Targetng Conservaton Investments n Heterogeneous Landscapes: A dstance functon approach and applcaton to watershed management Water Polcy Workng Paper # 2002-011 Prepared by Paul J. Ferraro Andrew Young School of Polcy Studes Georga State Unversty * The author acknowledges the fnancal support of the Insttute for the Study of World Poltcs, the U.S. EPA STAR program, and the Resources for the Future Joseph Fsher Dssertaton Award. Thanks to Rchard Bosvert, Jon Conrad, Ron Cummngs, Andrew Keeler, Davd Lee, Krstn Rowles, Loren Tauer and semnar partcpants at Duke Unversty, Economc Research Servce (USDA), Georga State Unversty, Unversty of Central Florda, and Unversty of Colorado-Boulder for comments on earler drafts and presentatons.
Targetng Conservaton Investments n Heterogeneous Landscapes: a dstance functon approach and applcaton to watershed management Abstract To acheve a gven level of an envronmental amenty at least cost, decson-makers must ntegrate nformaton about spatally varable bophyscal and economc condtons. Although the bophyscal attrbutes that contrbute to supplyng an envronmental amenty are often known, the way n whch these attrbutes nteract to produce the amenty s often unknown. Gven the dffculty n convertng multple attrbutes nto a undmensonal physcal measure of an envronmental amenty (e.g., habtat qualty), analyses n the academc lterature tend to use a sngle bophyscal attrbute as a proxy for the envronmental amenty (e.g., speces rchness). A narrow focus on a sngle attrbute, however, fals to consder the full range of bophyscal attrbutes that are crtcal to the supply of an envronmental amenty. Drawng on the producton effcency lterature, we ntroduce an alternatve conservaton targetng approach that reles on dstance functons to cost-effcently allocate conservaton funds across a spatally heterogeneous landscape. An approach based on dstance functons has the advantage of not requrng a parametrc specfcaton of the amenty functon (or cost functon), but rather only requrng that the decson-maker dentfy mportant bophyscal and economc attrbutes. We apply the dstance-functon approach emprcally to an ncreasngly common, but lttle studed, conservaton ntatve: conservaton contractng for water qualty objectves. The contract portfolos derved from the dstance-functon applcaton have many desrable propertes, ncludng ntutve appeal, robust performance across plausble parametrc amenty measures, and the generaton of rankng measures that can be easly used by feld practtoners n complex decson-makng envronments that cannot be completely modeled.
I. Introducton Gven the dffculty of measurng envronmental benefts n currency, many economc analyses focus on achevng effcency wthout optmalty [Baumol and Oates 1988: 159]. To acheve a gven level of an envronmental amenty at least cost, decson-makers must ntegrate nformaton about spatally varable bophyscal and economc condtons. In the case of endangered speces conservaton, for example, prevous analyses have focused on maxmzng, subject to a budget constrant, bologcal dversty measures [Solow et al. 1993; Wetzman 1992, 1993, 1998], habtat prorty ndces [Balmford et al. 2000], or the total number of speces conserved [Ando et al., 1998; Montgomery 1995; Polasky and Solow 1995; Polasky et al. 1993, 2001]. In the case of the mult-bllon dollar U.S. Conservaton Reserve Program, Babcock et al. [1996, 1997] focused on separately maxmzng ndvdual proxes of envronmental amentes. Other studes have looked at the allocaton of scarce budgets n the cleanup of hazardous waste stes [Hamlton and Vscus 1999; Vscus and Hamlton 1999]. Most studes of cost-effcent conservaton polcy nterventons have tended to use a sngle bophyscal attrbute (e.g., speces absence or presence, genetc dssmlarty between speces, erodblty of sol, dstance to surface water) as a proxy for an envronmental amenty. A narrow focus on a sngle attrbute, however, fals to consder the full range of bophyscal attrbutes that are crtcal to the supply of an envronmental amenty [Noss 1990]. Most realworld conservaton ntatves, lke the U.S. Conservaton Reserve Program [USDA 1999] or World Wldlfe Fund s Global 200 ntatve [Olson et al. 2000], dentfy multple bophyscal attrbutes (or amentes) of nterest. The use of a sngle bophyscal attrbute as a proxy for an envronmental amenty s understandable gven that scentsts and practtoners often fnd t dffcult to convert multple 1
bophyscal attrbutes nto a sngle envronmental amenty measure. Parametrc envronmental amenty functons are usually absent or controversal. Although the bophyscal attrbutes that contrbute to supplyng an envronmental amenty lke water qualty are often known (e.g., rparan sol type, dranage area), the way n whch these attrbutes nteract to produce the amenty s often unknown. Based on ths observaton, we ntroduce an approach that reles on dstance functons to cost-effcently allocate conservaton funds across a spatally heterogeneous landscape. Dstance functons allow one to descrbe a mult-nput, mult-output producton technologes wthout the need to specfy a prce vector (.e., attrbute weghts) or a behavoral objectve on the part of the producton unt (n ths case, a parcel of land). They have been used n economcs for many decades [Shephard 1970], but have seen resurgence n recent years [e.g., Chambers et al. 1996, 1998; Chavas and Cox 1999; Färe and Grosskopf 1990, 1998, 2000; Lynch and Musser 2001]. An approach based on dstance functons has the advantage of not requrng parametrc specfcaton of an amenty functon (or a cost functon). The approach only requres that the decson-maker dentfy mportant bophyscal and economc attrbutes. We apply the dstance functon approach emprcally to an ncreasngly common, but lttle studed, conservaton ntatve: conservaton contractng for water qualty objectves. The contract portfolos derved from the dstance-functon applcaton have many desrable propertes, ncludng ntutve appeal, robust performance across plausble parametrc amenty measures, and the generaton of rankng measures that can be easly used by feld practtoners n complex decson-makng envronments that cannot be completely modeled. Although we focus on the case of multple bophyscal attrbutes, the approach easly generalzes to cases n whch parametrc amenty functons are known but a conservaton agent s nterested n multple 2
