Unintended Consequences of Price Controls: An Application to Allowance Markets

Transcription

1 MPRA Munich Personal RePEc Archive Unintene Consequences of Price Controls: An Application to Allowance Markets Anrew Stocking Congressional Buget Office September 2010 Online at MPRA Paper No , poste 4. October :09 UTC

2 Working Paper Series Congressional Buget Office Washington, D.C. UNINTENDED CONSEQUENCES OF PRICE CONTROLS: AN APPLICATION TO ALLOWANCE MARKETS Anrew Stocking Microeconomic Stuies Division Congressional Buget Office Washington, D.C. September 2010 Working Paper Working papers in this series are preliminary an are circulate to stimulate iscussion an critical comment. These papers are not subject to CBO s formal review an eiting processes. The analysis an conclusions expresse in them are those of the author an shoul not be interprete as those of the Congressional Buget Office. References in publications shoul be cleare with the author. Papers in this series can be obtaine at (select Working an Technical Papers). This paper benefite from comments by an conversations with Dallas Burtraw, Terry Dinan, Harrison Fell, Sasha Golub, Janet Holtzblatt, Nathaniel Keohane, Joseph Kile, Deborah Lucas, Davi Moore, Aele Morris, Kevin Perese, Ceric Philibert, Stephen Salant, an one anonymous reviewer. Special thanks to Bob Shackleton an Brian Prest for constructing the sector-specific elasticities. Page 1

3 Abstract Price controls establishe in an emissions allowance market to constrain allowance prices between a ceiling an a floor offer a mechanism to reuce cost uncertainty in a cap-an-trae program; however, they coul provie opportunities for strategic actions by firms that woul result in lower government revenue an greater emissions than in the absence of controls. In particular, when the ceiling price is supporte by introucing new allowances into the market, firms coul choose to buy allowances at the ceiling price, regarless of the prevailing market price, in orer to lower the equilibrium price of all allowances. Those purchases coul either be transacte by a group of firms intening to manipulate the market or be inuce through the introuction of inaccurate information about the cost of emissions abatement that causes firms to purchase allowances at the ceiling. Theory an simulations using estimates of the elasticity of allowance eman for U.S. firms suggest that the manipulation coul be profitable uner the stylize setting an assumptions evaluate in the paper, although in practice many other conitions will etermine its use. Page 2

4 I. Introuction In light of growing concern about global climate change, some countries, incluing the Unite States, Australia, an New Zealan, are consiering establishing a cap-an-trae program, similar to that alreay enacte in the European Union an 10 states in the northeastern Unite States, to reuce emissions of carbon ioxie an other greenhouse gases (GHG). Uner such a program, the government woul set a limit, or cap, on total GHG emissions (measure as carbon ioxie-equivalent emissions, or CO 2 e, which is the amount of emissions of carbon ioxie alone that woul cause an equivalent amount of global warming) an woul require regulate entities, such as oil refiners, natural gas istributors, large electricity generators, an chemical companies, to hol rights, or allowances, for their emissions. After allowances were initially istribute, entities coul buy an sell them an woul be require each year to submit a number of allowances equal to their CO 2 e emissions from the previous year. The cost of those allowances an the cost of eliminating emissions in excess of those allowances represent the cost of complying with the cap-an-trae program. Allowance prices uner such a program woul change from ay to ay in response to changes in expectations about the marginal cost of reucing emissions an the eman for emissions-intensive goos an services. In the face of such uncertainty about compliance costs, some have propose placing controls on allowance prices in the form of a maximum price, sometimes calle a price ceiling or safety valve price, an a minimum price, or price floor. 1 Such controls, proponents argue, woul achieve a policy goal of traing off the economic costs with the environmental goals of a cap-an-trae program, an several economists have even conclue that such controls woul only minimally affect the emissions objective of the program. 2 That research, however, implicitly assumes that market participants will not use the pricecontrol mechanism to influence the price of allowances. The research presente here illustrates conitions uner which participants coul lower their cost of compliance with a cap-an-trae program by weakening the cap, thus reucing the environmental benefits of the program. That fining relies on the assumption that the cap-an-trae program woul aopt a price-control mechanism similar to that foun in most U.S. proposals: it woul maintain the price ceiling through the release of aitional allowances into the market when the allowance price threatens to excee the ceiling price, but woul not preclue such a release any time market participants Page 3

