The Economics of Pollution Trading and Pricing under Regulatory Uncertainty. Odin K. Knudsen and Pasquale L. Scandizzo. Abstract

Transcription

1 Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed The Economcs of Polluton Tradng and Prcng under Regulatory ncertanty by Odn K. Knudsen and Pasquale L. Scandzzo Abstract In ths paper, we explore the effects of uncertanty on prcng of polluton permts, through the use of a dynamc model of polluton markets. We consder two major sources of uncertanty that arsng from the volatlty of demand for the underlyng resource and that comng from the regulatory envronment. Both sources of uncertanty are common n polluton permt tradng as not only does the market respond to the volatlty of fundamentals but also to the vagares of the nsttutonal structure, created by publc polcy and enforced through regulaton. The paper shows that even n the presence of strategc behavor on the part of the agents nvolved, the tradng of permts effectvely reduces emssons, and prcng does reflect opportunty costs and envronmental objectves. Furthermore, and somewhat paradoxcally, the hgher uncertanty, the greater the mpact of regulaton. Introducton Polluton permts and tradng are becomng ncreasng mportant as a market frendly nstrument to control polluton at lower costs. Although such schemes have had ther brth wth sulfur doxde tradng n the nted States, they really dd not ht nternatonal promnence untl the Kyoto Protocol came nto force. By buldng nto Protocol carbon emsson tradng and wth the emergence of the European Tradng System (ETS), polluton tradng became a mult-bllon dollar market. Despte ther growth, the economcs underlyng these polluton markets are not well understood. Although t s assumed that these markets promote least cost means of meetng targets on carbon emssons, the economcs of prcng of permts

2 and penaltes are not well understood, along wth a host of other ssues assocated wth mportant polcy decsons, ncludng regulatory uncertanty. Because the markets for an externalty such as polluton are essentally artfcal markets, created by legslaton, an addtonal form of uncertanty s added to the normal randomness of prces: the vagares of regulatory enforcement. Ths regulatory uncertanty s qute evdent n the carbon emssons tradng of the Clean Development Mechansm (CDM) of the Kyoto Protocol and under the ETS wth a complex and judcal system of enforcement. nder the Kyoto Protocol and the Marrakesh Accords, three forms of emssons tradng were permtted:. The tradng of Certfed Emsson Reductons (CERs) under the CDM;. The tradng of Emsson Reducton nts ERs) under the Jont Implementaton mechansm; and 3. The tradng of Assgned Amount nts (AAs) under Internatonal Emssons Tradng. Each one of these mechansms for carbon tradng face hgh regulatory uncertanty. The CDM as the regulatons are enforced by a sem-poltcal CDM Executve Board whch has made nconsstent decsons and later reversed others. Wth each change the market has responded wth a major varaton n prces. Furthermore the Executve Board has reled on Desgnated Operatng Enttes (DOEs) to enforce the regulatons and standards set by the EB. Snce the DOEs are prvate, standards of valdaton and verfcaton dffer between DOEs. A project developer may fnd that dependng on the partcular DOE, even though certfed by the EB, a dfferent ntensty of enforcement. The other two markets face smlar regulatory uncertanty but of dfferent forms. The ERs n JI market depends on a supervsory body smlar to the EB of yet unknown dmensons and rgor. The market for AAs whle n theory the smplest, dependng only on governments to trade a relatvely known nstrument, has the uncertanty of not only how many AAs does a country actually possess but also on the poltcal demand by buyng countres that the AAs be greened, that s assocated wth some other envronmental nvestment scheme of unknown dmensons and rules.

