Environmntal Policy and Tim Consistncy: Emission Taxs and Emissions Trading Ptr W. Knndy 1 and Bnoît Laplant 2 1 Dpartmnt of Economics, Univrsity of Victoria, Victoria, British Columbia V8W 2Y2, Canada. 2 Dvlopmnt Rsarch Group, World Bank, 1818 H Strt, N.W. Washington, D.C. Unitd Stats. This rsarch was partially fundd by th Sustainabl Forst Managmnt Ntwork of Cntrs of Excllnc, Canada. Th findings, intrprtations, and conclusions xprssd in this papr ar ntirly thos of th authors. Thy do not ncssarily rprsnt th viws of th World Bank, its Excutiv Dirctors, or th countris thy rprsnt.
Excutiv Summary A ky considration in th choic of pollution control instrumnts is th incntiv for rgulatd firms to adopt clanr tchnologis. Th adoption of lss polluting production tchniqus holds th ky to long trm consumption growth with limitd accompanying nvironmntal damag. Mor immdiatly, it allows firms to achiv pollution rduction targts at lowr cost and with potntially smallr impact on thir intrnational comptitivnss. Ths issus ar of particular importanc to many dvloping countris whr high growth rats man that a larg numbr of ky industrial tchnology choics ar bing mad on a daily basis. It is ssntial that thos choics ar th right ons if th nt bnfits of growth ar to b maximizd. Thr is a wid array of pollution control policis availabl to rgulators and ach of thm hav diffrnt proprtis with rspct to incntivs for tchnological chang. In this papr w focus on mission taxs and missions trading. Ths markt-basd instrumnts ar bcoming incrasingly popular in practic du in part to thir dynamic incntivs. By attaching an xplicit pric to missions, ths policy instrumnts crat an ongoing incntiv for firms to continually rduc thir mission volums. In contrast, command-andcontrol typ mission standards crat incntivs to adopt clanr tchnologis only up to th point whr th standards ar no longr binding (at which point th shadow pric on missions falls to zro). Howvr, th ongoing incntivs cratd by markt-basd instrumnts ar not ncssarily th right incntivs. In particular, th rquirmnt that policis (th lvl of th tax rat or th numbr of prmits) b consistnt with th tchnology choic aftr tchnology adoption has takn plac (tim consistncy constraints) can potntially limit th ability of th rgulator to st policis that implmnt fficincy with rspct to tchnology adoption choics. This papr xplors ths issus for Pigouvian mission taxs and missions trading. W xamin th policy problm undr a rang of conditions rlating to th structur of th pollution markt and th natur of th nvironmntal damag. W show that tim consistncy constraints do not limit th ability of th rgulator to achiv a first-bst outcom if thr is a continuum of rgulatd firms or if th nvironmntal damag function is linar in aggrgat missions. Howvr, if thr ar rlativly fw rgulatd firms, such that thr is stratgic intraction btwn firms and th rgulator, and th nvironmntal damag function is strictly convx in aggrgat missions (that is nvironmntal damag incrass at an incrasing rat), thn tim consistncy problms do aris. In particular, th rational xpctations quilibrium undr mission taxs xhibits xcssiv incntivs for th adoption of a nw tchnology whil th quilibrium undr missions trading xhibits incntivs for adoption that ar too wak. Howvr, it should b notd that if an missions trading program is intndd to implmnt tchnological fficincy thn it is ncssary to continually adjust th supply of prmits in rspons to tchnological chang, vn whn th damag function is linar. This continual adjustmnt is not ndd for an missions tax whn damag is linar, a distinction that givs th missions tax a possibl advantag ovr missions trading. 2
Th incntiv to initiat tchnological dvlopmnt should, in principl, b th sam for tradabl prmits and taxs. OCDE (1999), p. 140. 3
1. Introduction A ky considration in th choic of pollution control instrumnts is th incntiv for rgulatd firms to adopt clanr tchnologis. Th adoption of lss polluting production tchniqus holds th ky to long trm consumption growth with limitd accompanying nvironmntal damag. Mor immdiatly, it allows firms to achiv pollution rduction targts at lowr cost and with potntially smallr impact on thir intrnational comptitivnss. Ths issus ar of particular importanc to many dvloping countris whr high growth rats man that a larg numbr of ky industrial tchnology choics ar bing mad on a daily basis. It is ssntial that thos choics ar th right ons if th nt bnfits of growth ar to b maximizd. Of cours, th right tchnology is not ncssarily th clanst tchnology availabl. This is spcially tru whn an xisting production tchnology is alrady mployd and th associatd invstmnt has bn sunk. Rtooling with a lss polluting production mthod or th rtrofitting of abatmnt quipmnt can b vry costly; that cost must b carfully wighd against th bnfits of rducd pollution from tchnological chang. Thus, it is not nough that policy instrumnts crat incntivs for tchnological chang; thy must crat th right incntivs, in th sns that thy induc tchnology adoption dcisions which corrctly balanc th bnfits and costs of altrnativ tchnologis. Thr is a wid array of pollution control policis availabl to rgulators and ach of thm hav diffrnt proprtis with rspct to incntivs for tchnological chang. In this papr w focus on mission taxs and missions trading. Ths markt-basd instrumnts ar bcoming incrasingly popular in practic du in part to thir dynamic incntivs. By attaching an xplicit pric to missions, ths policy instrumnts crat an ongoing incntiv for firms to continually rduc thir mission volums. In contrast, command-and-control typ mission standards crat incntivs to adopt clanr tchnologis only up to th point whr th standards ar no longr binding (at which point th shadow pric on missions falls to zro). Howvr, th ongoing incntivs cratd by markt-basd instrumnts ar not ncssarily th right incntivs. 4
