Integrating Farmer Decision-Making to Target Land Retirement Programs

Transcription

1 Paper Selected for Presentaton at the 2003 AAEA Annual Meetng, July 27-30, Montreal, Quebec Integratng Farmer Decson-Makng to Target Land Retrement Programs Wanhong Yang 1 and Murat Isk 2 1. Assstant Professor, Department of Geography, Unversty of Guelph, 2. Assocate Scentst, Center for Agrcultural and Rural Development, Iowa State Unversty,. All correspondence should be addressed to Wanhong Yang, Department of Geography, Unversty of Guelph, Guelph, Ontaro, Canada N1G 2W1; Tel: Ext Fax: Emal: wayang@uoguelph.ca May 6, 2003 Copyrght 2003 by Yang and Isk. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on such copes.

2 Integratng Farmer Decson-Makng to Target Land Retrement Programs Abstract Ths paper develops a model to examne the mpacts of uncertanty about crop producton and rreversblty of program partcpaton on determnng land rental payments and least-cost land retrement targetng n the Conservaton Reserve Enhancement Program. Results show that under rsk averson only, the margnal cost of abatement and the average land rental payment are less than those under rsk neutralty. However, under uncertanty and rreversblty, the margnal cost and the average land rental payment are consderably hgher than those under rsk neutralty or rsk averson only. It s mportant to ncorporate uncertanty and rreversblty nto the desgn of land rental payments and n determnng partcpaton constrants. Key Words: land retrement, CREP, rreversble decson, rental payments, targetng, uncertanty. 1

3 I. Introducton Snce md-1990s the Conservaton Reserve Program (CRP) has gradually movng towards a multfaceted envronmental mprovement program through the ntroducton of an envronmental beneft ndex (EBI) 1 (USDA 1997). Wth a bddng system, the CRP targets the retrement of cropland that exhbts hgh envronmental benefts relatve to economc costs (Feather, Hellersten and Hansen). In addton, the contnuous CRP and the Conservaton Reserve Enhancement Program (CREP) have been establshed to encourage land retrement for specfc conservaton practces such as flter strps and rparan buffers, and n areas of envronmental sgnfcance 2. The contnuous CRP and the CREP accept submtted contracts as long as the contracts address mportant conservaton needs such as proposng conservaton practces on the land to be retred or locatng n the program defnton area. Furthermore, ample program payments ncludng sol rental payments and addtonal ncentve payments are provded to encourage program partcpaton (Smth). As a result, program payments n the contnuous CRP and the CREP are hgher than those of the regular CRP and local cash rental rates. For example, n Illnos, the average CREP payment from 1998 to 2002 was $158 per acre n contrast to the average local cash rental rate $114 per acre (USDA 2003a, 2003b). Whle ths pattern can be explaned by addtonal ncentves for promotng conservaton practces contrbutng more envronmental benefts n the contnuous CRP and the CREP, a crtcal polcy queston remans: are the sgnfcantly hgher program payments economcally justfable? Theoretcally, rental payments n the land retrement programs should be desgned to compensate the losses of farmers expected returns from crop producton on the land to be retred. However, the determnaton of land rental payments requred for partcpaton s complcated for several reasons. Frst, farmers make ther partcpaton decsons under 2

4 uncertanty about croppng returns due to fluctuatons of crop yelds and output prces. Second, partcpaton n land retrement programs requres farmers to enter nto 10- to 15-year bndng contracts wth the USDA. Program partcpants are allowed to termnate ther contracts before the expraton date only f they pay back all government payments receved ncludng rental payments, cost-share payments and ncentve payments, plus nterests and a lqudatng cost calculated as 25% of the annual rental payments tmes the number of acres beng termnated 3 (Scott). Furthermore, farmers who ext the program wll lose ther nvestments on establshng conservaton covers and must bear addtonal costs for convertng conservaton covers nto cropland. From an economc perspectve, partcpaton n land retrement programs nvolves an rreversble decson because such a decson s very costly to reverse, as explaned n Dxt and Pndyck. Hence, the land rental payments requred for partcpaton depend on how farmers make ther partcpaton decsons. Understandng the role of uncertanty and rreversblty n determnng land rental payments and consequently, n targetng of a least-cost land retrement program s an mportant polcy queston that needs to be addressed. The purpose of ths paper s to develop a model to examne the mpacts of alternatve farmer decson-makng on determnng land rental payments and least-cost land retrement targetng n conservaton programs. By takng nto account uncertanty about crop producton and rreversblty of program partcpaton, t analyzes the mplcatons of desgnng approprate land rental payment schemes that compensate farmers losses of expected returns from crop producton on the land to be retred. The model s emprcally appled to an agrcultural watershed n the Illnos CREP regon and relevant polcy mplcatons are dscussed. From a socal planner s perspectve the typcal decson problem n land retrement programs s to select a small set of land to be retred from a large set of elgble land n order to 3

5 acheve specfed envronmental objectves whle mnmzng program payments. In addressng ths decson problem, a number of studes proposed a targetng approach for mprovng the cost effectveness of such programs. It has been shown that the CRP benefts could be mproved through better targetng based on off-ste benefts (Rbaudo, 1986, 1989; Hemlch and Osborn) or beneft to cost crtera (Babcock et al. 1996, 1997). Whle these studes examned CRP targetng at the regonal or natonal level, Khanna et al. developed a watershed-level land retrement targetng scheme to dentfy land parcels for retrement for achevng water qualty objectves at least costs. However, the costs of land retrement n these studes are typcally represented by forgone croppng returns that are estmated based on crop yelds, output prces and producton costs. In partcular, all of these studes dd not ncorporate how farmers make ther partcpaton decsons n examnng the cost effectveness of land retrement programs. Approprate assessment of the cost effectveness of land retrement programs requres ncorporatng farmer decson-makng nto the socal planner s land retrement targetng. Several studes have examned the mpacts of farmers rsk atttudes on the requred land rental rates for program partcpatons. Hope and Lngard revealed that ncreasng rsk averson would make land retrement more attractve to farmers for the set-asde program n the UK. Ths mples that lower program premum would be acceptable for hgh rsk-averse farmers. Consstently, several other studes also found that n the set-asde program addtonal ncentves could generate more land retrement for hgh rsk-averse farmers (Fraser; Roberts, Froud and Fraser). However, rsk averson would not justfy why the land rental payments n the contnuous CRP or the CREP are sgnfcantly hgher than the local cash rental rates. Consderng uncertanty about crop producton and rreversblty of program partcpaton s mportant n analyzng the requred land rental payments and the cost 4