amentes (e.g., affectng land use to secure bodversty and water qualty benefts). Conner et al. [1995] have emphaszed that a narrow focus on a sngle amenty can also lead to costneffcent nterventons. In the context of targetng habtat protecton nterventons, Prendergast et al. [1999] noted that feld practtoners and polcymakers rarely use the tools and results that have been developed n the academc lterature. In large part, the tools and results are not adopted because they are not developed and appled wth the objectves and approaches of practtoners and polcymakers n mnd. In the emprcal applcaton of ths paper, we use data routnely avalable to decsonmakers and consder explctly the actual approaches used by decson-makers n the feld. We also approach the problem at the geographc scale at whch decsons are beng made;.e., ndvdual parcels rather than large admnstratve dstrcts or GIS polygons on the landscape. In the next secton, the conventonal approach to targetng conservaton nvestments s ntroduced. In secton III, the alternatve approach to targetng conservaton nvestments usng dstance functons s presented. In secton IV, the emprcal case study s descrbed and n secton V, the results from ths case are presented. In secton VI, other aspects of the dstance functon approach are explored. II. Conventonal Approach to Targetng Conservaton Investments In the presentaton of the conventonal approach to targetng land conservaton nvestments, we use the followng notaton: p = e = Share of parcel under conservaton contract (p = 1 f parcel s fully contracted) Envronmental beneft from parcel (a scalar; often an ndex value or a measure of a key objectve, such as reducton n tons of sedment) 3
c = t = D = Contract cost for parcel (prvate opportunty cost of conservaton) Transacton costs for a contract on parcel (e.g., legal fees, montorng) Contractng agency s budget As n prevous analyses, we make several assumptons. Frst, each parcel can ether generate net returns of c to the prvate landowner or envronmental benefts of e to the contractng agent (and the ctzens that t represents). Second, the unt of analyss s the parcel, and each parcel s assumed to be homogenous (heterogeneous parcels can be dvded nto homogenous sub-parcels, each wth dfferent values of e and c). To dentfy the cost-effcent land portfolo that gves maxmum envronmental benefts per dollar expended, the decson-maker wants to solve max p p s. t. e [1] p ( c + t ) D [2] 0 p 1 [3] Ths approach s the same as that used by Babcock et al. [1996; n Babcock et al., e s ether a measure of a sngle bophyscal attrbute or an ndex] and s smlar n sprt to the approaches used n targetng nvestments for speces conservaton (the latter are often modeled as maxmum coverage problems or as the maxmzaton of a dversty measure subject to a budget constrant). Other characterstcs of ths approach are dscussed n the appendx. The degree to whch a contractng agent can dentfy the true cost-effcent land portfolo va expressons [1]-[3] depends on the degree to whch envronmental benefts, e, are 4
measured accurately. 1 Many conservaton ntatves have multple objectves. For example, n the emprcal example of ths paper, the Cty of Syracuse wshes to reduce sedment, chemcal, pathogen and nutrent loadng nto ts water supply. Even f the Cty were able to measure the way n whch a conservaton contract mght decrease each of the pollutants on a partcular parcel, the way n whch the loadngs of these pollutants combne to affect the man objectve, drnkng water qualty, s unknown. As n the Syracuse case, feld-level practtoners are generally not able to estmate pollutant loadngs, much less how they nteract to affect water qualty. In most cases, decson-makers know only the bophyscal attrbutes that contrbute to the conservaton objectve. In the Syracuse case, for example, a panel of scentsts and polcymakers has agreed that fve bophyscal attrbutes of rparan land are mportant n contrbutng to ther polcy objectve, but the way n whch the attrbutes combne to affect water qualty s unknown (see Secton IV). In order to estmate the benefts from an ndvdual parcel, Syracuse polcymakers have done what many conservaton groups and academc scentsts have done: they created a beneft ndex for each parcel based on ts bophyscal attrbutes. Such ndces are most often constructed from weghted lnear functons of the attrbutes or by assgnment of ponts to each parcel based on ts bophyscal attrbutes or land uses. Scorng methods lke these are qute common n the academc lterature [e.g., Voogd 1983; Lemunyon and Glbert 1993], n federal agency gudelnes [e.g., USFWS 1982; Terrell et al. 1982; Allen 1983; McMahon 1983; Allen and Hoffman 1984; FDEP 1999], n water qualty protecton ntatves [e.g., Smth et al. 1995; Rowles and Stlnger 1999; MDC 1999; FDEP 2000], and n the mult-bllon dollar conservaton 1 We assume that contract cost uncertanty wll eventually be resolved through negotaton or an aucton-type mechansm. In crcumstances wthout a mechansm for all landowners to reveal smultaneously ther wllngness-toaccept a contract, uncertanty over costs can make the ex ante targetng decsons dffcult (.e., wth whom does one start negotatng?). We wll argue that the dstance functon-based targetng approach offers advantages n such crcumstances. 5
