Carbon leakage: a mechanism design approach

Transcription

1 Carbon leakage: a mehanism design approah Lassi Ahlvik and Matti Liski Otober 5, 2017 Abstrat Polluting firms often press poliy makers to offer ompensations or roll bak regulations by threatening to reloate. Yet, only firms know if they an atually arry out the threat. Using a mehanism design approah, we show how exlusions and the intensity of regulation an be used to save on publi funds and alloate regulatory assignments effiiently. Some leakage is always optimal, and the intensity of regulation inreases when leakage is introdued; the regulation an even beome stronger than in the first best. We provide an illustrative quantifiation of the optimal arbon leakage poliy for the EU emissions trading program. Keywords: Climate hange; emissions trading; arbon leakage; private information; mehanism design. JEL odes: D82; L51; Q54; Q58 Ahlvik lassi.ahlvik@nhh.no: Eonomis department of the Norwegian Shool of Eonomis. Liski matti.liski@aalto.fi: Eonomis department of Aalto University. We thank Chang-Koo Chi, Baran Doda, Bård Harstad, Daniel Hauser, Johannes Hörner, Jussi Lintunen, Juan-Pablo Montero, Matias Pietola, Julia Salmi, Morten Sæthre, Po Yin Wong, Andrey Zhukov and partiipants at presentations in Athens EAERE, Bergen, Helsinki, Paris, Oslo, Toulouse 11th TSE onferene on limate and energy, and Zurih for valuable omments and disussion. Matti is grateful for funding from the Aademy of Finland program New Energy, and from the Aalto University projet SAGA. 1

2 1 Introdution It is triky to design loal regulations on global externalities. Firms may reloate and merely shift the externality-ausing ativities to another loation if the regulation is too ostly and inadequately ompensated. Yet, the true ease of moving is only known by the firm, and any ompensation sheme omes at a risk of paying unneessarily high transfers to some of the firms. Regulated industries fierely lobby for ompensations, emphasizing the ost of regulation and easiness to reloate prodution to other ountries. If the aim is to keep all the firms, these laims need to be respeted although they are diffiult to verify. But doing so will reate potentially large private rents to the industries. The issue has beome topial in the EU Emission Trading Sheme ETS, where industrial emitters onsidered to be suseptible to arbon leakage have reeived both generous alloations of free emission allowanes and diret monetary ompensations. 1 In onrete terms, the eletriity produers reeived windfall profits estimated to reah one billion euros between 2005 and 2013; the aviation setor, whih has been partly inluded in the EU ETS sine 2012, was estimated to have reeived two billion euros in windfalls. 2 total windfall for the european industries from ompensation shemes planned to prevent industry reloation has been estimated to be as high as 25 billion euros, with ompanies in ement, petrohemial and steel industries gaining the most. One reason suggested for this is industrial-sale lobbying from the vested interests whih has led to vast windfalls being handed to many ompanies in the energy-intensive setor. 3 This set-up raises an important question for the poliy design that we address in this 1 In total 43 % of the allowanes are given away for free during Setors deemed to be exposed to a signifiant risk of arbon leakage reeive 100 % of their estimated allowane need for free, whereas the free alloation to non-leakage setor is gradually redued to 30 % by year In addition, the most energy-intensive setors an be given monetary ompensation through national state aid shemes EC, Harrabin, Roger bn windfall from arbon trade. BBC, May 1. Nelsen, Arthur Airlines ould net 1.6bn windfall from EU arbon trading sheme, report says. The Guardian 11 January. 3 Krukowska, Ewa EU industry got $27 billion arbon plan windfall, study says. Bloomberg, Marh Carrington, Damian Carbon fat ats are killing the emissions trading mouse, The Guardian, February damian-arrington-blog/2013/feb/14/arbon-emissions- arbon-tax The 2

3 paper: how should suh loal regulations on a global problem be designed to reah environmental targets and to limit leakage without reating exessive private rents? In partiular, how muh industries under leakage risk should be ompensated, and how they should be ompensated with lump-sum transfers or by ompromising on the level of regulation? The main hallenge, that seems unavoidable, is that only firms know, firstly, the true osts of moving to another loation and, seondly, the ost of ompliane if staying in the regime. Taking a mehanism design approah, we study the optimal design of environmental poliies when firms have suh two-dimensional private information. Two main results arise from our analysis. First, we find that although arbon leakage is soially wasteful, the solution to the information problem alls for some positive leakage as an optimal outome. It is entral to the mehanism that there is a tool for disiplining threats. This an be ahieved by making firms responsible for emphasizing a low ost of reloation the mehanism holds firms aountable for the laims in the sense that they an be exluded from the regime. The optimal level of ompensation strikes a balane between firms marginal propensity to reloate, net damages due to leakage, and the soial ost of wasting publi funds to overompensate industries. Seond, we show that the industries exposed to the risk of leakage should not be given a lower level of regulation but leakage instead alls for a striter regulation, aompanied by lump-sum transfers. Without leakage, only the firms with low abatement osts reeive information rents, and a lower emissions prie is a way to redue those rents as, for instane, in Lewis With leakage, the low-ost firms are no longer ornered and may reloate without ontributing to emissions redutions, leading to an inrease in the optimal emissions prie attrating firms with low osts to stay. The other side of the same oin is that the higher emissions prie taxes the information rents of firms that merely buy the right the pollute but are not lose to moving. Together, these effets always inrease the level of regulation; the optimal emissions prie may even turn out to be higher than the Pigouvian first-best prie. The distortions in our mehanism stem from the regulator s urge to ompensate firms differently depending on their abatement osts on one hand, and the inability to ondition ompensation on the unobservable harateristis of the firm on the other hand. Figure 1 illustrates how the emissions prie an be used to target firms based on their unobservable osts. The regulator faes onstant marginal damages MD from emissions, and the marginal ost MC urve represents marginal abatement osts, aggregated over a mass of small firms. High-ost firms pay the emissions prie and fae the ost denoted by area A, whereas low- 3

