Ecological Economics 69 (2010) 1988–1994

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Ecological Economics

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Analysis

Does encouraging the use of wetlands in water quality trading programs makeeconomic sense?

Matthew T. Heberling a,⁎, Jorge H. García b, Hale W. Thurston a

a Sustainable Technology Division, National Risk Management Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency,26 West Martin Luther King Dr. (MS 498), Cincinnati, OH 45268, USAb Departamento de Economía, Universidad Javeriana, Edificio Gabriel Giraldo SJ, Calle 40 No 6-23 P7, Bogotá, Colombia

⁎ Corresponding author. US EPA/NRMRL, (MS 498), 2645268, USA. Tel.: +1 513 569 7917; fax: +1 513 569 7

E-mail address: heberling.matt@epa.gov (M.T. Hebe

0921-8009/$ – see front matter. Published by Elsevierdoi:10.1016/j.ecolecon.2010.05.014

a b s t r a c t

a r t i c l e i n f o

Article history:Received 15 January 2009Received in revised form 22 March 2010Accepted 26 May 2010Available online 22 June 2010

Keywords:Water quality tradingWetlandsEcosystem servicesIncentives

This paper examines a proposal to incorporate the use of wetlands in water quality trading (WQT) programsin order to meet national wetlands goals and advance WQT. It develops a competitive WQT model whereinwetland services are explicitly considered. To participate in a WQT program, an agricultural producer couldemploy wetlands as his nutrient management practice. Unlike most other management practices, wetlandsnot only remove nutrients from agricultural runoff but also provide ancillary benefits like wildlife habitat andflood control that do not exclusively accrue to the farmer. Thus, when appropriate, a WQT program should becoupled with additional incentives for wetland creation and restoration, such as using a wetland subsidy.Despite the water quality enhancement properties of wetlands, the model reveals that implementing awetland subsidy will not necessarily translate into water quality improvements. While wetland creation isexternally incentivized, the farm's opportunity cost of fertilizer usage in the WQT market is also reduced. Inthis sense, a wetland subsidy acts like a fertilizer subsidy. Conditions under which a wetland subsidy willhelp expand WQT include some degree of farmland area fixity, which is resembled in some, but not all,watersheds, and high efficiency of the wetland abatement technology.

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1. Introduction

Water quality trading programs or nutrient markets in the UnitedStates to date have usually taken the following form: a point source ofnutrient loading, often a municipal separate storm sewer system(MS4) facing a Total Maximum Daily Load (TMDL) restriction onnutrients, has the option of building more capacity or purchasingnutrient reductions from nonpoint sources in the watershed, usuallyfarmers (Woodward et al., 2002). Farmers have a variety of options toreduce nutrient runoff (e.g., reducing fertilizer use on their crops,creating stream buffers, using no-till techniques, or constructing orrestoring wetlands on their property). Agriculture is the leadingsource of impairment in assessed rivers and streams (37%) in theUnited States (US EPA, 2007a), but the runoff is largely unregulated.Therefore, water quality trading programs have the importantproperty of inducing voluntary participation of the agricultural sector.One recent proposal suggests that encouraging the use of wetlands ina water quality trading program will not only advance water qualitytrading and reduce the costs of meeting water quality goals, but it willalso help meet national wetlands goals (Raffini and Robertson, 2005;

Grumbles, 2006; USEPA, 2007b).1 Using economic theory, weexamine this proposal to see how farmers may react. We learn thatthe proposal has the potential to create unintended incentives.

Although there has been a net gain of freshwater wetlands onagricultural lands (Dahl, 2006), encouraging the use of wetlands in waterquality trading may be applicable in specific regions in the US. Forexample, a study on the hypoxia problem in the Gulf of Mexico finds thatmore wetlands are needed to control nutrients (US EPA, 2007c). Whencomparing the rates of wetland loss starting from the mid-1980s and thetotal nutrient yields delivered to the Gulf of Mexico from the MississippiRiver Basin, a clear connection can be made (e.g., Yaich, 2008; WSTB,2009). States with high rates of wetland loss, like Indiana, Iowa, andIllinois, also have large total phosphorus yields and total nitrogen yields.Regions that once had large areas of wetlands (e.g., the Corn Belt), butwere drained for agriculture, could prove promising for wetlandrestoration (US EPA, 2007c).

If wetlands were, in most respects, similar to other nutrientabatement technology, no further discussion on this topic would beneeded. Farmers would choose from a suite of available abatementtechnologies based on minimizing their costs and would choosewetlands if they represented the least cost method of reducing

ional Wetlands Policy Forum recommended a national goal of noetlands acres and functions and since then the NNL goal hasrt of the regulatory regime that governs watersheds in the US.

