Point-Nonpoint Nutrient Trading in the Susquehanna River Basin: Technical Appendices 1

Transcription

1 Pont-Nonpont Nutrent Tradng n the Susquehanna Rver Basn: Techncal Appendces 1 Rchard D. Horan a, James S. Shortle b, Davd G. Abler b a Assstant Professor, Department of Agrcultural Economcs 87 Agrculture Hall, Mchgan State Unversty, East Lansng, MI Tel: (517) , FAX: (517) , E-mal: horan@msu.edu b Professor of Agrcultural Economcs Department of Agrcultural Economcs and Rural Socology, Armsby Buldng The Pennsylvana State Unversty, Unversty Park, PA E-mal: jshortle@psu.edu, D-Abler@psu.edu

2 Our model of the Susquehanna Rver Basn conssts of: (a) an economc model of agrcultural producton and polluton control decsons, (b) pont source polluton control costs, (c) a model that quantfes nutrent transport, and (d) the economc costs of nutrents enterng the Chesapeake Bay from the SRB. Modelng Nonpont Sources Economc model. The vast majorty of nonpont loads are due to agrculture, wth corn producton beng one of the most mportant contrbutng agrcultural actvtes. Corn producton s modeled as a two-level, constant elastcty of scale (CES) technology that exhbts constant returns to scale at both levels [Sato 1967]. Followng pror work based on ths approach [Abler and Shortle 1992; Kawagoe et al. 1985; Thrtle 1985; Bnswanger 1974], producton n the th regon, denoted y, s a functon of a composte bologcal nput, B, and a composte mechancal nput, M,.e., y ' A ( B %(1& ) M ) 1/ (1) where A and are parameters, and = ( - 1)/, where s the elastcty of substtuton between the bologcal and mechancal nputs. Smlarly, B s produced usng land, L, and fertlzer, N : B ' K ( L %(1& )(u N ) ) 1/ (2) where K and are parameters, u s the proporton of ntrogen taken up by the plant, and K = ( B - 1)/ B, where B = s B + s M, s j (j = B, M) s the cost share of the jth nput n producton and L,N L,N s the elastcty of substtuton between L and N. Ntrogen s more or less a fxed proporton of fertlzer, and so we denote N as ntrogen. The mechancal nput s produced usng captal and labor. However, assumng the prces of these nputs reman fxed, there s no reason to further decompose M nto ts consttuent parts as captal and labor wll be used n fxed proportons. The prce of corn, denoted p, s fxed and does not vary wthn the SRB. The same s true of

3 the prces of ntrogen, w N, and the mechancal nput, w M. Land supply takes a constant elastcty form,.e., L ' b w L, where b s a parameter, w L s the prce of land, and s the elastcty of supply. Land supply s defned at the watershed level to reflect the opportunty cost of ths nput, whch s lkely to dffer n each regon n the SRB. NB c NPS Net benefts from corn producton n a compettve equlbrum (wthout tradng), denoted, equal profts plus the nfra-margnal rents that accrue to landowners,.e., NB c ' py c &w N N c &w M M c L & c (v/b, m ) 1/ dv where v s a dummy of ntegraton and the superscrpt c denotes all values are evaluated at 0 compettve levels. The benefts from producton n a tradng equlbrum, denoted NB T NPS, are where ˆx 0 NB T NPS ' py T &w N N T &w M M T &p x [x T L & ˆx 0 ] & T m 0 ( v/b ) 1/ dv, s the vector of the ntal allocaton of nonpont permts (denomnated n terms of expected loadngs or nputs) to the th regon, x T s a vector of fnal permt holdngs after trades occur, p x s the equlbrum vector of permt prces, and the superscrpt T denotes that all values are evaluated at levels that occur n the tradng equlbrum. Thus, regon s costs of nonpont controls under a tradng equlbrum are defned as the reducton n net benefts that result from tradng, c (N, L, M ) ' NB c &NB T (3) The economc model for nonpont sources s calbrated for each regon usng cost shares and producton shares developed from USDA [2000] and Pennsylvana data [PASS 1998]. For the elastctes,, and, we adopt exstng estmates provded n the lterature (Table A1). The L,N lterature often reports a range of values and, n consequence, these and other parameters of the model are not known wth certanty. Many studes ether gnore uncertanty by treatng estmated parameters as though they were certan or deal wth uncertantes by performng a smple senstvty analyss (.e., calculatng the optmal soluton under a few dfferent parameter values). Followng

