DISCUSSION PAPER. Refunding Emissions Payments. Cathrine Hagem, Michael Hoel, Bjart Holtsmark, and Thomas Sterner. February 2015 RFF DP 15-05

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1 DISCUSSION PAPER February 2015 RFF DP Refundng Emssons Payments Cathrne Hagem, Mchael Hoel, Bjart Holtsmark, and Thomas Sterner 1616 P St. NW Washngton, DC

2 Refundng Emssons Payments Cathrne Hagem, Mchael Hoel, Bjart Holtsmark, and Thomas Sterner Abstract We analyze two mechansm desgns for refundng emssons payments to pollutng frms: outputbased refundng (OB) and expendture-based refundng (EB). In both nstruments, emssons fees are returned to the pollutng ndustry, typcally makng the polcy more poltcally acceptable than a standard tax. The crucal dfference between OB and EB s that the fees are refunded n proporton to output n the former but n proporton to the frms expendture on abatement equpment n the latter. We show theoretcally that to acheve a gven abatement target, the fee level n the OB desgn exceeds the standard tax rate, whereas the fee level n the EB desgn s lower. Furthermore, the use of OB and EB may lead to large dfferences n the dstrbuton of costs across frms. Both desgns mply a cost-neffectve provson of abatement, as frms put relatvely too much effort nto reducng emssons through abatement technology compared wth reducng output or mprovng management. However, mantanng output may be seen as a poltcal advantage by polcymakers f they seek to avod actvty reducton n the regulated sector. Key Words: refunded charge, output-based, expendture-based, NOx, tax subsdy, polcy desgn JEL Classfcaton Numbers: Q28, Q25, H Resources for the Future. All rghts reserved. No porton of ths paper may be reproduced wthout permsson of the authors. Dscusson papers are research materals crculated by ther authors for purposes of nformaton and dscusson. They have not necessarly undergone formal peer revew.

3 Contents 1. Introducton A Model of Tax Compared wth Refunded Fees Standard Tax Mechansm Desgn for Output-Based Refundng Emssons Payments Expendture-Based Refundng (EB) A Comparson of Two Mechansms for Fefundng Comparsons wth Same Fee Level... 9 Proposton 1: Comparsons wth the Same Target Level of Abatement Effects on Ext and Entry of Frms Concludng Remarks References Appendces... 20

4 Refundng Emssons Payments Cathrne Hagem, Mchael Hoel, Bjart Holtsmark, and Thomas Sterner 1. Introducton It s well known that a unform tax, leved on all sources of emssons, s a cost-effectve nstrument to reduce unformly dspersed emssons. However, envronmental taxes tend to be lower than requred to correct for envronmental externaltes. One reason for ths s concerns that hgh taxes reduce domestc compettveness, leadng to frm closures and job losses. Furthermore, for transboundary pollutants, such as greenhouse gases, the welfare effect of reduced domestc emssons may be partly offset by ncreased producton and emssons abroad (carbon leakage) (see Hoel 1991). Moreover, powerful lobbes may overstate these and other arguments and thus make a cost-effectve tax regme poltcally nfeasble. All n all, the nablty to levy suffcently hgh envronmental taxes s a problem for the desgn of envronmental polcy. Wth tradable envronmental permts, the quantty-based alternatve to an envronmental tax, the problem can be allevated by allocatng permts for free. Ths lowers the revenue rased n the frst place, yet holds the permt prce constant (to the frst order), hence the abatement ncentve and economc effcency, though t creates a dfferent poltcal problem, that of how to allocate free permts. The same apples to the prce-based equvalent of free tradable permts, gvng away tradable thresholds for the emssons tax (Pezzey 2003), though ths opton s lttle known by polcymakers and hence undeveloped nsttutonally and legally. An alternatve, practcal f theoretcally suboptmal, way to make emssons taxes more poltcally feasble s to earmark the tax revenues for some envronmental purpose. Some people even see the use of the tax revenues as the envronmental purpose of the tax (see Sterner and Cora 2012). Kallbekken et al. (2011) show that recyclng the revenues to more narrowly targeted groups seems to ncrease support for taxaton. Varous ways of refundng the tax revenue ease the economc burdens on Hagem: Statstcs Norway, PO Box 8131, Dept. NO-033, Oslo, Norway; correspondenng author: cah@ssb.no. Hoel: Department of Economcs, Unversty of Oslo, PO Box 1095, Blndern, NO-0317, Oslo, Norway. Holtsmark: Statstcs Norway, PO Box 8131, Dept. NO-033, Oslo, Norway. Sterner: Department of Economcs, School of Busness, Economcs and Law, Unversty of Gothenburg, PO Box 640, SE , Gothenburg, Sweden; and unversty fellow, RFF. The fnancal support of the Norwegan Research Councl s hghly apprecated. Valuable comments by Taran Fæhn, Jack Pezzey, Katrn Mllock, Torbjørn Hægeland, and Arvd Raknerud, and research assstance by Ame Svärd, are gratefully acknowledged. 1