In particular, tim consistncy constraints on th stting of ths instrumnts can potntially limit th ability of th rgulator to st polics that implmnt fficincy as rational xpctations quilibria with rspct to tchnology adoption choics. This papr xplors ths tim consistncy issus for Pigouvian mission taxs and missions trading. W xamin th policy problm undr a rang of conditions rlating to th structur of th pollution markt and th natur of th nvironmntal damag. W show that tim consistncy constraints do not limit th ability of th rgulator to achiv a first-bst outcom if thr is a continuum of rgulatd firms or if nvironmntal damag is linar in aggrgat missions. Howvr, if thr ar rlativly fw rgulatd firms, such that thr is stratgic intraction btwn firms and th rgulator, and nvironmntal damag is strictly convx in aggrgat missions, thn tim consistncy problms do aris. In particular, th rational xpctations quilibrium undr mission taxs xhibits xcssiv incntivs for th adoption of a nw tchnology whil th quilibrium undr missions trading xhibits incntivs for adoption that ar too wak. Our papr contributs to a broad xisting litratur on incntivs for tchnological chang undr nvironmntal rgulation. 1 Downing and Whit (1986) xamin th incntiv ffcts of an missions tax but thy do not tak account of tim consistncy issus and whthr or not th outcoms xamind can in fact b rational xpctations quilibria. Malug (1989) argus that missions trading may not crat th right incntivs for nw tchnology adoption but his analysis is also flawd by a failur to xamin incntivs in quilibrium. Th firms in his papr do not bas thir invstmnt dcisions on a rational xpctation of quilibrium prics. Milliman and Princ (1989) similarly nglct quilibrium considrations in thir comparativ analysis of mission taxs and missions trading. Biglaisr, Horowitz and Quiggin (1995) xamin incntivs in a rational xpctations nvironmnt and claim that an missions tax dos not suffr from a tim consistncy problm. 5
Thir rsult is corrct in th contxt of thir modl but thy rstrict attntion to th cas of linar damag. Thy also claim that tchnology adoption is distortd undr missions trading bcaus of a tim consistncy problm for th rgulator. Howvr, this problm ariss in thir modl only whn th invstmnt dcisions of individual firms hav a significant ffct on aggrgat missions. This possibility is not consistnt with thir assumption of pric-taking bhavior on th prmit markt. If firms ar small playrs in th prmit markt thn thr is no tim inconsistncy problm in thir modl (which assums damag is linar) and no associatd distortion of tchnology invstmnt dcisions. Laffont and Tirol (1996a) and (1996b) also xamin tchnological chang undr missions trading. A primary focus of thir work is th tim consistncy problms arising from a nonunitary cost of public funds. Thy show that incntivs for innovation ar waknd if th rgulator cannot commit to distort futur prmit prics for th purpos of raising rvnu. Jung, Krutilla and Boyd (1996) compar th incntiv ffcts of mission taxs and missions trading but thy fail to account for tim consistncy issus. In particular, thy assum that firms xpct th tax rat to rmain unchangd aftr adoption of a clanr tchnology vn though this tax rat is sub-optimal x post. Similarly, thy assum that firms xpct th supply of prmits to rmain unchangd vn though that supply is sub-optimal x post. In thir modl ths xpctations ar fulfilld in quilibrium but only bcaus th rgulator fails to mak th optimal adjustmnts. Thus, th rgulator is assumd to b abl to commit to a policy that is not tim consistnt. This also raiss a problm with thir comparativ analysis of taxs and prmits bcaus th implicit objctiv of thir rgulator varis with th instrumnt usd to implmnt it. Th implicit objctiv undr a tax policy is to maintain th tax rat constant whil th implicit objctiv undr prmits is to achiv a givn lvl of missions. Ths objctivs ar not consistnt. 1 S Kmp (1997) for a survy of this litratur. 6
Our analysis focuss on th tim consistncy of policy and its implications for th importanc of xamining incntivs in quilibrium. Our rational xpctations framwork allows a dirct and consistnt comparison of mission taxs and missions trading. Th rst of th papr is organizd as follows. Sction 2 dscribs th modl on which our analysis is basd. Sction 3 charactrizs fficincy with rspct to tchnology adoption in th contxt of that modl. Sctions 4 and 5 thn xamin th circumstancs undr which fficint tchnology choics can and cannot b implmntd through a Pigouvian missions tax and missions trading rspctivly. Sction 6 concluds. 2. Th Modl Tim is dividd into two priods. In priod 1 ach of n firms uss a production tchnology with associatd abatmnt cost function c ( ), whr dnots missions, and 0 is th lvl 0 0 of missions corrsponding to no abatmnt. Thus, 0 rprsnts abatmnt. Abatmnt may involv a varity of masurs, including a rduction in output, a chang in inputs or som nd-of-pip rmdial action. Th abatmnt cost function masurs th last cost mix of abatmnt masurs. Abatmnt cost has th following important proprtis: c 0 > c 0 > 0. 0 and A clanr tchnology bcoms availabl at th bginning of priod 2. It can b adoptd by any firm at som fixd installation cost K. This tchnology has an associatd abatmnt cost function c ( ) with c 1 > 0 and c 1 > 0, whr and c < c 1 1 1 0 1 0 for any 0. Thus, any positiv lvl of abatmnt can b achivd at lowr cost with th nw tchnology. Polluting firms ar assumd to b pric-takrs on th product markt. This mans that privat and social marginal abatmnt cost coincid. It is important to not that this assumption can hold vn if th numbr of polluting firms in th rgulatd rgion is small sinc th rgulatd firms do 7