6 effectveness of land retrement programs because farmers partcpaton n the programs s smlar to technology adopton decson under uncertanty. Studes on nvestment under uncertanty show that decson makers could delay ther nvestment decsons to learn more about the value of technology or economc condtons before makng rreversble decsons (Dxt and Pndyck). A number of studes have recently appled the theory of rreversble nvestment to analyze the adopton of agrcultural technologes. The value of watng was shown to be very hgh and the farmers would delay nvestment decsons to learn more about the value of new technology and economc condtons (Purvs et al.; Wnter-Nelson and Amegbeto; Isk, Khanna and Wnter-Nelson; Carey and Zlberman). In ths paper, we extend the applcaton of the theory of rreversble nvestment to examne the mplcatons of farmer decson-makng for partcpaton n land retrement programs under uncertanty. We provde a framework for understandng the mpacts of uncertanty about crop producton and rreversblty of program partcpaton on determnng land rental payments and least-cost land retrement targetng. The next secton presents the theoretcal framework. Secton III descrbes the emprcal applcatons and data. The results of the emprcal applcatons are n Secton IV followed by the conclusons and polcy mplcatons. II. Theoretcal model The model s based on the socal planner s decson problem n targetng least-cost land retrement n an agrcultural watershed. Land parcels are dentfed to acheve an off-ste polluton abatement goal whle mnmzng program costs n terms of land rental payments to farmers. Assume that a watershed has N elgble land parcels, each parcel s of sze X acres, where = 1,, N. All other land parcels n the watershed are assumed to be unchanged n the 5

7 land retrement program. For smplcty we only consder off-ste sedment abatement as the envronmental benefts acheved by land retrement. The off-ste sedment abatement due to the land parcel taken out of crop producton s denoted by S ( C, O ), where C ndcates land characterstcs whch nclude land use, land qualty, dstance to the water body and other attrbutes, and O ndcates the mpacts of off-ste sedment generaton from other land parcels n the same surface runoff channel. The off-ste sedment abatement s the dfference n off-ste sedment loadng between when the land parcel s n crop producton and when t s n the land retrement program. The off-ste sedment abatement due to retrng of a land parcel depends not only on the sol characterstcs and land use of that parcel but also on the volume of runoff flowng n from upslope parcels; ths volume n turn depends on land use decsons and ste-specfc characterstcs of upslope parcels. The socal planner needs to compensate farmers losses due to the retrement of agrcultural land from crop productons. Let R ( η) be the mnmum per-acre land rental payment that needs to be provded to farmers for compensatng ther losses of expected returns on the land parcel from land retrement, dependng on ther decson-makng crtera (η ). Alternatve farmer decson-makng crtera that determne partcpaton constrants n the program wll be dscussed below along wth ther mplcatons for desgnng ncentve mechansms to nduce farmer partcpaton n the land retrement program. The socal planner s decson problem C The socal planner s problem s to dentfy land parcels to be retred to acheve a gven level of sedment abatement ( A ) n an agrcultural watershed whle mnmzng the total cost of the program n terms of land rental payments 4. Let θ be the proporton of the land parcel to be retred 5. The model s represented as follows: 6

8 (1) Mn mze θ X s.t. (2) θ X N θ = 1 N = 1 (3) θ 1. S( C, O ) A R( C η) The Lagrangan of the optmzaton model can be wrtten as: (4) L= N N θ X R( C η) + λ { A - = 1 = 1 θ X S( C, O ) }+ µ ( 1) where λ and µ are the Lagrange multplers assocated wth (2) and (3), respectvely (λ 0). The frst-order condtons are as follows: N = 1 θ (5) L L = X ( η ) R C -λ X S( C, O ) + µ 0 and θ = 0 θ θ. After rearrangement, (5) can be wrtten as: (6) λ X S( C, O ) - X R( C η) µ. On the left-hand sde of equaton (6) the margnal cost of sedment abatement λ, multpled by sedment abatement X S C, O ) from the retrement of land parcel, represents ( the socal benefts of land retrement. R ( η) could be consdered as the per-acre costs of the C retrement of the land parcel to the government. The dfference between the two, µ, ndcates the net socal benefts provded by land parcel f retred. Because the margnal cost λ s a constant at a gven sedment abatement constrant, equaton (6) also mples that a land parcel wth hgher beneft to cost rato, S C, O ) / R ( η), would be selected for land retrement. ( C 7