5 the polluters and thus lessen poltcal resstance to the tax. Refundng emssons can be seen as turnng a tax nto a fee, rebated to the polluters accordng to some specfed rules. A tax typcally mples that the revenues go toward the natonal budget. Revenues from a fee can be refunded or be seen as payment for a servce pad to a government agency or muncpalty. Ths paper compares two methods for refundng emssons payments: Refund n proporton to output, referred to as output-based refundng (OB). Refund n proporton to abatement expendture, referred to as expendture-based refundng (EB). (We also use the terms OB or EB desgns, schemes, or systems). Sweden has poneered the use of OB for ntrogen oxdes (NO x ), 1 sometmes referred to as refunded emssons payment (REP) n the lterature. 2 Among the reasons for the use of OB rather than a tax was the dffculty n settng a suffcently hgh prce on emssons to motvate abatement when faced wth a strong ndustral lobby aganst the tax (see further Sterner and Isaksson 2006). In Sweden, fees are refunded to the polluters strctly n proporton to useful output. In the French taxe parafscale, the fees (for NO x, SO 2, HCl, and VOCs) were used generally to subsdze research and abatement (see Mllock et al. 2004). The Norwegan NO x Fund goes a step further and drectly tes refundng to actual abatement costs at the frm level. 3 EB s an nterestng nnovaton for those stuatons where t s applcable and has hardly been analyzed prevously. 4 The contrbuton of ths paper s the theoretcal evaluaton of the 1 Ntrogen oxdes (NO x ) are waste gases emtted from the combuston of ol, gas, and bofuel that lead to acd ran, eutrophcaton, and ncreased concentratons of ground-level ozone. Emssons have ecosystem and health effects, and Norwegan and other countres emssons are regulated under the Gothenburg Protocol. 2 See, e.g., Fscher (2003), Gersbach and Requate (2004), Fredrksson and Sterner (2005), Höglund Isaksson (2005), and Cato (2010). Note also that OB corresponds to output allocaton or benchmarkng n a tradable permt system (see Fscher 2001). OB generates an output subsdy and thus gves ncentves for excess producton. Ths effect s harmful n a compettve envronment, but t can ncrease welfare under mperfect competton, where output s suboptmal (Gersbach and Requate 2004). Benchmarkng n unlateral CO 2 emssons polces s motvated by ts potental to reduce carbon leakage and loss of compettveness (Edwards and Hutton 2001; Fscher and Fox 2007). 3 For more nformaton about the Norwegan NO x Fund, see 4 There s a related lterature on two-part nstruments. A number of papers recognze that the Pgouvan tax level may be unattanable for varous reasons, and they therefore explore alternatves, such as varous combnatons of tax and subsdy. See, for nstance, Felder and Schlenger (2002), who analyze the trade-off between effcency and poltcal feasblty; and Fullerton (1997) who fnd that f a tax s nfeasble, a satsfactory alternatve may combne a subsdy to a clean substtute wth a tax on output. (See also Fullerton and Mohr 2003, Bernard et al. 2007, Svendsen et al. 2001, Parry et al. 2012, Johnson 2006, or Walls and Palmer 2001 for smlar ponts.) None of these artcles, 2

6 dfferences n performance of the EB and OB systems, ncludng a comparson of ther qualtes and propertes wth those of a standard envronmental tax. 5 EB mples a combnaton of a fee on polluton and a subsdy on abatement technologes where the latter s fnanced by the former. 6 By comparng the performance of the systems, we mplctly assume that all systems are applcable for the regulaton n queston. All systems requre measurable emssons. An addtonal prerequste for OB s measurable output, and EB works well only n stuatons where you can clearly dentfy and measure what s useful expendture on abatement technology, rather than general nvestment n new technology. In secton 3, we show that to acheve a certan abatement target, the fee level under OB must exceed the standard tax rate, whereas wth EB t must be set lower. Both OB and EB make techncal abatement relatvely cheaper than abatement through output reductons, compared wth a standard tax. Hence both EB and OB would be welfare nferor to the optmal standard tax system, as they lead to nferor output reductons. Ths comparson, however, assumes that the optmal tax s poltcally feasble, whch s often not the case because of resstance to hgh taxes. We cannot, n general, say whch of the systems devate most from the cost-effectve outcome. However, we dentfy the man drvng forces for the potental dscrepancy. In the real world, the regulator s welfare functon may nclude more than just pure economc costs, as the regulator may seek to avod job losses or gan poltcal support by avodng heavy tax burdens. In the concludng remarks, we dscuss welfare mplcatons of the dfferent systems and argue that EB and OB can be promsng systems n stuatons where there are such poltcal constrants on the regulator s use of taxes/subsdes and lump sum transfers. however, specfcally looks at refundng of the tax per se. Mllock and Nauges (2006) come the closest, analyzng the French taxe parafscale, where revenue was put nto a fund to whch frms could apply. The refundng was not automatc, however, as n the Norwegan case. 5 We focus on self-fnanced funds whose ncome comes exclusvely from fees or desgnated membershp contrbutons. An advantage of a standard tax wthout refundng s that t generates publc revenues. In ths paper, we do not take nto consderaton the effcency loss due to the revenue recyclng effect (Goulder et al. 1999). 6 Ths s not the type of subsdy where the polcymaker buys each unt of reducton from a baselne at a prce s (see, e.g., Kolstad 2000, chapter 7. Such subsdes clearly mply a perverse output subsdy. Inspred by the Norwegan and French NO x schemes, we nstead model subsdes as the partal payment for the costs of partcular abatement equpment. 3