efforts of the U.S. Conservaton Reserve Program [Feather et al. 1998], land trusts [e.g., The Nature Conservancy; Master 1991], nternatonal habtat protecton groups [e.g., World Wldlfe Fund; Olson et al. 2000], natonal wldlfe protecton ntatves [e.g., Partners n Flght; Carter et al. 1999], and farmland protecton ntatves (e.g., Amercan Farmland Trust). Scorng functons, however, are hghly subjectve and may not capture decson-maker preferences very well. Psychologcal experments and smple everyday experence ndcate that dentfcaton of crtera weghts s complcated even for experts [e.g., Narasmhan and Vckery 1988; Borcherdng et al. 1993] and that smple lnear preference functons can fal to capture actual decson-maker preferences [Keeney and Raffa 1976]. As wll be shown n the emprcal example, there are often many plausble scorng functons for approxmatng envronmental amentes. Uncertanty about the true value of e can make t dffcult to choose the optmal land portfolo. In the next secton, we draw from the lterature n producton effcency analyss to develop an alternatve cost-effcent targetng approach that does not depend on a parametrc specfcaton of an envronmental amenty functon. III. Dstance-Functon Approach to Targetng Conservaton Investments In many conservaton ntatves, the bophyscal attrbutes that are mportant n contrbutng to the desred envronmental amenty are largely agreed upon by practtoners and advsng scentsts. However, the way n whch these attrbutes (e.g., rparan exposure, dranage area) combne to produce the desred objectves (e.g., reduced pathogen loadng) s not smply a source of dsagreement, but rather completely unknown n many crcumstances. Instead of tryng to approxmate the envronmental amentes from each parcel through a specfc functonal form, t may be more approprate to target parcels based on ther effcency n producng the 6
desred bophyscal attrbutes. Such an approach s partcularly reasonable n a conservaton contractng ntatve for water qualty gven that bophyscal attrbutes have been shown to characterze well the underlyng hydrologcal and ecologcal features of aquatc ecosystems [Jensen et al. 2001]. In any conservaton contractng ntatve, one wants to assess the desrablty of contractng one parcel relatve to contractng the other avalable parcels. To compare parcels, one can treat each parcel as a producton unt that converts nput -- the costs of conservaton contractng -- nto multple jont outputs -- the parcel s bophyscal attrbutes that contrbute to the conservaton goal. In such an approach to targetng, one s only concerned wth the ablty of a parcel to obtan maxmal jont output gven the cost of contractng for that parcel (one assumes that more of the desrable attrbutes s always better than less). 2 The productvty of a parcel n producng the desred bophyscal attrbutes gven ts contractng cost can be measured by an nput dstance functon. A land attrbute producton fronter s estmated through nonparametrc programmng methods that place a lnear, faceted concal hull (convex cone) over the observed land parcels n the nput-output space, such that all parcels ether le on the surface of the cone or beneath t. Parcels can be ranked on relatve costeffcency by consderng a mnmal reducton n the contract cost that, gven the vector of parcel attrbutes, projects the parcel onto the effcent fronter. The pecewse-lnear hull approach to fronter estmaton was proposed n the 1950s by Farrell [1957], but dd not become popular untl programmng methods were developed for multple output-nput cases [Charnes et al. 1978]. In the general case of K nputs and M outputs, we denote nputs by the non-negatve K M vector x = (x 1,x 2,,x K ) R and outputs by the non-negatve vector (y1,y 2,,y M ). In the + R + 2 If more nformaton s known about the relatve mportance of each characterstc, that nformaton can also be ncorporated. See Secton VI. 7
case of conservaton contractng, nputs are the costs of conservaton contractng (e.g., the contract payment, the montorng cost), 3 and outputs are the desrable bophyscal attrbutes secured by the contract for conservaton (e.g., dranage area). We denote the nput dstance functon as D I ( x, y) = max{ x S ρ 1 ρ :(, y) S} = (mn{ ρ :( ρx, y) }), [4] where S s the land attrbute technology that descrbes the transformaton of contractng nputs nto desrable land attrbutes;.e., S = {( x, y) : xcan produce y}. S s assumed to be a convex, closed set and nputs and outputs are freely dsposable (outputs are dsposable n the sense that partal parcel contractng s allowed). The dstance measure ρ s the factor by whch all nput quanttes could be decreased whle stll remanng wthn the feasble nput set for the gven output level. The dstance measure s () greater than or equal to one, () equal to one f and only f a parcel belongs to the fronter, and () non-decreasng n x and ncreasng n y. Shephard [1970] showed that the nput dstance functon s the dual of the cost functon. The dstance functon defned by [4] can be estmated by mathematcal programmng methods. There are a varety of ways to specfy the programmng model, but all seek to use a subset of the N parcels to determne parts of the producton fronter surface (normally constructed as pecewse lnear). 4 To be effcent, a parcel vector must le on ths surface. Parcels not on the surface are termed neffcent and the nput dstance metrc provdes a 3 If all costs are n dollar terms, the nput vector has only one element. One can, however, defne the vector more broadly to nclude costs about whch a contractng agency s concerned but whch cannot be easly converted nto a dollar fgure; for example, lost forestry jobs when old growth forest s protected from loggng. 4 In the operatons research lterature, methods that use Free Dsposal Hull, Convex Hull, Starwse Hull, and Convex Cone approaches often go under the name Data Envelopment Analyss. The term was coned by Charnes et al. (1978), although others had proposed the method earler (see Coell et al. 1998 for references). 8