5 are willing to pay the ceiling price for allowances, an woul not inclue an equivalent mechanism for retracting those allowances shoul allowance prices later fall. That means that any release of aitional allowances woul permanently relax the allowance cap, regarless of the long-term marginal costs of emissions abatement. Thus, if one or more market participants were to purchase allowances at the ceiling price, whatever the actual equilibrium price, they woul be lowering the equilibrium price for all allowances, thereby proviing a public goo to themselves an other regulate entities by lowering the cost of all allowances. The provision of that public goo escribe throughout this paper as a manipulation is a possible unintene consequence of price controls not iscusse elsewhere in the literature. The analysis in this paper thus complements research on price manipulation in general an on manipulation specific to allowance markets by monopsonist buyers. 3 The unintene consequence may not conform to every reaer s efinition of manipulation, because it relies on a natural market response to price controls implemente as escribe in many cap-an-trae proposals. In aition, the manipulation oes not aversely affect other market participants, as many market manipulation strategies o, but instea leaves taxpayers worse off through lower government revenue an reuce environmental benefit. As a result, neither the legality of the manipulation nor the response of regulators is obvious, an for that reason this paper remains agnostic on any regulatory response or costs incurre by participants to avoi a regulatory response. The next section escribes the unintene consequences that woul appear to often accompany price controls, most of which were not preicte before their implementation. Section III escribes a hypothetical U.S. cap-an-trae program an explains qualitatively how the manipulation of price controls may be one such unintene consequence of such controls in a cap-an-trae market. Section IV brings theory to that explanation, an Section V escribes some of the key parameters efining the feasibility of the manipulation within the hypothetical program. Section VI uses those parameter estimates to escribe the payoffs of the potential manipulation an further characterize the manipulation from the perspective of market participants. Section VII conclues. Page 4

6 II. Historical Use of Price Controls Many economists believe that a tax is the most efficient mechanism to regulate GHG emissions. An some point out that a cap-an-trae program that inclues price controls coul mimic a tax by limiting the economic costs of a policy to reuce emissions. Furthermore, some suggest that because the cap-an-trae program woul be create through a government policy, it might operate ifferently than other markets, for example, energy an agricultural commoity markets. However, like price controls or price stabilization policies use in other markets, price controls in allowance markets may have unintene an etrimental consequences. In other markets, those various consequences ten to be largely unforeseen when the price controls are introuce. The unintene consequences of price controls in an emissions allowance market may or may not be similarly unpreictable. Generally, price controls can be implemente in one of two ways: regulation or supply management. The regulatory approach simply prohibits any buying or selling at prices above a maximum price or below a minimum price. Alternatively, controlling prices with supply management requires the market overseer in many cases a government entity to ajust the supply of the price-controlle commoity to eliminate excess supply in the case of a price floor an eliminate excess eman in the case of a price ceiling. Common examples of regulatory price controls inclue rent controls, which limit the rental rate a housing owner can charge renters, an the minimum wage, which places a floor on what an employer can pay employees. It is well establishe that price controls can create inefficiencies in the marketplace, for example, by preventing housing from being allocate to those willing to pay the most for it, or preventing jobs from being allocate to those willing to work for the lowest wage. But price controls can also have unintene consequences that are inirectly relate to the consumption of the controlle goo. For example, in the early 1970s the U.S. government place a maximum price on crue oil. Although intene to ampen the exposure of U.S. consumers to rising energy prices, those price controls create immeiate gasoline shortages an are thought to have create isincentives to prouce oil omestically, which ultimately contribute to a long-term reliance on foreign oil. 4 Regulatory price controls are also present in markets with active traing, which may offer market participants opportunities to capitalize on any inefficiency create by the controls. Most eregulate electricity markets in the Unite States currently have a price ceiling set at $1,000 Page 5

7 per megawatt-hour (MWhr), far above the typical price of between $30 an $100 per MWhr. 5 At that price, typically reache hours each year, the market overseer (calle the inepenent systems operator) of each regional electricity gri intervenes to clear the market by eciing which firms will prouce electricity, which firms will receive that electricity, an the price at which they will both transact. The infrequency with which those price ceilings are reache minimizes any negative consequences of such intervention. Other price controls in electricity markets, however, have prove less benign. For example, when the California electricity market was eregulate in the 1990s, that eregulation applie only to the price at which electricity istributors coul purchase electricity on the open market. California retaine a regulatory price ceiling for consumers, with the result that istributors were force to purchase electricity at market prices but coul pass on only a fraction of those costs (about $60 per MWhr) to California consumers. That iscrepancy between the price at which istributors ha to purchase electricity an the price at which they coul sell electricity create an opportunity for some market participants, such as Enron, to manipulate the market for their own profit. Although the opportunities for manipulation create by the price controls were not the sole cause of the California energy crisis, they are generally recognize as a contributing factor. 6 Supply management, the secon mechanism for controlling prices, has been use by the U.S. government at various times over the past century to stabilize prices of gol, tin, an silver. That type of price control requires the market overseer to have either a sufficiently large stock of the commoity to satisfy excess eman or a cash reserve with which to purchase excess supply. If excess eman or supply remains after the overseer s resources are exhauste, the market price will rise above the price ceiling or fall below the price floor. In theory, price controls implemente through supply management shoul have a stabilizing effect on the price, assuming the intention to implement an enforce the controls is creible to the market. 7 Perfect creibility, however, requires that the market overseer possess an inexhaustible supply of the commoity or cash. Without such creibility, as woul be the case if the government lacks the resources or authority to support a particular price uner any circumstance, market participants anticipating the reserve s imminent exhaustion woul be expecte to engage in a speculative attack on the price-controlle commoity. To o so, they woul buy the controlle item at the ceiling price to buil their own supply an exhaust the government s, an then, sell to the market when the price rises above the ceiling. 8 In a cap-an- Page 6