3 These regulatory uncertantes are coupled wth the normal market drvers of carbon, e.g. energy prces, ndustral actvty, economc growth etc. All these uncertantes are focused on the ETS market whch accepts for complance purposes EAs, CERs, ERs and ndrectly AAs. The rules of ths market are admnstered by the European Commsson (EC) and depend on the allocaton of EAs to the market and whch ndustres wll fall under the ETS and whch wll not. Furthermore, when there s a mscalculaton as wth the May 006 collapse of prce of EAs of 006 vntage because of an overallocaton of EAs, poltcs quckly emerges to try and adjust enforcement or standards. Enforcement mechansms on ndustres whch receve the EAs also are uncertan. The EC has the weapon to enforce complance but only at the natonal level through the European Court of Justce where fnes can be mposed on member states for non-complance wth EC regulatons. However the process s laborous, usually takng many years and wth uncertan results both on rulngs and penaltes. At the natonal level, each E government fnds ts own means of enforcement at the ndustry or entty level. Ths uncertanty creates a gamesmanshp between the EC, the E states and the ndustres that eventually have to face the mposton of regulaton and possble fnes. Furthermore the EC must pursue ts enforcement n a poltcal envronment and sometmes wthout the complete capacty to deal wth all the legal flngs, documentaton and defenses. Fnally, the master stroke of uncertanty s no one knows for sure f the markets wll contnue and f they do, what form they are lkely to take. The Kyoto Protocol expres n 0 and the EC has not announced the 008 allocatons or coverage. Meanwhle tradng of all these carbon emssons s takng place at a frenzy pace, and wth a great deal of fluctuatons n prces. The World Bank reports that tradng of all Kyoto nstruments has exceeded $0 bllon n 006. To model such a market n any detal would create such a black box that analytc lght s unlkely to emerge. Instead our purpose n the paper s to explore n smple abstract models how regulatory uncertanty could affect the market and prces of permts. Even though several authors have offered a basc treatment (Feld 997, Kahn 998 Tetenberg 000, Weber 00), economc and regulatory ssues behnd the propertes and use of these 3

4 nnovatve market nstruments stll need to be explored, partcularly when markets are dynamc and the fundamental drvers are themselves uncertan. In order to approach the problem gradually, we present a model that focuses on the lnk between polluton abatement penaltes and demand and supply of permts when market demand s stochastc and regulaton s uncertan. Tradng permts under uncertanty allows frms to behave strategcally, by optmally decdng when to exercse opportuntes and managng threats of penaltes from regulators. From the polcy perspectve, ths approach to polluton tradng under uncertanty brngs forth the effect of a polluton penalty on the market for permts and on the prce of output, how the transacton costs of the regulator affect the prce of permts, and how ncreased level of uncertanty n general affects the market. In dong ths, we are not attemptng to model exactly the complexty of any sngle market such as the ETS but to buld an approxmaton that yelds nsght nto the effect of varous polcy parameters on the market for permts and output. We model the behavor of the regulator as an agent that extracts penaltes on frms that exceed ther allowances supplemented by market purchased permts but does so only when t s able to cover the transacton costs of enforcement and when the volaton s not caused by a transtory ncrease n output demand of the frm. On the ndustry sde, the frm knows that the regulator wll not attack at any volaton but only when they suspect that the volaton s more permanent, n a sense, mbedded nto the fundamentals of the frm and market. But the frm does not know how the demand for output wll emerge over the future and may fnd tself n the poston of pollutng beyond ts allowances and be forced nto the market for permts when ther prces are hgh to avod the mposton by the regulator of penaltes. On the other hand, t may fnd that demand for ts output has fallen and that t s n a poston to sell to the market excess allowance. In a dynamc market and regulatory regme, the frm has to decde whether to be short or long n permts and by how much to buffer aganst the uncertanty of the market and the behavor of the regulator. In turn, the polcymaker has to decde what penaltes to mpose on volatons and how overall allocaton of permts wll affect the ndustry and the prce of output. The Basc Model The basc model s based on the dea that tradng permts under uncertanty allows frms to behave strategcally, by accountng for prce 4

