献县欧联玻璃容器有限公司

初始排污权核算技术报告

编制单位：献县欧联玻璃容器有限公司

20xx年9月15日

献县欧联玻璃容器有限公司

初始排污权核算技术报告

1. 企业概况

1.1. 企业基本信息

献县欧联玻璃容器有限公司于20xx年3月挂牌成立。公司前身是献县日新玻璃制品有限公司，20xx年建厂。20xx年10月美国OI公司收购，更名欧文斯献县玻璃容器有限公司。20xx年3月转为民营企业。公司位于献县东外环路与南环路交叉口东北角，占地面积150亩。

欧联公司前身日新玻璃制品有限公司，分别于20xx年6月和20xx年1月建设两个制瓶车间。按规定进行了环评，完工后通过了献县环保局的验收。并且核发了排污许可证。历年来环保部门对公司排污进行了检测。

1.2. 基本情况及项目组成

1.2.1. 基本情况：献县欧联公司总投资5300万元，拥有2座窑炉，6条制瓶生产线，年生产能力13万吨。公司主要生产玻璃包装容器，包括棕料、绿料和白料玻璃瓶，用于啤酒、白酒及各种饮料的包装

1.2.2. 项目组成

主体工程：两座煤气发生炉，两座玻璃窑炉，六条制瓶生产线及空压站等，附主要设备表。

辅助工程：原料库，成品库。

公用工程：高低压配电设施，办公设施、员工宿舍楼，供水系统，消防设施，食堂等。 环保工程：循环水系统，脱硫除尘设备和SNCR脱硝设备。

附表1. 主要设备一览表

附图1. 厂区平面图

1.3. 物耗能耗

附表2. 主要原料消耗

主要原料性质如下：

石英砂：是一种坚硬、耐磨、化学性质稳定的硅酸盐矿物，其主要成分是SiO2，颜色为乳白色或无色半透明状，油脂光泽，相对密度为2.65，不溶于酸，微溶于氢氧化钾溶液，是重要的工业矿物原料，广泛用于玻璃、铸造、陶瓷及耐火材料工业。

长石：是长石族岩石的总称，是一类含钙、钠和钾的铝硅酸盐类矿物，为地壳中常见的矿物，比例达到60%。长石常见乳白色，但常因含有杂质而被染成黄、褐、浅红、深灰等色，富含钾或钠的长石主要用于陶瓷、玻璃及搪瓷工业。

石灰石：主要成分是碳酸钙，分子量为100.09，属六方晶系，性状为白色粉末，无臭、无味，与稀醋酸、稀盐酸发生泡腾，并溶解。高温条件下分解为氧化钙和二氧化碳，露置空气中无反应。

纯碱：学名碳酸钠，易溶于水，呈弱碱性，在玻璃制品中提供氧化钠。被广泛用于制肥皂、纺织、印染、漂白、造纸、精制石油、冶金及其它化学工业。

附表3. 能源消耗

产品

玻璃瓶的特点是无毒、无味、透明、不透气，耐热、耐压、耐清洗，化学稳定性好，没有污染。缺点是易破碎。年产各种玻璃瓶2.5亿只。

2. 工艺流程和产污分析

2.1. 工艺流程

玻璃瓶生产工艺是利用煤气发生炉生产的半水煤气作燃料，在1530℃左右的温度把以石英砂为主的配合料熔化为玻璃液，经过澄清、均化等过程成为适合成型的玻璃态，通过行列式制瓶机制成各种玻璃瓶罐，经过退火、检验和包装后，成品入库。见附图2-工艺流程图

献县欧联玻璃容器有限公司

工艺流程图

玻璃的生产过程主要有以下几个环节：

煤气生产：在煤气发生炉中从底部进入发生炉的空气（一次风）和水蒸气的混合气体（气化剂）与成品煤炭发生氧化还原反应制得半水煤气。煤气经过除灰斗除去煤灰和煤焦油，送往窑炉。燃烧后的炉渣通过除灰器从灰盆出炉。

配料：石英砂、石灰石、长石、纯碱、碎玻璃等原料按照设计配方，经过称量、混合等工序混合为均匀的配合料，通过皮带输送机、斗式提升机等设备送到窑炉的料仓中。

熔化：本公司有二座蓄热式马蹄焰窑炉。煤气和空气分别通过上火侧煤气蓄热室和空气蓄热室吸收其中储存的余热，被加热到1100-1300度通过喷火口进入熔化池混和燃烧。燃烧后的烟气从另一侧喷火口进入回火侧煤气蓄热室和空气蓄热室，烟气经过蓄热室大量的砌体，除去烟尘，在烟气通道中适当的温度区域喷入氨水脱硝，再经过水膜除尘，最后经烟囱排入大气。来自配料岗位的配合料均匀加入窑炉的熔化池，经过分解、熔化、澄清，成为符合要求的玻璃液。

成型：玻璃液从窑炉经过供料道到供料机，用压缩空气吹制成成品瓶。 退火：制瓶机成型后的成品瓶通过电加热退火炉消除应力，提高热稳定性。 检验包装：退火后的瓶子经过自动检验机、灯检，合格的产品包装入库，不合格的瓶子通过废料系统作为原料回收利用。

缩空气吹制成型的，包装设备也使用压缩空气。空压站8台空压机为各工序提供压缩空气。

供电系统：供电局河街变电站10kV 566专线、和城关10kV 596备用线双回路为公司

提供电力。全厂有三台变压器，供给全厂生产生活用电。

供水系统：全厂生产生活用水由献县自来水公司供水管网提供。生产用水主要有空压机冷却水、制瓶机废料冷却水、煤气站水封用水等。冷却水循环使用，不外排。生活污水经化粪池处理后经污水管网排入献县污水处理厂。

2.2. 主要污染物产生和排放统计汇总见附表4

3. 环保措施及效果

3.1. 污染物防治措施

欧联公司高度重视环保工作，从人力、物力和财力方面提供保证。先后采取多项措施节能减排，至今已经初见成效。

首先，采取先进的工艺技术，降低能源消耗减少污染物排放。公司于20xx年和20xx年投资1100万元对两个车间窑炉进行了节能改造，疏通了蓄热室，更新了小炉。使得吨成品煤耗从改造前的250公斤降低到190公斤，全年减少煤耗3366吨，直接减少烟气排放1110万立方米，减少氮氧化物排放11吨。

第二，公司在二车间投资100万元，由沧州众诚环保公司建设脱硫、脱销、除尘一体化设备，于今年4月25日投入使用。

第三，公司投资90万元，由泊头得利隆环保设备公司建设两个车间SNCR

脱销系统。SNCR脱销工艺是减少氮氧化物排放的成熟技术。其工艺流程是20%的氨水经过计量泵稀释到需要的浓度，进入喷枪，用压缩空气雾化后喷入850-1000度的烟气中，在此温度区域，氨水与氮氧化物充分接触，反应生成氮气和水，然后经50米高的烟囱排放。此工艺没有废液和固体废物产生，没有二次污染，在国内外被广泛采用。此项目已经投入运行。

第四，保证一车间和二车间制瓶机冷却水循环使用。

第五，在原排水沟加装闸板，投资30万元新建厂区循环水系统。

第六，原煤气管道水封连续补水改为定时补水，不排放。

第七，保持空压机冷却水循环使用，不排放。 第八，修复公司通往污水处理厂的管道。

通过第四至第八项措施，一方面大大降低了消耗水量，生产用水实现零排放；另一方面，少量生活用水输送到污水处理厂。

附表5防治措施及治理效果

3.2. 环保污染防治投资估算 附表6

4. 初始排污权核算

依据建设期环评，欧联公司两座窑炉烟气排放量23000万立方米每年，生活废水年排放量7068吨，煤焦油33.81吨，炉渣5220吨。烟气中的SO2和废水中的氨氮和COD均按实际检测值计算排放量，氮氧化物和烟尘按照达标排放值计算排放量。详见附表7。 附表7

5. 核算结论

根据以上分析和计算结果，结合建设期环评控制排污总量，申请下一持证周期

污染物排放总量控制指标： SO2：21.68t/年， NOX：90.7 t/年， 烟尘：22.679 t/年

氨氮：0.13 t/年， COD：0.99 t/年。

6. 附件

组织机构代码证书

工商营业执照

建设项目环评报告

建设项目环境保护设施竣工验收报告

 