4 a Targeting ompensations to high-ost firms b Targeting ompensations to low-ost firms MC MC Emissions prie p p D MD p p A D B MD A B t C q q Total emissions q q Total emissions Figure 1: Illustration of the model and illustrations of seond-best poliies when the problem is leakage from a high-ost firms or b low-ost firms ost firms hoose to ut emissions faing osts in area B. Now, it is possible to target ompensations to high-ost firms by hoosing an emissions prie that is lower than the Pigouvian prie p < p as shown in Figure 1a; this redues the ost for firms in area A without affeting the inframarginal firms in area B. However, deviating from the Pigouvian level omes at a prie as it reates a deadweight loss area D. On the ontrary, ompensations an be targeted to low-ost firms by hoosing a higher emissions prie p > p, aompanied by a respetive lump-sum ompensation t, as shown in Figure 1b. This would redue the ost for firms in area B without affeting the osts of inframarginal firms in area A. This poliy reates firms that gain from regulation area C, and in addition, a deadweight loss area D. It is not a priori lear if more ompensation should be paid to high- or low-ost firms. This will be endogenous in our model and depend on empirially testable harateristis of the industry. We begin by analyzing the ase with no orrelation between abatement and reloation osts in Setion 3, whih aptures a general trade-off between two ountervailing effets. On one hand, low-ost firms are the most valuable to keep in the regime, as they reate the largest limate surplus, avoided global externality minus loal abatement osts, when utting emissions. In fat, suffiiently high-ost firms do not ut emissions even if they stay and hene their potential reloation does not ause arbon leakage as suh. This limate 4

5 surplus effet makes the regulator inlined to target ompensation to low-ost firms. On the other hand, the total ost burden of the regulation is the highest for high-ost firms, while low-ost firms may even gain from regulation as indiated by area C in Figure 1b. This abatement ost effet makes the regulator want to target ompensation to high-ost firms. We show that the abatement ost effet dominates when industries are relatively lean and the outside option is aurately known, leading to a downward distortion in regulatory stringeny Figure 1a. Conversely, the limate surplus effet dominates when industries are emission-intensive and there is a lot of unertainty about firms reloation osts, leading to an upward distortion in the level of regulation Figure 1b. For some industries, it may well be that abatement ost and reloation osts are orrelated, although is not a priori lear if suh a orrelation exists and if the sign should be positive or negative. 4 In the analysis of perfet orrelation Setion 4.1, we find that when there is a negative orrelation between reloation and abatement osts, the high-ost firms are first to reloate. To ompensate these high-ost firms, the regulator ompromises on the level of regulation, following the logi presented in Figure 1a. With a strong positive orrelation, low abatement osts are assoiated with the heapest reloation ost and only the low-ost firms move. To target ompensation to these low-ost firms, the regulator sets a higher level of regulation, in line with Figure 1b. Last, with a weak positive orrelation, the medium-ost firms leave the regime and the net effet on the emissions prie turns out to be ambiguous. A natural extension is to onsider a game between two uninformed loal poliy makers setting their environmental poliies non-ooperatively Setion 4.2. The firm s reloation deision is now altered sine the destination ountry may also have an environmental poliy in plae. We find that the information problem brings about a new strategi effet in this leakage game, absent in the strategi environmental poliy literature. Intuitively, the firm s reloation beomes environmentally less harmful when it moves to a regime with regulations in plae, whih in turn redues the need to ompensate firms for their limate surplus. One would expet that if firms have fewer options to esape regulations, the optimal emissions pries would go up. Yet, we find that the new strategi interation distorts 4 Ederington et al onsider U.S. manufaturing and trade data and find that the least footloose firms are the ones with the largest pollution abatement osts, suggesting a positive orrelation between moving and abatement osts. In ontrast, in a note written together with Ralf Martin we look at the firm level EU data from Martin et al and find evidene for a negative orrelation Ahlvik et al.,