5 uncertanty and antcpatng the regulator s strategy n mplementng the regulaton. We begn from an ndustral sector base, such as the power sector, where demand s assumed to be exogenous and stochastc and output adjusts to demand n every perod. Specfcally the output (and demand) of the ndustral sector Q s assumed to be a random varable followng a stochastc process of the Brownan moton varety: () dq = α Qdt + σqdz dz beng a random varable wth mean zero and varance equal dt. The parameters α and σ represent respectvely the drft or trend n demand and the varance. Wthn the sector, frms (depcted by the subscrpt ) are technologcally heterogeneous wth emssons y assumed for smplcty to be proportonal to ther output Q : () y = Qu The frm has a share w of the sectoral output and therefore s u Q of the sector s emssons where u s the emssons responsble for w per unt of output of the th frm. The more clean technologcally the frm, the lower s the emssons factor u. The government s assumed to have mplemented a cap and trade system where each frm s allocated an emssons allowance Y that t can supplement through market purchases or sell to other frms n the ndustry at a market determned prce p. The quantty of the permt q acqured n the market adds to ts overall allowances or f sold detracts from t. To deter frms from exceedng ther emsson allowances, the regulator s authorzed to mpose a fne at a rate of of the amount of emssons that exceed the allowance plus the net amount of permts derved from the tradng of emssons. However, mposng a sancton on the th frm has an mplementaton cost to the regulator of V. Because of ths mplementaton cost, the regulator n attemptng to lmt emssons reles not only on the collecton of the fne when t s worth dong, but also on the deterrent value of the threat to mpose ths sancton. 5

6 Furthermore the regulator realzes that because the output of emssons s stochastc, a temporary or random volaton of the allowance lmt may not be worth the transacton costs of mplement the procedures to collect the fne or penalty. But f the allowance s exceeded by a sgnfcant enough margn, the regulator s prepared to mpose the penalty. The frm on ts sde s attemptng to maxmze ts net worth as measured by ts net present value as any other company but also must decde whether to purchase emsson permts to cover the possblty of an ncrease n emssons as demand for example for electrcty randomly ncreases due to fluctuatons n weather. It also must manage the threat of the regulator mposng potentally stff penaltes on ts excessve emssons. Over the longer term, the frm can nvest n cleaner technologes but n the short term t faces both the vagares of the market for permts and the possblty of fnes from the regulator. value The frms s therefore tryng to maxmze ts expected net present Π : Pw Q (3) Π = C( w ) pq F( Q ), δ where P s prce of output, C w ) dc d C ( 0, > 0 d( w ) d( ) w ( s a concave cost functon ), C ndcatng rreversble nvestment and operatng costs approprately dscounted, and F( Q ) s the lablty threat comng from the regulator. The dscount factor δ s the dfference between the rsk free rate of nterest r and the drft α of the stochastc process or δ = r α. The term pq represents the value of permts acqured by the frm n polluton tradng. The last term of (3), F ( Q ), requres a longer explanaton. Because of uncertanty on both polluton levels and the regulator s behavor, the value of the term depends on the crcumstances. If the regulator s expected to mpose a fne on the frm, t wll have the value of the expected penalty; but Note that n many regulatory or legal stuatons, enforcement s not absolute. A smple reference to vehcle speedng where the polce may decde to let some unknown volaton of speed lmts take place or n over law enforcement, eg taxes or recreatonal drugs, where certan volatons may not be worth the effort of mposng the sancton. 6

7 obvously s zero f the regulator s expected to decde that the volaton s mnor and/or wll not persst and therefore s not worth the enforcement costs, ether drectly to the regulator or ndrectly to socety. If there s a volaton that could engage the regulator at some future tme, then the opton has a value n between these two extremes. To the frm, the possble mposng of the fne therefore s a contngent lablty, whose value depends on the opton held and/or exercsed by the regulator. The value of ths opton depends on uncertanty, the perod of the opton and the underlyng asset value, n ths case the possble fne, along wth other parameters such as the nterest rate. In turn, ths lablty opton s a call opton representng an asset opton for the regulator, who wll exercse t when the value of the emsson s hgh enough that the value of the contngent lablty opton equals the expected amount of the fne that can be collected mnus the costs of enforcement. Publc polcy and analyss set the rate of the fne for excess emssons at a level that reflects the margnal costs to socety of polluton above the targeted amount. 3 As we wll demonstrate later, there exsts a fne that corresponds to each polluton target and vce versa. The regulator therefore does not pursue fnes aganst the polluter at the pont when the expected amount of the fne s equal to the costs of enforcement, but wats untl the volaton has become excessve enough to justfy not watng any longer. At ths pont, the margnal ncrease n the opton value s just equal to the margnal expected present value of the net collecton of the fne or of the rate of the fne f ths s constant. 4 We assume that frms not only dffer n technology and emsson levels, but also, dosyncratcally, n the amount of transacton or economc costs that they generate when the regulator tres to sancton them. At any pont n tme, the opton s takng on a value that depends on ths expected net margnal fne and on the tme when the frm s lablty opton held by the regulator s expected to be exercsed. Ths s referred to as the value matchng condton. 3 Although the rate of the fne should be part of a complex analyss of benefts and costs, n practce, the regulator s estmaton s drven by a wde set of conflctng postons from ndustry, the general populaton, and cvl socety. After navgatng these poltcal and economc consderatons, the European non has set the rate of fne for the second phase (008 thru 0) of the ETS at Euro 00 per ton of CO. 4 Ths s called the smooth pastng condton. 7