1989M.T. Heberling et al. / Ecological Economics 69 (2010) 1988–1994

nutrients. Wetland creation or restoration, however, is usually moreexpensive relative to other abatement technologies (e.g., Byström,1998; Ribaudo et al., 2001) suggesting that additional incentiveswould be necessary for the proposal to work. Additional incentives inthe form of subsidies have also been suggested as a mechanism toreduce principal-agent problems inherent in current wetland mitiga-tion banking policy (Hallwood, 2007).

Wetlands provide a variety of services beyond nutrient abatement;wetlands may function as bird habitat, flood control, and sedimentretention (Knight, 1997; Tiner, 2003; MEA, 2005). These otherservices, referred herein as ancillary services or ancillary benefits,may accrue to the agent who constructs or maintains a wetland fornutrient reduction, to other agents in thewatershed, or to populationsoutside the market for nutrient reduction (Byström, 1998). Economictheory suggests that the producer will not consider the ancillarybenefits when choosing among the alternative abatement technolo-gies if the benefits do not enter into his profit-maximizing decision(i.e., positive externality of producing wetlands). To encourage asocially optimal provision of the services wetlands offer, all the socialcosts and benefits should enter into the decisions surrounding theconstruction and maintenance of wetlands (Ribaudo et al., 2001). Wefocus specifically on a wetland subsidy to internalize the ancillarybenefits and show the subsidy can affect a farmer's decision inunintendedways under certain circumstances. In fact, we find that thewetland subsidy can act as a fertilizer subsidy.

This paper examines the potential outcomes of encouraging wet-lands in water quality trading programs by developing a model wherewetland functions and services are explicitly considered. The paperproceeds as follows. First, we examine the existing literature onancillary benefits and environmental markets. Next, the basic tradingmodel illustrates how the social benefits and costs can impact themarket including the unexpected result of encouraging the use ofmore fertilizer. Finally, we discuss the issues highlighted by the modelincluding an alternative to the initial incentive approach.

2. Literature review

Earlier papers have modeled ancillary benefits in pollution tradingmarkets, but their approaches differ on certain key elements. Austinet al. (1997) examine cross-media effects, such as the ancillary airbenefits for reducing NOx emissions to meet a water quality standard(i.e., water quality goal). Montero (2001) develops a trading modelwith two pollutants where the reduction of one pollutant isaccompanied by the reduction in the other pollutants. Woodwardand Han (2004) use a similar model, but they also consider caseswhere the reduction of a given pollutant increases another pollutant.In this paper, we are not concernedwith the reduction in the pollutantthat “co-causes” the ancillary benefit; rather, it is the specificabatement technology that creates the ancillary benefits.

Feng and Kling (2005) and Elbakidze and McCarl (2007) argue thatthe carbon sequestration activities (e.g., agriculture practices) will leadto improvedwildlife habitat and soil erosion reductions, but the authorsalso assume that the ancillary benefits are functions of carbon emissionreductions (similar to Austin et al., 1997). Their approach assumes acorrelation between the pollutant reductions and ancillary benefits, butthis assumption is not applicable for the wetlands and water qualitytrading problem because there are many types of wetlands and theydiffer across space and time as do their services (see King et al., 2000).2

Horan et al. (2004) examine the coordination of water qualitytrading with agricultural conservation policies like Environmental

2 Where carbon markets cover large areas (possibly global in scope), water qualitytrading programs are by necessity organized at the watershed level limiting the size ofthe market. Water quality nutrient trading programs are further limited in scopebecause the emitters of nutrients tend to be point-source MS4s and nonpoint-sourceagriculture producers.

Quality Incentives Program (EQIP). When both the subsidy from theagricultural conservation policies and water quality trading affect thelast unit of abatement, farms operate efficiently. Although the authorsdo not explicitly model wetland services and functions, this resultsuggests that a subsidy based on the ancillary benefits of wetlandscould increase efficiency and encourage the use of wetlands in a waterquality trading program.

Although nutrient reduction credits are typically described as thecommodity traded in water quality trading, Shabman and Stephenson(2007) argue that credits, produced when the source reduces itsdischarge below a set baseline, lead to demand and supply uncer-tainty. Shabman and Stephenson prefer markets where allowances,permissions to discharge a fixed amount of a pollutant, are the tradedcommodity. We follow their recommendation and base the tradingmodel on Horan and Shortle (2005) and Horan et al. (2004) who useallowances rather than credits.

