the
environmental benefit per euro of payment. This is in this sense similar to the objective
of EQIP for instance (Cattanaeo, 2003).
4
See Bourgeon et al. (1995) for an endogenised treatment of the reservation utility.
5
Information rent can equivalently be defined as the difference between what is
received under asymmetric information and what would have been received under
perfect information.
the smaller is the cost to achieve effort a, and therefore the greater is
the incentive for the farmer to pretend facing higher costs. As the least
efficient farmer has
̲ no interest in imitative behavior, the information
rent is zero for θ . The Spence–Mirlees condition implies that efforts
asked of the farmers should be non increasing with respect to θ.
Solving problem (5)–(8) leads to the following condition (see
Appendix A.2):
2
BVðaðθÞÞ −
AV
GðθÞ A V
ðaðθÞ; θÞ =
ðaðθÞ; θÞ for all θaΘ
Aa
g ðθÞ AθAa
ð9Þ
Under perfect information, the optimal effort is such that marginal
environmental benefit and marginal cost are equal for all θ. The right
hand side of Eq. (9) therefore embeds the wedge due to asymmetric
information. Two factors play a role in this wedge: (i) the characteristics of the distribution of θ among farmers as summarized by GgððθθÞÞ,
and (ii) how the marginal cost of effort changes with θ.
For each additional unit of effort asked of one type of farmer, securing
a truthful direct revelation mechanism requires that additional rents are
given to all less efficient farmers. The implicit solution of Eq. (9) in a
defines the optimal transfer under asymmetric information, from which
one can derive the information rent. The following lemma compares the
optimal efforts under perfect information (a⁎) and under asymmetric
information (â).
Lemma 1. Under assumptions 1–3, the environmental effort under
asymmetric information is the same as under perfect information for the
most efficient farmer (θ̲), and lower for all other farmers. We thus have:
⁎
⁎
â ðθÞb a ðθÞ for all θaθ; θ̄ and â ðθÞ = a ðθÞ:
¯
¯
¯
This result is a straightforward consequence of Eq. (9). It highlights
the trade-off between information rent and allocative efficiency. As
soon as asymmetric information is taken into account, the presence of
information rents tends to reduce the required environmental effort.
3. A disaggregated information structure
3.1. Revelation mechanism under a disaggregated (finer) information
structure
In this section, the implications of a finer information structure, as
defined by Laffont and Tirole (1993), are specified. It is assumed that
the principal is able to segment the overall population of farmers
based on some observable characteristic, for instance on geographic
location. Furthermore, it is assumed that the farmers' population can
be split into a finite number of sub-divisions, each of which being
characterized by a distinct support regarding the distribution of θ.
Formally, the following definition is used:
Definition 1. (Laffont and Tirole, 1993)
A finer information structure allows a partition of the set of
̲
farmers into a finite number
of sub-divisions
defined by Θi = [θ̲i,θ i],
̲
̲
̲
with i = 1,…,K, θ̲1 = θ̲, θ i = θ̲i+1, and θ K = θ .
Individual farmers' opportunity costs remain unknown to the
principal. However, under the disaggregated information structure,
the principal can unambiguously enclose the type characterizing each
farmer within the narrower interval Θi based, for instance, on the
farm's location. Spatial targeting in this case takes the form of a
segmentation of the population of farmers aimed at reducing the
degree of asymmetric information.