8 We can express these concepts analytcally. Followng Dxt and Pndyck (994[OK]) the value of the contngent asset or opton for the regulator F Q ) at tme T can be expressed as: ( (4) F( Q = ) sup EQ e τ + T ρ ( s τ ) ( w Q u Y q ) ds V s For = to N. In (4) s the ad valorem rate of the fne, whle Y s the polluton cap mposed by the regulator on the th frm and V the cost of mplementng the sancton aganst the th frm. 5 Notce that the fne s rased on the dfference between the expected present value of the frm s emsson and total value of the ndvdual emsson cap and of the quantty of permts (expressed n emsson tons) owned by the frm. In other words, we assume that an rreversble nvestment n mplementaton costs has to be made by the agency n charge, n order to recover the fne, once a threshold has been exceeded by the frm. The regulator acts on the expected emssons over a perod. Because output s assumed to follow a geometrc Brownan moton and the emssons are proportonal to output, expected emssons are the same as pont emssons. The value of the contngent asset that the regulator holds (Dxt and Pyndck, 994) s: (5a) Q F( Q ) = ( w u Y q ) V δ f w Q Q when the frm n ts expected emssons has exceeded or s just at the trgger pont of the regulator Q u. For the frms that have not exceeded ths trgger pont but may be expected to exceed t some tme n the future, the value of the contngent asset s: w Qu β (5b) F( Q ) = ( ) [ ( u Y q ) V ] f w Q < Q Q u δ Q 5 It s reasonable to assume that the threshold level of emssons Y s fxed wth reference to the expected present value of emssons although some other crtera could be used by the regulator. 8

9 βδ V where δ = α ρ, Q u = ( Y + q + ) β and wqu β rt ( ) = Ee s the Q u expected dscount factor correspondng to the (stochastc) tme of enforcement t for the th frm. Consder the value of the frm under the threat of sancton n the case of expected acton by the regulator some tme n the future (the second case above). Substtutng expresson (5b) nto (3), we obtan: (6) Π = PwQ C( w ) pq δ wqu [ β ( Y + q β ] V + ) β Y ( V + q + ) β The expected present value of the frm s affected by the regulaton as a contngent lablty (the fourth term n equaton (6)). Because β n equaton (6) s nversely proportonal to volatlty of emssons and asymptotcally approaches as volatlty goes to nfnty (see Dxt and Pyndyck), the contngent lablty approaches the certanty fne, that s a fne equal to the amount of emssons tmes the rate of fne[ok]. As volatlty approaches zero or certanty ( β ), the contngent lablty also becomes zero (by assumpton the frm s emssons are below the trgger pont wth certanty n ths case). Obvously when emssons are above the trgger pont of the regulator s acton, the sancton s appled and the fne becomes equal to the rate of fne tmes the amount of emssons above the allowance. We now explore the behavor of the frm n the face of ths contngent lablty. We assume that each frm maxmzes net present value by selectng the frm output level as a share of the ndustral sector output w and the number of permts q whch t wll buy. Market prces for output and for the permts are determned by the condtons that supply and demand must be equal n both markets or: w = and = q 0. We frst fnd the value of the number of permts as long or short postons that maxmze the value of the frm, by takng the frst dervatve of (6) wth respect to q and equatng t to zero: 9