not ncssarily constitut th whol industry. Such is th cas, for xampl, whn polluting firms tak world prics as givn. Environmntal damag D(E) in any priod is an incrasing function of aggrgat missions E in that priod. That is, attntion is rstrictd to th cas of a dissipativ pollutant that is uniformly mixd rlativ to th rgulatd rgion. Two cass ar considrd with rspct to th damag function: D ( E ) > 0 (strictly convx damag) and D ( E ) = 0 (linar damag). 2 3. Efficincy W bgin with an analysis of a singl firm sinc this hlps to illuminat th ky issus with rspct to fficincy in tchnology adoption. W thn xamin th cas with many firms. 3.1 A Singl Firm Figur 1 illustrats th marginal damag schdul drawn for th cas of linar damag. Marginal damag is dnotd by δ. Also illustratd ar th marginal abatmnt cost schduls associatd with th old and nw tchnologis, labld c ( ) and c ( ) rspctivly. Th fficint 0 1 lvl of missions if th firm uss tchnology i is i such that c ( ) = δ. 3 i i i Th shadd ara in Figur 1 rprsnts th social bnfit obtaind if th firm adopts th clanr tchnology. This social bnfit compriss th rduction in damag associatd with th fall in missions from 0 to 1, rprsntd by ara (A+C) plus any rduction in abatmnt cost associatd with switching to th clanr tchnology, rprsntd by ara (B-C) in th Figur. Not that abatmnt cost could b highr undr th clanr tchnology sinc fficincy rquirs that mor abatmnt is undrtakn for that tchnology. Howvr, th ovrall social bnfit is ncssarily positiv. Lt G dnot that social bnfit. 2 Som nvironmntal problms ar possibly charactrizd by concav damag at vry high pollution lvls but w hav not xamind that cas hr. 8
Figur 2 illustrats an incrasing marginal damag schdul, labld D (E). Th fficint lvl of missions for th firm if it uss tchnology i is i such that c ( ) = D ( ). Th i i i i shadd ara in Figur 2 rprsnts th social bnfit obtaind if th firm adopts th clanr tchnology. It has th sam intrprtation as in th constant marginal damag cas. Whthr or not adoption of th clanr tchnology yilds a positiv nt social bnfit dpnds on th siz of th adoption cost K. Adoption is worthwhil if and only if G > K. It is clar from Figurs 1 and 2 that adoption of th clanr tchnology is most likly to b worthwhil if marginal damag is high and th diffrnc btwn marginal abatmnt costs is significant. 3.2 Many Firms Now suppos thr ar n > 1 rgulatd firms. Lt m dnot th numbr of firms to adopt th clanr tchnology. Efficint mission lvls for a givn valu of m ar givn by ( 0 m ) and 1 ( m) such that (1) c ( ( m)) = c ( ( m)) = D ( E( m)) 0 0 0 1 1 1 whr (2) E( m) = m ( m) + ( n m) ( m) 1 0 Not that if damag is linar thn th fficint mission lvls ar indpndnt of m. In contrast, if damag is strictly convx thn ( m) >, ( m) > and E ( m) < 0. Ths important 0 0 1 0 proprtis rflct th fact that if mor firms us th clanr tchnology thn marginal damag is lowr (whn D > 0 ), and so th balanc btwn marginal damag and marginal abatmnt cost calls for a highr lvl of missions from any individual firm using a givn tchnology. 3 For clarity, all graphs ar drawn for th cas whr = =. 0 1 9
Nxt considr fficincy with rspct to tchnology adoption. Figur 3 illustrats th cas of n = 2 and linar damag. Th shadd ara rprsnts th social bnfit from adoption of th nw tchnology by on of th firms. (Nt social bnfit is this shadd ara lss th cost of adoption). Efficincy rquirs that missions for th adopting firm fall from 0 to 1 ; missions for th non-adopting firm ar unchangd at 0, whil aggrgat missions fall from E (0) to E (1). Th social bnfit from adoption compriss th rduction in damag associatd with th fall in aggrgat missions plus any rduction in abatmnt cost for th adopting firm. Th pictur is somwhat mor complicatd whn damag is strictly convx. Figurs 4(a) and 4(b) illustrat th adoption of th nw tchnology by on of th two firms. Efficincy rquirs that missions for th adopting firm fall from 0(0) to 1(1), and that missions for th nonadopting firm ris from (0) to (1). Th fficint lvl of aggrgat missions falls from 0 0 E (0) to E (1). Th shadd aras in figur 4(a) rflct th rduction in abatmnt cost for th adopting firm: ara (B-A). Th shadd aras in figur 4(b) rprsnt th othr componnts of th social bnfit from adoption: ara D is th rduction in damag associatd with th fall in aggrgat missions; ara C is th rduction in abatmnt cost for th non-adopting firm associatd with th ris in its missions. Not that this lattr componnt of social bnfit dos not aris in th linar damag cas. Figur 4(c) combins th aras in figurs 4(a) and 4(b) to illustrat th ovrall social bnfit from adoption by on firm. Now considr th social bnfit from adoption by th scond firm. This is illustratd in figur 5. Efficincy rquirs that missions for th adopting firm fall from 0(1) to 1(2), and that missions for th xisting nw tchnology firm ris from 1(1) to 1(2). Th fficint lvl of aggrgat missions falls from E (1) to E (2). A comparison of figurs 5 and 4c rvals that th social bnfit from th scond firm adopting th nw tchnology is lss than th social bnfit from th first firm adopting. This is du to th fact that marginal damag falls whn th first firm adopts, so th social bnfit from th scond firm adopting is smallr. Sinc th cost of adoption 10
is constant, this mans that fficincy may rquir strictly partial adoption: som firms should adopt th clanr tchnology and som firms should rtain th old tchnology, vn though all firms ar idntical x ant. In contrast, strictly partial adoption is nvr fficint whn damag is linar sinc marginal damag is constant in that cas, and so th social bnfit from adoption by on firm is indpndnt of how many firms adopt. Efficincy in that cas rquirs adoption of th clanr tchnology ithr by all firms (if K is rlativly small) or by no firms (if K is rlativly larg). Of cours, a cornr solution can also b fficint in th strictly convx damag cas if K is larg nough or small nough. 4. Implmntation with an Emissions Tax 4 Th timing of th gam btwn th firms and th rgulator is as follows. In priod 1 th tax is st according to th Pigouvian rul for th prvailing tchnology. Th nw tchnology arrivs at th bginning of priod 2 and th rgulator announcs a tax rat for that priod. Firms thn dcid whthr or not to adopt th clanr tchnology, taking as givn th simultanous tchnology adoption dcisions of othr firms. Th rgulator cannot commit to a tax rat that is tim inconsistnt. That is, th tax rat announcd for priod 2 must b consistnt with th tchnology choics that th tax inducs. 4.1 A Singl Firm Th quilibrium to th gam btwn th firm and th rgulator dpnds importantly on whthr damag is linar or strictly convx. W xamin ach cas in turn. (a) Linar Damag 4 Th main rsults in sction ar rportd in mor dtail in Knndy and Laplant (1997). 11