6 emissions pries downwards, below the first best, in a non-ooperative Nash-equilibrium between two symmetri regions. In Setion 5, we provide an illustrative quantifiation of the optimal arbon leakage poliy for key setors in the EU emissions trading program, based on the firm-level data from Martin et al The data allow us to draw representative reloation risk distributions for five key setors that together form 62 per ent of the total industry emissions overed by the EU ETS. With representative values for the soial ost of arbon emissions and the soial ost of publi funds, we an quantify the optimal arbon leakage, distortions in the emissions prie, and the fration of the setoral ost that is optimally overed from publi funds. Two main results arise from our quantifiation: the optimal poliies vary heavily aross setors and the size of the distortions are non-negligible. The optimal arbon leakage is 3 24 per ent and the arbon pries are inreased upwards by per ent ompared to the benhmark without leakage. Total windfalls poketed by the five key setors under the optimal poliy are 7.6 billion euros. 1.1 Related literature Our study ontributes to the literature on environmental regulation under privately informed polluters. It is well known that the mere existene of private information does not need to lead to distortions from the first best: absent budgetary onerns, the regulator an reah the soially effiient outome by a Vikrey-Clarke-Groves -type mehanisms as in Dasgupta et al. 1980; see also Montero If firms annot hoose to opt out from regulation, the first-best an also be implemented through a Bayesian mehanism and any budgetary objetives an be satisfied by lump-sum transfers, following d Aspremont and Gérard-Varet 1979, Tehnially, our model differs from these papers as publi funds are valuable and firms privately known opportunity to move introdues a partiipation onstraint that prevents arbitrarily large lump-sum taxes on firms. It follows that the optimal seond-best poliy is distorted away from the first-best. Some studies onsider seond-best environmental poliies, where partiipation onstraint is either based on zero-profit ondition Spulber, 1988; Kim and Chang, 1993 or voluntary partiipation of firms Lewis, 1996; Montero, 2000 or ountries Helm and Wirl, 2014; Martimort and Sand-Zantman, Our study builds on this literature and extend the 5 Zero-profit ondition ensures that all firms prefer to stay in the market. Voluntary partiipation means 6

7 earlier analyses in three ways. First, arbon leakage is fundamentally different from, say, bankrupty as reloating firms will ontinue to produe global negative externalities. Seond, unlike previous studies, we allow the use of exlusions as a sreening devie. Leakage plays a similar role than exluding onsumers from using publi goods Hellwig, 2003; Norman, 2004 or preventing natural monopolies from serving the market Baron and Myerson, As a third differene, the ited studies assume that the regulator knows the firms outside option and an therefore offer just enough ompensation to make the high-ost firms indifferent between exiting and staying. With leakage, however, the regulator annot guarantee the indifferene as the outside option is not observable. To inorporate this effet, we solve a selfseletion model with random partiipation following Rohet and Stole 2002, where firms possess two-dimensional private information. 6 It follows that not just must the regulator leave positive information rents to some high-ost firms, but also some low-ost firms reloate. There is a vast literature on how poliies should be designed to take into aount a threat of arbon leakage. 7 Given that firms private information on the leakage propensity is indisputably an essential feature of the problem, it is rather surprising that it has reeived little attention. Greaker 2003 is among the first to introdue a model with one-dimensional asymmetri information about firms ease of moving in the ontext of strategi environmental poliy, but he leaves the formal analysis of a truth-revealing mehanism for future researh. Harstad and Eskeland 2010 onsider a signalling model where firms have private information about their need for permits, but there is no leakage in their model, an essenthat firms should make no loss relative to the ounterfatual situation. These two onditions are very similar in respet that, in the ase of optimal poliy, they only bind for high-ost firms who are left with no information rents. It follows that, to limit information rents, the regulator always distorts the level of the regulation downwards. This is in ontrast to the present study, where the level of regulation is often distorted upwards. 6 The upward distortion, one of the main results of this paper, is not a typial feature of previous models with random partiipation, suh as Rohet and Stole 2002; however it arises naturally in our setting with the global externality problem. 7 Carbon leakage, where the benefits of unoordinated limate poliies are offset by inreased emissions in unregulated regimes, may refer to at least three distinguishable phenomena: i leakage through hanges in fossil fuel pries Harstad, 2012; Harstad and Liski, 2013; Böhringer et al., 2014, ii inreased prodution in unregulated regimes via hanges in output pries Markusen, 1975; Hoel, 1996; Fisher and Fox, 2012; Meunier et al., 2014; Böhringer et al., 2014b or iii firms physially moving their prodution in ountries with laxer environmental regulation Markusen et al., 1993; Motta and Thisse, 1994; Hoel, 1997; Ulph and Valentini, 1997; Shmidt and Heitzig, 2014; Martin et al., This study fouses on the third ategory. 7

8 tial feature of the poliy design problem. The study that has motivated us most is Martin et al. 2014, who onstrut firm-level measures for the reloation risk and then derive what they all the fundamental eonomi logi of industry ompensation: [...] effiieny requires that payments be distributed aross firms so as to equalize marginal reloation probabilities, weighted by the damage aused by reloation. With private information, the optimal mehanism no longer follows this logi: the reloation propensities will be differentiated depending on observable ations or harateristis of the firms. Last, Meunier et al onsider how output-based alloations an be optimally used to manage leakage and volatility, with fous on unertainty rather than on asymmetri information. 2 The set-up Consider an industry with a unit mass of polluting firms, eah firm haraterized by a ost of reduing one unit of emissions [, ] 0 and a ost of reloation θ R. 8 Both and θ are private information to the firm. Regulator knows the distribution of firms types. The distribution of abatement osts follows ontinuous density funtion f, with F denoting the respetive umulative distribution. The onditional density and the umulative distribution for reloation osts are gθ and Gθ, respetively. The mass of firms with ost and migration ost less than θ is thus Gθ f. We make the usual assumptions that the distributions are regular : Assumption 1. Monotone hazard rate assumption. For all, θ, are non-dereasing in and θ, respetively. f 1 F and gθ 1 Gθ 8 It is natural to think that 0, but tehnially there is nothing preventing firms with negative marginal abatement osts for instane if firms postpone privately profitable abatement measures when expeting higher prie for them in the future. The assumption of full support for θ guarantees that some firms are immobile and have very large reloation osts so that there will always be a mass of firms with abatement ost staying in the regime. The ost of regulation may not be the only reason to reloate prodution, so there may be other privately known reasons affeting the outside option. These are all aptured by θ. Notably, some firms may move even with no regulation in plae; this is aptured by these firms having a negative θ. The assumption of full support makes the forthoming analysis tehnially simpler as we avoid points of non-differentiability at upper and lower bounds. 8