summary measure of the neffcency, whch, n the conservaton contractng case, s the reducton n the contract cost requred to put the parcel on the effcent fronter. We use a pecewse-lnear concal hull approach to estmate the dstance functon: 1 ( ( x, y)) = mnθ st D I θ,λ y + Yλ 0 [6] θx Xλ 0 [7] λ 0 [8] where θ s a scalar, λ s an Nx1 vector of constants, X s a KxN matrx of contract costs, and Y s an MxN matrx of bophyscal attrbutes (or amentes, n the multple-amenty context). The value of θ obtaned wll be the effcency score for the -th parcel and corresponds to the nverse of the dstance measure n [4]. By mnmzng θ, one acheves maxmal movement toward the fronter through a proportonal reducton of nputs (.e., radal contracton of the nput vector). The contracton of the nput vector, x, produces the projected pont (Xλ,Yλ) on the fronter surface. Ths projected pont s a lnear combnaton of the observed data ponts. The constrants [6]-[8] ensure that the projected pont cannot le outsde of the feasble producton set. By constructon, θ wll be less than or equal to one, wth a value of one ndcatng that the parcel s on the fronter. The program s solved N tmes, once for each parcel, thereby obtanng a value of θ for each parcel. 5 The way n whch the dstance functon ranks land parcels on the bass of productvty s llustrated n Fgure 1, whch depcts the smple case of one desred bophyscal attrbute. In the fgure, the boundary of S s represented by the ray emanatng from the orgn and passng [5] 5 Most recent nonparametrc programmng applcatons that estmate producton fronters add an addtonal convexty constrant, N 1 λ = 1, n order to allow for varable returns to scale (Coell et al. 1998: 150). In the appendx, we explan why ths convex hull approach s not approprate for the case of targetng conservaton nvestments. 9
through the parcel wth coordnates (1, 2). The parcel at (1, 2) yelds a dstance measure of θ = 1 and s classfed as effcent. Ths parcel would be the most desrable for conservaton contractng. The remanng parcels, whch are not on the fronter, are classfed as neffcent and yeld a dstance measure that ndcates the mnmal reducton n contract cost requred to project the parcel onto the fronter. For example, the parcel wth coordnates (4, 3.6) can be projected onto the fronter f ts contract cost were reduced by a factor of (1-θ) = (1-0.45) = 0.55, or $1.62. The projected pont s therefore (1.98, 3.6), and θ = 0.45 ndcates that the parcel s 45% of the way to the fronter. Parcels are ranked for acquston from the hghest value of θ to the lowest. Dstance Functons and Parcel Rankngs Output (Stream Feet) 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 Input (Contractng Cost) Fgure 1. Dstance Functons and Parcel Rankngs To understand how parcel acquston prortes based on expressons [1]-[3] and [5]-[8] dffer when e s an ndex constructed from a weghted lnear equaton of attrbutes, consder the case of one nput, acquston cost n dollars, and two bophyscal attrbutes, X and Y. In order to 10
present ths case n two dmensons, we normalze the attrbutes to attrbute per dollar spent on acquston. Fgure 2 presents four parcels n the attrbute space. The straght lne through parcel A represents one possble weghtng scheme n the lnear scorng equaton. Wth ths scorng equaton, parcel A s chosen frst, parcel B second (the lne s smply shfted down untl t ntersects wth another parcel), parcel D thrd and parcel C fourth. Usng (output) dstance functons, a productvty fronter would be estmated (stylzed by curved lne) and parcels would be ranked dependng on ther dstance from the fronter. In ths case, parcel A and D would be consdered equally as valuable, parcel B would be ranked thrd, and parcel C would be ranked fourth (the dstance-functon approach essentally allows the weghts on each attrbute to change across parcels, thereby allowng each parcel to be seen n ts best lght). Y A B C D X Fgure 2. Weghted Lnear Scorng Equatons and Dstance Functons Rankngs 11
Unlke n the applcaton of nonparametrc programmng and dstance functons to the analyss of frm effcency, the standard assumptons mpled by the use of an nput dstance functon and a nonparametrc approach to estmatng the fronter are not a problem n the conservaton targetng context. Frst, the land attrbute producton technology characterzed by the dstance functon s truly a jont producton technology. Second, usng a radal dstance metrc n nput space, rather than a radal output metrc or non-radal metrc, 6 makes perfect sense n the context of conservaton contractng because land attrbutes are not changeable; the only dscretonary varable s the amount of money pad by the contractng agency. 