Th unit tax rat on missions is st qual to marginal damag: t = δ. This is illustratd in Figur 1. Not that this optimal tax rat is indpndnt of which tchnology is in plac bcaus marginal damag is constant. Th firm rsponds to th tax by stting its missions lvl to quat its marginal abatmnt cost with th tax rat: c ( ) = t. Thus, th firm chooss 0 if it i i i uss th old tchnology, and 1 if it uss th nw tchnology. That is, th missions tax implmnts static fficincy for any givn tchnology. Th privat bnfit to th firm from adopting th clanr tchnology compriss th rduction in tax paymnts, t ( ), plus any rduction in abatmnt cost. Not that th rducd tax 0 1 paymnts corrspond xactly to th rducd nvironmntal damag sinc t = δ. It follows that th privat bnfit to th firm from adopting th nw tchnology is idntical to th social bnfit. Thus, th missions tax also implmnts fficincy with rspct to tchnology adoption. (b) Strictly Convx Damag Th rgulatory problm is somwhat mor complicatd whn marginal damag is incrasing. For an missions tax to implmnt th fficint lvl of missions for any givn tchnology i, th tax rat must b st qual to marginal damag valuatd at th fficint lvl of missions; that is, t = D ( ). Thus, th tax rat rquird dpnds on which tchnology is in us. This crats i i a potntial tim consistncy problm for th rgulator. If adoption of th nw tchnology is fficint thn th rgulator would lik to announc a tax rat t 1 for priod 2. Convrsly, if adoption of th nw tchnology is not fficint thn th rgulator would lik to announc a tax rat t 0 for priod 2. Th problm is that a tax rat of t 0 may actually induc th firm to adopt th nw tchnology, whil a tax rat of t 1 may induc th firm to rtain th old tchnology. In both cass th announcd tax rat would not b optimal x post and hnc could not b committd to x ant. Undr what conditions will this tim consistncy problm aris? Suppos adoption of th nw tchnology is not fficint; that is, G K. Thn th first-bst tax rat for priod 2 is t 0. Figur 12
6 illustrats th privat bnfit to th firm from adoption of th nw tchnology at this fixd tax rat. If th firm rtains th old tchnology thn it sts missions qual to 0. Convrsly, if it adopts th nw tchnology thn it sts missions qual to 1( t0 ). Lt B( t 0 ) dnot th privat bnfit from adoption at t 0. Comparing Figurs 2 and 6 rvals that B( t 0 ) > G. That is, th privat bnfit from adoption at t 0 xcds th social bnfit from adoption. This dos not ncssarily crat a tim consistncy problm. In particular, if B( t 0) K thn adoption of th nw tchnology is not privatly worthwhil for th firm, and so t 0 is optimal x post. In this cas th announcd t 0 tax rat is crdibl, and th Pigouvian tax policy implmnts fficincy with rspct to tchnology adoption. Howvr, if B( t 0 ) > K thn t 0 will induc adoption of th nw tchnology, and so t 0 will not b optimal x post. In this cas th rgulator cannot commit to th first-bst tax rat. Th bst th rgulator can do in this cas is to announc that it will st th tax at t 0 if th firm dos not adopt th nw tchnology, and st th tax at t 1 if th firm dos adopt th nw tchnology; no othr Pigouvian tax stratgy is tim consistnt. Milliman and Princ (1989) rfr to this policy as tax ratchting. Figur 7 illustrats th privat bnfit to th firm from adoption of th nw tchnology undr th tax ratchting policy. If th firm rtains th old tchnology thn it facs a tax rat of t 0 missions at 0. Convrsly, if it adopts th nw tchnology it facs a tax rat of t 1 and sts and sts missions at 1. Lt B( t, t 0 1 ) dnot th privat bnfit from adoption in this cas. Comparing Figurs 3 and 7 rvals that B( t 0, t1 ) > B( t 0). It follows that if B( t 0 ) > K G thn B( t, t 0 1 ) > K G. Thus, if fficincy calls for rtntion of th old tchnology but t 0 is not tim consistnt, thn th only tim consistnt policy is ratchting, and this policy inducs th infficint adoption of th nw tchnology. 13
Thr is no corrsponding problm if fficincy calls for adoption of th nw tchnology (that is, if G > K ). In this cas th first-bst tax rat for priod 2 is t 1. Figur 8 illustrats th privat bnfit to th firm from adoption of th nw tchnology at this tax rat. If th firm rtains th old tchnology thn it sts missions qual to ( t ). Convrsly, if it adopts th nw tchnology 0 1 thn it sts missions qual to 1. Lt B( t1 ) dnot th privat bnfit from adoption at t 1. Comparing Figurs 2 and 8 rvals that B( t1 ) < G. That is, th privat bnfit from adoption at t 1 is lss than th social bnfit. This dos not crat a tim consistncy problm if B( t1 ) > K sinc in that cas th firm will adopt th clanr tchnology at t 1 vn though B( t1 ) < G. Convrsly, if B( t1 ) < K thn t 1 is not tim consistnt and th only tim consistnt policy is tax ratchting. Howvr, if G > K thn B( t, t 0 1 ) > K sinc B( t, t 0 1 ) > G. Thus, if fficincy calls for adoption of th nw tchnology thn ratchting will always implmnt that outcom. Ths rsults indicat that th missions tax cannot induc too littl tchnological chang but it can induc too much tchnological chang. This problm with th missions tax stms from th fact that it dos not discriminat across units of missions according to th damag thy caus. Th tax rat is st qual to th damag causd by th marginal unit of missions and this tax rat is applid to vry unit of missions. This mans that whn marginal damag is incrasing th total tax paymnt xcds th total damag don. In assssing th privat bnfit to adopting a clanr tchnology, th firm thinks in trms of rducd tax paymnts but what mattrs from a social prspctiv is rducd damag. Sinc th rduction in tax paymnts undr ratchting xcds th rduction in damag, th firm s incntiv is distortd in favour of clanr tchnology adoption. This gnrats th wrong tchnology choic if fficincy calls for rtntion of th old tchnology. It is important to not that th dynamic incntiv problm associatd with th missions tax is not du to th assumd timing of th gam btwn th rgulator and th firm. W hav 14