9 We begin the analysis without orrelation between θ and in Setion 3, but to introdue the full model at one go, we use the general notation Gθ. What we define as firm an be interpreted more broadly as a unit of prodution suh that abatement osts are independently distributed aross prodution units that an be reloated individually. A real-world ompany an therefore onsist of several of these firms. Leakage may be aused by either firms atively reloating existing prodution units to other regimes, or investment leakage when firms expand into another loation for new prodution. Our model inorporates both kinds of leakage. Firms abatement ost an be seen as a tehnial parameter related to the abatement proess, and it is ustomary to treat it as private information Dasgupta et al., 1980; Montero, 2008; evidently, this is why market-based instruments are generally preferred over ommand-and-ontrol measures. The reloation ost should be interpreted as the net effet of the physial ost of moving and the expeted derease in profits due to hoosing another, supposedly less preferable loation. The firm may not know the reloation ost aurately, but it is reasonable to assume that the firm has more possibilities to estimate this parameter than the regulator, who may even be uninformed of where the firm ould potentially move to. 2.1 Firm s problem An individual firm faes two deisions. First, it either stays in the regime and omplies with the regulation, or reloates prodution to another loation with no regulation in plae. Seond, onditional on staying, the firm hooses how muh to ut emissions. Formally, x = [0, 1] is the amount that a firm uts its ounterfatual emissions that are normalized to unity. A firm reeiving monetary transfer t faes the following net ost of regulation: 9 Ct,, x = x t. 1 The regulator has two ways to ompensate the firm and redue the net ost of regulation; it an either offer a higher transfer t, or alternatively lower the required emission redution x. There is an important distintion between these two ways of ompensation, however: while the former is independent of firms abatement ost, the latter depends on it suh that a derease in x is more valuable for firms with high. If the offered ompensation is 9 The ase of general onvex abatement ost funtion is analyzed in Setion 4.3 9

10 insuffiient, the firm may find it worthwhile to avoid the regulation and fae the reloation ost. The ondition for this to happen is: Ct,, x > θ. 2 It is ritial that the transfer is onditional on firm s staying in the regime. Moreover, it is assumed that it is not possible to reloate a part of the prodution the prodution units an only move in entirety or not at all. After a unit moves, the regulator loses the possibility to regulate it or ollet lump-sum transfers. The problem is essentially one of two-dimensional private information. To arry on with the analysis, we follow the tehniques developed by Rohet and Stole 2002 and fous on non-stohasti mehanisms of the form {T ĉ, Xĉ}: we onsider a diret revelation mehanism where firms announe their abatement ost ĉ, taking the deision to stay as given. For any given mehanism proposed by the regulator we then alulate the net ost of regulation: Xĉ T ĉ, and solve for the mass of firms that have high enough reloation osts to stay in the regime. In other words, we model firms reloation deision as an indiret mehanism where no report on reloation ost ˆθ is made. This is without loss of generality, given the assumption that firms annot move partially, and the restrition to a deterministi mehanism. 10 truthfully announe their abatement osts : In inentive-ompatible mehanisms firms find it optimal to { } = arg min ĉ Xĉ T ĉ for all. 3 Let C be the indiret net ost funtion of the firm who truthfully reports his type. A firm stays in the regime if its net ost, when truthful, is lower than the reloation ost: C θ. The mass of firms of type for whih this holds, as a funtion of C and, is: 10 In a stohasti mehanism, firms would report both their abatement and reloation osts, after whih the regulator would arrange a lottery and randomly exlude a share of firms, using the probability of exlusions to sreen for both and θ. Aknowledging that suh a stohasti mehanism an be more effiient than the deterministi one, we follow the literature of random partiipation Rohet and Stole, 2002; Lehmann et al., 2014 and fous on the deterministi mehanism that have a simple market interpretation. A stohasti mehanism ould be implemented, for example, by a sheme of random audits with the probability of being audited depending on the reports. However, suh a mehanism may suffer from the known problems related to verifying randomization, see Laffont and Martimort

11 φc, = 1 GC f. 4 The mass of staying firms φc, is dereasing in C reahing zero as the net ost approahes to infinity. We use φ C, as shorthand for dφc, /dc. We also define the inverse hazard rate over C: ηc = φc, φ C, Regulator s problem The soial planner designs a regulation sheme for the industry by hoosing the level of ompensation T and the level of regulation X for firms of type who stay in the regime, so that the inentive ompatibility ondition is satisfied and the soial welfare is maximized: max X,T γ X λt φc, D 1 φc, X d 6 subjet to equations 3 and 4 holding. Planner s objetive funtion 6 onsists of four omponents. First, the government gets some benefit γ when a firm stays in the regime; this parameter aptures the firm s ontribution to soial surplus through profits, employment impats, or any possible diret politial benefits from having the firm. 11 Seond, the planner onsiders the ost of abatement, whih for firm of type, reduing X units of emissions, is simply X. Third, the revenue olleted by the mehanism is soially valuable, for instane, beause they an be used to derease distortionary taxes elsewhere. The soial ost of ompensating a firm is λt where parameter λ denotes the soial ost of publi funds. Last, the government onsiders damages due to pollution, with marginal damages assumed to be linear, D. 12 The loation of global emissions is irrelevant and therefore 11 The value of γ is industry-speifi, observable and does not depend on firm s type; it ould be exluded from the analysis with minor substantial hanges. However, it allows desribing pollution intensive industries as those with low value-added per unit of emissions low γ, and therefore variations in γ will help in analyzing how the optimal mehanism varies with observable harateristis aross industries. Also, γ will be a key parameter in our numerial alibration in Setion For limate hange, a onstant marginal damage is not a poor approximation. First, emissions from a single jurisdition are likely to have a small impat on the slope of the global damage urve. Seond, the 11