10 Π β (7) [ βδ V β Q = p + ( Y + q + )] ( wu ) = 0 q ( β ) δ Equaton (7) s a condton for a maxmum snce, as t can be easly checked, < 0 Π q permts q yelds: for all non zero values of q. Solvng for the amount of (8) q β Q Y δ β = ( ) ( ) wu p β V, The frm wll dsplay a postve or zero demand for permts ( q 0) f : Q p β β V (9) w u ( ) [( )( Y + )] δ β Note that n (9) the term on the left hand sde of the equaton s the trgger pont for the regulator n the absence of the holdng by the frm of permts. If the prce of permts s just equal to the ad valorem fne ( = p ), the frm wll be nduced to buy permts only f the expected present value of ts emssons at the permt prce s hgher than the threshold that the regulator wll enforce the sancton. On the other hand, f the prce of permts p s greater than the tax rate, the frm wll be nduced to buy permts only f ts producton s above the predctable threshold of sancton, whle the opposte wll be true f the tax exceeds the prce. For the frm sellng permts ( q < 0), on the other hand, a prce hgher than the tax rate wll be an ncentve to sell, wth respect to the ndfference case (emsson level equal to the threshold so that q = 0 ). In equlbrum, short and long postons should cancel each other N (demand equals supply),.e. q = 0 for N frms. Ths mples the followng equlbrum prce: = 0

11 Q / N = N δ / N (0) β β p = [ ] = ( ) β V / N ( Y + ) β In (0), the numerator of the expresson n parenthess N = w u denotes the expected emssons of an average frm, whle the denomnator of the same expresson, β V ( Y + ) / N β s the average value of the threshold of nterventon,.e. the value of emssons that would prompt the regulator to ntervene for an average frm wthout any permts. 6 In partcular, t can be easly shown (Dxt and Pyndyck, p ) that: / N / N β rt () ) = Ee ( rt Where Ee s the expected value of the dscount factor for the stochastc tme of the regulator s nterventon for the average frm that s not holdng permts. Snce holdng permts would postpone the day of reckonng, the tme n () s the earlest tme that the average frm wll be sanctoned. Expresson (0) thus predcts that the equlbrum prce of permts wll equal the expected present value of the fne ad valorem rate (expressed as a value per unt of output) for an average frm. As expresson () shows, the dscount factor s a functon of the rato between average emsson level and the level at whch the regulator would mpose a fne on a representatve frm producng the ndustry output wth an average technology. If ths rato were unty,.e. the regulator were exactly at the threshold for the average frm, the equlbrum prce of permts would be equal to the fne ad valorem rate. Whle a rato hgher than unty would not be permtted by a ratonal regulator, ts possble occurrence because of the regulator s neglgence wll cause the prce of permts to exceed the fne, because more frms wll be non complant and regulator acton wll appear overdue. Vce versa, for values of the thresholds above expected emssons, nterventon by the regulator wll 6 Note that Y, the polluton cap, can also be nterpreted as an amount that can be deducted from the fne base of emssons. Ths may nclude permts ssued by the government or any other element that causes emssons to declne (such as, for example, the adopton of a specfc abatement technology).

12 appear more remote and prce of permts wll tend to fall below the value of the fne. An ncrease n uncertanty, snce t wll mply an ncrease n the threshold value of nterventon, wll be assocated to a lower value of the prce of permts. Table and fgure show how the equlbrum prce would evolve under alternatve values of β and g V Y + =, f the value of the fne were fxed at 00 Euro per ton. 7 Note that the polluton rato g s a hybrd term between the rato of the targeted emssons cap Y relaxed by the aggregate bll (converted to emsson tons by the ad valorem fne rate) to the total emssons of the sector. Ths polluton rato s lkely always to be less than one unless the emssons gap s not very strngent and the enforcement costs are hgh. Also recall that the term β s nversely proportonal to the uncertanty of output and therefore emssons of the ndustry. 7 Ths value s the fne under the second phase of the European Tradng Scheme. However, under the ETS the fne s supplemented by the need to cover the gap n emssons to allowances by a market purchase. Also, purchases are allowed from the mechansms of Clean Development and Jont Implementaton. We have abstracted from these complcatons for smplcty of exposton.