assumd that th rgulator movs first by announcing a tax rat to which th firm rsponds with a tchnology choic. An altrnativ timing of th gam would hav th firm lading with a tchnology adoption dcision and th rgulator rsponding with th announcmnt of a tax rat. Undr this timing th only tim consistnt stratgy th rgulator can vr play is ratchting. Th outcom to this diffrntly timd gam corrsponds to th outcom of th gam w hav xamind whr th rgulator movs first but th tim consistncy constraint is binding. 4.2 Many Firms W now turn to th cas of many firms. For any givn m, whr m is th numbr of firms that adopt th nw tchnology, th optimal tax rat is qual to marginal damag valuatd at th fficint lvl of aggrgat missions: (3) t( m) = D ( E( m)) Thus, if D = 0 thn t ( m) = 0, and if D > 0 thn t ( m) < 0. This tax inducs th fficint mission lvls for givn tchnologis; that is, a firm with tchnology i chooss its missions i ( t( m)) such that (4) c ( ( t( m))) = t( m) i i i This implmnts quation (1); that is, ( t( m)) = ( m) i. i i Whthr or not th tax implmnts fficincy with rspct to clanr tchnology adoption dpnds again on whthr damag is linar or strictly convx. W considr ach cas in turn. (a) Strictly Convx Damag Rcall from th singl firm cas that th first-bst tax rat may not b tim consistnt whn damag is strictly convx. Th sam potntial problm ariss in th cas of many firms and is in fact mor acut. In particular, if fficincy rquirs strictly partial adoption of th nw tchnology ( 0 < m < n ) thn th corrsponding first-bst tax rat is nvr tim consistnt. 15
Why? If an announcd fixd tax rat of t( m ) inducs adoption of th nw tchnology by any firm thn it will induc adoption by all firms; it cannot induc strictly partial adoption among x ant idntical firms. Thus, if fficincy calls for strictly partial adoption thn th associatd first- bst tax rat, t( m ), cannot b tim consistnt. If th first-bst tax rat is not tim consistnt thn th only tim consistnt tax Pigouvian policy is ratchting. Ratchting in th contxt of many firms simply mans announcing that th x post tax rat will b st according to quation (3), basd on th numbr of firms that adopt th nw tchnology. Th quilibrium inducd by ratchting xhibits xcssiv incntivs for th adoption of th nw tchnology. This is illustratd in figur 9 for th cas of n = 2 and m = 1. Th shadd ara in figur 9 rprsnts th privat bnfit to th scond firm from adopting th nw tchnology. This privat bnfit compriss th rduction in tax paymnts plus any rduction in abatmnt cost. Comparing figurs 9 and 5 rvals that th privat bnfit xcds th social bnfit. Thus, thr is an xcssiv incntiv for th scond firm to adopt. Th basic intuition bhind this rsult is th sam as for th cas of a singl firm: th total tax paymnts mad undr th Pigouvian missions tax xcd th tru xtrnal cost of missions whn damag is strictly convx. (b) Linar Damag Whn damag is linar th optimal tax rat is indpndnt of th tchnologis usd and so thr is no potntial tim consistncy problm for th rgulator. Thus, th Pigouvian missions tax policy implmnts fficincy with rspct to tchnology adoption. Th intuition bhind th rsult is straightforward. Whn damag is linar th tax paymnts by a firm ar xactly qual to th damag causd by its missions. It follows that th privat and social bnfit from clanr tchnology adoption coincid. 4.3 A Continuum of Firms 16
It is worth noting that whn thr is a continuum of firms, th Pigouvian missions tax policy implmnts fficincy with rspct to tchnology adoption vn if damag is strictly convx. Th rason is straightforward. If thr is a continuum of firms thn ach firm is insignificant rlativ to th aggrgat, and so ach firm prcivs that its own tchnology adoption choic has no impact on th tax rat chosn by th rgulator. 5. Implmntation with Emissions Trading W now turn to th potntial tim consistncy problms associatd with missions trading. It is important to not at th outst that w assum th rgulator is committd to adjusting th aggrgat supply of prmits to maintain an fficint balanc btwn marginal damag and marginal abatmnt costs. Thus, w assum that th rgulator has th sam objctiv whthr th policy instrumnt of choic is an missions tax or an missions trading program. This nsurs a consistnt comparison btwn th two instrumnts. W xamin a tradabl prmit program that oprats in th following way. At th bginning of priod 1 th rgulator issus an aggrgat numbr of prmits corrsponding to th fficint lvl of missions basd on th xisting tchnology (usd by all firms in priod 1). It is not important for th problm at hand whthr prmits ar issud by auction or through som sort of grandfathring schm providd that th initial distribution dos not crat asymmtric markt powr. Each prmit allows on unit of missions during priod 1. W assum that no banking is allowd (which mans that prmits unusd in priod 1 cannot b carrid forward to priod 2). 5 Th nw tchnology arrivs at th bginning of priod 2 and th rgulator thn issus prmits for us in priod 2. Th rgulator may or may not thn hav to r-adjust that supply of prmits in rspons to th tchnology adoption that actually occurs in quilibrium, dpnding on whthr or not th first-bst prmit supply is tim consistnt. 17
Rcall that th first-bst tax rat undr an missions tax is th tax rat that inducs fficincy with rspct to tchnology adoption and at th sam tim gnrats th fficint lvl of aggrgat missions givn th tchnologis in plac. If this tax rat is not tim consistnt thn th rgulator must us tax ratchting. Similarly, th first-bst supply of prmits (and associatd quilibrium prmit pric) is that which inducs fficint tchnology adoption choics and at th sam tim corrsponds to th fficint aggrgat lvl of missions, givn thos tchnology choics. If this first-bst prmit supply is not tim consistnt thn th rgulator must us a rsponsiv policy, akin to tax ratchting, whrby th supply of prmits is st at th bginning of priod 2 and thn adjustd x post in rspons to quilibrium tchnology choics. As in th cas of an missions tax, th tim consistncy of th first-bst solution dpnds on th natur of th damag function and on th numbr of rgulatd firms. W bgin with a situation in which thr is a continuum of firms and thn considr a situation whr th numbr of firms is small nough that ach firm has som markt powr in th prmit markt. In both cass w xamin a situation with linar damag and a situation with strictly convx damag. 5.1 A Continuum of Firms (a) Linar Damag Rcall from sction 4 that whn damag is linar th rgulator dos not nd to rspond to tchnological chang if an missions tax is usd. Th tax rat is simply st qual to marginal damag and no adjustmnt is rquird. Morovr, this tax rat crats th corrct incntivs for tchnological chang to occur. Thus, th rgulator dos not nd to rspond to th advnt of a clanr tchnology. In contrast, th advnt of a nw tchnology rquirs a rassssmnt of th prmit supply undr an missions trading program vn whn damag is linar. In particular, th aggrgat supply of prmits that is fficint for an xisting tchnology will gnrally not b fficint if a nw tchnology is adoptd; th first-bst prmit supply dpnds on th tchnologis in us. Rcall 5 Allowing banking maks no diffrnc at all sinc th arrival of a nw tchnology in priod 2 with lowr abatmnt costs mans that th option to bank would nvr b xrcisd. 18