8 trae setting, a speculative attack woul not be expecte to occur if the government ha the authority to print an unlimite number of aitional allowances, as some proposals have allowe. A price floor can also invite a speculative attack. For example, when the Unite Kingom ecie in 1990 to join the European Exchange Rate Mechanism (ERM), it ha to guarantee that the poun s valuation woul fluctuate by no more than 6 percent relative to other member country currencies. In September 1992 both omestic an international pressures pushe the poun towar the lower boun of that range. In an effort to increase the value of the poun, the U.K. government sought to reuce supply by purchasing billions of pouns an repeately raising interest rates. Despite this, currency traers sol the poun short, in effect betting that the government woul fail to maintain the price floor. The government ultimately withrew from the ERM an allowe the poun to ecline in value, generating billions in profits for those currency traers who ha sol the poun short at the government-supporte floor. 9 A similar speculative attack occurre in 1985 when the International Tin Council faile in its effort to maintain a tin price floor. 10 Finally, price controls have also been observe to have behavioral implications for market participants. For example, the behavioral economics literature fins evience that the presence of price floors an ceilings causes participants in a laboratory to migrate towar those price bounaries, as if they provie significant information about the value of the commoity in question. 11 Another strain of economics research provies evience that price ceilings serve as a focal point for tacit collusion among proucers. Research suggests that the creit car inustry in the 1980s may have use state-specific interest rate ceilings as a focal point for setting interest rates, which then serve as stable equilibrium rates even in the presence of competition that shoul have force rates lower. As a result, the price ceiling may have actually raise consumer prices for creit car ebt. 12 Other behavioral reactions to price controls were observe uring the U.S. government s attempt to apply controls to the gol market in the 1960s. 13 In that episoe the government ha a strategic reserve of gol that it coul use to increase the supply an thus reuce gol prices if it felt that prices were too high. However, the government i not stipulate conitions uner which it might release gol from that reserve. The resulting uncertainty is creite with causing consumers an proucers of gol to require a higher return for their gol holings, which in turn cause the price of gol to increase at a faster rate than it woul have otherwise. Page 7

9 III. Manipulating Price Controls in the Emissions Allowance Market Proposals in the Unite States for implementing price controls in a cap-an-trae emissions allowance market vary, but all rely on the U.S. government s ability to ajust the supply of allowances to keep the equilibrium price between the ceiling an floor. Many recent proposals woul control prices by establishing a minimum price at which market participants can purchase allowances from the government, an a maximum price through the use of either a limite or an unlimite reserve of aitional allowances. The etails of their execution vary, but in most such proposals the reserve is intene to offer market participants an opportunity to purchase aitional allowances at a fixe ceiling price shoul there be excess eman at that price. For expositional simplicity, this paper will assume that participants can purchase those allowances at the ceiling price at their convenience that is, whether or not the ceiling price is bining an that the reserve is sufficiently large to support the eman escribe in this paper at the price ceiling. That oes not mean the reserve woul nee to be infinitely large, although it coul be, but only that it represent a sizeable fraction of the annual cap relative to the economy s responsiveness to changes in allowance prices (in practice, this coul mean the reserve woul be 5 to 20 percent of any one year s issue allowances). The efficacy of such a price ceiling esign rests on the assumption that market participants will not purchase allowances from the reserve if the allowance price oes not warrant such purchases. But the presence of the ceiling an the implications associate with the permanent relaxation of the cap whenever allowances are release from the reserve coul provie market participants with an incentive to purchase allowances from the reserve at the ceiling price even if the market price is significantly lower. That incentive stems from the fact that, all else equal, as the supply of allowances increases, the allowance price woul be expecte to ecrease. To motivate the analysis an provie a backrop for the remainer of the paper, suppose the Unite States aopte a cap-an-trae program that reuce emissions relative to 2005 levels by 80 percent in 2050, but by only a small amount in the first year of the program. Firms in the three sectors assume to be regulate uner such a hypothetical program electric utilities, refining, an large manufacturing woul generate approximately 5.1 billion tons of CO 2 e emissions in 2010 in the absence of a cap-an-trae program, accoring to baseline emissions Page 8

10 ata from the U.S. Energy Information Aministration (EIA). 14 To achieve the esire emissions reuction, the program woul issue approximately 5 billion allowances each year for the first 10 years an then reuce the number of allowances issue such that 130 billion allowances woul have been issue by Consistent with other cap-an-trae proposals, the hypothetical program use here woul inclue a price ceiling of $30 that is maintaine by an allowance reserve, with rules for its use as escribe above. Regulate firms coul use allowances issue in one year for compliance in any future year (i.e., they coul bank allowances) an, to a lesser extent, use allowances issue for future years for compliance in the current year (i.e., borrow allowances). Finally, the hypothetical program woul inclue provisions for entities not covere by the cap to generate emissions reuctions, calle offsets, an funing for other approaches to reucing carbon emissions similar to other cap-an-trae proposals. Thus, if the regulate firms were not to consier their nee for allowances beyon the first year (or if allowances coul not be save an use in later years), an if 5.2 billion allowances were release in that first year, the price for allowances that year woul be zero in the absence of a price floor, because the supply of allowances woul excee the eman even at a zero price. However, if only 5 billion allowances were release in the first year, the eman for allowances woul excee the supply by 0.1 billion allowances. Assuming that allowances are not allocate to regulate entities for free but must be purchase, the presence of the reserve woul give regulate entities two options for purchasing allowances. Either they coul purchase the necessary 5 billion allowances at the market price (reflecting the marginal abatement cost) an reuce their emissions by 0.1 billion tons, or they coul pay the ceiling price to introuce an aitional 0.1 billion allowances into the marketplace, thereby causing allowance scarcity to isappear an the market price for any aitional require allowances to fall to zero. Assuming an economy-wie elasticity of eman for allowances in the first year of an an equilibrium allowance price of $20, the ecision to purchase the necessary 5 billion allowances woul cost regulate entities $100 billion. But if some egree of collective action were open to them, they coul instea inuce the introuction of 0.1 billion new allowances to the market by buying them from the reserve at a cost of $3 billion (each reserve allowance costs $30) an then access the remaining 5 billion allowances at zero cost (because the market woul now contain 5.1 billion allowances, equal to business-as-usual emissions). Page 9