13 Table Equlbrum prce (Euro/ton), accordng to expresson () under alternatve hypotheses on uncertanty and polluton targetng (basc fne value = 00Euro / ton ) Inverse volatlty parameter : β Polluton Rato g

14 Fgure Equlbrum prce (Euro/ton), accordng to expresson () under alternatve hypotheses on uncertanty and polluton targetng (basc fne value = 00Euro / ton )

15 As the fgure shows, for plausble values of the polluton ratos and the uncertanty parameter, the prce of the permt wll tend to be a fracton of the value of the fne. It wll only slowly converge to such a value as the reducton target s stepped up and/or the uncertanty decreases. Substtutng p n (8), we fnd the expresson for the demand (supply) of permts for each level of producton for the -th frm: ωv V () q = ( ωy Y ) + ( ) where levels of ndustry. wuq ω = = wu w u s the -th frm s share of the emsson Equaton () states that n equlbrum frm demand ( supply) of permts wll not depend on stochastc demand Q of the ndustry but only on the extent to whch ts emsson cap (.e. ts deductble) and the mplementaton costs that t generates are smaller (greater) than ts share, respectvely, of polluton caps and mplementaton costs, based on ts contrbuton to total ndustry emssons. More specfcally, we can dstngush eght dfferent possbltes: ( Table Alternatve determnants of equlbrum demand and supply of permts ω Y Y ) ω V V ) Demand of Permts Demand of Permts ( < 0 0 f < 0 f V ωv V ωv ( ωy Y ) ( ) ( ωy Y ) < ( ) < 0 < 0 < 0 < 0 < f > 0 f ωv V ωv V ( Y ωy) ( ) ( Y ωy) < ( ) 5

16 In the four pure demand and supply cases (respectvely, frst and thrd row of Table ), demand of permts s postve or negatve (.e. supply s negatve or postve), because the actual assgnment of the polluton cap and the transacton costs to mplement the regulaton for the th frm, fall short (for postve demand) or exceed (for postve supply) ts theoretcal share on the bass of ts contrbuton to total polluton and to transacton costs. In the four mxed cases (thrd and fourth row of Table ), on the other hand, the frm wll demand (supply) permt, dependng on whether ts potental demand (supply) on the bass of ts polluton level s greater (smaller) than ts potental demand (supply) on the bass of ts contrbuton to mplementaton costs. In other words, a frm may demand permts because t values polluton more than the regulator does (n terms of allocated caps and mplementaton costs) or because the costs to recover a fne from t are suffcently hgher than the average costs or both. Substtutng () back nto (5b), we fnd that the output level that wll trgger the regulator s acton aganst the th frm s: Q Q βω V (3) u = w u = ( Y + ) δ δ β sng expressons () and (0), we can also derve the expresson for the expendture for permts of the -th frm: rt ωv V (4) p q = Ee [( ωy Y ) + ( )] Therefore n equlbrum, each frm wll spend (earn) n buyng (sellng) permts an amount equal to the expected value of the fne for the average frm multpled by the postve (negatve) devaton of ts (output based) shares from actual levels of emsson and mplementaton allowances. The Frm s Output level and Market Equlbrum We now go back to expresson (6) and fnd the proft maxmzng value of market share w. We assume that we are dealng n a regulated or sem-regulated ndustry lke wth the power utltes. We hypothesze that the 6

17 ndustry bases ts output on the expected prce for output. Each frm targets ts share of stochastc market demand, takng nto account the forecast of stochastc demand, the admnstered prce that t wll be allowed to charge, nvestment costs plus the costs nvolved by the threat of polluton fnes and/or of emsson permts. If the bds for producton are too low (the sum of the shares offered by the frms falls short of unty) as compared to demand, the government ncreases the admnstered prce, whle t lowers t f the output exceed expected demand. Market equlbrum s thus reached when the market prce for the output s such that expected demand s equal to the productve capacty allocated and each frm produces ts optmal share of total output. Dfferentatng proft n (6) wth respect to w, usng (3), equatng to zero and solvng for w, we obtan: (5) w = PQ δ 0 c ( Ee c rt )( ) Q u 0 β where Q0 s expected demand at the tme of the bd, Ee rt = ( ), and we have used a quadratc expanson to approxmate the cost functon, so that: C = c0 + cw + cw. It s easy to check from (6) that the second dervatve of proft w.r.t. w s always negatve, so that expresson (5) characterzes a relatve maxmum. Imposng the condton w = and consderng only the n N frms for whch expresson (6) yelds a postve value, we obtan the expresson for the equlbrum market prce of output: (6) c c + P = n rt + E( e )( Q / δ 0 Q ) u δ 7