from sction 3 that whn damag is linar, fficincy rquirs ithr adoption of th nw tchnology by all firms or rtntion of th old tchnology by all firms, dpnding on th magnitud of th adoption cost. If fficincy calls for univrsal adoption thn th first-bst aggrgat prmit supply is ) E 1 = n1 such that c 1( 1 1 = δ. In contrast, if fficincy calls for univrsal rtntion of th old tchnology thn th first-bst prmit supply is E = > such 0 n0 E1 that c ( ) = δ. 0 0 0 Considr first th cas whr fficincy calls for univrsal adoption. If th rgulator issus th corrsponding first-bst numbr of prmits thn adoption by all firms is th quilibrium rspons and th prmit supply is fficint x post. Th ky to this rsult is th fact that th x post quilibrium pric of prmits is qual to marginal damag; thus, th privat bnfit from adoption to any individual firm is, in quilibrium, xactly qual to th social bnfit. Similarly, if fficincy calls for rtntion of th old tchnology and th prmit supply is lft unchangd from priod 1, thn th x post pric of prmits in an quilibrium with no adoption is qual to marginal damag, and so th privat bnfit to adoption in that quilibrium is qual to th social bnfit. Thus, laving th supply of prmits unchangd btwn priods is tim consistnt and inducs fficincy. It is important to mphasiz that laving th supply of prmits unchangd in rspons to th advnt of a nw tchnology nsurs fficincy with rspct to th adoption of that tchnology only if fficincy calls for no adoption. If th rgulator dos not adjust th supply of prmits x ant thn th prmit pric in a candidat quilibrium in which all firms adopt th nw tchnology would b lowr than marginal damag and so th privat bnfit to adoption in that candidat quilibrium would b lss than th social bnfit. Th privat bnfit to adoption in th candidat quilibrium could thrfor b lss than th cost of adoption, in which cas adoption by all firms could not in fact b an quilibrium vn though adoption by all firms is fficint. Thus, nsuring fficincy whn fficincy calls for th adoption of th nw tchnology gnrally rquirs an 19
adjustmnt to th supply of prmits in rspons to th advnt of that nw tchnology vn whn damag is linar. (b) Strictly Convx Damag Rcall from sction 4 that whn damag is strictly convx th rgulator facs a tim consistncy problm with an missions tax whn thr is a rlativly small numbr of firms but that problm vanishs whn thr ar a continuum of firms bcaus ach firm is insignificant rlativ to th aggrgat and so prcivs an indpndnc btwn its own choics and th policis implmntd by th rgulator. Th sam is tru in th cas of missions trading with a continuum of firms: thr ar no tim consistncy problms associatd with implmntation of th first-bst policy vn whn damag is strictly convx. Th policy problm for th rgulator in this cas is in fact somwhat simplr undr missions trading than undr an missions tax. Rcall that strictly convx damag mans that fficincy may rquir strictly partial adoption of th nw tchnology. In that cas th rgulator must us tax ratchting sinc committing to th first-bst tax rat x ant cannot induc asymmtric tchnology choics by x ant symmtric firms, as rquird for an fficint quilibrium. In contrast, undr missions trading th rgulator can st th first-bst prmit supply at th bginning of priod 2, without th nd for x post adjustmnt, and nonthlss induc an asymmtric and tim consistnt quilibrium. Th ky to this rsult is th flxibility of th prmit pric to rspond to tchnology adoption choics in quilibrium. Th quilibrium pric of prmits is dcrasing in th numbr of firms that adopt th nw tchnology sinc th dmand for prmits is lowr whn mor firms us th nw tchnology. This quilibrating rol of th prmit pric mans that th privat bnfit to any firm from adopting th nw tchnology is dcrasing in th numbr firms using that tchnology, and this in turn allows an quilibrium to xist in which som firms adopt but additional potntial adoptrs find it unprofitabl to do so. No comparabl automatic adjustmnt to th pric of missions occurs undr a fixd tax rat policy; hnc th nd for xplicit tax ratchting. 20
Th quilibrium inducd by th first-bst supply adjustmnt is fficint. Each firm taks th prmit pric as indpndnt of its own action, and sinc ach firm is insignificant rlativ to th aggrgat, marginal damag is ffctivly constant with rspct to th missions of ach individual firm. Thus, th saving to th firm from having to hold fwr prmits at th first-bst quilibrium pric fully rflcts th rduction in damag. 5.2 A Small Numbr of Firms Th conditions rquird for a prfctly comptitiv prmit markt brakdown whn thr ar only a small numbr of firms. Howvr, missions trading can still yild valuabl fficincy gains undr such circumstancs and can still b an ffctiv rgulatory instrumnt if potntially dstructiv collusiv and prdatory practics can b controlld. Our approach hr is to abstract from ths potntial anti-comptitiv problms and focus on th implications of stratgic intraction btwn firms, and btwn individual firms and th rgulator, for th tim consistncy of prmit supply adjustmnt policy. W bgin with th cas of linar damag. (i) Linar Damag Th ky issu of intrst is th sam as in th cas with a continuum of firms: is it a tim consistnt policy for th rgulator to issu th first-bst numbr of prmits at th bginning of priod 2 without th nd for x post adjustmnt? Considr first th cas whr fficincy calls for rtntion of th old tchnology by all firms. (Rcall that fficincy rquirs all or nothing whn damag is linar). Suppos th rgulator issus prmits corrsponding to th associatd first-bst lvl of aggrgat missions: E 0) = n (0). Rtntion of th old tchnology by all firms will b an quilibrium rspons to ( 0 this policy if no firm has an incntiv to dviat from that quilibrium by adopting th nw tchnology. 21