11 Alternatively, consier the same initial setup where the regulate firms are 0.1 billion allowances short, but now new information is release to the market inicating larger baseline emissions an higher costs of reucing those emissions than previously expecte, which together suggest that the allowance price shoul be $38 instea of $ With a price ceiling of $30 an an elasticity of allowance eman of -0.10, market participants woul have excess eman at $30 an thus woul purchase allowances from the government s reserve until the equilibrium price falls to $30 or they exhaust the reserve. Uner those conitions, they woul purchase 0.1 billion allowances from the reserve, causing the allowance price to equilibrate at the ceiling price of $30. If that initial information about baseline emissions were subsequently etermine to be inaccurate, or were reverse by new information, the marketplace woul then hol 5.1 billion allowances, equal to baseline emissions, an the equilibrium price for all allowances woul fall to zero. These simple examples ignore the potential presence of a price floor an the fact that many regulate entities woul consier their allowance nees over a multiple-year time frame, an they assume that at least some large regulate entities woul prefer lower allowance prices to higher prices. 16 However, the examples illustrate three features of a cap-an-trae market with a price ceiling: 1) regulate entities coul lower allowance prices by eliberately inucing the introuction of new allowances into the market; 2) market participants coul be inuce by new information to purchase allowances at the ceiling, which woul result in a lower equilibrium price of allowances if that information were later reverse; an 3) each release of allowances from the reserve benefits every regulate entity, because the new supply lowers the allowance price for everyone. Although active manipulation is the focus of the remainer of this paper, it is straightforwar to exten the results to the information case or to consier a case where the manipulation involves the time introuction of information about high abatement costs when the allowance price naturally approaches the ceiling, to inuce others to purchase reserve allowances. The active manipulation of the price ceiling lowers overall compliance costs for those regulate entities involve in the manipulation if the compliance savings resulting from a lower equilibrium price excee the cost of manipulation. An, consistent with the stanar public goos game, where in this case the public is efine as the other regulate firms, compliance costs are further lowere as more regulate entities participate in the manipulation. However, Page 10

12 because the regulate entities benefit regarless of whether they participate in the manipulation, there woul be an incentive to free rie. 17 If a bining agreement among regulate entities is possible, they might agree to each purchase a select number of allowances from the reserve, or a few entities might agree to strategically release information to the market suggesting that the allowance price shoul be higher than the price ceiling, thus encouraging other market participants to purchase allowances from the reserve. However, that type of outright collusion is explicitly illegal, as is the intentional introuction of inaccurate information, an thus the regulate entities woul nee to rely on tacit, or unstate, cooperation to execute such a strategy. 18 The moel evelope in the next section provies insights into the profitability of such tacit cooperation to manipulate the allowance price. IV. Theory of Manipulation The moel cap-an-trae market issues Χ emission allowances uring a given perio T, where the length of that perio is measure in annual compliance cycles; both Χ an T are exogenous. Without loss of generality, it is assume that usage of allowances is optimal within each perio but that entities o not consier the optimal number of allowances to hol for compliance cycles subsequent to T. Thus, the length of each perio represents the planning horizon for regulate entities with respect to the use of allowances uner the program. 19 The market regulates the CO 2 e emissions of I firms such that in a static equilibrium, each firm i I enogenously uses x i emissions allowances to operate, where Χ= x I i, an abates any remaining emissions. The marginal cost of emission abatement, C ( a ), is assume to be increasing an convex ( C > 0 an C > 0 ), an the cost of no abatement is assume to be zero ( ( 0) 0 C = ). Let fi xi Χ be the fraction of total issue allowances use by firm i I in the static equilibrium, such that f = 1. The enogenous equilibrium price uring perio T is I i p e, which can be consiere the average price at which firms purchase allowances over the perio. The economy-wie elasticity of eman for allowances, ε 0, efine for a change in the number of allowances ( Δ ) relative to the total number of issue allowances ( Χ ), is approximate as: ΔΧ ε = (1) p p p ( ) Δ e e Page 11