4 Abler and Shortle [1995], Davs and Espnoza [1998], and Claassen and Horan [2001], a more robust senstvty analyss s acheved by examnng the dstrbuton of model results gven parameter dstrbutons nferred from the lterature. We take ths approach by performng K Monte Carlo smulatons for each of several tradng systems, where each smulaton represents a random draw of parameter values and parameter values are assumed known wth certanty. Ths process s descrbed n more detal n the man text. Nutrent loadngs model. Nonpont loadngs functons for each of the regons (where loads from a regon are defned as the amount of ntrogen enterng the Susquehanna Rver or ts trbutares from that regon) are derved from the results of a study by Carmchael and Evans [2000]. These researchers were part of a team that used the smulaton model Generalzed Watershed Loadngs Functon (GWLF) to develop Total Maxmum Daly Load (TMDL) recommendatons for Pennsylvana. Because models such as GWLF are too complex to easly lnk wth economc models for the purposes of optmzaton and economc analyss, Carmchael and Evans [2000] used Monte Carlo smulaton technques to generate data sets that could be used to statstcally parameterze the loadngs functons. We used ther data to parameterze GWLF accordng to the form r 'r 1 P 2 N C L %r 2 [P 2 N C ] 2 L %r 3 P (4) where P s precptaton, N C s the per acre concentraton of ntrogen leavng felds, and r q (q=1,2,3) are parameters. The parameters r q (q=1,2,3) were obtaned by applyng OLS to equaton (4) (plus an error term) usng data suppled by Carmchael and Evans. The results of those regressons are not presented here but they are avalable from the authors upon request. In most cases, each parameter was postve and sgnfcant at the 1% level. The varable N C s related to ntrogen accordng to the relaton N C ' (1&u ) N /(P L ) (5)

5 where s a parameter. Thus, the loadngs functon can be wrtten as r 'r 1 P (1&u ) N %r 2 [ P (1&u ) N ] 2 /L %r 3 P (6) The varable P s taken to be stochastc n our smulaton model. Thus there are two forms of uncertanty n the model: parameter uncertanty, whch s dealt wth by performng a Monte Carlo analyss (as mentoned above and explaned n greater detal n the man text), and uncertanty due to stochastc weather events, whch s dealt wth for each of the Monte Carlo smulatons (also elaborated on n the man text). P s taken to be gamma dstrbuted wth a mean and varance based on precptaton data for the regons (Table A1). There s lkely to be some uncertanty n the values for the mean and varance, and so we allow these dstrbutonal parameters to vary unformly by as much as ±15% between each of the Monte Carlo smulatons. Fnally, we scale each of our loadngs functons so that the expected loadngs that result from ntrogen and land use nputs defned by our base case data equal the nonpont loadngs defned by our base case data n Table 1 n the man text. Modelng Pont Sources Pont source abatement cost functons are derved usng data from a Susquehanna Rver Basn Commsson (SRBC) report [Edwards and Stoe, 1998]. The report provdes base level emssons (abatement) for the most mportant pont sources of ntrogen n the SRB, as well as costs for adoptng varous nutrent control technologes and the emssons levels for each source under these technologes. For most sources, there was data on at least two technologes: three stage annual treatment and fve stage annual treatment. 2 Data for these technologes was aggregated to the regonal level from ndvdual sources and used to calbrate an abatement cost functon. Followng Horan et al. [2001], we model abatement costs for smplcty as a decreasng, convex functon of emssons

6 c(e k ) ' z k e k k %F k (7) where z k >0 s a parameter, <0 s the elastcty of costs wth respect to emssons, and F k k s a fxed cost. There are three parameters n (7) to be calbrated, and so we also use nformaton provded by Camacho [1992] and Malk et al. [1994] to relate the margnal costs of abatement by nonpont sources wth pont source margnal abatement costs. Specfcally, we calculate the margnal costs of reducng ntrogen use by 10% (snce abatement s not well-defned for stochastc polluton), denoted k, and assume pont source margnal abatement costs are some multple of ths value,.e., k z k e k&1 k ' k (Table A1). Ths procedure enables us to calbrate pont source costs n a manner that avods scalng dfferences between pont and nonpont source costs. Fnally, loadngs from pont sources nto a regon are gven by aggregate emssons wthn the regon. Nutrent Delvery Nonpont source loadngs and pont source emssons are measured as loadngs nto the watershed n whch they orgnate. However, only a fracton of the loadngs or emssons generated from each watershed s delvered to become part of the ambent polluton concentraton n the Chesapeake Bay, whch s the chef area of concern for polcy purposes. The proporton of the load that s delvered s modeled as a constant delvery coeffcent, n a' j '1, so that total delvered loads are j j r % j s Ths relaton represents a frst-order approxmaton to the actual transport process, whch s thought to be reasonable n many cases [Roth and Jury 1993]. The delvery coeffcents are taken to be stochastc and gamma dstrbuted wth a mean and varance as reported by Carmchael and Evans [2000], as derved from the USGS SPARROW model [Smth et al. 1997] (Table A1). There s lkely to be some uncertanty n the values for the mean and varance, and so we allow these dstrbutonal parameters to vary unformly by as much as ±15% between each of the Monte Carlo k'1 j k e k (8)