7 2. A Model of Tax Compared wth Refunded Fees Consder a sector F consstng of frms ndexed by = {1,...,n}, each producng a commodty n quantty q. Producton causes emssons, e. Let e and q denote emssons and producton n the absence of envronmental polcy. Each frm can reduce emssons by nstallng new, measurable abatement technologes or by reducng producton. 7 For the sake of smplcty, we assume there s only one type of abatement technology (y) that s relevant for the sector n queston. However, frms wthn the sector may nvest n varyng levels. We have (, ) (, ), e r y = e a r y (1) where a( r, y) s the emssons reducton (abatement) functon and r s output reducton ( 0 q q ). Abatement s ncreasng n output reductons and abatement technology at a decreasng rate; a () > 0, a () < 0, a () > 0, a () < 0. Furthermore, we make the followng assumptons: r rr y yy (A.1)The abatement functon s strctly quas-concave, and both r and y are normal nput factors n the producton of a. (An nterpretaton of the abatement functon s gven n appendx A.) As a startng pont, we consder nternal solutons for frm producton decsons. Impacts on ext and entry decsons are dscussed n secton 3.3. Let E stand for the sector s total emssons, assumed to be unformly dspersed; that s: E = e. (2) F Furthermore, we defne total output and total abatement as Q= q, (3) F 7 We do not address the dynamc effect or rreversblty of nvestments (see, e g., Cora 2009 for such models). Furthermore, n ths paper, we do not delve nto the ncentves for technologcal progress created by refundng (see Sterner and Turnhem 2006). See also Jaffe et al. (2002), Löschel (2002), and Requate (2005) for surveys on technology nvestment ncentves under varous polcy nstruments. Note also that t may be sgnfcant n practce to dstngush between technologes that are easy to measure and control through smple nspecton and those that are ether too complex or too subtle to allow for smple montorng. 4

8 and 0 0. (4) F F A= a e E E E We assume that all market shares are so small that all frms take all prces, taxes/fees, and subsdes as gven Standard Tax Wth a standard tax, an ndvdual frm has the followng payoff: 0 p = pq c ( q ) my t ( e a ( r, y )), (5) where p s the product prce, 8 c ( q ) are producton costs of q, t s the tax rate on emssons, and m s the (annuty) cost per unt of abatement technology y. We apply the standard assumptons that margnal cost of producton s postve and ncreasng: c > 0 and c > 0. 9 Maxmzng the proft functons yelds the followng frst-order condtons: 10 m = t, (6) a ( r, y ) y p c = t. (7) a ( r, y ) r The left-hand sde of (6) expresses the margnal cost of reducng emssons through abatement equpment, and the left-hand sde of (7) expresses the margnal cost of emssons reductons through output reductons. The ntuton behnd the frst-order condtons s well known: the margnal cost of emssons reductons should equal the margnal beneft of emssons reducton 8 Wthout loss of generalty, we assume the same product prce for all producers. Ths may be nterpreted as ether a stuaton wth homogeneous goods or a stuaton wth heterogeneous goods and a choce of unts for each good makng all prces dentcal. In the latter case, total output Q must be nterpreted as the total value of producton. 9 In real lfe, abatement technologes may also affect the cost of producng q. However, our smplfcaton does not affect the man results of the paper. 10 Second-order condtons for an nternal soluton are gven n appendx B. 5

9 (t), whether the emssons reducton occurs through abatement technology (6) or output reducton (7). It s well known that (6) and (7) lead to a cost-effectve (cost-mnmzng) combnaton of output reducton and abatement technology deployment for all emssons levels, and an optmal emssons level allocaton as long as the level of t corresponds to the true socal margnal damage, often referred to as the Pgouvan tax level Mechansm Desgn for Output-Based Refundng Emssons Payments Wth a standard tax, the total tax revenue, te, s collected by the government as publc revenue. A fund system mples that the tax becomes a fee and the revenue s collected by the fund. We shall focus on such cases where all the revenue s rembursed fully to the polluters. We consder two stylzed schemes for refundng emssons fees: output-based refundng (OB) and expendture-based refundng (EB). In an output-based refundng scheme, fees are refunded n proporton to output q, and the payoff to frm s 0 E p = pq c( q) my t ( e a( r, y)) + qt, (8) Q where t s the fee (correspondng to a standard tax) and E Q s the average emsson. The refund per unt producton s E t Q. The budget constrant s satsfed as exactly to refundng the total fee revenue te n proporton to the frms market shares, F E qt = te. Ths corresponds Q q, as n Q the Swedsh NO x scheme. 11 As all frms market shares are assumed to be small, they take the average emssons ntensty E/Q as gven, 12 although the equlbrum value of ths average emssons ntensty s endogenous and a functon of t. 11 Gersbach and Requate (2004) use ths setup n the compettve verson of ther model. 12 See Fscher (2003) and Sterner and Isaksson (2006) for a model of an OB system where such strategc behavor s dscussed. See also Gersbach and Requate (2004) for an analyss of an OB system n the context of mperfect competton n the output market and prenvestment n cleaner technology. 6