13 where p Δ is the equilibrium price when there exist Χ +Δ allowances. That elasticity of allowance eman incorporates the response to changes in the allowance price resulting from both changes in the eman for emissions-intensive goos an services an changes in emissions abatement technologies. Similarly, the ith firm s elasticity of allowance eman, εi 0, is approximate as: where ε = i ( Δ ) ( ) x i xi xi p p p Δ x Δ i is the equilibrium eman for allowances by that firm when Δ new allowances are introuce into the market, causing the equilibrium price to fall to p Δ. In aition to knowing their own elasticity of eman for allowances, firms are assume to know the economy-wie elasticity an the allowance price (an its path) with certainty. Next consier a eviation from the equilibrium where a subset D purchase emissions allowances at the price ceiling ( p ) such that firm allowances, where e e I of the firms D purchases δ Δ= δ D. For expositional simplicity, each eviating firm will be assume to purchase a constant proportion ν (where ν = δ / x ) of its equilibrium allowance eman at the ceiling at exactly the same time an incur no transaction costs in the process, such that: Δ = f νθ D x δ (3) Χ where x is the equilibrium eman for allowances before the eviation by those firms that engage in the eviation, ν is the size of the eviation as a fraction of the preeviation equilibrium eman, an θ = f D is the size of the coalition participating in the eviation, measure as a fraction of aggregate equilibrium allowance eman. The assumption that each firm eviates by a constant proportion of its equilibrium eman allows one to consier only the aggregate eman of the firms participating in the eviation as a fraction of supply, measure by θ. Then the feasibility of the eviation can be etermine base on the actual market structure of the regulate firms, that is, whether 1 percent of emissions ( θ = 0.01) can be represente by a single eviating firm or requires 200 firms acting collectively. The eviation woul be profitable on net if the costs incurre uner the eviation were less than those incurre uner the noneviating, or truthful, scenario (i.e., purchasing only Χ (2) Page 12

14 allowances at the equilibrium price). Figure 1 graphically illustrates the costs uner the two scenarios. Uner the truthful scenario with an equilibrium price of p e, regulate firms incur costs equal to the sum of regions A through E, where regions B an E represent allowance acquisition costs an regions A, C, an D are abatement costs. The eviation is efine as the introuction of Δ z5 z3+ z2 z1 new allowances from the reserve, purchase at the ceiling price ( p ). That new supply causes the equilibrium price to fall to the new price p Δ, where all available allowances ( Χ z3 z2) can be purchase. Note that when consiere on an aggregate basis, for the equilibrium price to fall no further than p Δ, it must be the case that z5 = z4. Uner the eviation, when the equilibrium price falls to the new price, the aggregate of regulate firms a the cost of the shae region an region F but save the cost of regions A an B. Aggregate profits from the eviation can be expresse as: z2 z1 Π= C( a) a+ peχ C( a) a+ pδ+ p Δ Χ 0 0 The first two terms on the right-han sie of (4) represent compliance costs uner truthful participation, an the brackete term represents compliance costs uner the eviation. Before (4) rawing conclusions about (4), it will be useful to construct the comparable profit statement for the iniviual firm. Given heterogeneity in the firm-specific elasticity of eman for allowances, the profitability of the eviation will vary across firms. Following the formulation of (4), an assuming that Figure 1 epicts the marginal abatement costs for a particular firm an the eman for the goos prouce by that firm, the eviation will result in positive profits ( π ) for the eviating firm if the firm s cost of eviating is less than the cost of not eviating an purchasing allowances at the equilibrium market price: z2 z1 = + e + + Δ 0 0 ( ) ( ) ( ) (5) π C aa px C aa pδ x δ p where the th eviating firm purchases either x z3 z2 allowances uner the truthful scenario at the equilibrium price or δ z5 z3+ z2 z1 allowances at the ceiling price an then the remainer of its allowance requirement ( x Δ δ ) at the reuce price p, where Δ x z Δ 4 z is 1 Δ Page 13

15 the firm s increase eman at the new, reuce price. Only if every firm participates in the eviation will ν =Δ X ; otherwise, ν >Δ X an z5 z4. The profit escribe by (4) an (5) can be boune by two corner conitions, as escribe in Result 1. Result 1. a) Given the above setup, eviation profit is boune from below by the case where the aggregate firms (single firm) have a perfectly inelastic marginal abatement cost curve, an from above by the case where society has a perfectly inelastic eman for emissions-intensive goos an services prouce by the aggregate firms (single firm). b) Consequently, eviation profit will increase for firms that face a more elastic marginal abatement cost curve an more inelastic eman from consumers for their goos an services. Proof: See Appenix A. Incluing aggregate an firm-specific marginal abatement cost curves an the corresponing eman curves for the emissions-intensive goos an services prouce by the aggregate firms an each specific firm as uncertainty to the above moel while yieling only limite aitional insights. Given that the elasticity of eman for allowances incorporates both the marginal abatement cost curve an the eman curve for emissions-intensive goos an services into a single elasticity, this analysis focuses on the lower boun as a conservative estimate of profit, which can be estimate using only that elasticity. 20 Equation (4) can be reformulate to escribe the lower boun on profits as: ( ) Π= pe pδ Χ pδ (6) By rearranging (1) an combining with (3), p Δ can be efine as the higher of the new, reuce equilibrium price or the price floor ( p ). The floor may be unspecifie, or it may be zero, or it may be higher as etermine by the cap-an-trae market rules: vθ pδ = max pe 1 +, p ε (7) From (7), an noting that ε 0, the introuction of allowances from the reserve woul lower the equilibrium price by an increasing amount as the size of the coalition (θ ) increases an the Page 14