As we focus on the effects of improved ex-ante information, we first
assume that the principal has access to the disaggregated information
structure at no cost. The principal is therefore able to design payment
schedules that are specific to each subdivision. gi(θ) denotes the
conditional density of θ given that the farmer belongs to the i-th
J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
subdivision, with Gi(θ) representing the conditional cumulative
distribution function. The principal's program thus becomes:
max
ai ;ti
K
X
G θi
¯
i=1
+ 1
− Gðθi Þ
¯
Z
Θi
½Bðai ðθÞÞ − ti ðθÞgi ðθÞdθ
ð10Þ
subject to ti(θ) − V(ai(θ),θ) ≥ 0 for all i and for all θ ∈ Θ
ti ðθÞ − V ðai ðθÞ; θÞz ti θ̃ − V ai θ̃ ; θ for all i and for all θaΘi
Note that the participation constraint is common to all types of
farmers, whereas incentive compatibility constraints are specific to each
subdivision. Solving this program leads to the following conditions:
2
AV
G ðθÞ A V
BVðai ðθÞÞ −
ða ðθÞ; θÞ = i
ða ; θÞ for all θaΘ and for all i
Aai i
gi ðθÞ AθAai i
ð11Þ
The implicit solution in ai of Eq. (11) determines the effort and
transfer involved by the direct revelation mechanism under the finer
information structure. The only difference between Eqs. (9) and (11)
lies in the hazard rate. As the overall distribution does not change
under a finer information structure, the conditional density is given by
gi(θ) =g(θ)/(G(θ̲i+1) −G(θ̲i)). Likewise, we have Gi(θ) = ∫θθ̲i g(u)du/(G
(θ̲i+1) −G(θ̲i)). Under a finer information structure, it then follows that:
Gi ðθÞ
GðθÞ − Gðθi Þ
=
¯
gi ðθÞ
g ðθÞ
ð12Þ
By comparison with the case examined in Section 2, a disaggregated
information structure involves changes in (i) efforts asked of farmers,
and therefore costs and transfers, and (ii) information rents. As potential
imitative behaviors are restricted to farmers belonging to the same
subdivision, the information rent for farmer of type θ now writes:
Z
RðθÞ =
θ̄i
θ
AV ðai ðuÞ; uÞ
du
Au
ð13Þ
To assess the distributional impacts of the change in information
structure, we use
wðai ðθÞÞ = Bðai ðθÞÞ − hi ðai ðθÞ; θÞ
ð14Þ
where, following Melumad et al. (1995), hi ðai ðθÞ; θÞ = V ðai ðθÞ; θÞ −
R θ̄i AV ðai ðuÞ;uÞ
du may be interpreted as agent i's virtual cost.
θ
Au
In the absence of any cost to access to the disaggregated information structure, the principal can always implement the mechanism
corresponding to the standard asymmetric information case6 discussed in Section 2. Therefore, the principal's objective function unambiguously increases, that is, Ŵ ≤ Ŵ F, where the superscript F
indicates the optimal value under the finer information structure.
Proposition 1 summarizes the results regarding the distributional
effects of the change in the information structure compared to the
standard asymmetric information case.
Proposition 1. Under assumptions 1–3 and in the absence of any cost
for the principal to access to finer information structure,
(1) Farmers in the most efficient subdivision (i = 1) are asked the
same effort and their information rent is lower, âF = â, RF̂ ≤ R̂, and
ŵF N ŵ for all θ ∈ Θ1;
(2) Farmers in subdivisions i = 2,…,K − 1 are asked higher efforts
and the effect on information rent is ambiguous: âF N â, R̂F ≶ R̂, and ŵF ≶
ŵ, for all θ ∈ Θi, i = 2,…,K − 1.
6
Eq. (10) can be rewritten so as to make appear the initial objective function
Þ
(Eq. (5)) by recalling that gi ðθÞ = Gðθi + g1ðÞθ−
Gðθi Þ.
¯
¯
2117
(3) Farmers in the less efficient subdivision i = K are asked higher
efforts and their information rent is higher: âF N â, RF̂ N R̂, and ŵF ≶ ŵ for
all θ ∈ ΘK.
Proof. From Eq. (12), it is clear that G1(θ)/g1(θ) = G(θ)/g(θ) for all θ ∈
Θ1 and Gi(θ)/gi(θ) b G(θ)/g(θ) for all θ ∈ Θi, i = 2,…,K. Therefore, the
comparison of Eqs. (9) and (11) implies that efforts remain unchanged
for i = 1. For i = 2,…,K, efforts are higher under our assumptions: B″(a
2
3
(θ)) ≤ 0, AAaV2 ðaðθÞ; θÞN 0, AaA 2VAθ z 0. The comparison of information rents
derives from Eq. (13). An example where the net contribution of some
farmers to the overall objective is smaller under the finer information
structure, ŵ F b ŵ, is given in Section 3.2.
The proposition underlines the contrasted effects of disaggregated
information structure between the first subdivision (most efficient
farmers) and the other subdivisions. In subdivision i = 1, the hazard
rate is the same as in the standard asymmetric information case, and
so are the effort and the related cost. The sole effect of a disaggregated
information structure on these farmers results from the change in
information rent. As the lowest-cost farmers are pooled together in
this subdivision, the potential for imitative behavior from these
farmers is reduced, lowering the information rent needed to secure a
truthful direct revelation mechanism. In this context, AES that manage
to isolate the most efficient farmers decrease these farmers' utility.