10 Assumng that the frms under OB maxmze ther payoffs specfed n (1) and (8), the frst-order condtons are as follows: 13 m = t, (9) a ( r, y ) y p c E = t(1 ). (10) a ( r, y ) Qa ( r, y ) r r As n the standard tax system, we fnd that the margnal cost of emssons reductons through abatement technology should be equated wth the level of the fee for all frms, equaton (9). However, we see from (10) that the margnal cost of avoded emssons through output E reductons s no longer equal to the level of the fee t but multpled by the factor (1 ) Qa ( r, y ) r It should also be noted that the output based refundng may leave some frms wth a subsdy on producton. The rght hand sde of (10) s negatve for frms whch have lower margnal emsson E ntensty than the average emsson ntensty ( a r ( r, y ) < ). Hence, some frms may actually Q ncrease ther producton under an output based refundng scheme compared to a stuaton wthout any envronmental polcy Expendture-Based Refundng (EB) Wth an expendture-based refundng scheme, all fee revenues are refunded to the polluters n proporton to ther expendtures for abatement. The payoff to a frm s 0 p = pq c ( q ) (1 s) m y t ( e a ( r, y )), (11) where s s the subsdy rate for abatement cost expendture. As we consder compettve frms, they all take t and s as gven when makng ther decsons. However, t follows from the budget constrant that Second-order condtons equal the second-order condtons for the standard tax system (see appendx B). However, f we do not assume that the output share of each frm s treated as gven, there s an extra factor (1 - q /Q) n (9) and (10). When all frms share of total output s small, ths factor s neglgble (see further Fscher 2003 and Sterner and Isaksson 2006). 7

11 te s =, (12) my where Y = y. (13) F Assumng frms maxmze the payoffs specfed n (1) and (11), the frst-order condtons are 15 (1 sm ) = t, (14) a ( r, y ) y p c = t. (15) a ( r, y ) r By comparng (6) and (14), we see that the expressons for the margnal cost of reducng emssons through abatement technologes dffer between systems. The expendture-based refundng mples very strong ncentves for abatement. Not only are emssons taxed but abatement subsdzed. As s s a subsdy rate, not drectly addressng any externalty, we refer to the left-hand sde of (6) as the margnal socal cost of reducng emssons through abatement technologes, whereas the left-hand sde of (14) s the margnal prvate cost of reducng emssons through abatement technologes n the EB scheme. It thus follows from (14) and (15) that the socal margnal cost of reducng emssons through abatement expendture exceeds the socal margnal cost of reducng emssons through output reductons. 3. A Comparson of Two Mechansms for Fefundng In ths secton, we evaluate the EB and OB systems regardng cost-effectveness, and we compare the fee levels and dstrbuton of costs across frms. The standard tax system s used as a benchmark. However, we acknowledge that a standard tax system may, for poltcal or practcal reasons, not be achevable or preferred, as noted earler and dscussed further n secton 4. We 14 To ensure an nternal soluton, we assume that the regulator always sets t such that s < 1. In practce, the budget of the fund mght not have to balance exactly every year, and s may also be adjusted over tme. 15 Second-order condtons equal the second-order condtons for the standard tax system (see appendx B). 8

12 ntroduce the subscrpts ST, OB and EB to refer to the outcomes of the standard tax system, the OB system, and the EB system, respectvely. 3.1 Comparsons wth Same Fee Level As we saw from the prevous secton, the output effect of a fee under the OB system s weaker compared wth a tax under a standard tax system. Under the EB system, on the other hand, the fee on polluton s complemented wth a subsdy on abatement equpment, and thus makes abatement less costly. Comparng the two systems wth the outcome of a tax system, we must decde whether the comparson assumes equal tax rates or equal abatement. We start wth the former and show, n proposton 1, that EB gves more and OB gves less abatement than a standard Pgouvan tax of the same magntude. Proposton 1: Gven (A.1), we have that a EB () t > a ST () t > a OB () t for all t. Proof of proposton 1: The outcome of the EB system can be mmcked by a standard tax system wth prces on the a abatement technology equal to (1 sm ) < m, and t= t ST. We have that < 0 (see appendx B), m EB ST ST ST such that a ( t ) > a ( t ). The outcome of the OB system can be mmcked by a standard tax system wth a tax rate of t ST OB OB and p = p+ k, where k OB OB ST E a = t >0. We have that < 0 OB Q p OB ST ST ST (see appendx B), such that a ( t ) < a ( t ). 3.2 Comparsons wth the Same Target Level of Abatement Buldng on ths result, we swtch to a comparson between dfferent levels of fees, desgned to gve the same level of abatement. Proposton 2 shows us that the tax/subsdy (EB) requres a fee that s lower than the standard tax, whereas output-based refundng (OB) requres a hgher fee. Proposton 2: ST OB EB Consder a gven target for abatement, and let t, t, and t denote the tax/fee levels that ensure that the target s met n the standard tax system, the OB system, and the EB EB ST OB system, respectvely. Gven (A.1), we have t < t < t. 9