9 An mportant ssue n solvng the socal planner s problem above s to determne an ncentve mechansm that nduces farmer partcpaton n the land retrement program. Most of the prevous studes consder R ( η) as the opportunty cost of crop producton or croppng C returns on the land parcel to be retred. However, land rental payments requred for partcpaton n the program, R ( η), could also depend on how farmers make ther partcpaton decsons C n the land retrement program and ther rsk preferences. Thus, solvng the decson problem n (1) (3) requres ncorporatng farmer decson-makng nto the model, whch determnes partcpaton constrants. In other words, the socal planner must determne approprate value of R ( η) that makes farmers ndfferent between partcpatng n the land retrement program C and contnung ther rsky farmng operatons. We now ncorporate alternatve farmer decson-makng represented by η nto (1) and analyze mplcatons of those decson-makng scenaros for the margnal cost of sedment abatement. The expected returns from the land currently n crop producton depend on varous factors such as land characterstcs and how farmers make ther partcpaton decsons. Gven uncertanty about crop producton and rreversblty of program partcpaton, R ( η) would depend not only on the opportunty costs of crop producton but also on the farmer s decsonmakng crtera (η ). If the farmer s rsk neutral, R ( η) s the expected returns from crop producton on the land parcel to be retred, that s, R ( η) = ER C ). If the farmer were rsk averse, he would reduce the varablty of returns by partcpatng n the land retrement program and would requre less for land retrement. To determne the mnmum rental payments requred for partcpaton, we assume for smplcty that the utlty C C ( C functon s represented by a negatve exponental functon U φr = e, where φ s the absolute 8

10 rsk averson coeffcent. Wth a negatve exponental utlty functon and normally dstrbuted R ( C ), the certanty equvalent of expected returns under rsk averson for X acres land s 2 φx represented as X ER( C ) Var( R), where Var (R) s the varance of the returns and 2 φx 2 2 Var( R) s the rsk premum. Thus, under rsk averson only, X R( η) wll be replaced by C 2 φx X ER( C ) Var( R) n solvng the socal planner s decson problem gven n (1). 2 When the rreversblty of program partcpaton s taken nto account, farmers would requre the rental payment at least be Γ ER C ) to compensate ther losses of croppng returns for ( partcpaton n the land retrement program, where Γ > 1 s the opton value multpler (see Appendx). The extent to whch uncertanty and rreversblty affect the farmer partcpaton depends on the value of Γ (Dxt and Pndyck). Thus, uncertanty and rreversblty causes farmers to be compensated at least Γ ER C ) n order to partcpate n the land retrement ( program and therefore, R ( η) = Γ ER C ) n (1). C Margnal cost of sedment abatement under alternatve models ( Under rsk neutralty only, the condton for least-cost land retrement s λ X S( C, O ) µ X ER C ). We denote the margnal cost of sedment abatement under rsk ( neutralty as λ RN. Under rsk averson only, the condton for least-cost land retrement s 2 φx λ X S( C, O ) µ [ X ER( C ) Var( R)]. The margnal cost of sedment abatement 2 under rsk averson s defned as λ RA. Because Var(R) > 0, RN RA λ > λ. Under uncertanty and rreversblty, the condton for the least-cost land retrement s gven by 9

11 λ X S( C, O ) µ Γ X ER C ). The margnal cost of sedment abatement under uncertanty ( IR and rreversblty s denoted as λ. Snce Γ >1, λ > IR RN RA > λ λ. The model shows that when only rsk averson s consdered n land retrement programs, the margnal cost of sedment abatement s less than that under rsk neutralty, and ths would lead to lower program costs n terms of land rental payments. However, when rreversblty of program partcpaton s consdered, the margnal cost of abatement s hgher than that under rsk neutralty or rsk averson only. In addton to the margnal cost of abatement, solvng the above model emprcally would generate total costs of the program and the least-cost land retrement patterns. It s reasonable to expect that elgble land parcels n an agrcultural watershed are heterogeneous. How land heterogenety, n conjuncton wth uncertanty and rreversblty, mpact on determnng the changes n the magntude of land rental payments and least-cost land retrement pattern s an emprcal queston that wll be examned further. III. Emprcal applcatons and data We develop an emprcal model to apply the above theoretcal model to the Otter Creek Watershed n Fulton County of the Illnos Conservaton Reserve Enhancement Program (CREP) regon (Fgure 1). The Illnos CREP s a supplementary program of the CRP for mprovng water qualty n the Illnos Rver Basn. Wth about $500 mllon budget, the program ams at retrng 232,000 acres of cropland out of over 5 mllon acres of elgble land n order to acheve envronmental objectves such as reducng sedment loadng n the rver by 20% and ntrate loadng by 10%. To acheve these goals the Illnos CREP lmts enrollment prmarly to a narrow buffer zone adjacent to rvers and streams, 85% of whch are to be selected from rparan areas (defned as the 100-year floodplans of the Illnos Rver and ts trbutares and streams and wetlands). The remanng 15% could be selected from hghly erodble cropland adjacent to 10

12 enrolled rparan areas. These crtera make over 5 mllon acres of cropland elgble for enrollment n the program and CREP does not specfy any mechansm for dentfyng the land parcels that should be retred (Khanna et al.). The Otter Creek Watershed has 68,314-acre land, of whch 47% s cropland, 25% s grassland, 25% s woodland, and the remanng 3% s urban, water and mscellaneous land. The watershed s also relatve flat, wth 71% of the land under 5% slope. We parttoned the watershed nto 300-by-300 foot parcels (2.07 acres per parcel), resultng about 33 thousand parcels for the entre watershed. Ths parcel sze s chosen because t leads to relatve homogeneous land unts from avalable data sources. Because the Illnos CREP s essentally a buffer program n whch cropland on floodplans or adjacent slopng land s elgble, we defne cropland wthn 900-foot buffer of water bodes as elgble land n the emprcal model, beng consstent wth the program defnton. Ths leads to 4,691 elgble land parcels or 9,710 acres, whch s 30% of all the cropland n the watershed. The on-ste eroson and off-ste sedment generated by elgble land parcels are estmated wth the Agrcultural Nonpont Source Polluton (AGNPS) model, a hydrologc model that s wdely appled to smulate movements of sedment and nutrents n agrcultural watersheds. The AGNPS model requres fve parameters at watershed level and twenty-three parameters at the parcel level 6 (Young et al.; Young, Onstad, and Bosch). In the model, we use a typcal 5-year storm event wth 3.73 nches of ranfall wthn 12 hours based on ranfall data from Huff and Angle. Remote sensng data (Illnos Department of Natural Resources) s used to dentfy land use n each land parcel. Elevaton data (U.S. Geologcal Survey) s used to create flow paths or channels that drect runoff from upland parcels to nearest water body. Sol erodblty factor, texture and hydrologc sol group are derved from the sol data obtaned from Illnos Natural 11