As for subdivisions i = 2,…,K, two effects are at play. On the one
hand, finer information structure restricts the potential for imitative
behaviors, and thus tends to reduce information rents. On the other
hand, because of the decrease in the hazard rate, farmers can be asked to
undertake greater efforts, leading to higher costs and larger transfers,
which have an opposite effect on information rents. The impact on those
farmers' utility is ambiguous.
A (costless) disaggregated information structure has an overall
positive impact on the efficiency of agri-environmental policies. This is
indeed one of the main arguments in favor of spatial targeting. By
reducing the degree of asymmetric information, environmental efforts are
closer to their first-best levels. One might think that well targeted
contracts could ease acceptance of AES among farmers. However, our
results show that the most efficient farmers are worse off under a
disaggregated information structure than under the standard asymmetric
information case. This may create political conflicts and prompt defensive
actions by agents to protect their rent. Furthermore, although total welfare
increases, the net contribution of some farmers (the environmental
benefit of their effort minus costs) may diminish. Such redistributive
effects may also hinder the acceptability of AES. These results shed some
light on the wide diversity that prevails with respect to targeting in the
actual implementation of AES, with some countries opting for a ‘broadand-shallow’ approach while other favor more targeted measures.
3.2. Illustrative case
Let us illustrate the results on a̲ simple simulation with θ uniformly
distributed between θ̲ = 10 and θ = 20. The probability density is thus
GðθÞ
1
g ðθÞ = θ̄ −
and the hazard rate is gðθÞ = θ − θ. We further posit B(a
θ
¯
(θ)) = a(θ)¯ and V(a(θ), θ) = a(θ)2θ. These specifications satisfy
assumptions 1–2. Solving the principal's program (5)–(8) yields:
1
; 8θaΘ
4θ − 2θ
¯
θ
V ðaðθÞ; θÞ =
; 8θaΘ
ð4θ− 2θÞ2
¯
1
1
1
−
RðθÞ =
; 8θaΘ
4 4θ − 2θ
4θ̄ − 2θ
¯
¯
1
4θ − 3θ
wðθÞ = +
¯ ; 8θaΘ
2ð4θ −2θÞ2
4 4θ̄ − 2θ
¯
¯
aðθÞ =
ð15Þ
ð16Þ
ð17Þ
ð18Þ
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J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
Fig. 1. Optimal effort as a function of the farmer's type θ under perfect information,
standard asymmetric information, and disaggregated information structure with two
and four subdivisions.
Fig. 3. Information rent under standard asymmetric information, and disaggregated
information structure with two and four subdivisions.
Four scenarios are considered. Results are presented in Figs. 1–4. In
the first ̲ scenario, the mechanism is designed using the whole interval
Θ = [θ̲,θ ] (black solid line). The information structure thus corresponds to the standard asymmetric information case. We also
consider the cases where the principal is able to split Θ into two
(dotted lines) and four (thin dashed lines) sub-divisions. For the sake
of simplicity, the sub-divisions are assumed to be of equal length in
each case. Last, we depict the benchmark situation under perfect
information (grey thick dashed lines).
Fig. 1 presents the optimal level of efforts in each of the four cases.
Note that for all scenarios and on each subset, the level of efforts
decreases with respect to θ. Furthermore, on each subset, the most
efficient farmer is offered first-best efforts. Consider the case with a
disaggregated information structure into two subdivisions. Farmers in
the first subdivision (10 ≤ θ ≤ 15) are asked the same level of efforts as
under the standard asymmetric information case (the dotted and solid
lines overlap). By contrast, the less efficient farmers (15 ≤ θ ≤ 20) are
required to undertake a greater effort. In the standard asymmetric
information case, the efforts asked of the less efficient farmers have to
be low to deter mimicking behavior of more efficient farmers. Since
the potential for such behavior diminishes under a disaggregated
Fig. 2. Cost of effort under perfect information, standard asymmetric information, and
disaggregated information structure with two and four subdivisions.
Fig. 4. Net contribution to surplus under perfect information, standard asymmetric
information, and disaggregated information structure with two and four subdivisions.
J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
information structure, the optimal effort can be greater (or equal) for
all farmers.
The correspondence between Figs. 1 and 2 is immediate and
intuitive. As the cost is increasing with respect to the effort, V(.) is
greater (or equal) under a disaggregated information structure than
in the standard asymmetric information case. Therefore, higher costs
under a disaggregated information structure tend to increase the
transfers required to secure a truthful direct revelation mechanism.