第二篇：排污权初始分配

EnvironResourceEcon(2008)39:265–282

DOI10.1007/s10640-007-9125-4

ORIGINALPAPER

Theoptimalinitialallocationofpollutionpermits:

arelativeperformanceapproach

IanA.Mackenzie·NickHanley·TatianaKornienko

Received:24May2006/Accepted:30March2007/Publishedonline:3May2007

?SpringerScience+BusinessMediaB.V.2007

AbstractTheinitialallocationofpollutionpermitsisanimportantaspectofemissionstradingschemes.WegeneralizetheanalysisofB?hringerandLange(2005,EurEconRev49(8):2041–2055)toinitialallocationmechanismsthatarebasedoninter-?rmrelativeperformancecomparisons(includinggrandfatheringandauctions,aswellasnovelmecha-nisms).Weshowthatusing?rms’historicaloutputforallocatingpermitsisneveroptimalinadynamicpermitmarketsetting,whileusing?rms’historicalemissionsisoptimalonlyinclosedtradingsystemsandonlyforanarrowclassofallocationmechanisms.Instead,itispossibletoachievesocialoptimalitybyallocatingpermitsbasedonlyonanexternalfactor,whichisindependentofoutputandemissions.Wethenoutlinesuf?cientconditionsforasociallyoptimalrelativeperformancemechanism.

KeywordsRelativeperformance·Initialallocation·Pollutionpermits·Auctions·Rank-ordercontests

JELClassi?cationQ53·Q58·C72

1Introduction

Tradablepermitmarketshavebecomeanimportantpolicytoolinthecontrolofpollution.SchemessuchasRECLAIMandtheSO2marketintheUShaveshownthattradablepermitsareaviableandcosteffectivemarket-basedmechanism(e.g.Stavins1998;Schmalenseeetal.1998).Yetthereisstillanactivedebateabouthowtoallocatepermitendowmentsamongtheparticipating?rmsatthebeginningofeachtradingperiod.AsB?hringerandLange(2005)argue,someinitialallocationmechanismsmaycreateinter-temporaldistortionsandresultinsociallysuboptimaloutcomes.

I.A.Mackenzie(B)·N.Hanley·T.Kornienko

DepartmentofEconomics,UniversityofStirling,StirlingFK94LA,UK

e-mail:i.a.mackenzie@stir.ac.uk

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266IanA.Mackenzieetal.Inthispaper,weextendtheresultsofB?hringerandLange(2005)toaccommodatemostoftheexistingdynamicinitialallocationmechanisms(includinggrandfatheringandauctions,aswellasnovelmechanisms).Weshowthatusing?rms’historicaloutputsforallocatingpermitsisneveroptimal,whileusing?rms’historicalemissionsisoptimalonlyinclosedtradingsystemsandonlyforanarrowclassofallocationmechanisms.Instead,itispossibletoachievesocialoptimalitybyallocatingpermitsbasedonlyonanexternalfactor,whichisindependentofoutputandemissions.Weoutlinesuf?cientconditionsforasociallyoptimalrelativeperformancemechanismanddiscusstheissuesrelatedtothechoiceofasuitablemechanismforinitialallocation.

Inouranalysis,wediscusstwotypesofmechanismsthatarecommonlyconsideredforallocatinginitialendowmentsofpermits.The?rstmechanism,whichwecallanAbsolutePerformanceMechanism(APM),involvespermitallocationsbasedonthelevelsofindivid-ual?rmactivity.Thesecondmechanism,whichwecallaRelativePerformanceMechanism(RPM),involvespermitallocationsbasedonhowthelevelsofa?rm’sactivitycomparetothelevelsofother?rms’activities,oroninter-?rmrelativecomparisons.Thedistinctionbetweenthesetwomechanismsiscrucialas?rms’behaviourinthepermitmarketissubjecttowhether?rms’believetheyareobtainingpermitsindividuallyor,asunderaRPM,aspartofagamewherea?rm’sallocationisdependentonother?rms’actions.Weshowinthispaperthatamechanismthatallocatespermitsbasedon?rms’absoluteperformance(APM),asusedbyB?hringerandLange(2005),isaspecialcaseofageneralizedrelativeperfor-mancemechanism(RPM),andthusthatthetwomechanismsshareanumberofoptimalitypropertiesinadynamicsetting.Wehoweverarguethatmechanismswhicharebasedonrelativeperformancemightbesuperioroverthosebasedonabsoluteperformanceandofferapromisingalternativetoauctioningandgrandfathering,namelyarank-ordercontest.

Bothtypesofmechanismshavehadimportantapplicationsinexistingtradablepermitmarkets.Absoluteperformancemechanismshavebeenadvocatedintheformofrelativeemissionsorintensity-basedemissionscaps(Fischer2001,2003;EllermanandWing2003;KuikandMulder2004;Pizer,2005;NewellandPizer,2006).1Insuchaschemeintra-?rmrelativecomparisonsexist,wheretheperformanceofagiven?rmisevaluatedrelativetoitsownactivity,butnotrelativetotheactivityofother?rms.Ratherthanhavingacaponabsolutelevelsofemissions,anintensity-basedcapinvolvesaceilingontheemissionsinten-sity(i.e.emissionsperoneunitofoutput).Thistypeofapproachisbecomingincreasinglycommon,forexample,Bode(2005)notesthatanumberofparticipantsintheUKemissionstradingschemeweregivenanintensitytarget.Furthermore,theBushadministrationintheU.S.hasstronglyadvocatedthistypeofapproachtotackleclimatechange(Kolstad2005;Pizer2005).Whenatradingsystemisbasedonemissionsintensity,each?rmcanunilaterallyincreaseboththeiroutputandemissionswithoutchangingemissionsintensityandwithoutanyeffectonother?rms(thepermitallocationisanadjustablegrandfatheringmechanism).However,themajorityofdistributionruleswhichhavebeendiscussedarerelativeper-formancemechanisms.ThetwomostcommonRPMsincludeauctions(where?rms’areallocatedpermitsbasedontheirrelativebids)andgrandfatheringwitha?xedcap(where?rms’areallocatedpermitsbasedontheirrelativeemissionslevelswithrespecttosome?xedcap)(seeHahnandNoll1982;Lyon1982;1986;Oehmke1987;MillimanandPrince1989;VanDyke1991;Franciosietal.1993;Parry1995;Parryetal.1999;CramtonandKerr2002).1Wemakeadistinctionbetweenintensity-basedcapsandoutput-basedallocation(althoughtheydobothactasanimplicitoutputsubsidy).Inintensityrate-basedmechanismstheemissioncapisadjustedtomaintainaconstantemissionsintensityandhenceallocationisnotdependentonother?rms’behaviour(e.g.thelevelsofother?rms’emissionsandoutputchoices).Incontrast,output-basedmechanismsaltertheaverageallocationperunitofoutputtomaintaina?xedemissionscap(allocationisdependenton?rms’behaviour).123

Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach267However,thereisalargeselectionofRPMsthathavenotbeenextensivelyconsideredintheliterature.Forexample,yardstickcompetition,whereeach?rm’sperformanceisassessedrelativelytotheperformanceofother?rmshasbeensuggested(Shleifer1985;Franckxetal.2005;NalebuffandStiglitz1983a,b).Moreover,anovelRPMthatcouldbeenvisagedtoallocatepermitsistheuseofcontestsortournamentswhere?rmsspendresourcesinorderto‘win’aproportionofthepermitallocation(MoldovanuandSela2001,2006).

Inter-?rmcomparisonsusingrelativeperformancemechanismshaveanumberofgen-eralregulatoryadvantageswhichhavebeenwidelydocumentedintheliterature(LazearandRosen1981;Holmstr?m1982;GreenandStokey1983;NalebuffandStiglitz,1983a,b;Mookherjee1984;Shleifer1985;MoldovanuandSela2001,2006).Relativeperformancemechanismscanalsobeadvantageousinanenvironmentalcontext.Govindasamyetal.(1994)suggestedtheuseofatournamenttocontrolnon-pointpollution,andfoundthataRPMresultsinanumberofdesirableoutcomes.Franckxetal.(2005)extendedtheworkofGovindasamyetal.(1994)byusingadifferentRPM,yardstickcompetition,andconductedtheanalysisinamoregeneralenvironmentalregulatorysetting.They?ndthatthisRPMwillbedesirablewhenalargenumberof?rmsparticipateandcommonshocks(suchassimilartechnologyshocksoroilpricechanges)areexperiencedbyall?rms.