7 smulatons. Damages Polluton control costs and loadngs are standard nput for the analyss of polluton tradng [see e.g., Hanley et al. 1997]. However, gven the stochastc nature of loadngs, a crteron s needed to judge when one probablty dstrbuton of loadngs s superor to another. Followng Shortle s [1990] recommendatons for evaluatng the relatve effcency of polluton control allocatons under uncertanty, we use expected damage costs. More about the crtera for the use of damage costs n desgnng the tradng system s presented below. Economc damages from polluton are a secondorder approxmaton of actual damages, whch s taken to be an ncreasng, convex functon of a, D(a) ' d 1 a%d 2 a 2 (9) Damages are calbrated by settng ntal expected damages equal to a percentage of ntal nonpont net benefts and by choosng an elastcty of damages (Table A1). The percentage used to set ntal expected damages s taken from values reported by Smth [1992] for groundwater damages, although we allow for a range of larger values because we consder damages from both pont and nonpont sources (whereas Smth only consdered damages by agrculture) and because of the economc mportance of both use and non-use aspects of the Chesapeake Bay that are lkely to be adversely mpacted by ntrogen from the SRB.

8 References Abler and Shortle, Abler, D.G. and J.S. Shortle, Technology as an Agrcultural Polluton Control Polcy, Amercan Journal of Agrcultural Economcs, 77, 20-32, Bnswanger, H.P., The Measurement of Techncal Change Bases wth Many Factors of Producton, Amercan Economc Revew, 64, , Camacho, R., Fnancal Cost-Effectveness of Pont and Nonpont Source Nutrent Reducton Technologes n the Chesapeake Bay Basn, ICPRB Report, 91-8, Carmchael, J. and B. Evans, A Reduced Form Model of Non-Pont Polluton Loadng for Regonal Scale Analyss, Workng paper, The Pennsylvana State Unversty, Chambers, R.G. and U. Vasavada, Testng Asset Fxty for U.S. Agrculture, Amercan Journal of Agrcultural Economcs, 65, , Chavas, J.P. and M.T. Holt, Acreage Decsons Under Rsk: The Case of Corn and Soybeans, Amercan Journal of Agrcultural Economcs, 72, , Claassen, R. and R.D. Horan, Unform and Non-Unform Second-Best Input Taxes: The Sgnfcance of Market Prce Effects on Effcency and Equty, Envronmental and Resource Economcs, 19, 1-22, May Davs, G.C. and M.C. Espnoza, A Unfed Approach to Senstvty Analyss n Equlbrum Dsplacement Models, Amercan Journal of Agrcultural Economcs, 80, , Edwards, R.E. and T.W. Stoe, Nutrent Reducton Cost Effectveness Analyss, 1996 Update, Susquehanna Rver Basn Commsson Publcaton No. 195., Harrsburg, PA., Fernandez-Cornejo, J., Short- and Long-Run Demand and Substtuton of Agrcultural Inputs, N.E. Journal of Agrcultural and Resource Economcs, 21, 36-49, Hanley, N., J.F. Shogren, and B. Whte, Envronmental Economcs: In Theory and Practce, Oxford, New York, Hertel, T.W., Negotatng Reductons n Agrcultural Support: Implcatons of Technology and Factor Moblty, Amercan Journal of Agrcultural Economcs, 71, , Holt, M. T., A Multmarket Bounded Prce Varaton Model Under Ratonal Expectatons: Corn and Soybeans n the Unted States, Amercan Journal of Agrcultural Economcs, 74, 10-20, 1992.