13 Proof of proposton 2: The abatement n the standard tax system s an ncreasng functon of the tax rate for all frms ( a >0, see appendx B). Furthermore, we know from proposton 1 that a EB () ST () OB t > a t > a () t t, for all t. Hence the t OB ST ST OB OB ST that satsfes a ( t ) = a ( t ) t, and the must be larger than ST ST EB EB ST = t. must be smaller than t EB that satsfes a ( t ) a ( t ) The tax rate n the EB system can be set lower for dentcal emssons reductons, snce the tax effect s combned wth a subsdy on abatement. The OB system does have a hgher fee level, but thanks to the automatc refund, the average company pays nothng, and both theory and experence show that even hgh fee levels may be more easly acceptable under these crcumstances than a tax (see Fredrksson and Sterner 2005). However, t could be costly for frms wth emssons-ntensve producton and lmted abatement optons. Furthermore, outputbased refundng can be controversal to operate when frms produce dfferentated products and output s hard to measure. On the other hand, we assume abatements are easy to dentfy and measure and that the EB system redstrbutes the tax revenue only n terms of subsdes to abatement technologes; thus frms that have already mplemented relevant abatement technologes (or have clean producton) receve no refundng of the tax revenue and could complan that they are unfarly treated. In general, the two types of funds may lead to very dfferent dstrbutons of costs across frms. The magntude of the dfferences n tax levels necessary to acheve a specfc target depends nter ala on the frms senstvty to changes n varable producton costs and on total emssons. For nstance, consder a stuaton where outputs are senstve to changes n producton costs. Abatement nduced by a standard tax system n that case s acheved by sgnfcant reductons n output (as a tax on emssons mples hgher producton costs). As dscussed above, the output effect of an emssons fee under the OB system wll be absent or very modest. To compensate for ths, the fee level may be consderably hgher than the standard tax level n order to nduce suffcent nvestment n abatement technology. On the other hand, f output s nsenstve to changes n varable producton costs, the standard tax system nduces abatement 10

14 mostly through nvestment n abatement technology, and there s lttle dfference between the fee levels of the OB system and the standard tax system. We see from (12) that the hgher the tax base (E), the lower the t needed to provde a gven subsdy rate n the EB system. Hence the larger the emssons, the larger the dfference n the tax rate between the standard tax system and the EB system. Note that although the regulator, by approprate tax/fee levels, can acheve the same total abatement level n all three systems, both the EB and OB system wll lead to a combnaton of abatement and output reducton that s cost-neffectve compared wth the deal frst best (f and when that s achevable or applcable). In that frst best, a standard tax leads to a cost-mnmzng dstrbuton of output reductons, and abatement technology measures for all abatement levels. Proposton 3 formalzes ths. Proposton 3: Gven (A1), both the OB and the EB systems acheve the requred abatement level by too much nvestment n abatement technologes and too lttle output reducton, compared wth a standard tax system. Proof of proposton 3: See Appendx C. Although the desgn of the OB and EB dffer substantally, they both make abatement through technology nvestments relatvely cheaper than abatement through output reducton, compared wth a standard tax. Wth EB, ths follows from the subsdzed abatement technology, whereas the OB subsdzes output. In practce, OB and EB are lkely to be used when poltcal or practcal condtons make a suffcently hgh t n a standard tax system mpossble or undesrable. 16 Thus from a poltcal vewpont, the relevant comparson mght be between a standard tax system wth a low t, and thus low abatement target, and OB and EB systems wth a hgh(er) abatement target. In ths case, 16 Poltcans, who make many of the relevant decsons, rarely want output reducton n any sector. On the contrary, one of the man obstacles for any envronmental polcy s the threat to jobs. Although a reducton n jobs n some sector mght be part of an economcally optmal strategy, t rarely goes over well wth voters. Furthermore, the condtons under whch the polcy s optmal may not be met. Ths apples nter ala to cases where olgopoly exsts or small, open economes where there s a threat to compettveness through foregn compettors that do not face envronmental polces. 11

15 producton mght stll be hgher under the OB and EB systems, but certanly there wll be hgher expendtures on abatement actvtes. As mentoned, hgher producton s often consdered desrable by poltcans. The nvestments also create employment and may speed up the development of the abatement ndustry through scale effects and learnng by dong, possbly even creatng export opportuntes or other strategc advantages for domestc ndustry. As we dscussed n the ntroducton, the motvaton for refundng s often to appease busness and to prevent frm closure, job loss, and carbon leakage. We know that both the EB and OB refundng mechansms lead to hgher output and hgher nvestments n abatement technologes than the standard tax system (proposton 3). The more the outcome devates from the frst best, the hgher the total cost of achevng the emssons target wll be. On the other hand, the establshment of a fund s typcally motvated by a preference for a dfferent combnaton of output reductons and abatement technology than what follows from a standard tax system. To determne the preferred fund system, t s therefore vtal to know how the two dfferent funds perform regardng output reducton versus nvestments n abatement technology. However, that demands an emprcal nvestgaton of the regulated sector. Proposton 4: Gven a specfc emssons target ( E ) and (A.1), we cannot, n general, tell whether OB or EB leads to larger nvestment n abatement technologes and output. Proof of proposton 4: Proposton 4 can be proved by a numercal example. Assume that all n frms are dentcal, and let the emssons functon (1) be gven by Let cq ( ) 1 2 e r y = e a r y = Z + y (16) (, ) (, ) (q r) = q, p=10, n =5, m=1, and E =500. For the fxed cost Z = 50 we fnd, from (9), (10), (12), (14), and (15), that q OB = 9.68 < q EB = 9.86, whereas for Z=250, q OB = 8.84 > q EB = Fgure 1 depcts the level of output under OB and EB as a functon of the fxed cost Z, gven the model specfcaton from the proof of proposton 4. A hgher Z means that the busness-as-usual emssons ncrease. If we keep the emssons target constant, ncreasng Z 12