Ratherfewerauthorshavefocusedonrelativeperformanceissuesinemissionstrading.Usingarent-seekingmodel,MaluegandYates(2006)examinetheeffectsofcitizenpar-ticipationinapermitmarkettodeterminetheendowmentandpriceofpermits.They?ndthatcitizens’choiceoflobbyingandpermitpurchasesinamarketdependsontheinitialallocationmechanismchosen(auctioningorgrandfathering).Finally,GroenenbergandBlok(2002)outlineaninitialallocationmechanismforapermitmarketthatbasesdistributiononbenchmarkingtheproductionprocessofeach?rmand?nditeliminatesalargeamountofproblemsassociatedwithexistingallocationmechanisms.

Foranumberofdecadesthefreeallocation(grandfathering)ofpermitshasbeendiscussedasafeasiblemethodofallocation(e.g.Tietenberg1985).Indeed,themajorityofactualemis-sionstradingschemestodateusegrandfatheringastheprimaryallocationmechanismduetoitspoliticalviability:marketparticipantswillalwayslobbyforthefreeallocationofper-mits(Stavins1998).Grandfatheringmightalsobeseenasofferingacloser?ttoexistingregulatoryapproaches,sinceitdoesnotinvolveanyfundamentalchangeinpropertyrightscomparedwith,forinstance,asystemofperformancestandardsforpollutingemissions.Grandfatheringmightalsobepreferredbygovernmentsoncompetitiongrounds,sincetheavoidanceofalump-sumdistributionfromindustrytogovernmentcanavoiddisadvantagingdomestic?rmsrelativetotheirinternationalcompetitors.Onthenegativeside,grandfather-ingcouldbeseenasrewarding?rmswhohaveengagedinrelativelylowpollutioncontroleffortsinthepast.Asgrandfatheringisacommonlyusedtool,thediscussionsregardingtheeffectsofthemechanismhavebeenwidespread.Inparticular,RequateandUnold(2003)haveshownthatsubstantialinnovationincentivesexistfor?rmsinagrandfatheredemissionsscheme.However,Goulderetal.(1997)foundgrandfatheringtobearatherinef?cientallo-cationmechanismcomparedtoalternativeallocationprocedures.Recently,grandfatheringhasbeenadaptedtoincludeadynamicelement(Bode2006;B?hringerandLange2005).Inparticular,B?hringerandLange(2005)havediscussedupdatedgrandfatheringwhichcontinuallyupdatesthefreeallocationofpermitsbasedonhistoricalemissionsandoutput.2Theyfoundthatthedynamicallocationhastobecarefullyconsideredtoreducedistortionsintheproductandpermitmarket.

2SeeFischer(2001)forstaticanalysisofoutput-basedpermitallocations.

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268IanA.Mackenzieetal.Anotherimportantaspectofthemechanismsinquestioninvolvesmulti-periodchoiceproblemsinpollutionpermitmarkets.Severalstudieshavefocusedongeneraldesigncon-siderationsformulti-periodpermitmarkets(CronshawandKruse1996;Rubin1996;KlingandRubin1997;Schennach2000;LeibyandRubin2001;YatesandCronshaw2001),yetonlyafewstudieshavefocusedontheinitialallocationofpermitsinthissetting.Inthecontextoftheelectricitysector,Bode(2006)?ndsconsiderablevariationinthedistributionalimpactsamongdifferentallocationmechanismswithinadynamicemissionstradingscheme.JensenandRasmussen(2000)modelanumberofallocationmechanismsinadynamicsettingand?ndthatwelfareandemploymentvarydrasticallyacrossallocationmechanisms.

TheworkwhichisthemostrelevanttoourpaperisbyB?hringerandLange(2005),whocomparetheef?ciencyofdynamicpermitallocationsbasedonoutput,emissionsandalump-sumtransfer.Incomparingef?ciency,theymakeadistinctionbetweenmarketsthatareopen(i.e.when?rmscantradeoutsidethedomesticmarket)andclosed(i.e.whenparticipating?rmscannottradeinpermitsoutsidethedomesticmarket).Thisdistinctionisimportanttopolicyanalysisastradablepermitmarketsarebecomingincreasinglyvariedinsizeandscopeandhavethepotentialtohaveeitheranopenorclosedmarketstructure.They?ndinaclosedmarketitisoptimaltoallocatepermitsoncriterianotrelatedtooutput,whereasforanopenmarket,anef?cientallocationoccurswhenthepermitsaredistributedusingalump-sumapproach.However,intheirtreatmentoftheinitialallocationmechanism,B?hringerandLange(2005)assumethatthepermitdistributiontoa?rmisbasedonlyon?rms’absolutelevelsofoutputandemissions,sothatother?rms’sactionsdonotaffecttheallocationofagiven?rm.Yet,giventhe?xedemissioncapconsideredbyB?hringerandLange(2005),thepermitallocationtoa?rmisalsocruciallydependentonthebehaviourofrival?rms.Thisisbecausea?xedemissionscapimpliesthatifinthecurrentperiodrival?rms,say,increasetheiroutputandemissionsrelativetoagiven?rm,thenthecurrent-periodaggregateoutputandemissionsincrease,thusdecreasingtheproportionoffuturepermitsthateach?rmcanreceivepereachunitofcurrentoutputandemissions.Astheresult,evenifagiven?rmdoesnotalteritsownchoices,itsownfutureallocationofpermitswillchange.ThuswearguethattheinitialallocationprocessconsideredbyB?hringerandLange(2005)shouldtakeintoaccountother?rms’actionsandthusshouldbemodelledasarelativeperformancemechanism.

OurpaperthereforeattemptstoextendB?hringerandLange(2005)byimplementingamoregeneraldesignofadynamicinitialallocationmechanism,whichallowsforthealloca-tionofpermitstobebasedoneach?rm’schoicesrelativetoother?rms.FollowingB?hringerandLange(2005),weconsiderallocationmechanismswhicharebasedonchoicesofoutputandemissions,butinadditionweconsiderpossiblepermitallocationsbasedonan“external”factorwhichisindependentofoutputandemissions.Thisallowsustocreateanencompass-ingmodelformostexistingtypesofinitialallocationmechanismssuchasgrandfathering,auctioningandcontests.WeshowthataRPMcanef?ciently(sociallyoptimally)allocatepollutionpermitsifthecriteriausedtocompare?rmsisbasedonsuchanexternalfactor,inacontest.Giventhevarietyofpotentialexternalfactors,wesuggestanumberofcriteriathataregulatormaytakeintoaccountwhenchoosingasuitablefactor.Wealsoargueinfavourofanewmechanism,whichinvolvesaninter-?rmcontestdesignedtoachievetwogoalssimultaneously—thatis,theprimarygoalofef?ciencyandsomesecondarygoal,suchasgeneratingrevenue,achievinghealthandsafetytargets,noisereduction,reductionofotherpollutants,etc.Giventhepoliticaleconomyproblemswithbothauctionsandgrandfatheringasawayofinitiallyallocatingpermits,thisnewmechanismmaywellbeofinteresttopolicymakers.

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Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach269Ourcontributionisthustwofold.First,weextendtheresultsofB?hringerandLange(2005)toawiderclassofmechanisms,so-calledrelativeperformancemechanisms,suchasgrandfatheringwith?xedcap,yardsticks,auctions,contests,etc.Althoughsuchmechanismscreateasituationwhere?rms’choicesareinterdependent,thegeneralintuitionofB?hringerandLange(2005)holdsintheNashequilibriumoftheensuinggame.Thatis,forawiderangeofmechanisms,fortheinitialallocationtobecost-ef?cient,itshouldnotdependon?rms’outputs,andmaydependon?rms’emissionsonlyinlimitedcircumstances.Second,weproposethatthelump-sumdistributionadvocatedbyB?hringerandLange(2005)canbeimplementedbetterwitharelativeperformancemechanismbasedonanexternalfactor.Suchacost–ef?cientmechanismallowstheregulatortoachieveasecondarytarget,suchasraisingrevenue,—thus“killingtwobirdswithonestone”.

