超越对数成本函数

ANALYSISEnvironmentalefficiencymeasurementwithtranslogdistancefunctions:Aparametricapproach☆RafaelA.Cuestaa,1,C.A.KnoxLovellb,JoséL.Zofíoc,⁎aCajadeAhorrosdeAsturiasandDepartamentodeEconomía,UniversidaddeOviedo,E-33071Oviedo,SpainbDepartmentofEconomics,TerryCollegeofBusiness,UniversityofGeorgia,Athens,GA30602,USAcDepartamentodeAnálisisEconómico:TeoríaEconómicaeHistoriaEconómica,UniversidadAutónomadeMadrid,E-28049Cantoblanco,Madrid,SpainabstractarticleinfoArticlehistory:Received8October2007Receivedinrevisedform11December2008Accepted3February2009Availableonline4May2009Keywords:ParametricdistancefunctionsStochasticfrontieranalysisEnvironmentalefficiencyUndesirableoutputsJELclassification:C23D24L94Weintroducenewspecificationsandestimationproceduresoftraditionaldistancefunctionsthatallowresearcherstoundertakeenvironmentalefficiencyandproductivitystudieswithinaparametricstochasticframework.Relyingonatranslogdistancefunctionspecificationthattreatstheoutputs'vectorasymmetricallybyallowingequiproportionaldesirableoutputsexpansionandundesirableoutputscontraction,wediscusstherelevantpropertiesthatcharacterizetheenvironmentalhyperbolicdistancefunction,andshowthatitcanbeeasilyimplementedusingconventionaleconometrictechniquesbasedonmaximumlikelihoodestimation.WeillustrateourmodelestimatingtechnicalefficiencyscoresforapanelofU.S.electricitygeneratingunitsthatproduceelectricityandSO2emissionsasbyproduct.©2009ElsevierB.V.Allrightsreserved.1.IntroductionMostfirmsproducemultipleoutputsthataredifficultorundesir-abletoaggregate.Thisnecessitatesreplacingproductionfunctionswithdistancefunctionsinaprimalanalysisofproducerperformance.Input-andoutput-orienteddistancefunctions,introducedbyDebreu(1951),Malmquist(1953)andShephard(1953,1970),arenowthecornerstonesofprimalanalysisofproducerperformance.Nonpara-metricdistancefunctions(Charnesetal.,1978)dominateempiricalanalysis,althoughflexibleparametricdistancefunctionshavebeenemployed(Lovelletal.,1994;Morrison-Pauletal.,2000).Aparticularlysignificantexampleofmultipleoutputproductioninvolvesthesimultaneousproductionofdesirablemarketedoutputsandundesirable,typicallynon-marketed,byproductssuchasemis-sionsandpollutants.Becausebyproductsarerarelymarketed,theyarerarelypriced,andsoenvironmentalperformanceanalysisisfre-quentlybasedonaprimalrepresentationoftechnology,whichallowsthedeterminationofthetechnologicalopportunitycostofreducingundesirableoutputs.Moreover,whenabatementprogramsbasedonmarketincentivesexist,supplyanddemandforallowancesinteractdeterminingequilibriumpricesfortheemissionpermits,whichinturncanbeconfrontedtoaneconomicvaluationofthetechnologicalopportunitycosts,i.e.shadowprices;asitisthecaseforthe“capandtrade”programdealingwiththeSO2emissionsthatweconsiderintheempiricalapplication.Howeverconventionaldistancefunctionsarenotwellsuitedforenvironmentalperformanceanalysisbecausetheymeasureitradially,intermsoftheabilitytoexpandalloutputs(orcontractallinputs)equiproportionately.Theydonotdiscriminatebetweendesirableoutputsandtheirundesirablebyproducts.AsZofíoandPrieto(2001;67)remark,outputdistancefunctionstreatthetwosetsofoutputssymmetrically−abusinessasusualstrategy,whilewhatisrequiredisadistancefunctionthattreatsdesirableandundesirableoutputsasymmetrically.Färeetal.(1985)introducedsuchadistancefunction,ahyperbolicdistancefunctionthatmeasuresproducerperformanceintermsoftheabilitytoexpandoutputsandcontractinputsequiproportionately.Conventionalradialdistancefunctionsareorientedtowardexpandingoutputsorcontractinginputs,andsoarespecialcasesofhyperbolicdistancefunctions.LaterFäreetal.(1989)(FGLP)adaptedanonpara-metrichyperbolicdistancefunctiontothemeasurementofenviron-mentalperformance.ThisenabledthemtotreatdesirableandEcologicalEconomics68(2009)2232–2242☆WearegratefultoProfessorWilliamWeberforprovidinguswiththedatabaseonU.S.electricutilitiesthatweemployinourempiricalapplication.WehavebenefitedfromconversationswithCarlPasurka.Wearealsogratefultotwoanonymousrefereesforhelpfulcommentsonanearlierdraft.Anyremainingerrorsaretheresponsibilityoftheauthors.⁎Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddresses:[e-mail](R.A.Cuesta),[e-mail](C.A.K.Lovell),jose.zofi[e-mail](J.L.Zofío).1Tel.:[phone];fax:[phone]-8009/$–seefrontmatter©2009ElsevierB.V.Allrightsreserved.doi:10.1016/j.ecolecon.2009.02.001ContentslistsavailableatScienceDirectEcologicalEconomicsjournalhomepage:(1996),whointroducedanalternativecharacterizationoftheproduc-tiontechnologybywayofthedirectionaldistancefunction.Chungetal.(1997)presentedthefirstextensionofthisdistancefunctionforenvironmentalefficiencymeasurement.Thesetheoreticalbreakthroughshavespawnedagrowingliteratureinenvironmentalperformanceanalysis.Beyondtheseminalcontribu-tions,empirical