13 Resources Conservaton Servce. All the other AGNPS parameters are obtaned from the USDA publcatons (1972, 1986). Input data for all AGNPS nput parameters are adjusted n consultaton wth the Unversty of Illnos hydrologsts n order to ft nto the condtons wthn the study area. The AGNPS model run shows that a typcal 5-year storm event (3.73 nches of ranfall wthn 12 hours) would cause about 30,000 tons of sedment beng loaded nto water bodes n the watershed gven exstng pattern of land use. Summary statstcs for the elgble land parcels n the watershed s shown n Table 1. The land parcels dffer consderably n ther dstance from water bodes, slope, erodblty ndex, upland sedment nflow and on-ste eroson. The dstance from water bodes reflects the poston of all elgble land parcels wthn the watershed. The elgble land parcels wthn the watershed have an average dstance from water bodes 392 feet. The elgble land parcels are relatvely flat wth an average slope of 3.3%. However, relatve landscape varatons stll exst wth a slope rangng from 0.5% to 21%. The sol erodblty ndex ranges from 0.04 to 0.49 wth an average of 0.39, whch represents modest erodblty condton. The amount of upland sedment nflow vares from 0.0 to 133 tons per acre wth an average of 4 tons per acre. Whle some parcels generate as low as 0.3 tons on-ste eroson per acre, others could generate on-ste eroson as hgh as 162 tons per acre. The average on-ste eroson rate s 12 tons per acre. A dffculty n estmatng off-ste sedment abatement acheved by retred land parcels s to handle the nterdependence of land parcels n determnng off-ste sedment abatement benefts. In order to solve ths problem, we consder flow chans wthn the elgble regon, 900- foot buffer of water bodes, as decson unts, and each flow chan conssts of at most three 300- by-300 parcels. Of the runoff channels that cover the watershed, 2,594 runoff channels contan elgble cropland wthn 900 feet of water bodes. We defne all possble eght (=2 3 ) alternatve 12

14 land retrement optons for each flow chan wthn a surface runoff channel, those are CCC, GCC, CGC, CCG, GGC, CGG, GCG, and GGG, where C denotes crop producton and G denotes land retrement wth grass cover 7. Land uses of all the other parcels outsde the elgble regon are assumed to be unchanged n the land retrement program. The AGNPS model s run for the eght land retrement optons to obtan off-ste sedment abatement for each flow chan and each land retrement opton, denoted as A mp, where m = 1,,M denotes flow chans n the elgble regon and p denotes the eght land retrement optons. Whle the deposton rato for each parcel s stll dependent on ts own characterstcs and upslope runoff n the same runoff channel, by changng decson-makng unts from the land parcels to the flow chans we crcumvent the computatonal dffcultes arsng from the dependency of sedment deposton coeffcents of ndvdual land parcels. We obtan correspondng croppng returns for the eght land retrement optons n each flow chan, denoted as R mp. The estmaton of croppng returns s based on a crop budget model (FaRM Laboratory). Wthn the model, a typcal 700-acre farm wth corn-soybean rotaton and reduced tllage 8 s assumed. The returns are defned as total revenue mnus total varable costs, whch nclude machnery use, fertlzer and pestcde costs, crop nsurance premum, and nterests pad for captals. We obtan crop yeld nformaton based on sol productvty (Olson and Lang). The machnery use costs n terms of mantenance, repar and fuel and labour costs are estmated from a machnery program (Semens). The use of fertlzers, pestcdes and other chemcals s based on Illnos Agronomy Handbook (Cooperatve Extenson Servce). The crop nsurance premum s calculated based on the data from Rsk Management Agency. The nterest rate s based on average loan rates n 1998, whch s 5%. Based on above justfcaton croppng returns are estmated for each sol type and then assgned to elgble land parcels through GIS. 13

15 The elgble land s hghly productve n nature wth an average return of $145 per acre. However, sgnfcant dfferences n productvty exst across the land parcels. The mnmum of returns s $31 per acre whle the maxmum s $216 per acre (Table 1). Based on the theoretcal model the estmaton of expected returns depends on two key parameters: rsk averson coeffcents, φ, and the factor that affects the magntude of uncertanty and rreversblty, Γ. There s no consensus regardng the magntude of rsk averson coeffcents φ n the lterature (Babcock, Cho, and Fenerman; Weersnk, Dutka, and Goss). In ths study we choose low rsk averson coeffcent at and hgh rsk averson coeffcent at 0.01, beng consstent wth the range of rsk averson coeffcents evaluated by Lambert. The varance of the returns s estmated for each land parcel based on the sample of all elgble land parcels. The varances of the returns for each flow chan and land retrement opton are standardzed by coeffcent of varaton, CV. In ths study, CV = 0.38, whch s estmated from the croppng returns data n Fulton County of Illnos (USDA 2001). Thus, the mnmum rental rates requred for retrng an acre-land from crop producton for flow chan m and land retrement φ 2 opton p under rsk averson s [ Rmp ( CV * R mp ) ]. Usng the returns receved by farmers n 2 Fulton County, we also estmated the rreversblty factor β 1 Γ =, where β < 0 s the β 2 smaller root of 0.5 β ( β 1) αβ ρ = 0 σ (see Appendx). The drft parameter α s estmated as 2 = µ ( 0.5) σ, where µ s the mean of the seres ln( t 1 / Rt ) α + R + and σ s the standard devaton of the seres (Forsyth). We assume a 5% dscount rate n the estmaton of β. Usng the hstorcal data on the average crop returns from corn and soybean productons over the perod of n Illnos (USDA 2001), we estmate the rreversblty factor Γ =1. 45 for Fulton 14