18 where u = n u. Accordng to (6), output market prce wll equal average cost of producton plus the expected present value of the fne multpled by the target level of polluton corrected for the nequalty n the dstrbuton of emsson technologes. Substtutng (6) nto (5), we fnd: rt (7) w = E( e )( ) ( u u ). n c δ Q In equlbrum, the optmal share of producton for the th frm wll be larger, the smaller s ts threshold emsson level per unt of output compared wth the average emsson level that would prompt the regulator to mpose the fne. Whle the tradtonal crtcsm aganst the market for permts s that t allows pollutng frms to pollute more, the result n (7) shows that the system may actually work. Wth polluton permt tradng, the frms that are the more technologcally effcent n terms of reduced polluton per unt of output over the ndustral average wll preval n the market. The more severe the polluton cap the more ths effcency wll be reflected n market share for any level of uncertanty. Lkewse the hgher the fne the more s the market share from cleaner technologes for any level of uncertanty. Snce β s nversely related to uncertanty of underlyng demand or output, hgher levels of uncertanty reduce the expected dscounted value of the fne, thereby reducng the amount of mpact that technologcal advantage has on market share. Ceters parbus, the markets wth the hghest levels of output uncertanty wll have the lowest envronmental beneft of mproved technologes under a regme of emssons tradng and regulatory fnes. 4. The ndustry- wde polcy problem Multplyng w by u and summng over all, we fnd: 8

19 (8) w u _ = u Ee rt n Q σ δ u where u = n u and σ = ( u u). u n _ For β, expresson (8) s a non lnear equaton that has no general analytcal soluton. We can gan some nsghts n ts mplcatons, however, by consderng the lnear case,.e. β =. In ths case, average optmal polluton level s: (9) w u = δc V δc ( Y + ) V ( Y + ) + nq0σ u _ u As expresson (9) shows, for any gven level of Y and V, the average level of polluton s always less than the arthmetc mean,.e. average polluton under equal sharng, and so much so, the larger the level of the polluton tax. The average level of polluton depends negatvely on the degree of dversfcaton of producers emsson, measured by ts ndustrywde varance. In other words, a mean preservng spread of the dstrbuton of pollutng frms reduces total polluton, snce the threat of the fne s more effectve n determnng a dfferental ncentves for low versus hgh polluters. On the other hand, realzed average polluton level does not depend on how the polluton threshold and/or the transacton costs are dstrbuted across the frms. Even though expresson (9) cannot be solved explctly n terms of total polluton, t can be nterpreted as a relatonshp between one polcy target,.e. the average level of polluton u and two nstruments: the w polluton threshold Y and the tax. Denotng the target level of polluton wth R, we can solve (9) to derve the relatonshp between the two polcy nstruments for any gven value of the target: V Y + nq0 ( u R) β (0) = [ ] RQ / δ 0 c t 9

20 where u R t = σ u can be consdered, n analogy wth the Student t statstc, a measure of the sgnfcance of the gap between the polluton that would be expected wthout any publc acton and the polluton target set by the government. From expresson (0), we may conclude that t s not only the gap between the target and average polluton to determne the threshold and/or the ax level, but also ts sze relatve to the degree of dversfcaton of the ndustry. The more dversfed the ndustry, the easer, coeters parbus, s to acheve a szable reducton of polluton by favorng low emsson frms. Substtutng the value of Y of (0) nto (7), we fnd: ( u u)( u R) () w = [ ] n σ _ u _ Expresson () shows a remarkable result: once the government has fxed ts polluton target, the ensung optmal share of market capacty for the th frm does not depend on the value of the demand forecast (ndependent of the level of the stochastc varable Q), but only on the degree of emssons of the frm, the sze of the government target as compared wth the ndustry average and the varance of ndustry emsson. The condton for w to be greater than or equal to zero can be derved from () as: () u _ u+ ( _ σ u u R) whch can be wrtten n percentage terms as follows: u CV (3) + _ u ( u R) / u where CV s the coeffcent of varaton σ / u u. From (3), we can nfer, for example, that for a reducton target equal to 5 percent of the expected _ 0