Transfers also include information rents. Fig. 3 shows information
rents as a function of the farmer's type and under each information
structure. It again illustrates the results found in Proposition 1; a
disaggregated information structure does not necessarily reduce
information rents. In this illustrative example, information rents
increase under a more disaggregated information structure for the less
efficient farmers (17.5≤θ≤20). As higher efforts are asked of these
farmers, their net utility must increase to prevent mimicking behavior.
As shown in Proposition 1, the combined effects on effort, information rent and transfer may result, for some farmers, in a net
contribution to surplus w(ai(θ)) that is lower under disaggregated
information structure than under the standard asymmetric information case. This is illustrated in Fig. 4. The situation where ŵF b ŵ arises
in our example (with two subdivisions) for the most efficient farmers
in the second subdivision (θ slightly larger than 15). The same kind of
result holds when the information structure is further disaggregated
(from two to four subdivisions) for farmers characterized by θ slightly
greater than 12.5 and 17.5. Again, even though a disaggregated information structure has an overall positive impact, the net contribution
of some farmers may be reduced, questioning the political economy of
the measure.
4. Incentives and delegation
Delegation of the implementation of AES to sub-national authorities can be seen as a means of improving the regulator's ex-ante
information because local institutions may have a better knowledge of
agents' characteristics. Delegation may thus enable the principal to
access to the disaggregated information structure. However, as
delegation modifies the structure of the principal-agent problem, it
may influence the optimal transfers. This section discusses whether
combining disaggregated information structure and delegation can be
profitable for the principal.
Introducing a third level in the principal-agent relationship may
lead to a “deadweight loss of delegation” (Faure-Grimaud et al., 1999)
or, on the contrary, may have a positive impact through for instance
the reduction in communication costs or the possibility of renegotiation. Let λ measure the (net) effect of delegation on each unit of
transfer (λ N 0 corresponds to the case where delegation is costly).
Further assume that the principal must resort to delegation in order to
access to the disaggregated information structure. The impact of
delegation on transfers will then influence the effort asked of each
agent.
Using Eqs. (9) and (11), we can assess the effect of delegation on
the optimal effort. Within subdivision i, the efforts are higher under
the disaggregated information structure (with delegation) than in the
standard asymmetric information case if and only if:
ð1 + λÞ
!
AV
G ðθÞ A2 V
AV
GðθÞ A2 V
+ i
+
b
Aa
gi ðθÞ AθAa
Aa
g ðθÞ AθAa
ð19Þ
We focus first on the most efficient farmers (in the first
subdivision). We have seen in the previous section that these farmers
were asked the same effort under the standard asymmetric information case as under the disaggregated information structure. Therefore,
from Eq. (19), their effort will be larger only if delegation has a positive
impact on the social cost of transfers, i.e. if λ b 0.
2119
To illustrate the effect of delegation on the efforts of less efficient
agents, it is useful to consider a simple disaggregated information
structure with two subdivisions. Assume that θ is uniformly
distributed over Θ, with a share α of farmers belonging to the first
subdivision Θ1 and (1 − α) belonging to the second subdivision Θ2. In
this case, farmers in the second subdivision are asked larger efforts
under the disaggregated information structure than under the
standard asymmetric information case if and only if:
λ
b α θ̄ − θ
1+λ
¯
!
A2 V
AθAa
AV
Aa
A V
+ ðθ − θÞ AθAa
¯
2
ð20Þ
A few observations can be made from condition (20) on the
parameters influencing̲ the level of effort. First, the wider the overall
interval, the greater θ − θ̲, and the higher the efforts asked of the
farmers. Intuitively, a wide initial distribution reveals important
differences in farmers' opportunity costs. Therefore, isolating the less
efficient farmers favors allocative efficiency rather than information
rents in the payment schedule. Second, a low θ within one subdivision
implies a higher effort asked of the farmer as the contract offered is
now close to the first-best. Finally, the effort is increasing with respect
to α. A higher α results in a smaller size for the second sub-division,
which reduces all the more asymmetric information and increases
allocative efficiency for that subdivision.
The previous illustration emphasizes some key points. The impact
of delegation on allocative efficiency depends crucially on the
considered subdivision. Moreover, delegation may be intrinsically
costly, the regulator can still benefit from it if it is the way to isolate the
less efficient farmers. Generalizing condition (19) to the case of K
subdivisions and a uniform distribution yields:
!