16 County 9. The mnmum land rental rate requred to partcpate n the CREP under uncertanty and rreversblty s then represented as Γ Rmp. The socal planner s problem s to select a land retrement opton p n each flow chan m M 8 A mp m= 1 p= 1 to acheve the 20% off-ste sedment abatement goal A n the watershed, that s A, whle mnmzng the program costs n terms of land rental payments compensatng the losses of expected returns on the land parcels to be retred. Ths model s solved for each scenaro of rsk averson and rreversblty to obtan margnal cost of sedment abatement, total cost of the program, and the least-cost land retrement pattern n the watershed. IV. Results The emprcal model s run for dfferent scenaros of alternatve farmer decson-makng and partcpaton constrants to dentfy the least-cost land retrement patterns for achevng the 20% sedment abatement goal n the Otter Creek Watershed and the results are presented n Table 2. In the base scenaro under rsk neutralty, 451 land parcels or 934 acres of cropland need to be retred n order to acheve the 20% off-ste sedment abatement n water bodes of the watershed. The targeted acreage for land retrement s about 10% of the elgble land n the watershed. The program cost n terms of land rental payments for compensatng farmers croppng return losses s about $114,000 per year. The margnal cost of sedment abatement s $36 per ton and the average land rental payment that should be provded to the farmers n the watershed s $123 per acre. When farmers are assumed to be rsk averse or face an rreversble decson of partcpatng n conservaton programs, the requred land rental payments for compensatng farmers losses of expected croppng returns are dfferent dependng on the scenaros of rsk averson and rreversblty. When only rsk averson s consdered n modelng farmer 15

17 partcpaton, the program cost n terms of land rental payments s less than that n the scenaro of rsk neutralty. Ths s because rsk-averse farmers requre less compensaton for ther losses of expected croppng returns than that for rsk-neutral farmers. In the low rsk averson scenaro, 448 land parcels or 927 acres of the cropland need to be retred to acheve the 20% sedment abatement goal, whch s close to the land retrement acreage under the rsk neutralty scenaro. However, the program cost n terms of land rental payments s less than that under rsk neutralty, whch s about $102,000 per year. Correspondngly, the margnal cost of sedment abatement s $32 per ton and the average land rental payment to the farmers s $111 per acre. Under the scenaro of hgh rsk averson, 539 land parcels or 1,116 acres of cropland need to be retred n order to acheve the 20% sedment abatement goal. Whle the land retrement acreage s ncreased by 20% compared to the rsk neutralty scenaro, the program cost decreased by 25%, whch s about $86,000 per year. The correspondng margnal cost of sedment abatement s $26 per ton and the average payment to the farmers s $77 per acre. Because the rsk premum could vary across heterogeneous land parcels, land retrement patterns under rsk averson are dfferent from those under rsk neutralty (Table 2). In the scenaro of low rsk averson, 11 land parcels or 2% of the targeted land parcels are not overlappng wth the targeted land parcels n the rsk neutralty case. On the other hand, n the hgh rsk averson scenaro, the non-overlappng parcels reach 153 or 28% of the total selected parcels n the watershed. The cause of the spatal shft s that the beneft to cost ratos of elgble land parcels change when rsk averson factor s consdered, and the land retrement s moved towards the land parcels that have hgher beneft to cost ratos. Under uncertanty and rreversblty, land retrement patterns are smlar to those under the rsk neutralty scenaro because the rreversblty factor scales up the rental payments 16

18 requred to partcpate n the program. As a result, the program cost n terms of rental payments that need to be provded to the farmers ncreases consderably. Under uncertanty and rreversblty, the land retred s 451 land parcels, whch s the same as the scenaro under rsk neutralty. However, the total cost of the program reaches about $166,000 per year, whch s 45% hgher than that under the scenaro of rsk neutralty only. The correspondng margnal cost of sedment abatement s $52 per ton and the average land rental payment to the farmers s $178 per acre. As expected, the total cost of land retrement and margnal cost of abatement under uncertanty and rreversblty are also consderably hgher than those under rsk averson only. These results may provde a justfcaton for the sgnfcantly hgher program payments n the contnuous CRP or the CREP. For example, n Fulton County where the Otter Creek Watershed s located, the average sol rental rate was $87 per acre n 1998 for the 5-year Illnos CREP. However, the actual average program payments n 1999, 2000 and 2001 were $142, $152 and $167 per acre, respectvely, representng ncreases rangng from 63% to 92% (USDA 2003a, 2003b). Although the actual program payments are consderably hgher than the average sol rental rate, these payments are below the average land rental payment estmated under the scenaro of uncertanty and rreversblty ($178 per acre). Ths ndcates that when the rreversblty of the program partcpaton s consdered, the actual land rental payments n the CREP are reasonable n compensatng the losses of farmers expected croppng returns. Implcatons of a unform bd cap n the scenaro of uncertanty and rreversblty Whle a bddng cap s currently not applcable to the contnuous CRP or the CREP, the emprcal model s also appled to examne the mplcatons of a unform bddng cap that s practced n the regular CRP sgnups. It s mportant to examne the potental polcy mplcatons of ntroducng such a land rental nstrument for the contnuous CRP or the CREP. Typcally n 17