In our model, society directly benefits from both water qualityimprovements and wetland creation and restoration. Consistent withthe proposal, and with Horan et al. (2004), we assume the farmerparticipates in a water quality trading market and receives a subsidyfor wetland creation. Initiation of a program such as this is far fromimplausible; the Natural Resources Conservation Service (NRCS) ofthe US Department of Agriculture (USDA) is officially open to allowinglandowners to sell credits for management options that the NRCS hascost-shared (e.g., USEPA, 2008).

Unlike the above mentioned studies, farmland here is treated as anallocable input. Total abatement critically depends on this allocationdecision and on fertilizer use. Since wetlands cannot be used for cropproductionpurposes, the value of the forgoneproductionwhenwetlandsare in place represent an important part of abatement costs. Allocatingfarm land between cropland and wetland is thus central in this analysis.

In a related paper, Lankoski and Ollikainen (2003) focus on the jointproductionof commodities andnon-commodities bya farm(e.g., runoff,biodiversity, etc.) and how to optimally provide these outputs. Thestudy does not use water quality trading to address the runoff; instead,the authors present a fertilizer tax and buffer strip subsidy as policytools. Also,while it assumes that farmland is constrained, themodel thatwe present looks at both the constrained and the unconstrained cases.As shown later, these assumptions have important implications formodel prediction (e.g., Lankoski and Ollikainen, 2003, find that thesubsidy does not affect the marginal profitability of fertilizer use).

3. Model

We assume that there is a single point source (i.e., a MS4) and asingle nonpoint source (i.e., a farm) in a watershed, although weassume no market power. Emissions for the point source, e, generatemarginally decreasing benefits, b(e), to the MS4.

The farmer, on theotherhand, allocates land forboth theproductionofcrops z1 and abatement of runoff, namely wetland creation and/orrestoration, z2. We initially assume that land area is fixed and defined asz ̅=z1+z2. The production function for crops is Y(x, z1) where x isfertilizer use and z1 is land allocated to crops. Themarginal productivity ofboth inputs is positive and decreasing, YxN0, Yz1N0, Yxxb0, and Yz1z1b0,and the factors are assumed technically complementary, Yxz1N0 (e.g.,Beattie and Taylor, 1993).3 The nonpoint source profit function withoutregulation is defined as

πðx; z1; z2Þ = pyYðx; z1Þ−wxx−wzðz1 + z2Þ ð1Þ

3 To avoid confusion in terminology, Beattie and Taylor (1993) do not use the term‘complementarity’ when discussing Leontief production technology which has to domore with substitutability than factor–factor interdependence. For interdependence,output is not held constant and an increase in one factor changes the marginalproductivity of another factor.

1990 M.T. Heberling et al. / Ecological Economics 69 (2010) 1988–1994

where py is the price of the crop,wz is the rent of land (converting landto agriculture or to wetlands from its original use is assumed costless),and wx is the price of fertilizer. By substituting the land constraint inEq. (1), we obtain the following profit function:

π̂ðx; z2Þ = pyYðx;�z−z2Þ−wxx−wzð�zÞ: ð2Þ

It is easy to see that the optimal choice of wetlands is 0 since thefarmer's profit is decreasing in wetlands. The private optimum forfertilizer occurs where the marginal benefits equal marginal costs. Aspart of the production of Y, the farmer also creates nonpoint sourceemissions r(x,z2), where x is fertilizer use and z2 is the area of land inabatement technology such as wetlands. The first order derivativesare, naturally, rxN0, rz2b0 and the cross-partial derivative is rxz2b0.This indicates that the marginal productivity of fertilizer, x, producingrunoff, r, is decreasing in z2. In other words, fertilizer usage andwetland creation interact in runoff production as technically compet-itive factors (Beattie and Taylor, 1993). We assume that rxxN0 becausefertilizer can be washed away more easily at higher fertilizerapplications and rz2z2N0.4 In order to simplify the model and keepthe point of this paper clear, we eschew focus on the effects ofstochastic events on runoff; much of the literature on water qualitytrading has already focused on this aspect (Griffin and Bromley, 1982;Shortle and Horan, 2001). Based on the model described above, wehave joint production of crop, Y, and runoff, r, through the use ofallocable, but fixed, input z and nonallocable input x (Beattie andTaylor, 1993; Abler, 2004).