Tothebestofourknowledge,thisisthe?rstpapertointroduceageneralisedRPMintoapermitmarketwhichallowsustomodelmostexistingrelative-basedmechanismsandhastheaddedadvantageofencompassingAPMs.Thepaperisorganisedasfollows:Sect.2outlinesourmodelandpresentsthesocialoptimalityconditionsand?rm’soptimisationproblem.Asociallyoptimaldynamicinitialallocationmechanism,whenthemarketexperiencesbothexogenousandendogenouspermitprices,isconsideredinSect.3.Section4discussestheexternalfactor,whileSect.5concludes.

2Themodel

WefollowB?hringerandLange(2005)andconsideramulti-periodpartialequilibriummodel.Thetechnologyofa?rmi(i=1,2,...,n)attimet(t=1,2,...)isgivenbyacostfunctioncit(eit,qit),whereqitisthe?rm’soutputlevel,andeitthe?rm’semissionsresultingfromproduction.Costscitareassumedtobetwicedifferentiableandconvex,with?2?22c2c2c2c2cc>0.it≤0,it>0,?e,?q,?itit≥0and?q·?e?ititititititThe?rmsellsitsoutputinacompetitiveproductmarketatapriceofpt.Finally,the?rmisregulatedbyacompetitiveemissions-tradingprogramandreceivesaninitialallocationofpermitsAit.

Wefurtherassumethateach?rmialso“produces”afactorzitwhichhasnodirectrele-vanceintheproductandemissionsmarket,andthusisoutsidetheregulator’sinterestsand/orjurisdiction.This“external”factoris“produced”byeach?rmindependentlyofoutputandvemissionsatacostvit(zit)(possiblyzero),withdit≥0.Whilethisexternalfactorisirrel-evanttotheproductandemissionsmarket,itmaydetermine?rms’permitallocationsAitinamannertobespeci?edlater.

2.1Thegeneralisedallocationmechanism

B?hringerandLange(2005)consideredamechanismwherebypollutionpermitsareallo-catedbasedonthelevelsof?rm’shistoricalproductionqitandemissionseit.3We?rstextendthismechanismbyassumingthatinadditiontooutputandemissions,some“external”factormayplayaroleinhowmanypermitswillbeallocatedtoagiven?rm,butthisfactorhasnorelevancetotheproductandemissionsmarket,andthusisbeyondtheinterestorjurisdiction3B?hringerandLange(2005)consideredanumberofhistoricalobservationperiods,l=(1,2...,s).Forexpositionalsimplicity,werestrictourmodeltol=1(thehistoricalperiodissimplythepreviousperiod).Itisstraightforwardtogeneraliseourmodeltol>1historicalobservationperiods.

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270IanA.Mackenzieetal.oftheregulator(anditisthisfactorwhichdeterminesthelump-sumallocationsinthemodelofB?hringerandLange2005).

Examplesofapossibleexternalfactorincludepopulationsizeina?rm’slocality,a?rm’ssociallyresponsibleactivities,a?rm’semissionsofotherpollutants,arandomeventsuchalotterydrawandsoon.Wedenotesuchexternalfactorsaszit.WhilewewilldiscusstheexternalfactormoreinSect.4,itisworthnotingherethatthenatureoftheexternalfactordeterminesboththecostofthisfactortothe?rm,aswellasthedegreeof?rm’scontroloverthisfactor.Forexample,populationsizeisbothbeyondthe?rm’scontrolanditis“free”tothe?rm.Ontheotherhand,lotteryticketscanbeboughtby?rms,orcanbeallocatedto?rmsbytheregulator(andthusarebeyond?rms’control).Incontrast,inapermitauction,bothsuccessandcostsofeach?rm’sbiddependsonthebidsofotherparticipating?rms.Thus,theallocationmechanismbasedonabsoluteperformance(APM)isgivenby

t?1?t?11?APMAit=λq?(ei(t?1))+λtz?,ith(qi(t?1))+λe,itg,itf(zi(t?1))(1)

1λtz?,it≥0aretheweights(inperiodt)placedonperiodt?1’sperformance.Theweightsre?ecttherelativeimportanceofaparticularactivity,andcanvaryacrosstimeperiodsandacross?rms.

WeextendEq.1byallowingfor?rms’performancetobeevaluatedincomparisontoother?rms,i.e.howagiven?rmi’sperformanceattimetinproductionqit,emissionseit,anexter-nalfactorzitcomparesrelativelytotheperformanceofeveryother?rm?i={1,...,i?1,i+1,...,n}.Formally,?rmi’sperformanceattimetinoutputrelativelytoother?rms’outputq?itisgivenbyarelativeperformancefunctionh=h(qi(t?1),q?i(t?1)).Similarly,relativeperformanceinemissionsandexternalfactoraregivenbyg=g(ei(t?1),e?i(t?1)),andf=f(zi(t?1),z?i(t?1)),respectively.Weassumehi=,gi=,fi=it>0ititsothat,forgivenlevelsofother?rms’performance,higherlevelsofemissions,output,andtheexternalfactorresultinalargerpermitallocation.Wealsoassumethath?i=,?itt?1t?1?,gwhereh?,f?areincreasingandcontinuouslydifferentiablefunctions,andλq,it,λe,it,?g?f,f?i=≤0,sothatforagivenlevelof?rm’sperformance,itsallocationg?i=?it?itdoesnotincreasesifother?rms’increasetheirlevelsofemissions,output,ortheexternal

factor.4

Wetakearathergeneralviewoftherelativeallocationfunctions.Thatis,toallowforuncer-taintyoverallocations,wetreatthesefunctionsasexpectationsoverpossiblerealisations.Thusallocationscanbedistributedusingdeterministicrules(suchasyardstickcompetitions)devisedbytheregulator,aswellasbylotteries,auctions,orcontests.Foranalyticaltractabil-ity,weassumethattherelativeallocationfunctionsh,g,farecontinuouslydifferentiable.5Forexample,a?rm’srelativeallocationcanbedeterminedcontinuouslybasedonhowitsqitownoutputcomparestoaggregateoutput,e.g.h(qi(t?1),q?i(t?1))=α.Anotherit?i?itexampleofacontinuousrelativeallocationfunctionincludesTullock-type(winnertakesall)contestallocations,wherea?rm’sexpectedamountofpermitsisgivenbyallparticipating

qr?rms’outputsasfollows:h(qi(t?1),q?i(t?1))=β—i.e.thesizeofthepermit?i?ititlotβmultipliedbytheprobabilityofwinningthecontest(seeSkaperdas1996).

4Instead,onecanassumethathandgarenegative.ii

5Ourargumentwillnotchangeifwerelaxtheassumptionofcontinuitytoincluderelativeperformancemechanismssuchaswinner-payandall-payauctionsinvolvingdiscontinuitiesin?rms’payofffunctions.Todealwithsuchdiscontinuities,onetypicallyassumesthatall?rmsfacecommonlyknowncontinuouslydiffer-entiabledistributionof?rms’“types”,andthatall?rmsfollowsymmetricstrictlyincreasinganddifferentiablestrategy,sothateach?rm’sexpectedpayofffunctionbecomescontinuouslydifferentiable.

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Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach271Thus,thepermitallocationfor?rmiattimet,accordingtothegeneralizedRelativePerformanceMechanismis

t?1t?1t?1RPMAit=λq,ith(qi(t?1),q?i(t?1))+λe,itg(ei(t?1),e?i(t?1))+λz,itf(zi(t?1),z?i(t?1))(2)

Comparingthisrelativeperformanceallocationmechanismtothatbasedonabsoluteper-formance(1),onecanobservethefollowing:

Remark1Ifh?i≡g?i≡f?i≡0thenarelativeperformanceallocationmechanismreducestoanabsoluteperformanceallocationmechanism.

Inotherwords,theabsoluteperformancemechanismconsideredbyB?hringerandLange(2005)isaspecialcaseofrelativeperformancemechanismwhen?rmi’sallocationisinde-pendentoftheremaining?rms’actions.Inthiscase,theremaining?rms’actionshavenoimpacton?rmi’sallocation,anda?rmicanobtainpermitsbyoptimallychoosingqit,eitandzit,withoutconsideringother?rms’actions.