16 means larger abatement. Fgure 1 thus shows the mpact of larger abatement requrements on output under OB and EB, all other thngs beng equal. Fgure 1. The Outcome for Output under OB versus EB for Increasng Values of Z qob versus qeb as a functon of Z Output qob qeb Z By nsertng for s from (12), we can wrte (14) as m E a ( r, y ) =, (17) y EB EB t Y and rewrtng (10) gves p c OB q E a OB ( r, y ) = + (18) r OB t Q It follows from (A.1) that an ncrease n abatement requrement mples that Y ncreases and Q decreases. For a gven E, ths means that the last term on the rght-hand sde of (17) declnes, whereas the last term on the rght-hand sde of (18) rses. Thus an ncrease n Z wll ceters parbus decrease the ncentves for output reductons under OB and ceters parbus decrease the ncentves for nvestments n abatement technology under EB. Ths explans why OB EB q can be smaller than q for small values of Z and vce versa for larger values of Z. 13

17 3.3. Effects on Ext and Entry of Frms In modelng the performance of the two types of funds n the prevous sectons, we gnored potental mpacts on ext and entry. A dfference between a standard tax and a refunded fee s that the former generates publc revenue, whereas the fund systems are revenue neutral, as the emssons tax (fee) collected by the fund s redstrbuted to the frms. A standard tax may lead to a stuaton where some frms are no longer able to cover ther total costs for any output level, and thus t s proftable for them to close down producton. Compared wth a standard tax system, the fund systems may prevent closures as the frms receve an ncome from the rembursement of emssons taxes. Hence refundng could lead n prncple to a lower degree of ext compared wth a standard tax. We cannot tell n general whch of the fund systems, EB or OB, would have a stronger effect n preventng closures, as the two types of funds may lead to very dfferent dstrbutons of costs across frms. For nstance, as the EB system redstrbutes the tax revenue only n terms of subsdes to abatement technologes, t benefts frms wth large current optons for abatement nvestments (whch often may be coupled wth other nvestments decded by plant vntage). Frms that have low emssons levels compared wth the average would, on the other hand, tend to prefer OB over EB, as they receve a hgher-than-average refund of ther tax payment. We argued n secton 2.2 that frms whch have lower margnal emsson ntensty than the average emsson ntensty would ncrease ther producton under an OB scheme compared wth a stuaton wthout any envronmental polcy. Thus an OB system may nduce entry of new frms wth low emssons per unt output, as output-based refundng n that case works as a net subsdy on producton. On the other hand, an EB system mght also help avod the ext of a plant that has to undergo relatvely expensve reparatons or refurbshment, f the frm s able to get the nvestment classfed as an mprovement from the vewpont of abatement and thus get a subsdy, thereby reducng the expendture ncurred. It s worth notng that the ssue of montorng and enforcement could be qute trcky n some cases, partcularly f nvestments serve dual purposes of expanson and abatement. 4. Concludng Remarks Our pont of departure was that polcymakers and ndeed the publc at large usually emphasze a number of aspects of envronmental polcy n addton to effcency: actvty reductons n local ndustres, possble job losses, leakage effects (pollutng ndustres relocatng to other countres), and dstrbutonal concerns loom large. Hence the envronmental polcy nstrument preferred by most economsts, the Pgouvan tax, s seldom as popular as economsts 14

18 thnk t deserves to be (though a tax combned wth thresholds to lower the revenue rased rarely has been consdered as a potentally more acceptable varant). We have analyzed two alternatve mechansms that mply refundng emssons payments to pollutng frms: output-based refundng (OB) and expendture-based refundng (EB). Our man fndngs are as follows. Gven a certan emssons target, the tax/fee level that ensures that the target s met s lower n the standard tax system than n the OB system, but t s even lower n the EB system than n the standard tax system. These dfferences, n turn, lead to dfferences n the dstrbuton of cost across frms. Both refundng mechansms lead to cost-neffectve combnatons of abatement and output reducton, wth hgher output and more abatement than effcent from the vewpont of a smple economc model. However, ths effect may be seen as an advantage by polcymakers f they seek to avod actvty reducton n the regulated sector. Intutvely, one mght perhaps expect that an EB system would lead to hgher nvestment n abatement technologes than the OB systems. We found that ths s not a general result. The opposte occurs f the regulated sector s suffcently emssons nsenstve and the abatement requrement s suffcently large. Frms that already have mplemented abatement technologes before the ntroducton of a refund mechansm are lkely to prefer an OB system, whle a frm that stll has proftable nvestment optons n abatement technologes would prefer the EB system. An mportant dfference between the two systems s n the regulator s needs for nformaton to regulate the systems effectvely. All systems (ncludng a regular tax) requre nformaton about frms emssons. In addton, the OB system requres nformaton about output, whch s usually avalable but n many cases may be open to manpulaton (such as through transfer prcng. In the Swedsh NO x polcy case, the physcal heat and energy output of bolers was chosen as a readly verfable and relevant measure. It s not unlkely that the lack of applcatons n other areas s due to the dffculty of usng, for nstance, gross sales values as a measure. The EB system, on the other hand, demands knowledge about the frms costs of purchasng and utlzng the abatement technology. As a result of asymmetrc nformaton between the fund s manager and the frms, the frms may gan large nformatonal rents by overstatng the cost of the abatement technology. Recall here that emssons reductons often are a consequence of dfferent types of commercally proftable projects, such as rebuldng engnes for hgher effcency. Furthermore, n order to gan nformatonal rent, the frms may not choose the most cost-effectve abatement technology project, but nstead mplement technologes where ther prvate cost nformaton advantage s the greatest. 15