Pollution from both sources causes damages, defined as D(e, r),where each small increment of emissions or runoff increases the costs,DeN0, DrN0. Wetlands provide ancillary benefits A(z2) where Az2N0and Az2z2b0.5 Social welfare (W) can thus be defined as:6

Wðe; x; z2Þ = bðeÞ + π̂ðx; z2Þ−Dðe; rÞ + Aðz2Þ: ð3Þ

To have a closer look at the trade-off of gains and losses faced bysociety, wemaximize social welfarewith the appropriate assumptionsto ensure an interior solution (optimal values from this maximizationproblem will be identified as e⁎, x⁎, and z2⁎). Using the necessaryconditions, we obtain:

beπ̂x = rx

=De

Dr: ð4Þ

Note that π̂x/rx=π r̅, where π ̅is profit as a function of runoff. Eq. (4)thus represents the usual optimality condition where the ratio ofmarginal benefits of emissions and runoff activities should equal theratio of the marginal costs or damages. In addition to Eq. (4), we alsohave

beðπ̂z2 + Az2Þ= rz2

=De

Dr: ð5Þ

This allocation condition includes the ancillary benefits of wet-lands. The larger the benefits, the more society will relatively favor

4 One function that meets these restrictions is r(x, z2)=xγz2φ with γN1 and φb0.

However, we should point out that some minimum level of wetlands is necessary to beeffective at controlling runoff (Crumpton et al., 2008).

5 More fertilizer could lead to reductions in the ancillary benefits from wetlands(Ethridge and Olson, 1992; Knight, 1997), but for simplicity, the model does notaccount for this possible effect. We also avoid the implications about perceived costs ofwetlands due to various placement options (e.g., Gelso et al., 2008).

6 The underlying presumption with this type of research is that there is a sum ofmoney the government can use to finance the subsidy without impacting socialwelfare. In effect, we implicitly assume a set of lump sum taxes that are non-distortionary that help to finance public expenditures including externality-correctingsubsidies.

runoff reductions over emissions reductions. Using Eqs. (4) and (5),ancillary benefits have implications on fertilizer use since π̂x/rx=(π̂z2+Az2)/rz2. Larger ancillary benefits require higher marginal benefits offertilizer, π̂x, or lower marginal runoff, rx, which are both achieved atlower fertilizer applications.

3.1. Water quality trading

In a nutrient market, the regulator issues a given number ofpollution allowances and allocates them among the different sources.Sources cannot emit more pollution than the number of allowancesthey hold but they can buy (or sell) allowances in the pollutionmarket. When pollution is not perfectly mixed, as in our case, it hasbeen established that the regulator should also introduce a tradingratio, t, or a rate at which sources are allowed to trade their emissions(Tietenberg, 2006). Following existing water quality trading markets,we assume that all allowances are given to the farm and none to theMS4 (e.g., see Horan and Shortle, 2005). If the MS4 emits e units ofpollution, it should purchase et allowances from the farm. The profitfunction of the MS4 is thus given by B(e)=b(e)−pret where pr is theprevailingmarket price of pollution allowances, i.e., runoff reductions.The first order condition of maximizing the firm's benefits is:

be−prt = 0: ð6Þ

The profit function of the farmer can be represented by:

Π̂ = π̂ðx; z2Þ + pr ½r̂ 0−rðx; z2Þ� + sz2 ð7Þ

where r̂0 represents the total number of allowances given to the farmand r̂0− r(x,z2) is runoff abatement. Although there are a number ofapproaches to internalize the ancillary benefits of wetlands, we use aper acre subsidy for wetlands, s, that is determined by the regulator. Ineffect, the subsidy reduces the private cost borne by the farmerthereby making wetlands relatively more attractive to him as anutrient runoff reducing management practice.

The first order conditions for optimal input usage are:

∂Π̂∂x = π̂x−prrx = 0 ð8aÞ

∂Π̂∂z2

= π̂z2−prrz2 + s = 0: ð8bÞ

The farmer will choose abatement technology to minimize costssuch that the marginal control costs are equal to the marginal revenuegenerated. Conditions (8a) and (8b) provide insight into the gains andlosses the farmer faceswhen participating in the cropmarket andwaterquality tradingmarket given the allocable input and nonallocable input.Land for abatement, z2, must be chosen so that the gain in the nutrientmarket of converting land from z1 to z2 is equal to the lost value in thecrop market plus the subsidy. For the polluting input x, condition (8a)requires that the farmer balance themarginal benefits from fertilizer (interms of the decrease in abatement costs) with the marginal costs (interms of the lost opportunities in the nutrient market).