Considr th incntivs for a potntially dviating firm. This firm is not a pric-takr sinc th prmit markt is not charactrizd by prfct comptition. Th firm must instad sll prmits through individual bargaining with othr firms. Th spcific trading schdul th potntial dviant facs dpnds on th numbr of firms in th markt and th natur of th bargaining gam btwn firms. Howvr, that schdul must hav two gnral proprtis. First, th trading schdul cannot li abov δ sinc no firm will b willing to purchas a prmit if th asking pric is highr than its marginal abatmnt cost. Sinc c (0)) = δ at th candidat 0( 0 0 quilibrium, and sinc c 0, it follows that th potntial dviant cannot sll a prmit for a pric 0 > highr than δ. Scond, th trading schdul cannot b downward sloping (sinc c 0 ). An 0 > xampl schdul satisfying ths two proprtis is illustratd as SS is figur 10. Facd with this trading schdul th dviating firm sts missions at ~ 1 and th privat bnfit from its nw tchnology adoption is th shadd ara in figur 10. A comparison with figur 1 rvals that th privat bnfit to th dviating firm cannot b gratr than th social bnfit from that dviation (and will gnrally b lss). Sinc th social bnfit is lss than th cost of adoption (by natur of th fact that fficincy hr by construction involvs no adoption), it follows that th privat bnfit is also lss than th cost of adoption, and so th dviation is not privatly optimal. Thus, univrsal rtntion of th old tchnology is a tim consistnt quilibrium rspons to th first-bst prmit supply policy whn univrsal rtntion of th old tchnology is fficint. Th first-bst policy is also tim-consistnt whn fficincy calls for univrsal adoption of th nw tchnology. Th argumnt is xactly analogous to on just mad. Figur 11 illustrats th privat bnfit to a dviating firm that rtains th old tchnology whn all othr firms adopt th nw tchnology. Th dviating firm cannot purchas prmits for lss than th lowst marginal abatmnt cost of th othr firms, and so th dviating firm s trading schdul cannot li blow δ for prmit pruchass. Thus, th privat cost (or forgon bnfit) of rtaining th old tchnology for th dviating firm (th shadd ara in figur 11) must xcd th social bnfit from adoption, which in turn xcds th cost of adoption. Thus, th avoidd cost of adoption for th dviating firm is lss than th cost of th dviation, and so th dviation is not worthwhil. 22
Thus, univrsal adoption of th nw tchnology is a tim consistnt quilibrium rspons to th first-bst prmit supply policy whn univrsal adoption is fficint. (ii) Strictly Convx Damag In sction 4 w argud that strictly convx damag combind with rlativly fw firms mans that a Pigouvian missions tax is gnrally not abl to implmnt fficincy with rspct to tchnology adoption. In particular, unlss fficincy involvs a cornr solution, th only tim consistnt tax policy is ratchting, and this policy crats xcssiv incntivs for tchnology adoption. A similar problm ariss undr missions trading but with th opposit implication for incntivs. Figurs 9 and 12 illustrat th comparison btwn th tax policy and th missions trading policy for th cas of two firms and whr m = 1. Rcall that th shadd ara in figur 9 rprsnts th privat bnfit (undr ratchting) to th rmaining old tchnology firm if it dviats from th first-bst solution. In comparison, th shadd ara in figur 12 illustrats th maximum privat bnfit to th rmaining old tchnology firm if it dviats from th first-bst solution undr missions trading, whr th supply of prmits has bn fixd at its first-bst lvl. This ara can b xplaind as follows. Th maximum pric th dviating firm can obtain for prmits sold to th nw tchnology firm is th lattr firm s marginal abatmnt cost. Th schdul labld SS in figur 12 plots that maximum pric. Facd with this trading schdul, th dviating firm will st missions at ~ 1 and so drivs a privat bnfit from th dviation qual to th shadd ara. A lss favorabl bargaining solution for th dviating firm will man a smallr bnfit than th shadd ara. Comparing figurs 9 and 12 shows that th privat bnfit to th dviating firm is strictly lss undr missions trading than undr an missions tax. Thus, th privat bnfit to dviation undr missions trading is lss likly to xcd th cost of adoption than undr th missions tax. This mans that undr som conditions th first-bst prmit supply policy will b tim consistnt (and so implmnt fficincy) whil th missions tax policy lads to xcssiv tchnology adoption. 23
Whn th privat bnfit to dviation from th first-bst solution dos xcd th cost of adoption, th first-bst prmit supply policy will not b tim consistnt: th prmit supply corrsponding to th first-bst tchnology choics will not implmnt thos choics and so will not b optimal x post. In such cass th only tim consistnt prmit supply policy is a typ of ratchting, whrby th rgulator initially issus th sam numbr of prmits in priod 2 as in priod 1 but thn buys back prmits to adjust th supply in rspons to tchnology adoption choics. Suppos th rgulator cannot xpropriat prmits but must rpurchas prmits from willing sllrs. Thn th only tim consistnt policy is to announc that prmits will b rpurchasd at a pric qual to marginal damag valuatd at th optimum, givn th tchnologis in plac. This is illustratd in figur 13. At th bginning of priod 2 both firms ar using th old tchnology and th rgulator issus E (0) prmits accordingly. Suppos on of th firms thn adopts th nw tchnology, in which cas th fficint lvl of aggrgat missions falls to E (1). Th rgulator thn offrs to buy prmits at pric p ( 1) = MD( E(1)). At that pric th adopting firm is willing to sll 0) (1) prmits. Th non-adopting firm is willing to pay a pric highr 0( 1 0( 0 than p (1) for 1) (0) prmits and so th adopting firm slls this many prmits to th nonadopting firm. Th rmaining E( 0) E(1) prmits ar sold back to th rgulator. Th rsulting quilibrium is fficint, givn th tchnologis in us. No othr rpurchas pric will induc an fficint supply adjustmnt and so no othr policy is tim consistnt. Th shadd ara in figur 13 rprsnts th maximum privat bnfit to th singl adopting firm undr th prmit supply ratchting policy. This bnfit compriss th paymnt rcivd from th rgulator for rpurchasd prmits, plus th maximum possibl paymnt from th adopting firm for tradd prmits, plus any rduction in its own abatmnt costs. In comparison, rcall from figur 4(c) th social bnfit from adoption by on firm. It is clar that th privat bnfit undrrprsnts th social bnfit. Thus, th prmit supply ratchting policy tnds to crat an undrincntiv for th adoption of th nw tchnology. Rcall that th opposit rsult obtains for an 24