7 By usng an nput-orented metrc, we also obtan an effcency measure that s useful to a conservaton agent that must negotate wth landowners: the dstance functon allows negotators to evaluate the change n a parcel s relatve rankng f the estmated contract cost changes durng ste vsts and negotaton (see Secton VI). A radal metrc also has the desrable property that the effcency measure s unts nvarant. In the next secton, we descrbe the case study n whch alternatve targetng approaches are emprcally evaluated. IV. Case Study: Lake Skaneateles Watershed Program The use of conservaton contracts to acheve water qualty objectves s becomng an ncreasngly popular polcy tool [Johnson et al. 2001]. For example, the New York Cty Watershed Management Plan wll spend $250 mllon on conservaton contractng wth prvate landowners n the Catskll-Delaware watershed over the next ten years to protect the Cty s water 6 Usng a concal hull approach, the estmated effcency measures are the same under the radal output and nput orentaton, but ther nterpretaton s dfferent. 7 If the landowner can change land attrbutes (e.g., reforestaton), one could construct a dfferent producton unt (.e., dfferent output and nput vectors) for each nterventon and compare each parcel-nterventon combnaton to every other parcel-nterventon combnaton. Wth the excepton of the case n whch a sngle parcel may defne the fronter under more than one of the avalable nterventons, one smply ranks parcels under each parcel s most productve nterventon. In the case of one parcel defnng the fronter under more than one nterventon, one would need to pck the fronter-defnng parcel s most desrable state usng other crtera. 12
supply and mantan ts fltraton waver from the Envronmental Protecton Agency [NRC 2000: 213-239]. Examples of other contractng ntatves for water qualty nclude North Carolna s $30 mllon Clean Water Management Trust Fund, Massachusetts s $80 mllon dollar effort to acqure rparan land to protect Boston s Wachusett Reservor, and Costa Rca s $16 mllon per year effort to secure conservaton contracts n, among other areas, the watersheds of muncpal water supples and hydroelectrc dams. In partcular, scentsts and polcymakers have dentfed the establshment of vegetated rparan zones that protect surface waters from nputs of nutrents, pestcdes, sedment and pathogens as an mportant polcy for mprovng surface water qualty [Tlman et al. 2001]. One such rparan buffer acquston ntatve s currently underway n upstate New York. The Cty of Syracuse (populaton 163,860) obtans ts drnkng water from Lake Skaneateles, whch s outsde of the Cty s regulatory jursdcton. The 16 mle-long lake has a 60 square mle watershed that covers three countes, seven townshps and one vllage. The populaton of the watershed s about 5000 resdents, concentrated largely n the northern half of the lake where the Cty s ntakes ppes are located. Land use s manly a mx of forest (40 percent) and agrcultural land (48 percent), on whch croppng and dary farmng are most common. The water from the lake s of exceptonally hgh qualty and the Cty, usng only dsnfecton by chlornaton, meets drnkng water standards wthout coagulaton or fltraton. 8 In recent years, however, the Cty has come under ncreasng pressure to consder fltraton n order to satsfy the provsons of the Envronmental Protecton Agency s (EPA) Surface Water Treatment Rule. In 1994, the Cty sgned a Memorandum of Agreement (MOA) wth the New York State Department of Health that allows the Cty to avod flterng water from the lake. The 8 An estmated 20-65 mllon Amercans drnk unfltered surface water [DeZyane 1990], ncludng ctzens n the ctes of New York, Boston and San Francsco. 13
MOA requres that the Cty commt to a long-term watershed management program to reduce pathogen, chemcal, nutrent and sedment loadng nto the lake. An mportant part of the management program s a conservaton easement acquston program through whch up to $5 mllon wll be spent over the next seven years (2001-2008) to secure easements on prvately owned rparan parcels. By securng easements on rparan buffers n the watershed, the Cty hopes to avod, or delay, the estmated $60-$70 mllon cost of a new fltraton plant. The Cty wants to allocate ts lmted budget across the watershed n a way that wll have the greatest effect on mantanng and mprovng water qualty n the lake [Meyers et al. 1998]. In the analyss, we focus on prortzng the acquston of easements from an avalable populaton of 202 rparan parcels n the upper watershed of Lake Skaneateles (see Fgure 3). Bophyscal and economc data on these parcels were obtaned from the Geographc Informaton Systems database of the Cty of Syracuse s Department of Water. The southwestern end of the lake s protected publc land and s thus excluded from the analyss. Data on parcels n the southeastern end of the lake were not avalable at the tme of analyss, but because these parcels are far from the Cty s ntake ppes, excludng them wll have only mnor effects on the fnal results. Beneft Data The Cty wshes to reduce sedment, chemcal, pathogen and nutrent loadng nto ts water supply. Sophstcated hydrologcal models, however, are not avalable for the Lake Skaneateles watershed. To measure the contrbuton of each parcel to the Cty s water qualty objectves, the Cty s Department of Water convened a scentfc panel to help t develop a parcel-scorng system based on known land attrbutes n the watershed [Myers et al. 1998]. The 14