16 fraction of equilibrium eman that each firm purchases from the reserve (ν ) increases. This leas to the following result: Result 2. a) For the eviation to be profitable at a given equilibrium price ( p e ), the absolute value of the economy-wie elasticity of allowance eman must be less than the ratio of the equilibrium price to the price ceiling, ε < pe p. b) Uner that conition, the profitability of the eviation increases as the equilibrium price approaches the price ceiling. Proof: See Appenix A. Intuitively, the eviation requires firms to pay p to increase the supply of allowances in the market, which becomes less costly relative to the truthful scenario as the equilibrium price approaches p. Result 2 emonstrates that a necessary but not sufficient conition for a profitable eviation is that ε > 1, which is the limit at which the equilibrium price equals the ceiling price. However, if the equilibrium price is below (e.g., half of) the ceiling price, a more inelastic eman for allowances is necessary for the eviation to be profitable. Similarly, the lower boun of equation (5) can be reformulate as: ( ) π = p x pδ x δ p (8) e Δ Rearranging (2) an combining with (7) prouces the eviating firm s increase eman at the price escribe by (7): Δ x Δ ε = x 1+ νθ ε where ε is the firm-specific elasticity of allowance eman for eviating firms. The lower (9) equilibrium price prouce by the eviation causes all firms to eman more allowances than they woul uner the truthful scenario. Firms with a more elastic eman for allowances woul want more allowances at the new equilibrium price than firms with a more inelastic eman. Profits earne by the th firm, normalize for the quantity of allowances purchase in the truthful scenario by that firm, can be expresse by substituting (7) an (9) into (5) an rearranging: x ( p pe) p θ π ν eν 1 ν ε 1 νθ = ε + + ε (10) Page 15

17 The first term on the right-han sie of (10) is negative an represents the cost that each participating firm woul incur by participating in the eviation; this term will be ientical for each participating firm. The sign of the brackete term cannot be etermine an represents the combination of increase eman an reuce cost at the lower price. That leas to the following result: Result 3. A necessary but not sufficient conition for the lower boun on eviation profits to be positive is that ν ε < 1. If that conition is satisfie, the lower boun on profits increases as a) the equilibrium price approaches the ceiling price; b) the economy exhibits more inelastic eman for allowances; or c) more firms participate in the eviation. Proof: See Appenix A. Setting firm profits in equation (10) equal to zero, iviing the whole equation by the size of each firm s eviation (ν ), an taking the limit as ν approaches zero, one can calculate the minimum coalition size necessary for a firm to be inifferent between eviating an not eviating: θ min p p e ε = pe 1+ ε (11) Corollary to Result 3. Assuming 1< ε < 0, the minimum size of the coalition necessary for a profitable eviation a) falls as the equilibrium price approaches the price ceiling an b) falls as the economy-wie eman for allowances becomes more inelastic. Proof: See Appenix A. Finally, equation (7) suggests that suggests that the price floor may impose practical limits on the benefit of increasing coalition size or the size of each firm s eviation. Assuming that the new, eviation-prouce equilibrium price is constraine by the price floor ( p ) an reformulating (8) as π = δ + ( δ ) p x p x p e Δ prouces the constraine version of (10): ( ) ( )( 1 ) π x = ν p p + p p + ε p p (12) e e e Page 16

18 Equation (12) is strictly ecreasing as the fraction of allowances purchase by a eviating firm increases, because at the price floor, purchasing aitional allowances from the reserve will not further lower the equilibrium price. Setting profits in (12) to zero prouces the following expression for the largest profitable eviation given a price floor: ν p p p e max = 1+ ε p p pe The fact that (12) an (13) are not a function of coalition size (θ ) comes as a consequence of the iniviual nature of a firm s profit uring the eviation. When the combination of participation an eviation size causes the price to fall to the price floor, a larger coalition will no longer prouce a positive externality on price. Thus, at the point where the price is constraine, there is a maximum eviation, represente by equation (13), where each eviating firm is inifferent between eviating an not eviating. That maximum eviation hols true for any coalition size above that where the eviation prouce by (13) causes the equilibrium price to fall to the price floor. That coalition can be characterize using (7) an setting p = Δ p such that % θ = ε( p p e 1) νmax (14) (13) If the coalition increases in size beyon θ %, the eviation can become no more profitable, because the price floor is bining. However, firms can lower their eviation to increase their profitability, as escribe in Result 4. Result 4. The eviation that prouces the maximum profit ( ˆmp ν ) for any given egree of participation (θ ) is efine as: Proof: See Appenix A. ( p p ) ( p ) ( ) 1+ ε + ε e eθ ε p ˆ ν mp = min, 1 21 θε ε θ p e (15) V. Moel Parameters in the Hypothetical Cap-an-Trae Program Given the ambiguity in the sign of (10), one can gain insight into the conitions uner which manipulation of the price ceiling woul be profitable by consiering (10) in light of some Page 17