12 pollution damages our either when a share of firms 1 φc, reloates, or when firms stay but do not ut emissions φc, 1 X. The last term of equation 6 is the sum of these two omponents. It is immediately lear that in our model the firms reloation deisions are not equally harmful; the regulator is more onerned about leakage by firms who ould ut emissions with low abatement ost. To see this, we define the net losses from reloation as the derease in soial welfare when a firm of type leaves: X, T, = γ + D X λt 7 Let us denote this term in short. When firms do not ut emissions X = 0 their reloation does not ause emission leakage as suh, for they would pollute the same amount in either regime. In that ase the regulator only dislikes reloation beause of the fixed omponent γ and beause these firms ontribute to the publi funds via a negative T, for instane when they pay the emissions tax or buy emissions permits in an aution. Emission leakage only ours when a firm that uts emissions X > 0 moves, and then limate surplus D X will be lost. The low-ost emission redutions reate the largest limate surplus and, other things equal, the regulator suffers the most when the firms with lowest abatement osts move. The regulator is keen to keep the low-ost firms in the regime but annot diretly pay ompensation to those firms unless abatement osts are observable. This will be the key driver behind the distortions in our leakage mehanism The leakage mehanism There are two main aspets of the poliy we are interested in. The first is the level of regulation, that is, the total amount of required pollution redution in setors under the global expeted damage hanges only slowly over time, and therefore it will be a matter of deades before the soial ost an be seen to hange as a funtion of emissions; the marginal damage an hange in the near term only if severe limate impats beome material see Gerlagh and Liski Third, onstant damages an well approximate the preditions of the omprehensive limate-eonomy models Golosov et al., 2014; van den Bijgaart et al., We will extend the analysis to the more general ase where the damages from emissions may be onvex in Setion This is a differene to the model developed by Rohet and Stole 2002 where, onditional on trade taking plae at a given prie, the monopolist does not are about ustomers privately known valuation parameter. Here, the regulator diretly ares about partiipating firms type-dependent surplus as seen in equation 7. 12

13 leakage risk. The seond aspet is the level of ompensation: how muh of the private ost of regulation should be overed from the publi funds? Intuitively, we an think that the regulator sells two tikets, one for the right to stay in the regime and another for the right to pollute if the firm hooses to stay. The tikets offered may vary aross firms having different observable harateristis. The right-to-pollute tiket implements the level of the regulation and the right-to-stay gives the level of ompensation whih an also be negative. We first onsider a situation where these tikets an be onditioned on abatement ost. Also, throughout setion 3 we fous on the ase without orrelation between and θ. 3.1 Benhmark: publi, θ private information We begin by onsidering a benhmark where the regulator observes abatement ost of eah firm, and reloation ost θ is the only parameter that is private information to the firms. We an think that the regulator must offer a single ontrat for pools of observationally idential dimension but in fat heterogeneous firms θ dimension, and define industryspeifi ontrats this way. Although perhaps unrealisti, this ase is useful for the more omprehensive mehanism where both and θ are private information. Tehnially, the regulator maximizes soial welfare 6 but without inentive ompatibility onstraint 3. Proposition 1. When is publi information and θ is firms private information, the optimal poliy X B, T B takes the following form: X B = { 1 if B = D 1+λ 0 otherwise φ C B, λφc B, = 0 intensive margin extensive margin where C B = X B T B. The first part of Proposition 1 is the modified Pigouvian rule for priing externalities: firms ut emissions when their marginal abatement ost is lower than marginal damage from pollution, when expressed in terms of publi funds D/1 + λ. 14 Where revenues are not valuable to the regulator λ = 0 the rule ollapses to the famous Pigouvian priniple, 14 This is similar to Laffont and Tirole But the distortions in their paper are different than those in our analysis sine they onsider government monopoly priing of permits using a single instrument the prie, rather than the optimal mehanism. 13

14 setting the marginal abatement ost threshold equal to the marginal damages from pollution, B = D. Where λ > 0, firms that ut emissions pay lower taxes, implying a loss of tax revenues that are valued as suh. Private resoures are spent on redutions to avoid emissions taxes and therefore they are ostly in terms of publi funds, diminishing the effetive weight put on marginal damages. This first part of the Proposition gives the intensive margin of the regulation, that is, it tells us how muh is required from the firms that stay in the regime. The seond part of Proposition 1 gives the extensive margin of the regulation in the sense that it determines the types to be exluded from the program the optimal leakage. The ondition represents a well-known trade-off between effiieny leakage and rent-extration overompensation. Consider a marginal inrease in ompensation for type : i it redues surplus losses from marginal firms leaving the regime with mass φ C B, and ii it inreases the overompensation paid to all the remaining firms of type with mass φc B,. Some arbon leakage is part of the optimal seond-best poliy, although it is learly ineffiient given that under perfet information, any exluded firm ould simply be exempted from regulation these exempted firms would pollute the unregulated amount but the regulator would not have to suffer the loss of γ. Firms private information about θ therefore leads to ineffiienies in the extensive margin in this benhmark ase with known. The benhmark ompensation that implements these distortions is haraterized as: Corollary 1. When is observable: i For > D, the optimal ompensation shedule is flat, 1+λ T B = 0. ii For = D, the optimal ompensation jumps disontinuously 1+λ lim T B lim T B =. D/1+λ D/1+λ + iii For < D, the optimal ompensation satisfies 1+λ { > 0 iff λη T B C B > 1 = < 0 iff λη C B < 1 Part i of the Corollary tells us that all firms that do not ut emissions are paid the same ompensation regardless of their abatement ost. For firms that do not ut emissions, their abatement ost beomes irrelevant both in terms of soial welfare and their private ost of 14