2
λbðθi − θÞ
¯
¯
A V
AθAa
AV
Aa
A V
+ ðθ − θi Þ AθAa
¯
2
ð21Þ
where θ̲i represents the lower limit of subdivision i. The RHS of
condition 21 is increasing in θ̲i. Therefore, the following proposition
can be added.
Proposition 2. The impact of delegation on the set of contracts proposed
depends on the subdivision considered. The less efficient the group of
farmers, the more likely delegation would still increase the efforts asked
of the group.
Spatial targeting improves the net benefit of AES for different
reasons, which vary according to the relative efficiency of the group of
farmers considered. Therefore, the impact of delegation is asymmetric.
Initially, an important distortion had to be made for the farmers with
the highest opportunity costs. It was the condition for a truthful
reporting from the other farmers. As it is now possible to discriminate,
it becomes possible to increase the efforts asked of the less efficient.
Then, the cost of delegation can be important without questioning the
efficiency of the policy. However, for the most efficient farmers, a
disaggregated information structure does not intrinsically increase the
efforts asked. There are gains in terms of information rents but they
are more likely to be balanced when delegation introduces negative
distortions.
In terms of policy recommendations, the size and grouping of
delegated authorities should then be one of the main characteristics of
the mechanism design. It is likely that the cost of delegation is a
decisive criterion to measure the net benefits of AES in the areas with
the most efficient farmers. Furthermore, it is also for the most efficient
farmers that the loss in net utility (information rents) is the most
important. Therefore, it should be in the interest of the principal to try
and keep direct control over those farmers. Conversely, isolating the
less efficient farmers is sufficient to increase their efforts. The
potential cost of delegation becomes less of an issue for these farmers
2120
J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
and the principal can afford to delegate the control over those farmers
to local authorities.
As the regulator seeks to implement truthful revelation mechanisms, we need:
5. Concluding remarks
θaarg max π θ̃ = t θ̃ − V a θ̃ ; θ
θ̃
Environmental concerns related to agricultural activities are often
characterized by asymmetric information and spatial variability in
farmers' efficiency. In such situations, spatial targeting may improve
the regulator ex-ante information and therefore simplify the trade-off
between allocative efficiency and information rents. If spatial
targeting is achieved through delegation, delegation costs need to
be accounted for when measuring the relative efficiency of the policy.
This work analyzes various information structures and highlights their
key role in the design of agri-environmental schemes. The results also
illustrate that spatial targeting and delegation, when combined, have
asymmetric impacts on farmers' payoffs.
Compared to the existing literature on spatial targeting, our approach
emphasizes the distributional effects of disaggregated information
structures. Some farmers' net utility, the most efficient ones, decrease
when the principal obtains finer information. Furthermore, other
farmers' contributions to the overall surplus of the measure are reduced.
These redistributive effects should not be neglected when considering
the overall efficiency of local agri-environment programs. Furthermore,
AES require complex administrative structures to acquire information
and monitor the environmental effects of the measures. A key insight of
this model is that for a given cost of delegation, the impact on farmers'
efforts is greatly asymmetric, the most efficient farmers most likely
being negatively affected. In the debate that opposes ‘wide-and-shallow’
versus more targeted schemes, our intermediate position is to say that
more targeted schemes will only be efficient if the regulator is able to
keep a direct control over the most efficient farmers. In other words, an
AES policy design could be to delegate authority when farmers'
opportunity cost is high but to supervise the implementation of the
policy at the EU level for the most efficient farmers.
Further research is needed in several directions. First, farm-type
based models operating at fine geographic resolution could be used to
assess the spatial distribution of the costs of agri-environmental
schemes (see for instance De Cara et al. (2005) in the case of
greenhouse gas emissions). It would provide an empirical basis for
calibrating the spatial distribution of opportunity costs for environmental measures. Another important issue concerns the enforcement
of such a policy. Following the methodology proposed by Florens and
Foucher (1999) in the case of oil pollution, further research could
investigate the issue of the optimal investment policy to enforce
contracts. For instance, various instruments are available to measure
carbon sequestration, like remote sensing or sampling, and it would
be relevant to endogenize farmers' responses to the choice of one of
these instruments.
Acknowledgements
The functions t(θ), a(θ) and R(θ) are supposed fully differentiable.