19 In ths paper, we have mentoned varous reasons why polcymakers may prefer refund systems over a standard tax system. In separate papers ( 2012, 2014), we have descrbed and analyzed the emprcal data on one applcaton of the EB refundng for NO x n Norway. Our man concluson s that, although t s not effcent n a standard statc sense, and although there are some poltcal economy peculartes, ths stll remans an nterestng addton to the polcy nstruments avalable, partcularly for cases when t s not possble to mplement a tax that s suffcently hgh (but when t s possble to dentfy dscrete abatement nvestments that are desrable). An area for future research s to analyze more specfcally how the optmal choce of emssons polcy mechansms depends on how the polcymakers emphasze the varous polcy targets (e.g., emssons reductons, ndustres actvty level, ncome dstrbuton, dffuson of abatement technologes). We beleve that economsts have put nsuffcent nterest on the use of revenues collected by envronmental taxes. For busnesses, NGOs, and poltcans alke, ths s often a very mportant ssue. Our model has shown how refundng, ether n proporton to output or to pay partally for abatement, can mprove the ncentves under some condtons. Experence from Sweden, Norway, and other countres has shown that ths type of refundng can make the polces more poltcally acceptable, at least n such cases as NO x from large ndustral sources. Whether there may be a case for applcatons n the clmate area s an nterestng ssue left for future research. 16

20 References Bernard, A. L., Fscher, C., Fox, A. K Is There Ratonale for Output-Based Rebatng of Envronmental Leves? Resource and Energy Economcs 29 (2): Cato, S Emsson Taxes and Optmal Refundng Schemes wth Endogenous Market Structure. Envronmental and Resource Economcs 46 (3): Cora, J Taxes, Permts, and the Dffuson of a New Technology. Resource and Energy Economcs 31(4): Edwards, T. H., and J. P. Hutton Allocaton of Carbon Permts wthn a Country: A General Equlbrum Analyss of the Unted Kngdom. Energy Economcs 23 (4): Felder, S., and R. Schlenger Envronmental Tax Reform: Effcency and Poltcal Feasblty. Ecologcal Economcs 42 (1 2): Fscher, C Rebatng Envronmental Polcy Revenues: Output-Based Allocatons and Tradable Performance Standards. Dscusson paper Washngton, DC: Resources for the Future Market Power and Output-Based Refundng of Envronmental Polcy Revenues. Dscusson paper Washngton, DC: Resources for the Future. Fscher, C., and A. K. Fox Output-Based Allocaton of Emssons Permts for Mtgatng Tax and Trade Interactons. Land Economcs 83 (4): Fredrksson, P.G., and T. Sterner The Poltcal Economy of Refunded Emssons Payments Programs. Economc Letters 87 (1): Fullerton, D Envronmental Leves and Dstortonary Taxaton: Comment. Amercan Economc Revew 87 (1): Fullerton, D., and R Mohr Suggested Subsdes Are Sub-optmal Unless Combned wth an Output Tax. B.E. Journal of Economc Analyss & Polcy 2(1). Gersbach, H., and T. Requate Emsson Taxes and Optmal Refundng Schemes. Journal of Publc Economcs 88 (3): Goulder, L.H., I.W.H. Parry, R.C. Wllams, and D. Burtraw The Cost-Effectveness of Alternatve Instruments for Envronmental Protecton n a Second-Best Settng. Journal of Publc Economcs 72 (3):

21 Hagem, C., B. Holtsmark, and T. Sterner Mechansm Desgn for Refundng Emssons Payments. Dscusson paper 705. Oslo, Statstcs Norway Om den norske poltkken for reduksjon av utslpp av NO x. Samfunnsøkonomen, 5. Hoel, M Global Envronmental Problems: The Effects of Unlateral Actons Taken by One Country. Journal of Envronmental Economcs and Management 20 (1): Höglund Isaksson, L Abatement Costs n Response to the Swedsh Charge on Ntrogen Oxde Emssons. Journal of Envronmental Economcs and Management 50 (1): Jaffe, A., R. Newell, and R. Stavns Envronmental Polcy and Technologcal Change. Envronmental and Resource Economcs 22 (1): Johnson, K. C An Effectve Regulatory Instrument for Cost-Constraned Envronmental Polcy. Energy Polcy 34 (18): Kallbekken, S., S. Kroll, and T. L. Cherry Do You Not Lke Pgou, or Do You Not Understand Hm? Tax Averson and Revenue Recyclng n the Lab. Journal of Envronmental Economcs and Management 62 (1): Kolstad, C. D Envronmental Economcs. New York: Oxford Unversty Press. Löschel, A Technologcal Change n Economc Models of Envronmental Polcy: A Survey. Ecologcal Economcs 43 (2 3): Mllock, K., and C. Nauges Ex Post Evaluaton of an Earmarked Tax on Ar Polluton. Land Economcs 82 (1): Mllock, K., C. Nauges, and T. Sterner Envronmental Taxes: A Comparson of French and Swedsh Experence from Taxes on Industral Ar Polluton. CESfo DICE Report, 1, Parry, I. W. H., J. Norregard, and D. Hene Envronmental Tax Reform: Prncples from Theory and Practce. Annual Revew of Resource Economcs 4: Pezzey, J. C. V Emsson Taxes and Tradeable Permts: A Comparson of Vews on Long Run Effcency. Envronmental and Resource Economcs, 26 (2): Requate, T Dynamc Incentves by Envronmental Polcy Instruments: A Survey. Ecologcal Economcs 54 (2 3):