The optimal trading ratio can be obtained by manipulating theprivate optimal conditions (6), (8a) and (8b) to obtain:

beπ̂x = rx

= t ð9Þ

beðπ̂z2 + sÞ = rz2

= t: ð10Þ

Comparing condition (9) with condition (4), it is clear that theoptimal trading ratio should be t=De(e*,r*)/Dr(e*,r*), where e⁎ and r⁎

1991M.T. Heberling et al. / Ecological Economics 69 (2010) 1988–1994

are the socially optimal levels of emissions and runoff frommaximizing Eq. (3). Further, in order for Eq. (10) to match thesocially optimal condition given by Eq. (5), the wetland subsidyshould equal themarginal benefits of wetlands, that is s=Az2(z2⁎). Theoptimal level of wetlands, z2⁎, is greater than 0 provided that thebenefits of wetlands are large enough to induce an interior solution.Thus, when the ancillary benefits provided by wetlands are accountedfor through a subsidy, the optimal trading ratio takes its traditionalform where the objective is to induce exchange of pollution that hasequivalent environmental impact rather than raw exchange ofpollution (Montgomery, 1972; Tietenberg, 2006). (For an in-depthstudy of second best trading ratios, see Horan et al., 2004). Holding allelse constant, a larger subsidy (or a higher marginal ancillary benefit)will also lead to a situation where firms need not purchase as manypermits to cover their emissions. Finally, the regulator should issuethe optimal number of allowances, that is r̂0= r(x⁎,z2⁎)+ te⁎.

3.2. Comparative statics

In this section, we study how a wetland subsidy, based on theproposal of Raffini and Robertson (2005), changes the farmer'sbehavior within the water quality trading program, ceteris paribus.In particular, we want to examine how a marginal increase in thesubsidy will affect wetland acres, fertilizer use and the supply ofrunoff abatement. The farm's optimal input choice given exogenousprices, can be represented as x(py, pr,wx,wz,s) and z2(py,pr,wx,wz,s).Substituting these expressions in optimal conditions (8a) and (8b) weobtain:

π̂xðxð·Þ; z2ð·ÞÞ−prrxðxð·Þ; z2ð·ÞÞ = 0 ð11Þ

π̂z2ðxð·Þ; z2ð·ÞÞ−prrz2ðxð·Þ; z2ð·ÞÞ + s = 0: ð12Þ

Differentiating with respect to the subsidy and using Cramer's Rule(see Appendix A), we find the sign for the change in wetlands is givenby:

∂z2ðpy;pr;wx;wz; sÞ∂s = ð−1Þðπ̂xx−prrxxÞ N 0: ð13Þ

In particular, since π̂xxb0 and prrxxN0, Eq. (13) confirms that thewetland subsidy increases wetland area, as expected. Next, weexamine how fertilizer use will change given the subsidy on wetlands

∂xðpy;pr;wx;wz; sÞ∂s = ðπ̂xz2−prrxz2Þ?0 ð14Þ

where the questionmark denotes an indeterminate sign. Althoughwecannot readily sign this expression, its general structure is veryintuitive. It shows how the fertilizer allocation rule changes inEq. (8a), due to an increase in wetland area, as seen in Eq. (13).Because the farmer participates in two markets, we have to examinethe cross-partials in both the crop market and the nutrient market.Note that π̂xz2=pyYxz1(−1)b0 given the assumption Yxz1N0. Withrxz2b0, there are two counteracting effects present in Eq. (14). Thedecrease in cropland demands less fertilizer use, due to thecomplementarities of these factors in crop production. At the sametime, the farmer also has an incentive to use more fertilizer since alarger share of runoff will be trapped in thewetlands and the foregonebenefits in the runoff market due to fertilizer usage are reduced.7 Inthis sense, the wetland subsidy has the same effect of a subsidy onfertilizer. The total change in fertilizer use is ambiguous and dependson which cross-partial is dominant.

7 One may also think of runoff exports as an input in production. In order to producecrops, some runoff is necesessary. The wetland subsidy reduces the burden related tothis input, so incentives to use it more intensely are provided.

Since less land is allocated to crops, there is a clear incentive to useless fertilizer in production. The extent to which this may swamp theeffects in the water quality trading market depends on specificcircumstances. Specifically, note that an increase in wetland areareduces the associated costs of fertilizer use in the water qualitytrading market by prrz2 since rz2b0. An important incentive fornutrient application emerges if two conditions are satisfied. First, thenewly implemented wetlands must be particularly effective (rz2bb0).According to Crumpton et al. (2008), there are two main factors thatdetermine how effective wetlands are at reducing nutrients: a)position in the landscape to capture significant loads and b) adequatesize to retain nutrients for an appropriate time. Second, the price ofrunoff pr must be relatively large. This presumption may not berealistic if many farms participating in the water quality tradingmarket drive prices down through competition.

We now turn to determine how runoff changes throughsubsidizing wetlands. Differentiating the optimal runoff with respectto the subsidy, we have

∂r∂s = rx

∂xðpy;pr ;wx;wz; sÞ∂s + rz2

∂z2ðpy;pr;wx;wz; sÞ∂s ?0: ð15Þ

Condition (15) depends on both conditions (13) and (14) and themarginal productivities of fertilizer and wetlands in the production ofrunoff. Thus, the change in the supply of runoff abatement in the nutrientmarket due to amarginal increase in the subsidy ∂(r̂0−r)/∂s=−∂r/∂s isundetermined. A scenario in which the wetland subsidy increases runoffproduction is therefore possible. As we attempt to answer the questionregarding how to incentivize the use of wetlands in a water qualitytrading program, to understand condition (15), we need farm specificdata on the production functions for runoff, crops, and wetland services.