19 regular CRP sgnups, a sol-based bd cap s set at the county level and land parcels wth hgher EBI scores relatve to bds would be accepted to the program. Apparently, the bd cap could be set dfferently dependng on the alternatve farmer decson-makng crtera examned above. Then, an mportant queston would be how a unform bd cap determned assumng rsk neutralty would work when farmers actually make ther partcpaton decsons under uncertanty of crop producton and rreversblty of program partcpaton. We frst determne a unform bd cap requred to acheve the 20% sedment abatement goal n the watershed assumng that farmers are rsk neutral. A heurstc procedure s bult nto the least-cost targetng model to dentfy the unform bd cap that would nduce land retrement n order to acheve the 20% sedment abatement goal. In the begnnng a low bd cap s set, land parcels wth croppng returns below the cap are selected, and the sedment abatement acheved by these parcels s summarzed. The bd cap s ncreased by small ncrements untl the envronmental goal n the watershed s acheved. The model ndcates that a unform rental rate of $140 per acre would acheve the 20% sedment abatement by enrollng farmlands wth the expected returns at most $140 per acre. We examne the mpacts of ths unform bd cap set assumng rsk neutralty when farmers actually make an rreversble decson of land retrement under uncertanty. The unform bd cap under rsk neutralty scenaro s appled to the scenaro of uncertanty and rreversblty to dentfy land parcels that would be retred, and the sedment abatement and the cost of abatement are estmated. As a result, 493 acres of cropland are selected for retrement. The acheved sedment abatement s only 42% of the abatement target 6,000 tons (Table 3). The sedment abatement acheved under uncertanty and rreversblty s sgnfcantly lower than the program goal. The result strongly suggests that f a unform bd cap s determned 18

20 wthout consderng uncertanty and rreversblty, then applyng the polcy nstrument would not acheve the program goal. Otherwse, the unform bd cap needs to be rased. These results provde nsghts for settng approprate level of bddng caps for nducng farmers partcpaton n land retrement programs. The results also mply that the programs lke CREP does not mpose bd caps because they encourage farmer partcpaton by provdng addtonal ncentves n order to meet the program goals. V. Conclusons and polcy mplcatons Ths paper develops a model to examne the mpacts of alternatve farmer decsonmakng on determnng land rental payments and least-cost land retrement targetng n agrcultural conservaton programs. It takes nto account uncertanty about crop producton and rreversblty of program partcpaton to analyze the economc ncentves necessary for nducng farmer partcpaton n land retrement programs. The model s emprcally appled to the CREP n the Otter Creek Watershed n Illnos. Results show that n achevng the 20% sedment abatement goal n the watershed, the margnal cost of sedment abatement and the average land rental payment under rsk averson are less than those under rsk neutralty. However, when rreversblty of the program partcpaton s consdered, the margnal cost of sedment abatement and the average land rental payment are consderably hgher than those under scenaros under rsk neutralty or rsk averson only. Furthermore, the model results show that f a bddng system were ntroduced, a unform bd cap determned under the assumpton of rsk neutralty would acheve far less sedment abatement than the program goal when t s appled to the scenaro of uncertanty and rreversblty. The success of land retrement programs hghly depends on approprate desgn of land rental payment nstruments to compensate the losses of farmers expected returns. Statstcs 19

21 reveals the land rental payments n the contnuous CRP or the CREP are sgnfcantly hgher than the local cash rental rates. The results from ths paper ndcates that when rreversblty of the land retrement program partcpaton s consdered, the land rental payments needed for nducng farmers partcpaton n the program should be hgher than the payments determned under the assumpton of rsk neutralty only. Furthermore, f a bddng system were mplemented, the unform bd caps determned wth the assumpton of rsk neutralty would not be attractve to many farmers who make program partcpaton decson under uncertanty and rreversblty. As a result, the bd caps need to be rased n order to encourage more farmers to partcpate n the program. The results have mplcatons for the desgn of polcy nstruments n land retrement programs. Gven that uncertanty about crop producton and rreversblty of program partcpaton, ncentve payments n addton to the land rental payments based on local land markets should be provded to farmers to account for the value of watng. Currently, only contnuous sgn-ups n the CRP or the CREP provde addtonal ncentves to farmers for mplementng conservaton practces that provde more envronmental benefts such as flter strps and buffers or for retrng land n areas of envronmental sgnfcance. In lght of our modelng results, the bddng system and payment level of regular sgn-ups n the CRP need to be re-examned. 20

22 Footnotes 1. The EBI s composed of sx envronmental factors: wldlfe, water qualty, eroson, endurng benefts, ar qualty, and state or natonal conservaton prorty area. 2. The contnuous CRP s dfferent from the general CRP and provdes producers the opportunty to enroll acreage n specfc conservaton practces and areas year-around. The CREP s a jont federal-state program to address envronmental problems of state sgnfcance. Enrollment s usually conducted under the contnuous CRP wth ncentves from both federal and state governments. 3. The Federal Agrcultural Improvement and Reform Act of 1996 allowed partcpants wth contracts sgned before 1995 to wthdraw from the CRP wthout penalty. However, certan envronmentally senstve CRP acres were nelgble for early termnaton. The purpose was to release those CRP acres that contrbuted less envronmental benefts through the sgn-ups wth sol eroson crtera. 4. The socal planner s problem could also be formulated as maxmzaton of envronmental benefts subject to a budget constrant. However, the budget constrant s typcally set at the natonal, state, or regonal level. In a specfc watershed, the budget constrant s unknown because program funds are not further allocated at the watershed level. Therefore, we model the socal planner s problem as mnmzng program costs subject to the envronmental objectves set by the programs. 5. It s possble to assume that θ s a bnary decson varable, takng the values one f a parcel partcpates and zero f t does not. Snce t s theoretcally possble to enroll some proportons of a parcel to the program, we do not restrct θ to be one or zero n theoretcal model. 21