21 polluton level, and for a coeffcent of varaton of 0%, a frm would have to expect a level of emssons not greater than twce the average to enter the market. Ths upper lmt rases to 4 tmes the average n the case of a CV equal to 0% and to 0 tmes the average for a CV equal to 00%. On the cost sde, consderng a quadratc approxmaton of the cost functon, substtutng the value of w obtaned from () : 0 t (4) C = nc + c + c ( + ) n Total producton cost (the total level of producton s equal to total demand and thus s assumed to be exogenous and random) s thus postvely related to the square of the reducton of average emssons that the government wants to acheve. As equaton (4) shows, however, cost s unquely determned by the polluton target and the ndustry structure (ts degree of dversfcaton) and cannot be affected by a separate polcy nstrument. The only feasble nstrument to reduce the costs determned by the polluton target would thus be an mprovement n productvty (.e. a reducton of the values of the parameters of the cost functon). Conclusons In ths paper, we have explored the effects of uncertanty on prcng of polluton permts through the use of a dynamc model of polluton markets. We have brought n two major sources of uncertanty that arsng from uncertan demand for the underlyng resource and that comng from regulatory uncertanty. Both sources of uncertanty are common n polluton permt tradng as not only does the market respond to the volatlty of fundamentals but also to the vagares of the nsttutonal structure beng created by publc polcy and enforced through regulaton. The dynamc uncertanty nherent n polluton permt markets and the strategc decson-makng that s demanded of partcpants n the market both on the part of frms and the regulator create market behavor that s not evdent from smple statc models of supply and demand. As we have shown usng a real optons model operatng under dynamc uncertanty, the effect of regulaton on permt prcng s not straghtforward. The regulator operatng also under uncertanty had two nstruments at ts dsposal: the rate

22 of the fne and the tmng of the mposton of the fne. The frm on the other hand has several nstruments: the amount of output or market share, the amount of polluton permts t secures from the market and the effcency by whch t uses technology to reduce pollutng emssons. We have found that under uncertanty the combnaton of the threat of the sancton and the market for permts may be effectve n reducng the emsson levels by shftng the compettve advantage n favor of less pollutng frms. Ths wll occur both because of the reducton of frm value to the potental mposton of the sanctons and because less pollutng frms wll be able to sell part or all of ther allowances to the more pollutng ones. ncertanty, however, tends to reduce the value of the market prce of permts, snce n equlbrum ths s smply equal to the expected present value of the fne. Thus, hgher uncertanty wll requre, for the regulaton to be effectve, comparatvely hgher fnes. Even under uncertanty of regulaton and demand for output, the effect of polluton permt tradng s postve to achevng a cleaner ndustral base. Frms that are more technologcally effcent n reducng polluton wll tend to acqure larger market shares, wth the exact effect dependng on the uncertanty of demand for output and the severty of the fne. sng ths type of real optons approach, we beleve that avenues of research are open. For example, through relatvely smple analytc models other ssues wth respect to permt tradng can be explored, for example, the effect on new entry nto the market when wll new frms wth cleaner technologes enter the market when demand s uncertan and the behavor of the regulator uncertan. We wll explore ths ssues and others n later papers. References Dxt, A. K. and Pndyck, R. S Investment under ncertanty. Prnceton Prnceton nversty Press. Feld, B. C Envronmental economcs: An ntroducton. nd ed. Hghtstown, N.J.: McGraw-Hll.

23 Kahn, J. R The economc approach to envronmental and natural resources. nd ed. Fort Worth, Tex.: Dryden. Tetenberg,T Envronmental and natural resource economcs, 4th ed. New York: Harper-Collns. Weber, D. W. 00. Polluton permts: a dscusson of fundamentals. The Journal of Economc Educaton 3