15 regulation. We all this the base ompensation level. To understand part ii, onsider a marginal firm with osts = D/1 + λ so that the regulator is indifferent between this firm utting emissions and polluting. Beause of this indifferene, the firm is guaranteed the same ost of regulation C irrespetive of the hoie of X and it follows that the transfer has to jump by D/1+λ, to exatly over the ost of ation X = 1. Part iii of the Corollary 1 shows how the optimal benhmark ompensation varies with abatement ost for firms that redue emissions. Should more or less be paid to firms with the lowest abatement ost? There are two ountervailing effets. On one hand, as shown in equation 7, the regulator wants the low-ost firms to stay and redue emissions, beause they reate the largest limate surplus: this surplus grows with slope 1 when marginally dereases. We all this the limate surplus effet. On the other hand, the regulation is heaper for the low-ost firms as they an ut emissions with low osts. As the private net ost of regulation dereases linearly in when a firm uts emissions, the low-ost firms need a smaller ompensation to stay; see equation 1. This redued transfer in turn hanges the soial surplus by λη C. This is what we all the abatement ost effet. Whether the low-ost firms are paid the most then ultimately depends on whih of these two effets dominates, as shown by the ondition for the slope of the shedule in part iii of Corollary Complete mehanism: and θ private information When both abatement and moving osts are firms private information, the transfers an no longer be made onditional on the observable harateristis dimension. They an only be made onditional on firms observable ations. Proposition 2. When both and θ are firms private information, the optimal poliy X, T takes the following form: X = { 1 if = D 1+λ + µ 1+λφC, 0 otherwise intensive margin where µ = [ ] φ C, λφc, d. Compensation to firms that do not ut emissions X = 0, > is T = T and given 15

16 by φ T, λφ T, = f 1 F µ, extensive margin while firms that ut reeive T = T +. As shown in the Appendix, the poliy problem an be formally solved by hoosing two pries: a flat baseline ompensation level T, and a top-up for those who ut T = T +. In ontrast to Proposition 1, there are now two types of distortions as both the intensive and extensive margins will differ from the benhmark with observable abatement osts. To understand the soure of the distortions, onsider a small inrease in the intensive margin. This hange makes firms around to ut emissions but also, due to the inentive ompatibility ondition, leads to higher transfers to all the firms with lower than. The net welfare effet of this inrease, integrated over all the types that ut emissions, is aptured by the distortion term µ. Next, notie that keeping the intensive margin fixed, any base transfer T paid to high-ost firms that do not ut emissions must also be paid to the low-ost firms the welfare effet of this, it turns out, is aptured by the same distortion term µ. For a positive µ the regulator values the extra ompensation paid to low-ost firms and onsequently hooses a striter level of regulation higher and a higher base level of ompensation higher T for > than in the benhmark. For a negative µ the regulator dislikes the extra ompensation to low-ost firms, and sets a lower level of regulation lower and a lower base ompensation level lower T for >. Setors with no leakage. To illustrate, let us look at the speial ase where firms are immobile and will stay in the regime regardless the net ost of regulation they fae. 15 Now the only relevant piee of private information is the firm s abatement ost. This is an extreme ase of Proposition 2 where φ C, = 0 and φc, = f, so that the distortion term beomes: µ = λf d < 0 8 It an immediately be seen that with no leakage, the level of regulation is thus always distorted downwards. Solving the integral in 8 and plugging it in the optimal poliy we get: 15 We an interpret the situation as one where the firms outside option beomes publily known and thus the firms an be made indifferent between staying and leaving. 16

17 = D 1 + λ λ F 1 + λ f. 9 This result is familiar from earlier studies on optimal seond-best environmental poliies, see for instane Lewis 1996: only the low-ost firms reeive information rents, and a lower emissions prie offers a way to redue those rents at the ost of effiieny see also Baron and Myerson By ontrast, when firms an reloate and the reloation ost is their private information, a mass of soially valuable firms with low abatement osts will also have low moving osts and will move. Therefore the regulator is now more onstrained to extrat their rents and will optimally inrease the emissions prie to enourage the low-ost firms partiipation. In addition, and in ontrast to the model without leakage, a mass of firms with high abatement ost will also reeive information rents those whih also have high reloation osts. The higher prie serves to extrat a fration of these rents. Corollary 2. All else equal, industries with arbon leakage are always assigned a striter level of regulation higher emissions prie than industries without leakage. This follows from omparing the distortion term in Proposition 2 with φ C > 0 and where some firms reloate φc, < f to that presented in equation 8. Comparison to benhmark with observable. Whether the optimal seond-best poliy entails upward µ > 0 or downward µ < 0 distortions is endogenous in the model and depends on the harateristis of the industry. To be more preise, it will depend on the interplay of the previously introdued limate surplus and abatement ost effets: on one hand, the low-ost firms are the most valuable to keep in the regime for their emission redutions but, on the other hand, these firms have low ost of ompliane and are therefore less likely to reloate. To better grasp this result, we make a link between the ase of unobservable and the benhmark ase with known. Proposition 3. The sign of distortions, term µ, is positive negative if limate surplus effet abatement ost effet dominates: λη C B < >1 for all <. The proposition tells us whether the level of regulation is higher or lower than the Pigouvian 17