23 6. The fve parameters at the watershed level are watershed name, cell area, total number of cells, precptaton, and ranfall energy-ntensty value. The twenty-three parameters at the parcel level are cell number, flow drecton, recevng cell number, channel ndcator, runoff curve number, slope, slope length, slope shape, channel slope gradent, channel sde slope, Mannng s roughness coeffcent, sol texture, sol erodblty, croppng management factor, conservaton practce factor, surface condton coeffcent, fertlzaton applcaton level, fertlzaton ncorporaton level, chemcal oxygen demand factor, pont source ndcator, eroson from other sources, terrace mpoundments and feedlots. 7. For example, GCG ndcates the frst and thrd parcels from a water body are n grass cover and the second parcel s n crop producton. 8. Reduced tllage has less ntensve operaton on sol than conventonal tllage such as smaller cultvaton equpment. 9. In realty, the value of Γ could vary across heterogeneous sol characterstcs and therefore across R mp. Because we do not have the hstorcal data at the sol type level n ths county and the study area s relatvely small, we smplcty assume that the value of Γ are on average the same for all the land parcels consdered here. 22

24 References Babcock, B.A., E.K. Cho, and E. Fenerman. Rsk and Probablty Premums for CARA Utlty Functons. Journal of Agrcultural and Resource Economcs 18(1993): Babcock B.A., P.G. Lakshmnarayan, J. Wu, and D. Zlberman. The Economcs of a Publc Fund for Envronmental Amentes: A Study of CRP Contracts. Amercan Journal of Agrcultural Economcs 78, no.4 (1996): Babcock B.A., P.G. Lakshmnarayan, J. Wu, and D. Zlberman. Targetng Tools for the Purchase of Envronmental Amentes. Land Economcs 73, no.3 (1997): Carey, M.J. and D. Zlberman. A Model of Investment under Uncertanty: Modern Irrgaton Technologes and Emergng Markets n Water. Amercan Journal of Agrcultural Economcs 84, no. 1(2002): Cooperatve Extenson Servce. Illnos Agronomy Handbook. Department of Crop Scences, Unversty of Illnos at Urbana-Champagn, Dxt, A. K., and R.S. Pndyck. Investment under Uncertanty. Prnceton, NJ : Prnceton Unversty Press, FaRM Laboratory. Crop and Lvestock Budgets: Examples for Illnos AE Department of Agrcultural and Consumer Economcs, Unversty of Illnos at Urbana-Champagn, Feather, P., D. Hellersten and L. Hansen. Economc Valuaton of Envronmental Benefts and the Targetng of Conservaton Programs: The Case of the CRP. Agrcultural Economc Report No. 778, ERS, USDA, Forsyth, M. On Estmatng the Opton Value of Preservng Wlderness Areas. Canadan Journal of Economcs 33 (2000), Fraser, R. Nce Work f You can Get It: An Analyss of Optmal Set-Asde. Oxford Agraran Studes 19, no.1 (1991): Hemlch, R.E. and C.T. Osborn. After the Conservaton Reserve Program: Macroeconomcs and Post-Contract Program Desgn. A Task Force Report to the Great Plans Agrcultural Councl, Rapd Cty, South Dakota, Hope, J. and J. Lngard. The Economcs of Set-Asde: Lnear Programmng Analyss. Farm Management 7, no. 6 (1990): Huff, F.A. and J. R. Angel. Frequency Dstrbutons of Heavy Ranstorms n Illnos. Crcular 172. Illnos State Water Survey, Champagn, IL,

25 Illnos Department of Natural Resources. Illnos Geographc Informaton System. CD ROM, Illnos Natural Resource and Conservaton Servce. Illnos Watershed Boundares. CD ROM, Isk, M., M. Khanna, and A. Wnter-Nelson. Sequental Investment In Ste-Specfc Crop Management Under Output Prce Uncertanty. Journal of Agrcultural and Resource Economcs 26 (2001): Khanna, M., W. Yang, R. Farnsworth and H. Onal. Cost-Effectve Targetng of CREP to Improve Water Qualty wth Endogenous Sedment Deposton Coeffcents. Amercan Journal of Agrcultural Economcs (Forthcomng). Lambert, D.K. Rsk Consderatons n the Reducton of Ntrogen Fertlzer Use n Agrcultural Producton. Western Journal of Agrcultural Economcs 15, no.2 (1990): Olson, K.R., and J.M. Lang. Productvty of Newly Establshed Illnos Sols, , Supplement to Sol Productvty n Illnos. Department of Agronomy, Unversty of Illnos at Urbana-Champagn, Purvs, A., W. G. Boggess, C. B. Moss, and J. Holt. Technology Adopton Decsons under Irreversblty and Uncertanty: An Ex Ante Approach. Amercan Journal of Agrcultural Economcs 77 (1995): Rbaudo, M. O. Consderaton of Offste Impacts n Targetng Sol Conservaton Programs. Land Economcs 62, no.4 (1986): Rbaudo, M. O. Targetng the Conservaton Reserve Program to Maxmze Water Qualty Benefts. Land Economcs 65, no.4 (1989): Rsk Management Agency Crop Insurance Partcpaton Data. Onlne. Avalable at December Roberts, D., J. Froud and R.W. Fraser. Partcpaton n Set Asde: What Determnes the Optng n Prce? Journal of Agrcultural Economcs 47, no.1 (1996): Scott, L Termnaton of CRP contracts. Personal communcaton wth staff n Illnos FSA. Semens, J. Machnery Cost Program. Department of Agrcultural Engneerng, Unversty of Illnos at Urbana-Champagn, Smth, M. Agrcultural Resources and Envronmental Indcators: Land Retrement. Ag Handbook No. AH722. ERS, USDA,

