Should We Pay for Ecosystem Service Outputs, Inputs or Both?

Abstract

Payments for ecosystem service outputs have recently become a popular policy prescription for a range of agri-environmental schemes. The focus of this paper is on the choice of contract instruments to incentivise the provision of ecosystem service outputs from farms. The farmer is better informed than the regulator in terms of hidden information about costs and hidden-actions relating to effort. The results show that with perfect information, the regulator can contract equivalently on inputs or outputs. With hidden information, input-based contracts are more cost effective at reducing the informational rent related to adverse selection than output-based contracts. Mixed contracts are also cost-effective, especially where one input is not observable. Such contracts allow the regulator to target variables that are “costly-to-fake” as opposed to those prone to moral hazard such as effort. Further results are given for fixed price contracts and input-based contracts with moral hazard. The model is extended to include a discussion of repeated contracting and the scope that exists for the regulator to benefit from information revealed by the initial choice of contract. The models are applied to a case study of contracting with farmers to protect high biodiversity native vegetation that also provides socially-valuable ecosystem services.

Appendices

Appendix 1: Input-Based Contracts Asymmetric Information

The analysis of the theoretical model is greatly simplified by the fact that the IC for the l-type farm and the IR constraint for the h-type farm are the only constraints that are binding Following Laffont and Tirole (1993, p. 59) The incentive compatibility constraint for the low cost farmer (IC-l) is:

$$\begin{aligned} f_l -(c_e (\theta ^e ,e_l )+c_x (\theta _l^x ,x_l ))\ge f_h -(c_e (\theta ^e ,e_h )+c_x (\theta _l^x ,x_h ))\end{aligned}$$

(45)

The individual rationality constraint for the h-type (IR-h) $f_h -(c_e (\theta ^e ,e_h )+c_x (\theta _h^x ,x_h ))\ge 0$ implies:

$$\begin{aligned} f_l -(c_e (\theta ^e ,e_l )+c_x (\theta _l^x ,x_l ))\ge (c_e (\theta ^e ,e_h )+c_x (\theta _h^x ,x_h ))-(c_e (\theta ^e ,e_h )+c_x (\theta _l^x ,x_h ))\ge 0 \end{aligned}$$

As $f_h$ is at least $(c_e (\theta ^e ,e_h )+c_x (\theta _h^x ,x_h ))$, Thus we can ignore the IR-l constraint as it is implied by IC-l

If we now optimize (15) with respect to IC-l and IR-h it is possible to check that IC-h is satisfied from the first order conditions (17) and (18), $x_l >x_h$ and $e_l >e_h$

If we restate the IC-l constraint:

$$\begin{aligned} r_l\ge & {} r_h -((c_e (\theta ^e ,e_h )+c_x (\theta _l^x ,x_h ))+(c_e (\theta ^e ,e_h )+c_x (\theta _h^x ,x_h )) \\\ge & {} r_h -c_x (\theta _l^x ,x_h )+c_x (\theta _h^x ,x_h ) \end{aligned}$$

Where $r_i$ is the rent The IC-h is:

$$\begin{aligned} r_h\ge & {} r_l -((c_e (\theta ^e ,e_l )+c_x (\theta _h^x ,x_l ))+(c_e (\theta ^e ,e_l )+c_x (\theta _l^x ,x_l ))\\\ge & {} r_l -c_x (\theta _h^x ,x_l )+c_x (\theta _l^x ,x_l ). \end{aligned}$$

Bringing the constraints together:

$$\begin{aligned} 0\ge (c_x (\theta _h^x ,x_h )-c_x (\theta _l^x ,x_h ))-c_x (\theta _h^x ,x_l )+c_x (\theta _l^x ,x_l ). \end{aligned}$$

The assumption that the IC-h constraint is implied by the IR-h and IC-l constraints holds as long as $c_x^{{\prime }{\prime }{\prime }} (\theta _i^x ,x_i )\ge 0$

Appendix 2: Equivalency Between Mixed Contracts and Second-Best Input-Based Contracts

The regulator maximizes:

$$\begin{aligned} \mathop {{ Maximum}}\limits _{x_i ,y_i ,f_i } \sum _i {\phi _i \left\{ {vg(x_i ,e_i (x_i ,y_i ))-c_e (\theta ^{e},e_i (x_i ,y_i ))-c_x (\theta _i^x ,x_i )-\lambda f_\mathrm{i} } \right\} } \quad i\in l,h \end{aligned}$$

Subject to the participation for the high-cost type

$$\begin{aligned} f_h -c_e (\theta ^{e},e(x_h ,y_h ))-c_x (\theta _h^x ,x_h )=0 \end{aligned}$$

and incentive compatibility constraint for the low cost type:

$$\begin{aligned} f_l -c_e (\theta ^{e},e(x_l ,y_l ))-c_x (\theta _l^x ,x_l )=f_h -c_e (\theta ^{e},e(x_h ,y_h ))-c_x (\theta _l^x ,x_h ) \end{aligned}$$