NotethatB?hringerandLange(2005)implicitlyassumethatthegrandfatheringmecha-nismisanabsoluteperformancemechanism.However,witha?xedemissioncap,foragivenbehaviourofother?rms,ifaparticular?rmincreases/decreasesitsoutputand/oremissions,thatwouldaffecttheaggregateoutputandemissionsofdomestic?rms,ultimatelyaffectinghowmanypermitsboththat?rmandallother?rmswillreceive.Thus,itisimplicitinB?hrin-gerandLange(2005)thatthefactorweightswillchangeeachperiodtore?ectchangesin?tistheaggregateactivities.Toseethis,supposethatattimeta?xedamountofpermitsEallocatedamongn?rmsproportionallytoeach?rm’soutputqit.Inotherwords,each?rm?tE.Thus,theoutputweightγthastobeireceivesanallocationγtqit,whereγt=it?i?itadjustedeachperiodtore?ectchangesinaggregateproduction.Itiseasytoseethatsuchaq?t?xedcapgrandfatheringmechanismisaRPMwithh(qi(t?1),q?i(t?1))=E.it?i?itWhenarelativeperformancemechanismisused,?rmi’schoicesaffectthenumberofpermitsallocatedto?rmj=i,andthusaffect?rmj’spro?ts,andviceversa.Inotherwords,aRPMcreatesasituationwhere?rmschoicesareinterdependent.Insuchasitua-tion,arational?rmwillmakeitschoicesstrategically,bytakingintoaccounttheanticipatedactionsofitsrivals.Therelativeperformancepermitallocationmechanismthusresultsinagameamongparticipating?rms,whichleads?rms’behaviourtobetypicallydifferentfromtheirbehaviourwhenfacedwithanAPM.Toexplorethedistortionaryeffectofsuchbehaviour,we?rstneedtoconsiderthesociallyoptimalsituation.

2.2Thesociallyoptimaloutcome

Wenowconsidertheregulator’spointofview.FollowingB?hringerandLange(2005)weassumethattheregulatorcaresaboutpro?tsandcostsassociatedwiththeproductionofoutputandemissionsofthespeci?cpollutant,aswellasthetradeinthepollutionpermits,butisnotinterestedintheexternalfactorssuchaspopulationsize,lotterydraws,orauctionbids(wewillcomebacktothisassumptioninSect.4).Thus,theregulator’sobjectiveistomaximise(minimise)theaggregatepro?t(cost)thatallthedomestic?rmsincurwhileproducingtheproductoftheregulator’sinterestsorjurisdictionwhilstbeingconstrainedbytheemissionsprogram.

Whentradeinemissionspermitsisnotrestrictedtotheregulator’sjurisdiction,?rmscanimport/exportemissionsacrossthesystem’sborders.Fromaregulator’spointofview,thisisa(small)openemissionstradingsystem,wherethepermitpriceisexogenouslydeter-mined,andtheaggregateemissionsinthejurisdictionarenotcapped.Thismayoccurwhen

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272IanA.Mackenzieetal.themarketisopentotransactionsfromother(possiblylarger)schemes.Forexample,intheEuropeanUnionEmissionsTradingScheme(EU-ETS),memberstatesallocatepermitsdomestically,but?rmsineachmemberstatecantradepermitswith?rmsinothermemberstates.

Insuchasystem,theregulator’sobjectivetakesintoaccountthebalanceofthetradeintheemissionpermits.Thus,giventhesetofprices(σt,pit),theregulator’sobjectiveisto

?n?n?????Maxpitqit?cit(eit,qit)?σteit?t(3)qit,eitti=1i=1

whereσtistheexogenouspermitpricedeterminedbythe(international)demandandsupplyofpermitsintheopenmarketandtisthedomesticemissionscapattimet.Foreach?rmiandeachofit’srival?i={1,...,i?1,i+1,...,n},thesociallyoptimalconditionsareasfollows:6

pit=

??citit(4)(5)?cjt?cit=?(=σt)itjt

foralli,j=i,t.Thatis,atperiodtall?rmswillsimultaneouslyequatetheirmarginalproductioncoststotheir?rm-speci?cproductprice(4).Also,intheequilibrium,?rms’mar-ginalabatementcostswillbeequalized(5),andwillbeequaltothe(exogenouslydetermined)commonpermitprice.

Incontrast,inaclosedemissionstradingsystem,asingleregulatordistributes?thetotalsupplyofpermits,andthusensuresthattheaggregateemissionsarecapped:ieit=t.Theemissionspermitpriceisendogenouslydeterminedbythe(domestic)demandandsupplyintheclosedmarket.Theregulatorsobjectivefunctionisthus:

??nn???Maxpitqit?cit(eit,qit)subjecttoeit=t(6)qit,eitti=1i=1

Thesociallyoptimalconditionsareidenticaltotheconditions(4–5),exceptthat?rms’mar-ginalabatementcostswillbeequaltotheshadowpriceofabatement.

2.3Firmoptimisation

We?rstextendedtheallocationmodelofB?hringerandLange(2005)byallowingforeval-uationsbasedonanindependentexternalfactorsuchaspopulationsize,sociallyresponsibleactivities,emissionsofotherpollutants,lotterydraw,andsoon.Wenowfocusouratten-tiononthe?rm-speci?cproblem.Giventhepro?leofother?rms’actions,thesetofprices(σt,pit),anditspermitallocationAitforthetargetpollutant,a?rmiwillchoosealevelof?,e?,z?)tomaximiseitstotalstreamofpro?ts:emissions,outputandanexternalfactor,(qit,it,it

qit,eit,zitMax?[pitqit?cit(eit,qit)?vit(zit)]?σt(eit?Ait)t=1

6WefollowthelanguageofB?hringerandLange(2005)andrefertotheleast-costoutcomeandcorrespondingconditionsassociallyoptimal.

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Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach273Thus,whenarelativeperformancemechanism(2)isusedtoallocatepollutionpermits,?rmi’sobjectivefunctionis:??Max[pitqit?cit(eit,qit)?vit(zit)]?σteitqit,eit,zitt=1

t?1t?1+σt[λq,ith(qi(t?1),q?i(t?1))+λe,itg(ei(t?1),e?i(t?1))?t?1+λz,itf(zi(t?1),z?i(t?1))]]

Foreach?rmianditsrivals?i={1,...,i?1,i+1,...,n},theoptimalchoicesaredeterminedbythe?rstorderconditionsasfollows:

tpit+σt+1λq,i(t+1)hi(qit,q?it)=?c

it

?c

it(7)(8)

(9)σt?σt+1λte,i(t+1)gi(eit,e?it)=?σt+1λtz,i(t+1)fi(zit,z?it)=dv

dzit

SimilarlytotheabsoluteperformanceallocationmechanismofB?hringerandLange(2005),whena?rm’scurrentoutputandemissionsdetermineitsfutureallocationofpermits(andthusitspro?ts),each?rmwilltakethisintertemporaleffectintoaccount.7Thus,relativetothesociallyoptimalconditions(4)and(5),amechanismwhichusespastperformanceinoutputandemissionswillgenerateanintertemporaldistortionof?rms’incentives.

Importantly,thisholdsbothfortheabsoluteperformancemechanism(1)butalsofortherelativeperformancemechanism(2).Toseethat,compareequations(7)to(4),aswellas(8)to(5).Giventhatgiandhiarebothpositive,suchamechanismcreatesanimplicitincentivetoincreaseproductionandemissionsbeyondsociallyoptimallevels.8Becausetheexternalfactorzisoutsidetheinterestsorjurisdictionofthesocialplanner,itdoesnotdistortincen-tiveswheneitherarelativeorabsoluteperformancemechanismisused(9).Foragivenpro?le?,optimally,sothatthemarginalcostofother?rms’actions,?rmichoosesexternalfactorzitofobtainingthefactorequalsthemarginalfuturebene?tobtainedfromthepermitallocation.Insummary,wehavethefollowinggeneralizationoftheintuitionofB?hringerandLange(2005):

Remark2When?rms’permitallocationsareatleastpartiallydeterminedbyoutputandemissions,allpermitallocationmechanismsofthegeneralform(2)createdistortionaryincentivesintheproductandpermitmarkets.

Aswenotedabove,theabsoluteperformancemechanism(1)isaspecialcaseoftherelativeperformancemechanism(2).Thus,anymechanismthatallocatespermitsbasedonhistoricaloutputand/oremissionswilldistort?rm’sincentivestoproduceoutputandemis-sionsoptimally.Notonlywouldthedistortionsoccurwhentheadjustablecapgrandfatheringscheme(whichisanAPM)isused,butalsoanyotherschemewhichutilizes?rms’relativeperformancewithrespecttoeachotherinoutputand/oremissions.