19 actual parameter values, specifically, the economy-wie an firm-specific elasticity of eman for allowances. For purposes of this paper, sector-specific elasticities proxy for firm heterogeneity across sectors, an an aggregate economy-wie elasticity is etermine inepenent of the specifics of any cap-an-trae proposal, using an approach evelope by the Congressional Buget Office (CBO) that relies on parameters an inputs from several other publishe moels. 21 In aition, CBO has evelope a moel to estimate the cost of cap-antrae proposals between 2012 an 2050 that incorporates the effects of offsets an other programs esigne to reuce the cost of a cap-an-trae program. 22 That moel is use to estimate an economy-wie elasticity that reflects the various features banking, borrowing, offsets, an other cost-reucing components of this paper s hypothetical program. Complicating the estimation of elasticities for use in the simulations is the fact that both firm-specific an economy-wie elasticities are expecte to change over time. As the economy grows, new technologies an abatement solutions are expecte to become available that will cause the elasticity to increase in absolute value over time; i.e., the eman for allowances across the economy becomes more elastic with respect to the allowance price. Similarly, the eman for emissions-intensive goos an services will ajust to the increase price for those goos an services, which will further cause the economy-wie elasticity to increase in absolute value. Selecting the appropriate elasticities that incorporate changes to both those supply an eman conitions over time thus requires one to consier the time perio in which the manipulation escribe above might occur an be most profitable to regulate entities. The first few years of the program woul appear to be the best caniate years for consiering the manipulation, because uring that perio, regulators an other oversight agencies woul be the least accustome to the market s operation an therefore coul be less likely to ientify behavior of market participants that woul be abnormal. At the same time, any cap-an-trae program woul be expecte to inclue some regulate entities that engage in highly sophisticate traing practices in other energy markets an thus have the resources necessary to quickly unerstan the ynamics of the allowance market. In aition, many proposals for a price ceiling stipulate that it rise more rapily over time than the expecte rate of allowance price increase, meaning that the ceiling price will be closest to the allowance price at the start of the program. For those reasons, the elasticities use in the simulations are estimates for the first 10 years of the program. Page 18

20 Elasticity, economy-wie (ε ). There are two approaches to estimating the economy-wie elasticity of allowance eman in the first few years of the program. First, one coul estimate an aggregate elasticity that incorporates both the supply of abatement technologies an the eman for emissions-intensive goos an services for the group of regulate entities. Over the first 10 years of the program, the estimate elasticity for the regulate sectors ranges from to -0.14, with a mean of That range accounts for ifferent assumptions about the evelopment an introuction of abatement technology for those sectors an the ease with which regulate entities can shift their prouction an consumption of carbon-intensive goos an services to less carbon-intensive alternatives. That elasticity, calculate for just the regulate sectors, approximates the elasticity for a cap-an-trae program that oes not inclue other features, such as energy efficiency programs, offset allowances, or carbon capture an sequestration. The secon approach to estimating the elasticity involves incorporating some of the features that are inclue uner the hypothetical cap-an-trae program an woul be expecte to increase the responsiveness of the economy to changes in the allowance price. That is, any changes in the cost of abatement in sectors covere uner a cap-an-trae program will trigger responses throughout the economy, but program features are intene to give firms increase flexibility for ajusting to those changes. In the secon approach to estimating elasticities, the economy is assume to be in equilibrium, given a combination of allowances an program features over the planning horizon of the regulate entity, an a change in the allowance supply causes regulate entities to reequilibrate over their planning horizon given the new supply of allowances. Over the first 10 years of the program, the elasticity of allowance eman that incorporates those features, estimate using CBO s climate moel, ranges from to For moeling purposes an elasticity of is use, although a range between to is use for sensitivity analysis, where the more inelastic values represent conitions at the beginning of a program an the more elastic values represent conitions more than a ecae into the program. Elasticity, sector-specific ( ε i ). Electric utilities woul account for approximately 40 percent of total emissions, accoring to EIA, an the average elasticity for those electric utilities over the first 10 years is expecte to range from to -0.27, with the larger elasticities occurring in the later years. 24 The transportation sector, which inclues petroleum proucts companies, woul Page 19