panel developed two potental systems: an nterval-scale scorng equaton and a rato-scale scorng equaton. The equatons, whch are descrbed n the appendx, are weghted lnear functons of bophyscal attrbutes and assgn a score to each parcel; the hgher the score, the hgher the beneft from easement acquston. The panel dentfed fve bophyscal attrbutes that affect the Cty s water qualty objectves (see appendx). These fve attrbutes are combned n the lnear scorng equatons to generate a score, e, for each parcel that can then be used n the optmzaton approach n expressons [1]-[3]. We refer to ths optmzaton approach as the E-max approach (for envronmental score maxmzaton ). In the dstance-functon approach, whch we wll refer to as the Nonparam approach (for nonparametrc ), the fve attrbutes are treated as outputs and cost (easement and transacton) s treated as a sngle nput. We also derve easement portfolos under another parcel-scorng method for water qualty objectves: the Parcel-Pollutant-Weghtng (PPW) equaton [Azzano et al. 2002], whch s descrbed n the appendx. Cost Data A regonal apprasng company estmated that easements around Lake Skaneateles would cost between 40 percent and 60 percent of the assessed land value of a parcel [Gardner 2000]. In the analyss, we use 50 percent. A change n the percentage affects the number of parcels that can be acqured for a gven budget, not the order n whch the parcels are acqured. There were not enough observatons on sales of propertes wth easements n the regon to estmate a hedonc equaton of easement costs. Based on transacton cost nformaton from the local Fnger Lakes Land Trust, we also assume that there s a transacton cost of $5000/easement. 15
V. Results In ths secton, we examne two aspects of the performance of the dstance-functon approach: (1) the ways n whch the NonParam portfolo dffers from the portfolos derved usng the E-max approach under the three parcel-scorng methods; and (2) the total parcel scores generated by the dfferent portfolos when scored under each scorng method. The pont of ths latter exercse s to examne the robustness of the NonParam portfolo across plausble beneft measures;.e., what would be lost f a conservaton agent used the dstance-functon approach when, n fact, one of the scorng equatons was the true measure of parcel benefts? We begn wth an exploraton of the second aspect. For each scorng method, we calculate the total score generated by the parcel portfolo chosen usng the conventonal targetng approach emboded n expressons [1]-[3];.e., the E-max approach. A portfolo score s calculated at each of thrty-four budget levels, rangng from $0 to $11.8 mllon. The maxmum budget level s equvalent to enough money to buy rparan easements across the entre upper watershed, gven the assumed cost of contractng (.e., 202 = 1 ( c + t ) ). We refer to ths amount as the Total Watershed Cost. We refer to the sum of all parcel scores under a gven scorng method as the Total Watershed Beneft (.e., 202 e = 1 ). We also calculate the scores generated by the Nonparam portfolo at each budget level. 9 Fgure 4 llustrates the results for the nterval-scale scorng equaton. The x-axs represents the budget levels n percent of the Total Watershed Cost. The y-axs represents the envronmental benefts acheved as a percentage of the Total Watershed Beneft. By defnton, 9 Eght parcels le on the fronter and are equally effcent (θ =1), but these parcels cost only $135,050, whch s less than the frst budget level used n the analyss. Thus there was no need to resort to other crtera to dscrmnate among the effcent parcels. 16
the E-max approach acheves the maxmum score per dollar expended, and thus ts curve s on the outsde. The Nonparam portfolo curve tracks the E-max curve qute closely. For example, wth a budget of about $2.7 mllon, the E-max approach acheves 62% of the total watershed benefts, whle the NonParam approach acheves 51%. Under a budget of about $5 mllon, the E-max approach acheves 85% of the total benefts, whle the NonParam approach acheves 84%. % Total Watershed Beneft 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % Total Watershed Cost Emax NonParam Fgure 4 Portfolo Performance (Interval-Scale Scorng Equaton) Rather than present the correspondng fgures for each scorng method and then pck out specfc budget ponts for llustratve purposes, we consder the performance dfferences between the two approaches by comparng the areas under the curves and above the 45 lne n each fgure [Babcock et al. 1996]. If F(B) s the fracton of the Total Watershed Beneft acheved wth the 17
expendture of B, then one wants to calculate = 1 1 A F( B) db. For each parcel-scorng 0 2 method, we estmate an area equal to 2A by usng trapezods at each of the thrty-four budget ntervals. The greater the dfference between 2A under the E-max curve and the equvalent area under the NonParam curve, the greater the loss of effcency f the parametrc scorng-equaton were accurate and one chose the NonParam portfolo rather than the E-max portfolo. The same areas are also calculated for the portfolos derved usng the other scorng methods; e.g., the E- max portfolo selected usng the rato-scale equaton s scored wth the nterval-scale equaton and compared to the E-max portfolo selected usng the nterval-scale equaton. Ths emprcal exercse s smlar to the exercse one mght do when comparng parametrc and nonparametrc statstcal tests; one wants to know the effcency loss from choosng a nonparametrc or erroneous parametrc procedure when n fact the underlyng populaton was of a partcular parametrc form. The areas under the curves are lsted n Table 1. The data n the table answers the queston, What f one were to choose a portfolo based on one beneft measure, when another beneft measure s more accurate? For example, under the nterval-scale scorng equaton, the area under the E-max curve s 0.55, whle the area under the NonParam curve s 0.48, ndcatng that there s about a 12% overall loss n effcency f one were to choose the NonParam portfolo when, n fact, the nterval-scale scorng equaton s the correct way to measure parcel benefts. If, however, the nterval-scale scorng equaton were the most accurate way to measure benefts (Area = 0.55) but one nstead chose the portfolo derved under the rato-scale scorng equaton (Area = 0.37), there would be a 33% overall loss n effcency. By vrtue of the dstance-functon approach s ablty to acheve maxmal attrbutes at mnmal cost, the cost-effcency of the NonParam portfolo s robust across scorng functons. In contrast, an E-max portfolo chosen 18