7Moreover,thelongerhistoricalperiodoverwhich?rm’shistoricalrelativeperformanceinoutputandemis-sionsistakenintoaccountbytheschemedesigners,themoreimportantistheeffectofeachcurrentchoiceonfutureallocations.Becauseweassumethatonlyonepreviousperiodaffectscurrentallocation,wedonotexplicitlyaddressthispointhere.

8Similarly,ifeitherorbothgandharenegative,therewouldbeanincentivetodecreaseeitherproductioniioremissionsorbothtoasuboptimallevel.

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274IanA.Mackenzieetal.Thisproblem,ofincreasedoutputandemissions,isassociatedwiththe“ratcheteffect”—usingcurrentperformancetodeterminefuturetargetsandfutureinitialallocations(Weitzman1980;Freixasetal.1985;Berglandetal.2002).Ifa?rmdecidednottoincreaseemissions(output)thentheirpermitallocationwouldbe“ratcheted”down,astheiremissions(output)wouldberelativelylowerthanallother?rms.Ifsuchasystemwasimplemented,?rmsthatactivelyloweredemissions(output)wouldbeimplicitlypunished.Therefore,each?rmhasanincentivetoincreaseitsrelativeemissions(output)tostoptheirfuturepermitallocationfrombeinglowered.Thus,bothRPMsandAPMswillcreatedistortionsintheoutputandpermitsmarketwhenthecriteriausedtoallocatepermitsisbasedonhistoricaloutputand/oremissionsinformation.

However,RPMspossessanadditionalimportantfeaturethatAPMsdonot,namely,thataRPMresultsinagameamongparticipating?rms.Thisisbecausewheneach?rmisevalu-atedrelativelytoother?rms,?rms’actionsbecomeinterdependent.IntheNashequilibrium?,e?,z?)accordingtoEquats.7–9giventheofthisgame,each?rmchoosesapro?le(qitititequilibriumbeliefsaboutother?rms’choices.

3Sociallyoptimalallocationmechanisms

Inthelastsectionweexaminedtheinef?cienciescausedbyageneralisedrelativeperfor-mancemechanismwherethecriteriausedtoallocatepermitswerebasedonhistoricaloutput,emissions,andanexternalfactor.InthissectionwewillextendtheargumentofB?hringerandLange(2005)againsttheuseofhistoricaloutputsingeneralizedrelativeperformancemechanisms.Moreover,whenthesystemisopen,sothatthepermitpriceisdeterminedexog-enously,theexternalfactorshouldbethesoledeterminantofthe?rm’sallocations.Whentheclosedsystemisused,wherethepermitpricecanendogenouslyadjusttotheaggregatesupplyofemissions,thereisapossibilityofusingalinearperformanceschemeinemissions.

3.1Opensystem

Recallthatina(small)openpermittradingsystem,theaggregatesupplyofpermitsisdeter-minedjointlybythedomesticallocationofpermitsandbytheallocationsofpermitstoallotherforeignparticipants.Thus,thepermitpriceisdeterminedexogenously.FollowingB?hringerandLange(2005),themarketequilibriumoutcome(8),canbetransformedintothesociallyoptimaloutcome(5),byimplementingthesuf?cientconditionλte,i(t+1)=0foralli.Similarly,onecanensurethattheindividuallyoptimalproductionlevel(7)correspondsttothesociallyoptimalproductionlevel(4),bysettingλq,i(t+1)=0foralli.Thisleadsustothefollowing:

Proposition1Ina(small)opentradingsystem,asociallyoptimaloutcomecanbeachievedbyallocatingpermitsbasedonrelativeperformanceinanexternalfactorzitonly.Thatis,ant?1t?1optimalmechanisminvolvessettingλq,it≡λe,it≡0,foralli,tintheallocationequation

(2):

1Ait=λtz?,itf(zi(t?1),z?i(t?1))(10)

Thatis,inopentradingsystems,toachievethesociallyoptimaloutcome,aregulatorshouldplaceazeroweightforhistoricaloutputandemissions,anddesignasystemthatisbasedsolelyon?rms’performanceinanexternalfactor,whichisnotrelatedtotheoutputandemissionschoicevariables.Byrestrictingallocationtovariablesthatdonotaffectthepermit123

Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach275andproductmarket,the?rms’incentivesremainundistorted.Thisoccursbecauseusinganexternalfactorbreakstheintertemporallinkbetweenthepermitrent(outputsubsidy)andtheincentivetoalterthechoicevariables.Ourresultsagreewiththecommonlyheldviewthatonecanobtainasociallyoptimaloutcomebydistributingpermitsbasedonanexternalfactor(Goulderetal.1997;CramtonandKerr2002).Becauseanabsoluteperformancemechanismisaspecialcaseofrelativeperformancemechanism,theaboveresultcanbereducedtotheresultofB?hringerandLange(2005,Proposition2).Thatis,iftheallocationfunctionforeach?rmiisindependentofrivals’actions,itissociallyoptimaltousehistoricalexternalfactortoallocatepermits.

3.2Closedsystem

Wenowconsideranemissionsprogramwherethepermitpriceisendogenouslydeterminedbythedemandandsupplyinaclosedpermitmarket.Thisincludesaconventionalclosedmarketsystemwherethesolesupplyofpermitsoriginatesfromoneregulatorandwherethepermitpriceisdeterminedbytheaggregatelevelofemissionsintheemissionsprogram.Comparingequations(4)with(7)andequations(5)with(8)onecanobtainthefollowingsociallyoptimalconditionsforoutputandemissions:

tλq,i(t+1)hi(qit,q?it)=0

tλte,i(t+1)gi(eit,e?it)=λe,j(t+1)gj(ejt,e?jt)(11)(12)

?i,j=iand?i={1,...,i?1,i+1,...,n}.

Similartotheexogenouscase,Eq.11suggeststhattoachievesocialoptimality,themar-ginalbene?tto?rmifromincreasingoutputshouldbeequaltozero.Thus,asuf?cientconditionforachievingsocialoptimuminvolvestheregulatorplacingazeroweightoneach?rm’shistoricaloutput:

tλq,i(t+1)=0?i,t(13)

Incontrast,Eq.12suggeststhatthemarginalpermitallocationshouldbeequalacross?rms.Thisconditionisdif?culttoensureforall?rmsandforallfunctionalformsofg.Wecould?ndonlyonesetofsuf?cientconditionsforsocialoptimalityinemissionswhichholdsforallfunctionalformsofg,whichissimilartothesuf?cientconditionsforoutput:

λte,i(t+1)=0?i,t(14)

thatis,theregulatorshouldputazeroweightoneach?rm’shistoricalemissionschoices.Theseconditionsnotonlyensuresocialoptimalityforanyrelative(andthusabsolute)perfor-mancemechanism,butalsorequireslessproblemsolvingbytheregulatorandparticipating?rms.

Instead,ifanon-zeroweightforhistoricalemissionschoicesisselectedthenonlyanarrowclassofRPMssatisfythesocialoptimalitycondition(12).Inotherwords,onlyRPMsthatcreateanidenticalmarginalallocationcanobtainasociallyoptimaloutcome.Anexampleofsuchmechanismisayardstickmechanismthatallocatespermitstoeach?rmbasedonhowitshistoricalemissionscomparetheother???to????rms’averagehistoricalemissionse.g.

eEt+1?itg(eit,e?it)=1foralliandt(aswellasits“absolute”+αteit?counterpartg(eit)=e,i(t+1)

makestheproblemeasier.αteit).Obviously,equatingemissions“weights”λe,ite,i(t+1)across?rms

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276IanA.Mackenzieetal.Thus,anyRPMwithidenticalmarginalallocationsacross?rmscansociallyoptimallyallocatepermitsbasedon?rms’relativeperformanceswithrespecttohistoricalemissionsandanexternalfactor.OurresultsagreewithB?hringerandLange(2005)whowereabletoprovethattheoptimalityresultholdsforalinearAPM.Therefore,RPMsandAPMsthathaveidenticalmarginalallocationsacross?rmscanobtainasociallyoptimaloutcome.Thus,itfollowsfrominspectionofequations(11)and(12)that:

Proposition2Inclosedtradingsystem,asociallyoptimaloutcomecanbeachievedbyallocatingpermitsbasedonrelativeperformanceinanexternalfactorzitaswellasusingsuitablychosenrelativeperformanceschemesinhistoricalemissions,andignoring?rms’t?1historicaloutputs,i.e.λq,it≡0,foralli,t.Thus,theallocationequation(2)becomes:

???1?t?1?Ait=λtge,efz,z+λi(t?1)?i(t?1)i(t?1)?i(t?1)e,itz,it

wherefunctionsgarechosensuchthatcondition(12)issatis?ed.