21 make up 34 percent of emissions, with an average elasticity for firms in that sector uring the first 10 years between an The upper en of the range is efine as a case where there are significant technological improvements in automobile emissions reuction options. The remaining 26 percent of emissions woul come from the manufacturing sector, with an average elasticity ranging between an For moeling purposes an elasticity of is taken as representative of the eviating firm. Result 1 states that those firms with the most elastic eman for allowances are most likely to profit from the eviation, although that increase profit will not be observe when moeling the lower boun on profits, as is one here. Firm Planning Horizon an Issue Emissions Allowances ( Χ ). The planning horizon use by the regulate entities woul affect the amount of capital require to implement the manipulation an the feasibility of the manipulation given a finite reserve of allowances available in any given year. Returning to the hypothetical cap-an-trae example, if all firms were optimally banking an borrowing allowances over the 40-year perio from 2010 to 2050, with 130 billion allowances issue over that perio, the introuction of a 400-million-allowance eviation from the reserve woul represent only 0.3 percent of total allowances issue over those 40 years. At the estimate mipoint elasticity of eman for allowances (-0.12), the introuction of that quantity of allowances woul be expecte to reuce the price by only 2.5 percent. However, the effective elasticity of eman over 40 years is expecte to be closer to -0.50, which suggests only a 0.6 percent reuction in price. If instea firms have a 3-year planning horizon uring which they optimally bank an borrow allowances, those aitional 400 million allowances woul represent 3 percent of the total issue allowances, which, with a elasticity of eman, woul be expecte to reuce the price by closer to 25 percent. Table 1 presents the number of permits issue in each year an the number of permits require to increase supply by 3 percent in the hypothetical cap-an-trae program for planning horizons of 3, 5, an 10 years. The fourth column presents the size of the allowance reserve necessary to create that 3 percent supply increase, as a percentage of the first year s allowances. Those selecte horizons are consistent with the range of elasticities selecte above. If the hypothetical cap-an-trae program were implemente, one might expect the planning horizon uring the first few years of the program to be relatively short. Uncertainties in the early years of the program, particularly those relate to the ability of the economy to evelop technologies to Page 20

22 abate emissions an to the long-run commitment of policy makers to enforce the cap, coul cause regulate entities to aopt planning horizons shorter than 10 years. It is unlikely that any firm woul aopt a 1-year planning horizon, assuming the program was expecte to remain in operation the following year; however, the 3-year case coul be reasonable if the continuation of the program were politically uncertain. Once the cap-an-trae program has evelope an operational preceent an feasible low-carbon technology has been emonstrate, regulate entities coul be expecte to exten their planning horizon, making any type of manipulation more ifficult. Price ceiling ( p ) an price floor ( p ). The hypothetical cap-an-trae program is assume to have an allowance price ceiling of $30 an a price floor of $10, which is largely consistent with propose cap-an-trae programs in the Unite States given their emissions reuction objectives. Coalition size (θ ). As escribe earlier, the coalition size is efine as the percentage of emissions represente by the firms engaging in the manipulation (the eviating firms), which is assume comparable to the percentage of allowance eman. Although the Environmental Protection Agency estimates that a cap-an-trae program coul cover approximately 7,400 firms, only 18 firms 5 oil an gas firms an 13 power companies woul account for 40 percent of total U.S. emissions. 25 Twelve of those companies alone woul each represent at least 1 percent of total emissions, an three woul each represent more than 5 percent. Thus, a coalition representing 1 to 10 percent of allowance eman in a U.S. cap-an-trae program coul involve fewer than three firms. VI. Moeling an Results The results illustrate in Figures 2 through 6 are all for the lower boun on the eviation profit, as erive above. Only in Table 2 are the upper an lower bouns isplaye for comparison purposes. Using elasticity estimates from the previous section an parameters from the hypothetical cap-an-trae program, Figure 2 illustrates four regions of the space elineate by the size of the eviation an of the coalition. The area outline by the thick soli line (regions 1 an 2) represents the combinations of coalition an eviation size where the eviation woul be profitable, given the moel s assumptions. The bounary of that region represents the Page 21

23 conition where participants woul be inifferent between eviating an not eviating. The upwar-sloping section of the thick soli line is efine by solving equation (10) for zero profit. The flat section of that line is efine by the maximum eviation, from equation (13). That region of profitability, however, is ivie by a thin otte line that represents the price manipulation bounary, or the minimum combination of coalition an eviation necessary to cause the new equilibrium price to be constraine by the price floor, from equation (7). Beyon this line, larger eviations or larger coalitions cannot cause the price to fall any further an only reuce the participants profits. The thick otte line efines the maximum profit for eviating firms, as escribe by equation (15). Points above an below that line woul still be profitable, but less so. The other regions (3 an 4) in Figure 2 woul not be profitable. The area outsie the thick line but to the left of the thin otte line (region 3) woul not be profitable either because the eviation woul not be large enough or because the eviating coalition woul not be large enough. An the area above the thick flat line (region 4) woul not be profitable because the equilibrium price woul be constraine by the price floor. For the remaining iscussion, the region below the thin otte line an to the right of the thick soli line (region 1) is referre to as the profitable eviation triangle. Figures 3 an 4 quantify the magnitue of the conclusions from Result 3 uner the parameters escribe in the previous section. In each figure, the top panel shows the profitable eviation triangle in the coalition-eviation space for various estimates of one parameter. The lower panel shows the largest profit obtainable assuming the lower boun on profit uner the eviation as a function of coalition size, assuming that all eviating firms are optimally eviating as efine by equation (15). Maximum profit is expresse as a percentage of truthful expenitures ( π pex ), which means that if a firm were to spen $100 uner the truthful scenario with a 50 percent profit, it woul be spening $50 uner the eviation scenario. Given the moel, an equilibrium price closer to the price ceiling woul require fewer participants for a profitable eviation (see Figure 3). For example, a eviation coul be profitably implemente with 3 percent of emissions represente in the coalition if the price were $6 below the price ceiling; if the price were $15 below the ceiling, at least 13 percent of emissions woul nee to be represente in the coalition for a profitable eviation. In aition, the maximum profit from a eviation increases as the equilibrium price approaches the price ceiling (lower panel of Page 22