under one scorng method may not reman cost-effcent f ts parcels true values are reflected best by another method. 10 Table 1 Portfolo Performances under Alternatve Beneft Measures Areas Under Portfolo Curves n Beneft-Cost Space Portfolo Interval-Scale Rato-Scale PPW Interval-Scale 0.55 0.57 0.47 % E-max 100% 87% 72% Rato-Scale 0.37 0.65 0.48 % E-max 67% 100% 74% PPW 0.35 0.54 0.65 % E-max 64% 83% 100% NonParam 0.48 0.57 0.57 % E-max 88% 87% 87% More nsghts nto the relatve performances of the dfferent portfolos can be obtaned by comparng the desrable bophyscal attrbutes secured by each portfolo at a gven budget level. The Cty of Syracuse plans to spend $1 - $2.5 mllon dollars and then evaluate whether further easement acqustons are requred. For purposes of llustraton, we choose a budget of $2.5 mllon and summarze the portfolo characterstcs n Table 2. The qualtatve results are mantaned over all budget levels (they are more dramatc as the budget approaches zero, and less dramatc as the budget approaches $11.8 mllon). In each attrbute category except one, the 10 The nterval-scale portfolo performs well when scored under the rato-scale equaton because (1) the parcel scores under each equaton are strongly postvely correlated (ρ = 0.96), and (2) the rato-scale equaton scores almost onequarter of the parcels as zero (no beneft from an easement). These two factors make t relatvely easy for the nterval-scale portfolo to perform well when scored by the rato-scale equaton. 19
NonParam portfolo domnates the other portfolos. The parcels n the NonParam portfolo are farther on average from the Cty s water ntake ppes. Table 2 - Portfolo Characterstcs Budget = $2.5 mllon Acres of Acres of 100-ft HSL Buffer Average Dstance to Intake Ppes (mles) Stream Total Number of Portfolo Exposure (ft.) Acreage Parcels Interval- Scale 177,310 3034 1041 398 2.0 112.5 Rato-Scale 185,509 3309 1134 422 1.8 86.9 PPW 179,741 3920 1092 417 2.0 71.0 NonParam 205,722 4112 1193 470 2.4 84.7 Maxmum Possble 228,961 4204 1285 513 1.6 (mnmum) The NonParam portfolo performs best n obtanng stream exposure, total acreage and acres of hydrologcally senstve land (HSL) and worst n obtanng nearby parcels because stream exposure, total acreage and acres of HSL are postvely spatally correlated (ρ [0.55, 0.72]) and they are negatvely correlated wth dstance to ntake. Furthermore, the spatal varabltes of stream exposure, acres and acres of HSL are smlar (Gn coeffcents of 0.44, 0.59 and 0.41, respectvely), whle the spatal varablty of dstance to ntake s hgher (Gn coeffcent of 0.65;.e., more spatally concentrated). Smulatons wth artfcally generated landscapes of two bophyscal attrbutes (see appendx for detals) suggest that the NonParam portfolo performs best when correlatons are postve and spatal heterogenety s low, and that dfferences n spatal heterogenety among the attrbutes have a greater effect on performance than do the correlatons among attrbutes. When one attrbute has low varablty and another has hgh varablty, the effects on dstance-functon performance are ntensfed: the dstance-functon portfolo performs even better n obtanng the 20
low varablty attrbutes and even worse n obtanng the hgh varablty attrbutes. Gven the moderate to hgh spatal varablty of the desred bophyscal attrbutes n the Lake Skaneateles watershed (whch reduces the performance of the dstance-functon approach), the robust performance of the NonParam portfolo suggests that the dstance-functon approach to targetng conservaton nvestments may perform equally as well n other conservaton contexts. VI. Other Advantages of the Dstance-Functon Targetng Approach Despte decades of research on conservaton targetng, manly by bologsts, Prendergast et al. observed that practtoners had not adopted sophstcated targetng methods. They argued that practtoners often have a general antpathy toward what s seen as a prescrptve approach to conservaton.(p.484). The E-max approach n expresson [1]-[3] tends to generate results that practtoners perceve as too prescrptve, and t does not allow practtoners to easly compare parcels relatve to one another. The E-max approach generates rankngs n unts of parcel benefts dvded by contract cost, a measure not easly nterpreted when the parcel beneft s an artfcal ndex. In contrast, the dstance functon approach generates rankngs n terms of contract costs, whch are more easly understood. Moreover, the concept of maxmzng artfcal ndex numbers s not easly communcated, whereas the concept of tryng to obtan as many of the desrable bophyscal attrbutes as possble gven a fxed budget s clearer. Furthermore, the dstance measures allow for more ntutve categorzatons of parcels by comparng all parcels to a reference set of effcent parcels. The dstance functon approach also has advantages n conservaton ntatves lke the Lake Skaneateles program, n whch no mechansm exsts to smultaneously elct all landowners offer prces for acceptng a conservaton contract on ther land (e.g., a procurement 21