3.3. The unconstrained land case

Farmland area has been assumed constrained or fixed in themodelto this point. This assumption is realistic in short-run analyses whereland is a sunk cost and also in circumstances where the area of land inthewatershed that can be allocated to agriculture and/or wetlands is alimiting factor (e.g., see Taylor and Kalaitzandonakes, 1990; Leathers,1992). In the long run, however, land is not fixed and both croplandarea and wetland area are two separate choice variables. In somelocations, farmers could easily expand crop production by using lessproductive idle lands or changing uses from grassland pasture. Thefarm's profit function in this case is given by Eq. (1) instead of π̂(x,z2).To derive the social optimum and study the water quality tradingmarket and wetland subsidy, we follow a similar procedure to thatpresented above. From the analytical viewpoint, the only differencebetween the constrained and unconstrained problems is that farmingentails three, instead of two, choice variables. It can be shown that theexpressions for the optimal subsidy, the trading ratio, and the numberof allowances derived for the land constrained problem hold for theunconstrained one.When looking closer into the effects of the subsidyon the water quality trading market some new insights emerge (seeAppendix B for detailed comparative statics for the unconstrainedland problem). A marginal increase in the subsidy increases thewetland area, fertilizer usage, and cropland area. While morewetlands reduce runoff, more fertilizer usage increases it, and thenet effect is ambiguous. As mentioned earlier, the wetland subsidydoes not only incentivize wetland creation, but it also acts like asubsidy on fertilizer usage. Since fertilizer and cropland are techni-cally complements, the subsidy is also an incentive to expand thecropland area. This result is particularly sensitive since the wetlandsubsidy can actually induce the loss of other lands (e.g., forested landsor encourage farmers to move marginal lands into production) incertain areas. Therefore, it may limit programs that encourage the

1992 M.T. Heberling et al. / Ecological Economics 69 (2010) 1988–1994

retirement of marginal lands, like the Conservation Reserve Program.Based on the assumptions used in themodel and the results presentedabove, Eq. (16) reveals that the effect of the subsidy on runoff (andrunoff abatement) is undetermined.

∂r∂s = rx

∂xðpy; pr ;wx;wz2; sÞ∂s + rz2

∂z2ðpy;pr ;wx;wz2; sÞ∂s ?0 ð16Þ

Finally, while we have focused on changes in a wetland subsidyhere, the reader should keep in mind that the supply of runoffabatement also depends on other policy variables such as the numberof permits and the trading radio.

4. Discussion and conclusions

Using an economic model of water quality trading, we haveaddressed the question of whether a policy maker could encouragethe use of a particular pollution control technology through a subsidy.The idea to incentivize wetland abatement technology is linkeddirectly to the existence of ancillary benefits. We find that thisparticular approach can lead to an efficient result and increase the useof wetlands, but it also may lead to some unintended outcomes.Because a change in the crop market has impacts in the nutrientmarket and vice versa, (i.e., a small increase in wetlands reduces cropproduction, but increases nutrient control and a small increase infertilizer increases crop production, but also increases runoff), thefinal outcome in the water quality trading program depends on howthe factors are interrelated in each market. Although the subsidy willincrease the use of wetlands, we cannot confirm how the farmer'sbehavior might change in terms of fertilizer use or how runoffultimately will be affected by the subsidy.

In particular, when the farm area is fixed, wetland subsidiesdecrease cropland area. Since cropland and fertilizers are comple-ments, the incentives to use fertilizer are reduced. On the other hand,the fact that farmers may use more fertilizer because wetlands abatenutrients is somewhat unexpected. A wetland subsidy reduces theopportunity cost of fertilizer use in the water quality market, and this,indirectly, makes farming more profitable. By the same token, whenthe farm area is not constrained, a wetland subsidy may havepervasive effects on how the farmer uses other lands, such as forestedland. Given the assumptions in the model, the subsidy on ancillarywetland services encourages the farmer to expand the cropland areaand to increase fertilizer use. The change in runoff will depend on therelative effectiveness of wetlands as nutrient sinks.