18 a Abatement ost effet dominates b Climate surplus effet dominates T B B B B Figure 2: Optimal ompensation in the benhmark dashed line and in the mehanism solid line for the two ases: a abatement ost effet dominates, b limate surplus effet dominates. benhmark, B = D/1 + λ.16 The two ases are illustrated in Figure 2. The benhmark ompensation, haraterized in Corollary 1 and depited as dashed line in the Figure, an be onditioned on firm s abatement ost as is observable. But when is not observable, the regulator is restrited to offer the same ontrat for all firms with the same ation the ontrat offered is hosen to minimize the deviations from the benhmark, weighted by the mass of type firms. If the abatement ost effet dominates λη C B > 1 as in Figure 2a, the benhmark ompensation is inreasing in < see Corollary 1 and the regulator wants to limit ompensations to the low-ost firms in the benhmark. The optimal ontrat seeks to ahieve this same by distorting the intensive margin, that is, the emissions prie downwards µ < 0. In ontrast, if the limate surplus effet dominates λη C B < 1, the benhmark ompensation is dereasing in < and the regulator would like to target ompensation to the low-ost firms and tax the high-ost firms. In the optimal mehanism this is ahieved by distorting the intensive margin upwards µ > Intuitively, by 16 Clearly, the ondition in Proposition 3 is suffiient but not neessary sine the benhmark shedule an be nonmonotoni. We provide further omparative statis results in the next Setion. 17 The appearane of upward distortion is not standard in models of random partiipation, but it stems 18

19 σ Better known reloation ost Upward distortion µ > 0 Downward distortion µ < Lower emission intensity γ Figure 3: Sign of the distortion as a funtion of pollution intensity and reloation ost setting a high prie for emissions, the regulator taxes those firms that will not move in any ase high θ and for whom abatement is not an option high. The ombination of a high baseline T together with a high prie on emissions thus implements a tax-subsidy sheme where firms self-selet to be taxed or subsidized, depending on their abatement osts. Comparative statis. For a more omplete grip on the fators that determine how different industries should be treated, we arry out a sensitivity analysis with respet to two key industry-speifi harateristis. We make an additional assumption for the distribution desribing the outside options, namely that the hazard rate gθ /1 Gθ in Assumption 1 is not just inreasing, but also onvex in θ for all. A orresponding assumption has been exploited before Rohet and Stole, 2002, and it holds for many ommonly used distributions suh as the normal distribution. First, we look at how the distribution of outside from our limate surplus effet, or more exatly, from the fat that firms privately known type appears diretly in regulator s welfare funtion 6. This is not true in Rohet and Stole 2002 and, in their setting, assuming a non-dereasing inverse hazard rate or η 0 is suffiient to eliminate any upward distortions. In our model the limiting ase for upward distortions is η 1 see Proposition 3 where the right hand side equal to 1 is exatly the limate-surplus effet. 19

20 options shapes the optimal mehanism. To this end, we introdue another parameter σ > 0, whih aptures the degree of unertainty about the industry s reloation osts. Taking θ as a zero-mean risk, we an onsider a mean-preserving spread around a positive mean ˆθ ontrolled by the preision parameter σ, so that the ondition for firm s leaving beomes: C > θ σ + ˆθ. Hene σ aptures the ase where the outside option is perfetly known; smaller values of σ denote more unertainty about the outside option. Seond, we arry out sensitivity analysis with respet to γ. For very pollution-intensive industries, the value-added per unit of pollution, γ, beomes small and the ompensation is mainly motivated by damages aused by emissions. For industries that pollute a little, γ is relatively large. Proposition 4. All else equal, for industries with lower pollution intensity higher γ or more unertain reloation ost higher σ: i When is an observable harateristis, the ompensation of osts is greater, T B / γ > 0 for all, and the sign of T B / σ is ambiguous. ii When is private information and η x < 0, the distortion term, µ, is stritly lower, µ / γ < 0 and µ / σ < 0. Broadly speaking, there are two reasons in the model why the regulator dislikes firms reloation: the loss of fixed-value omponent given by γ and the loss of limate surplus D X that depends negatively on the abatement osts. For pollution intensive industries the latter effet beomes relatively very valuable, whih alls for ompensations to low-ost firms by distorting emissions prie upwards. Conversely, for firms that have high value per pollution unit high γ, the latter effet beomes small and the inentive to distort emissions prie upwards disappears see Figure 3. When the outside option beomes aurately known large σ, we approah the model of Lewis 1996 where the firms with high abatement osts an be made indifferent between staying and moving, leaving them with no information rents. Choosing a lower emissions prie is a means to extrat information rents from the low-ost firms. For very inaurately known outside options small σ, on the other hand, the mass of esaping low-abatement ost firms inreases, so they must be ompensated by lump-sums and tighter regulation, that is, the value of their ontribution to redutions must be inreased. 20