missions tax but th undrlying rason is of th sam natur. Th ratchting policy undr missions trading crats an undr-incntiv for adoption bcaus th paymnt rcivd from th rgulator for th rpurchasd prmits undr-stats th social valu of th rducd damag. 6. Conclusion In this papr w hav xamind th tim consistncy proprtis of a Pigouvian missions tax and missions trading. Our main rsults can b summarizd as follows. If damag is linar thn fficincy with rspct to tchnology adoption involvs ithr univrsal adoption of th nw tchnology or univrsal rtntion of th old tchnology dpnding on th cost of adoption. Th first-bst tax policy and th first-bst prmit supply policy ar both tim consistnt undr ths conditions, and th inducd quilibrium is fficint. If damag is strictly convx thn fficincy may rquir strictly partial adoption of th nw tchnology. In this cas th first-bst tax policy is not tim consistnt and tax ratchting must b usd. Ratchting will nonthlss induc an fficint quilibrium if thr is a continuum of firms. If thr ar rlativly fw firms thn ratchting crats xcssiv incntivs for adoption of th nw tchnology. Thus, th rsulting quilibrium may involv too much adoption. Th first-bst prmit supply policy is tim consistnt if thr is a continuum of firms and inducs th fficint solution. If thr ar rlativly fw firms thn th first-bst policy may not b tim consistnt, and th rgulator must us prmit supply ratchting. This policy crats an undrincntiv for firms to adopt th nw tchnology. Thus, th rsulting quilibrium may involv too littl adoption. Sinc both th Pigouvian mission tax and missions trading both potntially fail to induc fficincy whn damag is strictly convx and thr ar rlativly fw firms, our rsults do not spak strongly in favour of on instrumnt ovr th othr. Howvr, it should b notd that if an missions trading program is intndd to implmnt tchnological fficincy thn it is ncssary 25
to continually adjust th supply of prmits in rspons to tchnological chang, vn whn damag is linar. This continual adjustmnt is not ndd for an missions tax whn damag is linar, a distinction that givs th missions tax a possibl advantag ovr missions trading. 26
Rfrncs Biglaisr, Gary, John K. Horowitz and John Quiggin (1995), Dynamic pollution rgulation, Journal of Rgulatory Economics, 8, 33-44 Downing, Paul B. and Lawrnc J. Whit (1986), Innovation in pollution control, Journal of Environmntal Economics and Managmnt, 13, 18-29. Jung, Chulho, Krry Krutilla and Roy Boyd (1996). Incntivs for advancd pollution abatmnt tchnology at th industry lvl: an valuation of policy altrnativs, Journal of Environmntal Economics and Managmnt, 30, 95-111. Kmp, Rn (1997), Environmntal Policy and Tchnical Chang, Edward Elgar: Brookfild. Knndy, Ptr W. and Bnoit Laplant (1997), Dynamic incntivs and th Pigouvian tax, Univrsity of Victoria Discussion Papr 97-01. Laffont, Jan-Jacqus and Jan Tirol (1996a), Pollution prmits and complianc stratgis, Journal of Public Economics, 62, 85-125. Laffont, Jan-Jacqus and Jan Tirol (1996b), A not on nvironmntal innovation, Journal of Public Economics, 62, 127-140. Malug, David A. (1989), Emission crdit trading and th incntiv to adopt nw pollution abatmnt tchnology, Journal of Environmntal Economics and Managmnt, 16, 52-57. Milliman, Scott R. and Raymond Princ (1989), Firm incntivs to promot tchnological chang in pollution control, Journal of Environmntal Economics and Managmnt, 17, 247-265. Organization for Economic Co-Opration and Dvlopmnt (1999), Implmnting Domstic Tradabl Prmits for Environmntal Protction, OECD, Paris. 27
$ c ( 0 ) c ( 1 ) t = δ A B C 1 0 E FIGURE 1 Social bnfit from tchnology adoption (linar damag) 28
$ c ( 0 ) D ( E ) c ( 1 ) 1 0 E FIGURE 2 Social bnfit from tchnology adoption (strictly convx damag) 29
$ c ( 0 ) c ( 1 ) δ 1 E(1) E(0) 0 E FIGURE 3 Social bnfit from tchnology adoption by on firm (linar damag) 30
$ c ( 0 ) D ( E ) c ( 1 ) A B (1) (0) 0 1 0 (1) E(1) E(0) E FIGURE 4a Adoption by on firm: rduction in abatmnt cost for th adopting firm (strictly convx damag) 31
$ c ( 0 ) D ( E ) c ( 1 ) C D (1) (0) 1 0 0 (1) E(1) E(0) E FIGURE 4b Adoption by on firm: rduction in damag and rduction in abatmnt cost for th non-adopting firm (strictly convx damag) 32
$ c ( 0 ) D ( E ) c ( 1 ) (1) 1 0(0) 0 (1) E(1) E(0) E FIGURE 4c Social bnfit from adoption by on firm (strictly convx damag) 33
$ c ( 0 ) D ( E ) c ( 1 ) 1 ( 1) 1 ( 2) 0 ( 1) E( 2) E( 1) E FIGURE 5 Social bnfit from adoption by th scond firm (strictly convx damag) 34
$ c ( 0 ) D ( E ) c ( 1 ) t 0 ( t ) 1 0 0 E FIGURE 6 Privat bnfit from tchnology adoption ( at t 0 ) 35
$ c ( 0 ) D ( E ) c ( 1 ) t 0 t 1 1 0 E FIGURE 7 Privat bnfit from tchnology adoption undr ratchting 36
$ c ( 0 ) D ( E ) c ( 1 ) t 1 1 ( t ) 0 1 E FIGURE 8 Privat bnfit from tchnology adoption ( at t 1 ) 37
$ c ( 0 ) D ( E ) c ( 1 ) t( 1) t( 2) 1 ( 1) 1 ( 2) 0 ( 1) E ( 2) E( 1) E FIGURE 9 Privat bnfit to th scond adopting firm (strictly convx damag) 38
$ c ( 0 ) c ( 1 ) S δ S ~ ) 1 0 (0 E FIGURE 10 Privat bnfit to a dviating firm that adopts th nw tchnology (linar damag) 39
$ c ( 0 ) c ( 1 ) S δ S 1 ( n) ~ 0 E FIGURE 11 Privat bnfit to a dviating firm that rtains th old tchnology (linar damag) 40
$ c ( 0 ) D ( E ) c ( 1 ) S S 1 ( 1) ~ 1 0 ( 1) E( 1) E FIGURE 12 Privat bnfit to th scond adopting firm at th first-bst prmit supply (strictly convx damag) 41
$ c ( 0 ) D ( E ) c ( 1 ) p(1) (1) (0) 0 1 0 (1) E(1) E(0) E FIGURE 13 Privat bnfit from adoption by on firm undr prmit supply ratchting (strictly convx damag) 42