Both constraints enter as equalities. The four first order conditions for $x_l , y_l , x_h , y_h$ are:

$$\begin{aligned}&\displaystyle v=\frac{(1+\lambda )c_x^{\prime } (\theta _l^x ,x_i )+(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i))\hbox {e}_{x_l}}{g_{e_l } \hbox {e}_{x_l } +g_{x_l } }&\end{aligned}$$

(46)

$$\begin{aligned}&\displaystyle v = \frac{(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))}{g_{e_l } }&\end{aligned}$$

(47)

$$\begin{aligned}&\displaystyle v = \frac{\left( {\begin{array}{l} c_x^{\prime } (\theta _h^x ,x_h )+c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_h } +(\lambda /\phi _h )(c_x^{\prime } (\theta _h^x ,x_h ) \\ -\phi _l (c_x^{\prime } (\theta _l^x ,x_h )+c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h } -\phi _l c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h } ) \\ \end{array}} \right) }{g_{e_h } \hbox {e}_{x_h } +g_{x_h } }&\end{aligned}$$

(48)

$$\begin{aligned}&\displaystyle v = \frac{(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))}{g_{e_h } }+\frac{\lambda \phi _l }{\phi _h }(c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))-c_e^{\prime } (\theta ^{e},e(x_h ,y_h )))&\end{aligned}$$

(49)

First we establish that the low cost farmer selects the first-best solution. Rearrange (47) to give:

$$\begin{aligned} vg_{e_l } =(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i )) \end{aligned}$$

(50)

and (47) to give:

$$\begin{aligned} v(g_{e_l } \hbox {e}_{x_l } +g_{x_l } )=(1+\lambda )c_x^{\prime } \left( \theta _l^x ,x_i\right) +(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_l } \end{aligned}$$

(51)

Substituting for $vg_{e_l }$:

$$\begin{aligned} (1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_l } +vg_{x_l } =(1+\lambda )c_x^{\prime } (\theta _l^x ,x_i )+(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_l} \end{aligned}$$

This simplifies to:

$$\begin{aligned} vg_{x_l } =(1+\lambda )c_x^{\prime } (\theta _l^x ,x_i ) \end{aligned}$$

Establishing that the solution is identical to the optimal solution to the input-based contract, on the basis of (49) effort is also identical.

The area and effort for the high cost farmer can also be shown to be the same as for the input-based contract. From (49) the last term is zero as the effort costs are identical and rearranging:

$$\begin{aligned} vg_{e_h } =(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_h ,y_h )) \end{aligned}$$

(52)

Rearranging (48) and substituting in (52) adding and subtracting $\lambda c_x^{\prime } (\theta _h^x ,x_h )$ to the rhs and rearranging:

$$\begin{aligned} (1+\lambda )c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h } +vg_{x_h}= & {} (1+\lambda )c_x^{\prime } \left( \theta _h^x ,x_h\right) - \lambda c_x^{\prime } \left( \theta _h^x ,x_h\right) +c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h } \\&+(\lambda /\phi _h )(c_x^{\prime } (\theta _h^x ,x_h )-\phi _l (c_x^{\prime } (\theta _l^x ,x_h )\\&+c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h } -\phi _l c_e^{\prime } (\theta ^{e},e(x_h ,y_h ))\hbox {e}_{x_h}) \end{aligned}$$

Using the fact that $c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_h} -\phi _l c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_h} =\phi _h c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_h}$

$$\begin{aligned} (1+\lambda )c_e^{\prime } (\theta ^{e},e(x_h ,y_h )) \hbox {e}_{x_h} +vg_{x_h }= & {} (1+\lambda )c_x^{\prime } (\theta _h^x ,x_h )+(1+\lambda )c_e^{\prime } (\theta ^{e},e(x_i ,y_i ))\hbox {e}_{x_h }\\&+(\lambda /\phi _h )(-\phi _h c_x^{\prime } (\theta _h^x ,x_h )+c_x^{\prime } (\theta _h^x ,x_h )-\phi _l (c_x^{\prime } (\theta _l^x ,x_h )) \end{aligned}$$

This simplifies to:

$$\begin{aligned} vg_{x_h } =(1+\lambda )c_x^{\prime } (\theta _h^x ,x_h )+(\lambda \phi _l /\phi _h )(c_x^{\prime } (\theta _h^x ,x_h )-\phi _l (c_x^{\prime } (\theta _l^x ,x_h )) \end{aligned}$$

and this is identical to the first order condition for the input-based contract (18).