Again,becauseabsoluteperformancemechanismsareaspecialcaseofrelativeperfor-mancemechanism,theaboveresultcanbereducedtotheresultofB?hringerandLange(2005,Proposition1).Importantly,onecanachievesocialoptimalityintheclosedsystembyusingthesamepermitallocationschemeasintheopensystem:

Corollary1Inclosedtradingsystem,asociallyoptimaloutcomecanbeachievedbyallocat-t?1t?1ingpermitsbasedonrelativeperformanceinanexternalfactorzitonly,i.e.λq,it≡λe,it≡0,foralli,t.Thus,theallocationequation(2)becomes:

1Ait=λtz?,itf(zi(t?1),z?i(t?1))(15)(16)

Inotherwords,regardlessofthenaturetradingsystem,onecanimplementthesociallyoptimalpermitallocationmechanismbasedontherelativeperformanceintheexternalfactor.Thus,theexternalfactorplaysakeyroleinoptimalpermitallocationscheme,callingforfurtherissuestobeconsideredbytheallocationmechanismdesigner.

4Theexternalfactor

Wearguedintheprevioussectionthatonecanachievesocialoptimalityintheproductandtargetpollutantmarketsbyusing?rms’relativeperformancewithrespecttoanexternalfac-tortoallocatetargetpollutionpermits.Inthissection,wewilldescribetheexternalfactor,possiblemechanismsbasedonrelativeperformanceinthisexternalfactor,aswellasthebene?tsofthisapproach.

4.1Criteriaforthechoiceofanexternalfactor

Wede?netheexternalfactorasanythingwhichhasnodirectrelevancetotheproductandtargetpollutantemissionsmarkets,andwhichisthusbeyondtheinterestorjurisdictionoftheregulator.Examplesofpossibleexternalfactorincludepopulationsizein?rm’slocality,?rm’ssociallyresponsibleactivities,?rm’semissionsofotherpollutants,arandomeventsuchalotterydraw,andsoon.Sincetheexternalfactorcantakeavarietyofforms,theregu-latorfacesachoiceofasuitableexternalfactor.However,thereisnumberofissuesinvolvedintheexternalfactorchoice.

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Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach277Independence:Toachievesocialoptimality,the“production”oftheexternalfactorhastobeindependentof?rms’outputandemissionsofthetargetpollutant.Obviously,iftheexternalfactoriscorrelatedwith?rm’soutputand/oremissions,?rms’incentiveswillbedistorted,andsocialoptimalitywillnotbeachieved.

Easeofuse:Asthemainobjectiveoftheregulatoristominimisetheaggregatecostoftheemissionsprogram,adesirableexternalfactorshouldbeeasyfortheregulatortoobserve.RewardofEffort:Theregulatormaychoosetheexternalfactortoreward?rms’efforts.Whenheterogeneityof?rms’issubstantial,theexternalfactormaytakeaformof“inten-sity”,orwithin-?rmrelativeassessment—forexample,proportionof?rm’scommunityactivitiesrelativelytothesizeoflocality.

EqualOpportunity:Theregulatormaywishtoensurethatall?rmshaveequalopportunitytoobtainpermitallocations,andthusthattheexternalfactorcanbeproducedbyeveryparticipating?rm.Whentheregulated?rmsbelievetheyarebeingtreated“fairly”inasenseofequalityofopportunity,thentheemissionsprogrammayhaveahigherchanceofsuccess.

PoliticalAcceptabilityoftheExternalFactor:Thesuccessoftheallocationschememaydependonpoliticalacceptabilityoftheexternalfactorbytheregulated?rmsandregulator(aswellaspossiblybythegeneralpublic).

FairAllocations:Aspsychologistssuggest,judgmentsofallocativefairnessareaffectedbytherelativemeritsoftherecipients,thussuggestingthatrelativeperformancemech-anismsmaybeperceivedtobe“fair”aslongastheexternalfactorisconsideredtobemeritorious.9

DoubleDividend:Ofparticularinterestmaybethoseexternalfactorswherethemarginalbene?tswilltypicallyexceedthemarginalsocialcosts.Inotherwords,theexternalfactormaybechosensothatitconferssomeadditionalbene?ttotheregulatorotherthanthecontrolofemissions.Theregulatorcouldde?neacostlyzitinsuchawayasitwouldprefertoobservehigher(orlower)values.

Asthelastthreeoftheseissuesmaybeofparticularinteresttomechanismdesigners,wewilldiscussthemindetail.

4.2Anon-monetaryexternalfactor

Asitwasmentionedabove,oneofthepossiblereasonswhyregulatorsavoidallocatingper-mitsbasedon?rmsperformanceinexternal“monetary”factor—suchasauctionbids—isthatitispoliticallyunpopular.Wethussuggestthatperhapsamechanismthatisbasedonrelativeperformanceinanon-monetaryexternalfactor,mayhaveabetterpoliticalaccept-ability,inparticulariftheyinvolveapossibilityofsocialbetterment.Whenanon-monetaryexternalfactorischosenasabasisforpermitallocations,therearenodirect?nancialtrans-fers.Firmsinsteadarerewardedforthe(non-monetary)actionstheychoose.Thisreasoningisverysimilartotheargumentsthatadvocateagrandfatheringsystemratherthananauction(Stavins1998).However,asweshowedabove,grandfatheringschemesinvolvinghistoricallyupdatedoutputsandemissionsaredistortive.Yetwesuggestthataregulatorcanchooseanon-monetaryexternalfactorthatisagreeablefor?rms(oratleastlesscontroversialthanothercriteria).

9Notefurtherthat,asMellers(1982,1986)demonstrated,theallocations(ofsalariesandtaxes)judgedtobe“fair”byhumansubjects,dependedontherankofeachrecipient’smeritinthemeritdistributionofthecom-parisongroup.Inotherwords,arank-basedcontestmaybeagoodcandidatefora“fair”relativeperformancemechanism.

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278IanA.Mackenzieetal.Thereisavarietyofpossiblenon-monetaryexternalfactors.Charitableactivitiessuchassupportofimprovementsineducationandhealthinfrastructureinthelocalcommunitymaybeviable.Thismayprovetobeameritoriousallocationprocess;?rmsaregiventhe“right”topollutebasedonthedegreeoftheirsocialresponsibilitieswithinacommunity.Anothersetofalternativeexternalfactorsmaybeofparticularrelevancetoenvironmentalregulator.Thesemayincludereductionofanexternal“basket”ofenvironmentalpollutantsorenvironmentalindicators,forexamplenoisepollution,orinvestmentsinenergyef?ciency.Thatis,?rmscouldbeallocatedpermitsforthetargetpollutantbasedontheirreductionofcompletelyseparateandindependentpollutants.

However,wehavetoemphasizeagainthat,toachievesocialoptimalityinoutputandemissionsmarkets,apotentialnon-monetaryexternalfactorzithastobeindependentfromthe?rm’semissionsandoutputchoices.Thusspecialcarehastobetakeninregulator’schoiceofnon-targetpollutantsasexternalfactorsasemissionsofsomepollutantscanbecorrelatedwithemissionsofthetargetpollutant,leadingtopotentialinef?cienciesintargetpollutantemissionsmarket.

4.3Theregulator’ssecondaryobjective

Aswementionedabove,theremayexistexternalfactorswhichareirrelevanttotheproductandtargetpollutantemissionsmarket,butneverthelesstheregulatormaybeinterestedin?rmsengaginginproductionofthisexternalfactor.Ifthisisthecase,theregulatormayhaveaprimaryobjectiveofcontrollingemissionsatlowestsocialcost,aswellasasecondaryobjectiveofincreasingtheaggregateamountoftheexternalfactor,oritsnetbene?ts.