26 USDA. Natonal Engneerng Handbook, Secton 4, Hydrology. Washngton D.C., USDA. Urban Hydrology for small Watershed. Washngton D.C. Sol Conservaton Servce (SCS), USDA, FSA. The Conservaton Reserve Program. Onlne. Avalable at USDA. Agrcultural Statstcs, Annual Issues, Onlne. Avalable at 81/pedb/, Natonal Agrcultural Statstcs Servce, Washngton D.C., June USDA. CRP Monthly Actve Contract Fle Upload - Project Summary - Payment Summary for Actve CREP Contracts by Program Year. Onlne. Avalable at a. USDA. Agrcultural Land Values and Agrcultural Cash Rents. Onlne. Avalable at b. U.S. Geologcal Survey. USGS Geographc Data Download: 1:24,000 Scale Dgtal Elevaton Model SDTS Format. Onlne. Avalable at ndcdb.html, September Weersnk, W., C. Dutka, and M. Goss. Crop Prce and Rsk Effects on Farm Abatement Costs. Canadan Journal of Agrcultural Economcs 46 (1998): Wnter-Nelson, A., and K. Amegbeto. Opton Values to Conservaton and Agrcultural Polcy: Applcatons to Terrace Conservaton n Kenya. Amercan Journal of Agrcultural Economcs 80 (1998): Young, R.A., C.A. Onstad, D.D. Bosch, and W.P. Anderson. AGNPS User Gude Young, R.A., C.A. Onstad, and D.D. Bosch. AGNPS: An Agrcultural Nonpont Source Model. In Computer Models of Watershed Hydrology, ed., V.P. Sngh, pp Hghlands Ranch, CO: Water Resources Publcatons,

27 Appendx We model a rsk-neutral farmer s optmal partcpaton decson n the land retrement program under uncertanty and rreversblty. Let V be the rental rate to be determned, whch nduces the farmer s partcpaton n the land retrement program. We assume that net farmng returns R s stochastc and evolve accordng to the followng geometrc Brownan moton process: dr = α Rdt + σrdz (A.1) where dz s the ncrement of a Wener process wth mean zero and unt varance; α s the expected growth rate; and σ s the volatlty n the growth rate. A number of studes show that returns from agrcultural producton or output prces can be represented by a geometrc Brownan moton process (Purvs et al., 1995; Isk et al., 2001; Carey and Zlberman, 2002). By ncorporatng uncertanty and rreversblty of the land retrement program partcpaton, the farmer s partcpaton decson n the land retrement program s modeled usng dynamc optmzaton technques. The farmer s decson problem s to maxmze the net returns from partcpaton n the land retrement program by choosng an optmal tme t to partcpate n the land retrement program subject to (A.1) as: F ( V R ) ρ t ( R) = max E t t e dt t 0 (A.2) where ρ s the dscount rate. Dynamc optmzaton technques are used to derve the optmal partcpaton rule. The Bellman equaton s ρ F ( R) dt = E[ F( R) ]. Usng Ito s Lemma to expand the rght-hand sde of ths expresson, F (R) can be shown to satsfy 26

28 ( σ R F ) + αrf ρr = 0. We solve ths dfferental equaton wth respect to the boundary R R condtons: F ( 0) = 0, F( R) = V R, and F R ( R) = 1. Solvng the dfferental equaton subject to the boundary condtons reveals that the threshold return to be receved at whch t s optmal to partcpate at year 0 s gven by (Dxt * β 1 and Pndyck): V0 = ΓR0, where Γ = > 1 β wth β < 0 beng the smaller root of 2 0.5σ β ( β 1) αβ ρ = 0. The magntude of ths factor determnes the extent to whch uncertanty and rreversblty affect the partcpaton decson. Ths factor ncreases wth an ncrease n σ and/or a decrease n α. Ths decson rule requres the farmer to be compensated at least Γ R0 to partcpate n the land retrement program today. 27

29 Table 1. Summary Statstcs of Elgble Land n the Otter Creek Watershed Varables Mean (Std.Dev) Mn. Max Dstance From Water Bodes (Feet) (242.2) Slope (%) 3.3 (2.8) Erodblty Index 0.39 (0.06) Upland Sedment Inflow (Tons/Acre) 4.0 (6.3) On-Ste Eroson (Tons/Acre) 12.2(13.3) Quas-Rent ($/Acre) 145.2(29.7) Total No. of Elgble Land Parcels 4,691 Elgble Acres 9,710.4 Total Sedment Loadng (Tons) 29,996.3 Table 2. Characterstcs of Land Retrement under Dfferent Scenaros of Rsk Averson and Irreversblty Scenaros Varables Certanty Low Rsk Hgh Rsk Irreversblty Averson Averson Number of Parcels Enrolled Land Enrolled (Acres) , Percentage of Overlappng Parcels Compared to Certanty Case (%) Total Cost of Abatement a ( $) 114, , , ,013.9 Average Cost of Abatement ($/Ton) Margnal Cost of Abatement ($/Ton) Average Payment to Farmers ($/Acre) a. Total cost of abatement s represented by the total rental payments made to farmers to retre ther land. Table 3. Impact of a Unform Bd Cap under Rsk Neutralty on Land Retrement and Cost of Abatement under Irreversblty Varables Irreversblty Unform Bd Cap under Rsk Neutralty ($/acre) Land Enrolled (Acres) Abatement Acheved (Tons) Percentage of Abatement Target Acheved (%)

30 Fgure 1. The Otter Creek Watershed n Illnos Watershed boundary Elgble land 0 5 km 29