The results of our model suggest that wetland subsidies are morelikely to induce expansion of water quality trading, while alsoreducing the risks to forested and other lands where cropland areais already constrained in a particular watershed. This constraint(referring to our initial assumption of fixed land area, z ̅) may occurdue to natural, economic, or legal factors. In somewatersheds, like themidwest of the US, for instance, farming is already the predominantland use and there is little to no room for further expansion. Forexample, Lubowski et al. (2006) finds that 58% of total land in the CornBelt Region (Illinois, Indiana, Iowa, Missouri, and Ohio) is in croplandcompared to 12% in the Northeast Region (Maryland and statesnorth). In some regions, the use of land might have already beendetermined by law, although this may be susceptible to politicalpressure and changes in the future. It is very important toacknowledge differences across regions and watersheds whenformulating such joint policies. Making subsidy eligibility conditionalon limiting farmland expansion can be a feasible arrangement worthexploring. The particulars of this, and other mechanisms, will dependon relevant socio-economic, ecological and institutional factors.

Our results ultimately depend on the actual abatement cost func-tion, pollution damage function, profit functions, and wetlandancillary benefit function. Requiring this type of information at the

farm level may limit the effectiveness of the proposal; it certainly isthe case that estimating the wetland values in one watershedmay notbe appropriately transferred to other watersheds (e.g., see Elbakidzeand McCarl, 2007).

Although we only discuss the wetland subsidy, other options couldavoid some of the problems related to the subsidy, but they may alsocreate new ones. For example, the producer of wetlands could sell thenutrient trading capacity of the wetland in the nutrient market(assuming it is the primary market) and sell the ancillary wetlandservices, like biodiversity credits, in other markets, should they exist.“Multiple markets” refers to the producer's ability to sell different typesof allowances or credits in different markets (Kieser and Associates,2004;Woodward andHan, 2004; ELI, 2005). Ifwell-functioningmarkets(as described earlier)were to exist for the different services provided bywetlands, the ancillary benefits would be accounted for and sold and noexternalities would exist (i.e., the benefits enter directly into the profit-maximizing decision). The incentive for constructing or restoringwetlands, then, becomes the additional income from trading in othermarkets. Remember, though, most nutrient markets are not well-functioning; creating other markets that have the right requirementswill prove challenging as well.

Regardless of the policy approach, the results of this researchhighlight the importance of considering all of the potential outcomesof using market mechanisms to address environmental problems(e.g., see Goulder and Parry, 2008). Understanding how the marketparticipants will behave is essential to developing policy or tradingrules. As this area of research matures and policy makers are aware ofand able to address the unintended incentives, the inclusion ofwetlands as a nutrient abatement technology in certain water qualitytrading programs appears desirable because of the ancillary benefitswetlands produce that other technologies will not. Economic theorywill not provide all of the information for choosing among thedifferent policy options; it will depend on many issues including legaland ecological issues. Therefore, future research will require amultidisciplinary approach that focuses on empirically measuringthe benefits and costs (e.g., land conversion and maintainingwetlands) of the many types of wetlands, including restored, created,or enhanced, across space and time and examining the potentialoutcomes of other options for incentivizing wetland use. Otherrecommendations for providing insight into market implicationsinclude focusing on the marginal rate of substitution betweenfertilizer and crop land across different crops, incorporating theeffects of stochastic events on runoff, and studying the relationshipbetween the wetland subsidy and the optimal trading ratio.

Acknowledgements

The views expressed herein are strictly the opinions of the authorsand in nomanner represent or reflect current or planned policy by theUSEPA. Jorge H. García would like to acknowledge that part of thisresearch was conducted under a postdoctoral research associateshipprovided by the National Academy of Sciences, National ResearchCouncil. We thank Jake Beaulieu, James Shortle, Marc Ribaudo, andtwo anonymous reviewers for insightful comments.

Appendix A. Comparative statics for the constrained land problem

Rewriting the farm's optimal conditions, Eqs. (11),(12), anddifferentiating with respect to the subsidy, s, we have:

∂xðpy;pr;wx;wz; sÞ∂s ðπ̂xx−prrxxÞ+

∂z2ðpy;pr;wx;wz; sÞ∂s ðπ̂xz2−prrxz2Þ = 0

ðA1Þ

1993M.T. Heberling et al. / Ecological Economics 69 (2010) 1988–1994

∂xðpy;pr ;wx; sÞ∂s ðπ̂z2x−prrz2xÞ+

∂z2ðpy;pr;wx; sÞ∂s ðπ̂z2z2−prrz2z2Þ+1 = 0:

ðA2Þ

Rewriting Eqs. (A1) and (A2) into matrix notation, we have

π̂xx−prrxx π̂xz2−prrxz2π̂z2x−prrz2x π̂z2z2−prrz2z2

� � ∂xðpy;pr ;wx;wz; sÞ= ∂s∂z2ðpy; pr ;wx;wz; sÞ= ∂s

� �= 0

−1

� �:

ðA3Þ

Let us denote the left hand matrix by D. Notice that this is thematrix of second derivatives of the objective function, П̂(x,z2). UsingCramer's Rule, we have:

∂xðpy;pr;wx;wz; sÞ∂s =

j 0 π̂xz2−prrxz2−1 π̂z2z2−prrz2z2

jjDj ðA4Þ

∂z2ðpy;pr;wx;wz; sÞ∂s =

j π̂xx−prrxx 0π̂z2x−prrz2x −1 j

jDj ðA5Þ

The second order conditions for a maximum require the secondprincipal minor of D be positive or |D|N0. The numerators thus definethe signs of Eqs. (A4) and (A5). The other second order condition isthat the first principal minor of D should be negative, that is π̂xx−pyrxxb0. It is easy to verify that this condition is met given theassumptions on π̂ and r.

Appendix B. Comparative statics for the unconstrainedland problem

The farm's profit functionwhen land is not fixed is given by Eq. (1),the profit in the nutrient market and the wetland subsidy. That is,

Πðx; z1; z2Þ = πðx; z1; z2Þ + pr½r̂ 0−rðx; z2Þ� + sz2: ðB1Þ

The first order conditions for a private optimum are:

∂Π∂x = πx−prrx = 0 ðB2Þ

∂Π∂z1

= πz1 = 0 ðB3Þ

∂Π∂z2

= πz2−prrz2 + s = 0: ðB4Þ

From these conditions, factor demand functions x(py,pr,wx,wz,s),z1(py,pr,wx,wz,s) and z2(py,pr,wx,wz,s) can be derived. Substitutingthese functions back into optimal conditions (B2)–(B4) anddifferentiating with respect to the subsidy, s, we obtain:

∂xðpy;pr;wx;wz; sÞ∂s ðπxx−prrxxÞ +

∂z1ðpy;pr;wx;wz; sÞ∂s ðπxz1Þ

+∂z2ðpy;pr ;wx;wz; sÞ

∂s ð−prrxz2Þ = 0

ðB5Þ

∂xðpy;pr;wx;wz; sÞ∂s ðπz1xÞ +

∂z1ðpy; pr ;wx;wz; sÞ∂s ðπz1z1Þ = 0 ðB6Þ

∂xðpy;pr;wx;wz; sÞ∂s ð−prrz2xÞ +

∂z2ðpy; pr ;wx;wz; sÞ∂s ð−prrz2z2Þ = −1:

ðB7Þ

Rewriting these equations into matrix notation gives

πxx−prrxx πxz1 −prrxz2πz1x πz1z1 0

−prrz2x 0 −prrz2z2

0@

1A ∂xðpy;pr ;wx;wz; sÞ= ∂s

∂z1ðpy;pr ;wx;wz; sÞ= ∂s∂z2ðpy;pr ;wx;wz; sÞ= ∂s

0B@

1CA =

00−1

0@

1A:

ðB8Þ

The left hand side is the matrix of second derivatives of theobjective function Π(x,z1,z2) and we denote it as D′. Using Cramer'sRule, the solution of this linear system of equations is given by:

∂xðpy;pr;wx;wz; sÞ∂s =

j 0 πxz1 −prrxz20 πz1z1 0−1 0 −prrz2z2

jjD′j ðB9Þ

∂z1ðpy;pr;wx;wz; sÞ∂s =

jπxx−prrxx 0 −prrxz2πz1x 0 0

−prrz2x −1 −prrz2z2j

jD′j ðB10Þ

∂z2ðpy;pr;wx;wz; sÞ∂s =

jπxx−prrxx πxz1 0πz1x πz1z1 0

−prrz2x 0 −1 jjD′j : ðB11Þ

The signs of the expressions above are:

∂xðpy;pr;wx;wz; sÞ∂s =

−prrxz2πz1z1

jD′j N 0 ðB12Þ

∂z1ðpy;pr;wx;wz; sÞ∂s =

−prrxz2ð−πz1xÞjD′j N 0 ðB13Þ

∂z2ðpy;pr;wx;wz; sÞ∂s =

ð−1Þ½ðπxx−prrxxÞðπz1z1Þ−π2xz1�

jD′j N 0: ðB14Þ

Second order conditions for a maximum indicate that the thirdprincipalminor ofD′ is negative or |D′|b0. The signs of the numeratorsin Eqs. (B12) and (B13) are derived directly from the assumptions onthe farm's profit and runoff functions. The numerator in Eq. (B14) isequal to the negative of the second principal minor ofD′. We know thesecond principal minor should be positive in order to have amaximum; therefore, (B14) has a positive sign.

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