Oneobviousexampleofmultipleregulatoryobjectivesisthe“doubledividend”argumentfortheuseofauctionsforpermitallocations.AsCramtonandKerr(2002,p.335)suggest,apermitauctioncanraiserevenuewhilstenforcingemissionscontrol.Thisrevenuecanbeusedtoreducedistortionarytaxesintheeconomy(e.g.Parry1997)orreducetheburdenonauctionparticipantsthrougharevenueneutralauction(HahnandNoll1982;Hahn1988).Alternatively,therecanbetwo(non-competing)regulatorswithdifferentobjectives.Forexample,theenergy(electricity)industrymayberequiredtoparticipateinanemissionsprogramwhilstsimultaneouslybeingoverseenbysocial/publicpolicyregulatortopromote?rms’anti-discriminatorypersonnelpolicies.Theenvironmentalpolicyregulatoraimstocontrolaggregateemissionsatthelowestpossiblecostandisnotconcernedaboutthesizeorcostoftheexternalfactorinanyway.Thesecondregulatorispossiblyasocial/publicpolicyregulatorwho’saimistomaximisetheaggregateexternalfactorproducedbytheparticipating?rms.Anotherexampleofadoubleobjectivemaybetheregulationoftwoenvironmentaltargets,withonetargetbeingcontrolledbytargetpollutantpermitmarket,andanothertargetcurrentlybeingunregulated—forexample,emissionsofCO2andabasketofothergreenhousegases.Inanycase,thesecondaryobjectiveinvolvesmaximizationof?rms’aggregateactivities,expenditures,orefforts(forasimilarobjectiveseeforexampleMoldovanuandSela2001).

Aswearguedabove,onecanachievethesociallyoptimaloutcomeinproductandtar-getpollutantmarketsbyallocatingpermitsusinganexternalfactoronly.Therefore,usingsuchanapproachsimultaneouslyachievestheprimarytargetofsociallyoptimaloutcomeinthetwomarketsandasecondarytargetofmaximisationoftheaggregateexternalfactor.Formally,let?∈(0,1]representtherelativeimportanceoftheprimarytarget(emissionscontrol),andletusconsider(small)opensystem(theargumentfortheclosedsystemwillbeonlyslightlydifferent).Inthiscase,the“combined”regulatoryobjectiveis:

123

Theoptimalinitialallocationofpollutionpermits:arelativeperformanceapproach

n??

ti=1n?i=1279qit,eit,zitMax[?(pitqit?cit(eit,qit))?(1??)zit]subjecttoeit=t(17)

The?rstorderconditionsforemissionsandoutputareidenticaltothesociallyoptimalequations(4)and(5).Moreover,thiscombinedregulatoryobjectiveallowsfor?rms’indi-viduallyoptimalchoiceoftheexternalfactor.ItfollowsfrominspectionofEqs.7–9and17that:

Remark3IfaRPMisusedtoallocatepermitsbasedonacostlyexternalfactorthenasec-ondary(regulatory)targetcanbeachievedwhilststillachievingthesociallyoptimaloutcomewithrespecttothetargetpollutant.

Inotherwords,byallocatingtargetpollutantpermitsamong?rmsbasedontheirrelativeperformanceinasuitablychosenexternalfactor,aregulatorcan“killtwobirdswithonestone”byachievingemissioncontrolatthelowestsocialcostinoutputandpermitmarkets,andmaximizingaggregateproductionofasociallybene?cialexternalfactor.

5Conclusion

Thepurposeofthispaperwastoanalysetheimpactandoptimalityofimplementingagen-eralised(dynamic)relativeperformancemechanismfortheinitialallocationofpollutionpermits.WeextendtheresultsofB?hringerandLange(2005)toaccommodatemostoftheexistingdynamicinitialallocationmechanisms,includinggrandfatheringandauctions,aswellasnovelmechanisms,suchasrank-ordercontests.Weshowthatusing?rms’historicaloutputsforallocatingpermitsisneveroptimal,whileusing?rms’historicalemissionsisoptimalonlyinclosedtradingsystemsandonlyforanarrowclassofallocationmechanisms.Instead,itispossibletoachievesocialoptimalitybyallocatingpermitsbasedonanexternalfactorwhichisindependentofoutputandemissions.Weoutlinesuf?cientconditionsforasociallyoptimalrelativeperformancemechanismanddiscusstheissuesrelatedtothechoiceofasuitablemechanismforinitialallocation.

Duetothesepotentialbene?ts,weadvocateusingarelativeperformancemechanismwithanexternalfactorforthedynamicallocationofpermits.Thenumerousadvantagesofusingarelativeperformancemechanismincludeitsadaptabilitytochangingeconomic,technological,andotherconditions,aswellasapossibilityoftransferringriskofpossiblesystemicshocks(suchasoilpricechanges)totheregulator.Theadvantageofusinganexter-nalfactorinvolvesapossibilityofachievingsecondaryregulatorygoals,suchasrevenuemaximization,socialbettermentorreductioninotherenvironmentalproblems.Moreover,ifthesecondarygoalispoliticalagreeable,thepermittradingschememayalsoenjoygreaterpublicacceptance.

Allocatingpermitsforatargetpollutantbasedon?rms’relativeperformanceinexter-nalfactorincreases?rms’?exibilityinmeetingbothregulatorygoalsbychoosingthemostcost–effectiveapproach.Thatis,?rm’scost–effectivebehaviourmaydependonwhetherithascomparativeadvantageinabatementofthetargetpollutant,orintheproductionoftheexternalfactor.Wethinkthatsuchpotentialasymmetriesamong?rmsareimportantfortheoptimaldesignofpermitallocationschemes,atopicofpotentialfutureresearch.

Wealsoproposeanovelallocationmechanisminvolvingarank-ordercontest,whichisageneralizationofanall-payauction.Inanexternalfactorrank-ordercontest,?rmsarerankedintheorderoftheirrelativeproductionoftheexternalfactor,anditis?rm’srank,andnottheleveloftheexternalfactor,thatdetermines?rm’spermitallocation.Asthetheoretical

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280IanA.Mackenzieetal.literaturesuggests,anallocationschemewithasuitablychosen“prize”structureisexpectedtoachievethesecondarygoalofmaximizingaggregateproductionoftheexternalfactor—thegoalwhichmaynotbeachievablewithotherallocationmechanisms.Inotherwords,byallo-catingtargetpollutantpermitsamong?rmsusingarank-ordercontestinsociallydesirableactivities(includingabatementofunregulatedgreenhousegasesorevencharitableactivities)aregulatorcan“killtwobirdswithonestone”byachievingemissioncontrolatthelowestsocialcostinoutputandpermitmarkets,andmaximizingaggregateamountofasociallybene?cialactivity.

Theexternalfactorrank-ordercontesthassomeadvantagesoverthepresentlyusedgrand-fatheringscheme.Whileregulatorsseemtoprefergrandfatheringduetoitspoliticalagree-abilityamongtheregulated?rms,theseschemescanbeunpopularwiththegeneralpublic.Incontrast,anexternalfactorcontestnotonlyhasapotentialofachievingsocialoptimality,butalsoitachievesasecondaryregulatorygoal(whichmaybeperceivedasachieving“fair-ness”),whilethegrandfatheringschemeinvolvinghistoricaloutputandemissionsachievesnoneofthesetwogoals.

WhilewehavepresentedargumentsinfavourofusingRPMsbasedonanexternalfactorinallocatingpermits,weneverthelessappreciatethepotentialpracticaldif?cultiesinvolv-inginthechoiceofasuitableexternalfactor.Thesuccessofthetradingschemerestsontheregulator’sabilityto?ndanexternalfactorthatisdesirable,politicallyagreeable,inde-pendentfromoutputandemissions,andallowsforanadequatecomparisonbetween?rms.Weneverthelesshopethattheargumentspresentedinthispapermaybeofrelevancetotheenvironmentalpolicymakers.

AcknowledgementsTheauthorswouldliketothankPaulAllanson,PaulHare,EdHopkins,MattiLiski,MiguelRodriguez,JayShogren,JoeSwierzbinski,participantsattheEuropeanAssociationofEnvironmen-talandResourceEconomists(EAERE)2005conferenceandtwoanonymousrefereesfortheirvaluablecommentsandsuggestions.TheEconomicandSocialResearchCouncil(ESRC)provided?nancialsupport(PTA-030-2004-00560).

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