9 Horan, R.D., J.S. Shortle, D.G. Abler, and M. Rbaudo, The Desgn and Comparatve Economc Performance of Alternatve Second-Best Pont/Nonpont Tradng Markets, Department of Agrcultural Economcs Staff Paper , Mchgan State Unversty, Kawagoe, T., K. Otsuka, and Y. Hayam, Induced Bas of Techncal Change n Agrculture: The Unted States and Japan, , Journal of Poltcal Economy, 94, , Keeney, D.R., Ntrogen Management for Maxmum Effcency and Mnmum Polluton: Farmed Sols, Fertlzer, Agro-systems, n Ntrogen n Agrcultural Sols, edted by F.J. Stevenson, Amercan Socety of Agronomy, Madson, WI, Lee, D.R. and P.G. Helmberger, Estmatng Supply Response n the Presence of Farm Programs, Amercan Journal of Agrcultural Economcs, 67, , Malk, A.S., B.A. Larson, and M.O. Rbaudo, Economc Incentves for Agrcultural Nonpont Source Polluton Control, Water Resources Bulletn, 30, , Natonal Research Councl (NRC), Sol and Water Qualty: An Agenda for Agrculture, Natonal Academy Press, Washngton, DC, Nzeymana, E., B.Evans, M. Anderson, G. Peterson, D. DeWalle, W. Sharpe, J. Hamlett, B. Swstock, Quantfcaton of NPS Polluton Loads Wthn Pennsylvana Watersheds, Fnal Report to the Pennsylvana Department of Envronmental Protecton, Envronmental Resources Research Insttute, The Pennsylvana State Unversty, Pennsylvana Agrcultural Statstcs Servce (PASS) Statstcal Summary & Pennsylvana Department of Agrculture Annual Report. Pennsylvana Department of Agrculture. Harrsburg, PA, Peterson, G.A. and W.W. Frye, Fertlzer Ntrogen Management, n Ntrogen Management and Ground Water Protecton, edted by R.F. Follet, Elsever, Amsterdam, Ray, S.C., A Translog Cost Functon Analyss of U.S. Agrculture, , Amercan Journal of Agrcultural Economcs, 64, , Roth, K. and W.A. Jury, Modelng the Transport of Solutes to Groundwater Usng Transfer Functons, Journal of Envronmental Qualty, 22, , Sato, K., A Two-Level Constant-Elastcty of Substtuton Producton Functon, Revew of Economc Studes, 34, , Shortle, J.S., The Allocatve Effcency Implcatons of Water Polluton Abatement Control Cost Comparsons, Water Resources Research, 26, , 1990.

10 Smth, R.A., G.E. Schwarz, and R.B. Alexander, Regonal Interpretaton of Water-Qualty Montorng Data, Water Resources Research, 33, , Smth, V.K., Envronmental Costng for Agrculture: Wll t be Standard Fare n the Farm Bll of 2000?, Amercan Journal of Agrcultural Economcs, 74, , Tegene, A., W.E. Huffman, and J.A. Mranowsk, Dynamc Corn Supply Functons: A Model wth Explct Optmzaton, Amercan Journal of Agrcultural Economcs, 70, , Thrtle, C.G., Accountng for Increasng Land-Labour Ratos n Developed Country Agrculture, Journal of Agrcultural Economcs, 36, , USDA, Economc Research Servce, Corn Costs and Returns, http//

11 Table A1. Factor Cost Shares, Producton Shares, and Dstrbutons of Uncertan Parameters Determnstc and Uncertan Parameters That Vary by Regon Regon Producton Shares Pont and Nonpont Transport Coeffcents Dstrbuton Mean Varance Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma Determnstc and Uncertan Parameters That Do Not Vary by Regon a Parameters Dstrbuton Mean Varance Sources and/or Justfcaton for Values Land Cost Share None (determnstc) USDA [2000] Fertlzer Cost Share None (determnstc) USDA [2000] Mechancal Cost Share Elastcty of substtuton between composte nputs Elastcty of substtuton between land and fertlzer Elastcty of land supply None (determnstc) USDA [2000] Unform Bnswanger, [1974]; Chambers and Vasavada, [1983]; Fernandez-Cornejo, [1992]; Hertel, [1989]; Kawagoe et al., [1985]; Ray, [1982]; Thrtle, [1985] Unform Same as for the elastcty of substtuton between composte nputs. Unform Chavas and Holt [1990]; Holt [1990]; Lee and Helmberger [1985]; Tegene et al. [1988] Uptake Unform Keeney [1982]; Peterson and Frye [1989], NRC ]1993] Rato of PS margnal abatement costs to NPS margnal abatement costs Unform Malk et al. [1994] Precptaton Gamma Carmchael and Evans [2000] Elastcty of damages Unform The dstrbuton permts a range of convexty a The dstrbutons of uncertan parameters do not vary by regon, but the values of these parameters do vary across

12 regons for each Monte Carlo smulaton as each uncertan parameter s drawn ndependently for each regon.

13 Notes 1. Ths research was funded n part by Cooperatve Agreement number 43-3AEL wth the U.S. Department of Agrculture, Economc Research Servce, Resource Economcs Dvson. We are grateful to Jeff Carmchael, Barry Evans, and Bob Edwards for access to ther data. All remanng errors are our own. The vews expressed here are the authors and do not necessarly reflect those of ERS or the USDA. 2. Accordng to the SRBC data, three stage annual treatment provded the same reducton as fve stage seasonal treatment, but at a lower cost. Smlarly, fve stage annual treatment provded the same reducton as the lmt of technology, but at a lower cost.