The first order condition of the agent's profit maximization is:
:
AV
ðaðθÞ; θÞȧ ðθÞ = 0
t ðθÞ −
Aa
By definition of R(θ):
: AV dR
AV = t θ̃ −
a θ̃ ; θ ȧ θ̃
a θ̃ ; θ
−
dθ
Aa
Aθ
θ̃ = θ
θ̃ = θ
:
AV
ðaðθÞ; θÞ
RðθÞ = −
Aθ
ðA:5Þ
Eq. (A.3) must be satisfied θ, which means:
d Aπ
=0
dθ Aθ̃ θ̃ = θ
ðA:6Þ
which is equivalent to:
A2 π
A2 π
+
=0
2
Aθ
Aθ̃Aθ
ðA:7Þ
As the first term on the left hand side of this equation is necessarily
negative (second order condition of profit maximization), the second
one has to be positive. We have:
2
2
A π
A V :
= −
aðθÞN 0
AaAθ
Aθ̃Aθ
ðA:8Þ
This is the Spence–Mirrlees condition: the marginal disutility of
efforts increases with the type, the efforts asked of the farmers must
be decreasing in θ. So, we can rewrite the constraints as follows:
:
AV
ðaðθÞ; θÞ
RðθÞ = −
Aθ
ðA:9Þ
:
aðθÞ V 0
ðA:10Þ
RðθÞz 0
ðA:11Þ
Budget constraints justify that the third constraint is rewritten as
follows:
ðA:12Þ
A.2. Resolution
We proceed as follows. First, the second constraint is neglected.
The fact that this condition is satisfied is checked at the end of the
process. The surplus function is:
Z
S=
θ
¯
A.1. Simplification of the program
θ̄
½BðaðθÞÞ − V ðaðθÞ; θÞ − RðθÞg ðθÞdθ
ðA:13Þ
The last part of this integral is rewritten as follows:
The agents' program is:
θ̃
ðA:4Þ
Combining Eqs. (A.3) and (A.4) yields:
Appendix A
max π θ̃ = t θ̃ − V a θ̃ ; θ
ðA:3Þ
R θ̄ = 0
The authors would like to thank two anonymous referees for useful
suggestions that improved the clarity of the paper. We also wish to
thank Laurent Gillotte, Mireille Chiroleu-Assouline, and Pierre Dupraz
for their helpful comments and discussions. We are also grateful to the
participants to various seminars and working groups, especially the
members of GREQAM in Marseille.
ðA:2Þ
Z
ðA:1Þ
θ
¯
θ̄
θ̄
RðθÞg ðθÞdθ = ½RðθÞGðθÞθ −
¯
Z
θ
¯
:
RðθÞGðθÞdθ
θ̄
ðA:14Þ
J. Canton et al. / Ecological Economics 68 (2009) 2114–2121
Substituting Ṙ(θ) by its value given by the first constraint of the
program yields:
Z
θ
¯
θ̄
Z
RðθÞg ðθÞdθ = 0 +
θ
¯
θ̄
AV ðaðθÞ; θÞ
GðθÞdθ
Aθ
ðA:15Þ
So, the principal's program can be rewritten:
Z
θ̄
S=
θ
¯
AV ðaðθÞ; θÞ
½BðaðθÞÞ − V ðaðθÞ; θÞgðθÞ −
GðθÞ dθ
Aθ
ðA:16Þ
The first order conditions, for each θ, become:
AV ðaðθÞ; θÞ
A2 V
BVðaðθÞÞ −
g ðθÞ −
GðθÞ = 0
Aa
AaAθ
ðA:17Þ
Rearranging this expression yields:
AV
GðθÞ A2 V
=
Aa
g ðθÞ AθAa
BVðaðθÞÞ −
ðA:18Þ
By totally differentiating condition 38, sufficient conditions to
respect the second constraint are determined:
da
=
dθ
A2 V
AθAa
+
GðθÞ A3 V
gðθÞ AaAθ2
BWðaðθÞÞ −
ð Þ A2 V
+ 1 − GðgθðÞgθÞVθ
2
AaAθ
A2 V
Aa2
− GgððθθÞÞ AaA 2VAθ
3
b0
ðA:19Þ
A V
A V
Sufficient conditions
are Aa2 Aθ z 0, AaAθ2 z 0 and the monotonicity of
the hazard rate GgððθθÞÞ , condition respected for most of unimodal distributions (see Bagnoli and Bergstrom (2005) for further explanations).
3
3
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