aucton). Conservaton practtoners often use two cost dscovery methods: (1) wat for a landowner to express nterest n a conservaton contract and then negotate over the contract prce (often the approach used by land trusts); or (2) estmate ex ante the lkely wllngness-toaccept of each landowner and then negotate wth landowners sequentally by parcel rank. Thus, practtoners need a way of assessng the mplcatons of new nformaton on contract costs wthout havng to contnually update and re-solve a programmng model. We argue that the output from the dstance-functon approach s easer for practtoners to adapt n the feld and wll lead to more accurate conservaton targetng. Assume, for example, that the contractng budget s $2.5 mllon and Parcel 002-04 s n both the E-max nterval-scale portfolo and the NonParam portfolo. A rparan easement on the parcel s estmated to cost $12,000. After negotatng wth the landowner, the contractng agent dscovers that the contract cost s hgher than orgnally estmated. To consder the effect of a contract cost change n the E-max approach, the contractng agent must mnmze the portfolo contractng cost subject to a portfolo total score target n order to derve the allowable ncreases and decreases n contract cost under whch the current bass remans optmal. The mnmzaton suggests that contract cost could ncrease by as much as $15,985 wthout a change n the optmal bass. Usng the dstance functon approach, the contractng agent would know that Parcel 002-04 s 96% of the way to the fronter (θ = 0.96). Through smple arthmetc, 11 the agent can calculate that f the contract cost of Parcel 002-04 were to ncrease by $15,985, the parcel would shft to about 41% of the way to the fronter. In ths case, ten other parcels that formerly were not part of the soluton would have hgher effcency scores and would be consdered preferable 11 Dvde the parcel s target cost of (0.96*$12,000) = $11,520 by the new contract cost of $27,985. 22
to Parcel 002-04. When more than one contract cost changes, the ease wth whch relatve rankngs can be updated usng the dstance functon approach s even more mportant. 12 A nonparametrc programmng approach to targetng has the advantage that only the bophyscal attrbutes of the landscape need be consdered. Knowledge about the way n whch the attrbutes combne to produce the desred envronmental amentes s not needed. A pror knowledge about the relatve mportance of the dfferent attrbutes n contrbutng to the envronmental objectve can, however, be ncorporated nto the nonparametrc approach through constrants on the multplers n [5]-[8], whch are currently only restrcted to be non-negatve. Restrctons on the multplers wll alter the surface of the fronter and thus alter the estmated effcences of the parcels. Proposed technques for mplementng multpler restrctons nclude placng upper and lower bounds on ndvdual multplers [Dyson and Thanassouls 1988; Roll et al. 1991]; mposng bounds on the rato of multplers; appendng multpler nequaltes [Wong and Beasley 1990]; and requrng multplers to belong to gven closed cones [Charnes et al. 1989, 1990]. VII. Concluson Polcymakers and conservaton practtoners throughout the world seek flexble tools to ntegrate spatally heterogeneous bophyscal and economc data nto cost-effcent conservaton plans. In ths paper, we recognze the dffculty assocated n estmatng the envronmental amentes provded by a unt of land. We argue that there s often greater certanty about whch 12 Ths statement assumes that no parcel s prce decreases enough to greatly transform the surface of the fronter. Such a transformaton s most lkely to occur wth changes n contract costs for parcels found close to the fronter and near the area of ncreasng returns to scale on a convex hull over the data. It s n ths area of the attrbute-cost space that small absolute changes n contract costs can have a large mpact on a parcel s relatve poston n attrbute-cost space. The parcels n such areas can easly be dentfed ex ante through a modfcaton of the orgnal programmng model. 23
bophyscal land attrbutes contrbute to supplyng an envronmental amenty than there s about the way n whch these attrbutes combne to produce the amenty. Based on ths observaton, we ntroduce an alternatve, nonparametrc dstance functon-based method for ncorporatng bophyscal and economc data to mprove the targetng of conservaton nvestments. We emprcally compare dfferent conservaton targetng approaches by usng GIS data from a rparan easement contractng ntatve n upstate New York. In ths emprcal applcaton, we use data avalable to decson-makers, explctly consder actual approaches used by decson-makers, and approach the problem at the geographc scale at whch decsons are beng made. We demonstrate that n the absence of a wdely agreed upon specfcaton for an envronmental amenty functon, polcymakers may do well to consder a non-parametrc dstance functon-based approach to conservaton targetng. The land portfolos generated by the dstance-functon applcaton have many desrable propertes, ncludng ntutve appeal, robust performance across plausble parametrc amenty measures, and the generaton of rankng measures that can be easly used and manpulated by feld practtoners. Although we apply the dstance-functon approach to the case of rparan land contractng for water qualty objectves, the approach can be used for any conservaton ntatve. For example, conservaton practtoners nterested n habtat conservaton may dentfy speces dversty, habtat sze, genetc dssmlarty ndces of crtcal speces, and dstance from protected areas as key habtat attrbutes. The way n whch these attrbutes combne to produce habtat qualty s unknown. A reasonable conservaton approach would thus be to maxmze the jont output of these attrbutes subject to the cost of securng them. 13 Even n cases n whch specfc functonal forms are known for key envronmental objectves (e.g., a sedment loadng 13 Issues assocated wth substtutablty and complementarty among parcels, however, may be complcated to ncorporate nto the dstance-functon approach wthout specfyng all of the possble combnatons. More research on ths aspect of conservaton nvestment targetng s needed. 24
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