22 Sterner, T., and J Cora Polcy Instruments for Envronmental and Natural Resource Management. New York: RFF Press. Sterner, T., and L.H. Isaksson Refunded Emsson Payments Theory, Dstrbuton of Costs, and Swedsh Experence of NO x Abatement. Ecologcal Economcs 57 (1): Sterner, T., and B. Turnhem Innovaton and Dffuson of Envronmental Technology: Industral NO x Abatement n Sweden under Refunded Emsson Payments. Ecologcal Economcs 68 (12): Svendsen, G. T., C. Daugbjerg, L. Hjollund, and A. Branth Pedersen Consumers, Industralsts and the Poltcal Economy of Green Taxaton: CO 2 Taxaton n OECD. Energy Polcy 29 (6): Walls M., and K. Palmer Upstream Polluton, Downstream Waste Dsposal, and the Desgn of Comprehensve Envronmental Polces. Journal of Envronmental Economcs and Management 41 (1):

23 Appendx A Interpretaton of functon a(r,y) Output q s gven by an ncreasng and strctly concave producton functon of an nput v wth prce p v, and emssons are a functon of output as well as technology varable y : q= Fv () e= Gqy (, ) We assume G q >0, G y <0, and G yy >0. It s not obvous what the sgns of G qq and be; we dscuss ths below. Wth ths setup, the cost functon cq ( ) s for F <0. Wthout any envronmental polcy, c q 0 ( )= p 0 q and 0 e are gven by cq pf q 1 ( )= v ( ) G qy should, and c >0 0 0 e = Gq (,0) The abatement functon ar (, y ) s gven by a r y e G q r y 0 0 (, )= (, ) wth propertes a = G >0 r q a a y rr = G >0 y = G qq a yy = G <0 yy a = G ry qy We assume that G qq >0, mplyng a rr <0. If, for example, e s proportonal to v for a gven y, we have G qq >0 due to F <0. Wth these sgns, ar (, y ) wll be strctly concave (and hence strctly quas-concave) n (, r y ) provded G qy s suffcently close to zero (postve or negatve). For both r and y to be normal factors, a / a must be declnng n r and ncreasng n y. It s straghtforward to see that a suffcent condton for ths s that G qq >0 and G qy are r y 20

24 suffcently close to zero. The condton G qq >0 and Gqy suffcently close to zero s hence suffcent both for the concavty of ar (, y ) and for r and y beng normal factors. Appendx B In ths appendx, we derve second-order condtons for global proft maxmum and show how the equlbrum outcomes change wth t, m, and p n the standard tax system. We wrte the second order dervatves of the proft functon as follows: π π π π π π = πq, = π y, = πqq, = π yy, = = πqy. Gven that the second-order q y q q y y q y y q condtons for global proft maxmum are satsfed, we must haveπ = ta < 0, 2 π qq = c + ta rr < 0, and π π ( π ) > 0. π = ta,. yy qq yq qy To fnd how the equlbrum outcomes of the standard tax system change wth t, m, and p, we totally dfferentate the two equatons (6) and (7). Gven the second-order condtons and our assumpton about the abatement functon (see A.1), we are able to sgn some of the effects: r y yy yy y a π + a π = t D y qq r qy >0 (see below), (19) q r a r π yy + a y πqy = = < 0 t t D (see below), (20) y π qq = < 0, (21) m D q π = m D qy, (22) y p p = D qy, (23) q r p yy = = > 0, (24) p p D 21

25 where D = π π π > (25) 2 yy qq ( yq ) 0 We fnd that a 2 r y r, y ( y ) r, r ( r ) y, y ( y ) ( ) y t a a a a a a a a c r + = a y + a r = > 0 (26) t t t D Snce we have assumed that a( r, y ) s strctly quas-concave, we know that the term wthn the frst square bracket n the numerator of (26) s postve. (The term equals the second prncpal mnor of the bordered Hessan matrx of the abatement functon, whch s postve for a strctly a quas-concave functon.) As ( c ) s assumed to be postve, we have that t >0. We have also assumed that r and y are normal nput factors n the producton of abatement. As y q r abatement s an ncreasng functon of t, we must have that >0 and = < 0. t t t Furthermore, we fnd that r y a r + a y a a m m r πqy + a y πqq y = = = < 0, (27) m D D t r y a r + a y a a p p r p yy + a y pqy q = = = < 0. p D D t (28) 22

26 Appendx C In ths appendx, we prove proposton 3. Due to the quas-concavty of the functons a, y and q are ncreasng functons of the rato a r a y (for gven values of a ). From (6) and (7), we have ST ST a r p c ( q ) =. a y m From (9) and (10), we have EB a r a y EB a r p c ( q ) =. Assume y a OB ST y and hence also q y (1 sm ) OB E OB ST p c a r a ( q ) + t ST r Q p c ( q ),.e.,. a y a y m m OB OB E p c ( q ) + t Q =. From (14) and (15), we have m OB q ST. Ths requres E Snce t 0 Q > and 0 OB ST c, ths mples q > q, whch contradcts our ntal assumpton. OB ST OB ST Hence t must be true that y > y and q > q. Assume y q EB q ST. Ths requres EB a a r r a y a y OB,.e., EB y and hence also ST EB ST p c ( q ) p c ( q ). (1 sm ) m EB ST Snce s >0 and c 0, ths mples q > q, whch contradcts our ntal assumpton. Hence t EB ST EB ST must be true that y > y and q > q. 23