21 4 Extensions 4.1 Correlated private information So far we have assumed no orrelation between the reloation and abatement osts; it is not a priori lear whih way the orrelation should go in a given industry. For instane, in some industries the firms with the lowest loation-speifiity of produtivity may also have the heapest abatement options. Then, firms with low an be the most prone to move, that is, they are footloose and pollution-free. 18 In some other industries, the ease of reloation may inrease together with abatement osts. 19 The orrelation is an empirial question, and potentially important sine, it turns out, it links losely to the pattern of ompensations and distortions. 20 The general reasons for the distortions outlined in our main analysis do not hange with orrelation, but the analysis with orrelation helps to identify new irumstanes where downward and upward distortions arise. To introdue orrelation to the model in a tratable way, we follow the literature on typedependent partiipation onstraints Lewis and Sappington, 1989; Maggi and Rodriguez- Clare, 1995; Jullien, 2000 and analyze a perfet orrelation between θ and : θ = b + k 10 Here b is a saling fator and k is publily known parameter depiting the sign of the orrelation suh that for k > 0 the lowest ost firms fae the lowest reloation ost and k < 0 is the opposite ase. Firms still possess private information about both their abatement and reloation osts, but full orrelation renders this information one-dimensional: truthful reporting of the firm s abatement ost immediately reveals also the outside option to the regulator. For ease of exposition, let us adopt the onvention that the firm s type is. Using 18 This is the title of Ederington et al who find, using U.S. manufaturing and trade data, that the firms with largest pollution abatement osts also tend to be the least geographially mobile. 19 Levinson and Taylor 2008 find that pollution abatement osts, despite being small fration of valueadded, have an eonomially signifiant impat on U.S. trade volume with Canada and Mexio. While not diret evidene, the result is onsistent with a negative orrelation between mobility and abatement osts. 20 We looked at the question of orrelation empirially using the data from Martin et al in a note written together with Ralf Martin. We find support for a negative orrelation between the propensity to move and a measure of abatement osts, ontraditing the positive orrelation found in Ederington et al

22 equation 10, the ondition for leaving, equation 2, an be rewritten as: X T > b + k. 11 We an distinguish three situations, whih turn out to be substantially different. First, if the ost of moving and abatement have a negative assoiation k < 0, high-type firms high have the lowest ost of moving. In that ase, the firm always wants to overstate its type as this way it an exaggerate both the ease of moving and ost of ompliane. In this sense, the inentives to lie in both dimensions are onurring. Seond, with strong positive orrelation k > 1, the two types of osts are positively assoiated. The low-type firms still have the lowest ost of utting emissions but they an also easily move: the firm annot simultaneously overstate ompliane osts and the ease of moving. However, sine the orrelation is strong, the latter effet dominates and despite these onfliting inentives, the firm always has an inentive to understate its type. Third, with weak positive orrelation 0 < k < 1, the firm faes ountervailing inentives: it wants to understate its type to emphasize the willingness to leave if it is not required to ut emissions X = 0, and overstate its type to emphasize the high ompliane osts when required to ut X = 1. When the regulator ares suffiiently about the publi funds λ high enough, it is always optimal to exlude some firms from the regime to save on ompensations. Similarly, if externality ost D is suffiiently large, it will be optimal to require uts at least from some firms. These two onditions ensure that the mehanism implements an interior outome as follows: 21 Proposition 5. The interior optimal mehanism under perfet orrelation. i Conurring inentives, k < 0: firms ut X = 1 where = D 1 + λ λ F 1 + λ f, and firms with > = T + b/k leave where f = kλf, 21 This is a tehnial differene to the basi model: with full orrelation, the finite support of determines the support for θ by equation 10 whih an no longer be infinite, in ontrast to what we assumed in Setion 2. To failitate omparison with the results of the basi model, we only fous on the interior solution where some firms ut emissions and some are exluded from the regime. 22

23 and >. All staying firms reeive T, but T + if they also ut. ii Confliting inentives, k > 1: firms ut, = D 1 + λ + λ 1 + λ but leave when < = T + b + /1 k where 1 F, f f = 1 kλ 1 F, and <. Staying firms reeive T, but T + if they also ut. iii Countervailing inentives, 0 < k < 1: firms leave when < < where f = k 1λF f = kλ 1 F and = T + b + /1 k and = T + b/k. Firms ut and reeive T + while staying firms pollute and reeive T. The same priniples that we saw in Proposition 2 for the two-dimensional ase with no orrelation between the parameters apply here as well. First, it is optimal to distort the intensive margin, that is, to deviate from the Pigouvian rule, to manage the rents of those who stay in the regime. Figure 4 helps to understand the elementary differenes between the three reported ases. For onurring inentives, k < 0, the level of regulation is distorted downwards, < D/1 + λ, beause this limits the rents of the low types and allows for targeted ompensation to those with high types, following the logi in Figure 1a. Seond, the extensive margin strikes a balane between reloation loss by marginal firms and overompensating the remaining firms. For onurring inentives, the marginal exluded firm is a polluter see Figure 4 and therefore there is no pollution leakage. However, there is a leakage of eonomi value-added and thus ondition f = kλf is a trade-off between pure loation-speifi eonomi losses and inframarginal ompensations paid to the remaining firms. For onfliting inentives, k > 1, the intensive margin is distorted upwards, > D/1 + λ. Quite intuitively, by setting a high prie for emissions, the regulator wants to tax the high ost firms who pollute and stay in the regime but are nowhere lose to leaving see Figure 4; simultaneously, utting firms reate a large limate surplus and reeive a generous 23