NBER WORKING PAPER SERIES WHAT ARE THE COSTS OF MEETING DISTRIBUTIONAL OBJECTIVES FOR CLIMATE POLICY? Ian W.H. Parry Roberton C.

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1 NBER WORKING PAPER SERIES WHAT ARE THE COSTS OF MEETING DISTRIBUTIONAL OBJECTIVES FOR CLIMATE POLICY? Ian W.H. Parry Roberton C. Wllams III Workng Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambrdge, MA October 2010 We are grateful to Don Fullerton, Bll Randolph, an anonymous referee, and partcpants n the Chcago- RFF-Illnos Symposum on Dstrbutonal Aspects of Energy and Clmate Polcy for helpful comments and suggestons. And we thank Fanqng Ye for her excellent research assstance. The vews expressed heren are those of the authors and do not necessarly reflect the vews of the Natonal Bureau of Economc Research. NBER workng papers are crculated for dscusson and comment purposes. They have not been peerrevewed or been subject to the revew by the NBER Board of Drectors that accompanes offcal NBER publcatons by Ian W.H. Parry and Roberton C. Wllams III. All rghts reserved. Short sectons of text, not to exceed two paragraphs, may be quoted wthout explct permsson provded that full credt, ncludng notce, s gven to the source.

2 What Are the Costs of Meetng Dstrbutonal Objectves for Clmate Polcy? Ian W.H. Parry and Roberton C. Wllams III NBER Workng Paper No October 2010 JEL No. H22,H23,Q48,Q54,Q58 ABSTRACT Ths paper develops an analytcal model to quantfy the costs and dstrbutonal effects of varous fscal optons for allocatng the (large) rents created under prospectve cap-and-trade programs to reduce domestc, energy-related CO2 emssons. The trade-off between cost effectveness and dstrbuton s strkng. The welfare costs of dfferent polces, accountng for lnkages wth the broader fscal system, range from negatve $6 bllon/year to $53 bllon/year n 2020, or between mnus $12 to almost $100 per ton of CO2 reductons! The least costly polcy nvolves auctonng all allowances wth revenues used to cut proportonal ncome taxes, whle the most costly polces nvolve recyclng revenues n lump-sum dvdends or grandfatherng emssons allowances. The least costly polcy s regressve, however, whle the dvdend polcy s progressve, and grandfatherng permts s both costly and regressve. A dstrbuton-neutral polcy entals costs of $18 to $42 per ton of CO2 reductons. Ian W.H. Parry Resources for the Future 1616 P Street, NW Washngton, DC parry@rff.org Roberton C. Wllams III Department of Agrcultural and Resource Economcs Unversty of Maryland, Symons Hall College Park, MD and NBER rwllams@arec.umd.edu

3 1. Introducton One of the most mportant ssues n the desgn of domestc, market-based clmate polcy s what to do wth the rents or revenues created under cap-and-trade or emssons tax systems. 1 How these polcy rents are allocated and used crtcally affects not only the dstrbutonal mpacts of the polcy, but also ts overall cost-effectveness. There are many ways to allocate polcy rents. One s to grandfather allowances n a capand-trade system, that s, gve them away free to exstng sources, typcally based on ther hstorcal emsson rates. The man motvaton for ths approach s poltcal provdng compensaton for producers affected by the regulaton may make t easer to move legslaton forward. Almost all of the allowances n the US program to cap SO 2 emssons from power plants were gven away for free and smlarly n the ntal phases of the European Unon s CO 2 tradng program. However, more recent European and US federal clmate ntatves have moved away from full grandfatherng, as t s wdely apprecated that ths approach substantally overcompensates emtters for ther complance costs. 2 More recently, the dstrbutonal concern n the Unted States has been on the household sde, partcularly nsulatng low-ncome households from the prospectve ncrease n energy prces from clmate polcy. Some proposals nvolve grantng free allowances to local dstrbuton companes wth the expectaton that the value of these allowances wll be rebated to households n the form of lower electrcty blls. Another approach that has recently ganed tracton s known as cap-and-dvdend, whch nvolves a cap-and-trade program wth full allowance auctons wth all the revenue returned n equal lump-sum transfers for all ndvduals. An argument for ths approach s that all ndvduals have equal ownershp rghts to the envronment and therefore proceeds from chargng for use of the envronment should be shared equally. A key drawback of both of these approaches s that they forgo the potentally large effcency gans from usng allowance aucton revenues to cut other dstortonary taxes. Personal 1 Other key ssues nclude the overall strngency of the polcy, ts sectoral coverage (ncludng provsons for emsson offsets), whether cap-and-trade should nclude prce stablzaton mechansms, and to what extent supplementary nstruments are warranted to address other possble market falures (e.g., technology spllovers). For a general dscusson of these ssues see, for example, Aldy et al. (2010). 2 Power companes n the European Unon earned large wndfall profts when the CO 2 cap was frst ntroduced (e.g., Sjm et al., 2006). At least for a moderately scaled CO 2 permt system, only about percent of allowances are needed to compensate energy ntensve ndustres for ther loss of producer surplus, so the huge bulk of the allowances could stll be auctoned (e.g., Bovenberg and Goulder, 2001, Smth et al., 2002). 1

4 ncome and other taxes dstort captal and labor markets by depressng net factor returns. They also dstort household consumpton decsons by allowng exemptons or deductons for partcular types of spendng (e.g., employer medcal nsurance). Therefore, usng revenues to lower the rates of these dstortonary taxes produces gans n economc effcency that can substantally lower the overall welfare costs of clmate polcy (though ths approach may do lttle to help wth dstrbutonal objectves). In fact, wthout ths counteractng revenue-recyclng effect, the welfare costs of market-based clmate polces are substantally hgher n the presence of dstortonary taxes, because those dstortons rase producton costs and product prces, and thereby lower real factor returns and factor supply (e.g., Goulder et al., 1999, Fullerton and Metcalf, 2001). To date, no clmate blls have been ntroduced n the US Congress that would use polcy revenues to reduce margnal ncome tax rates, though some nclude uses that would have smlar effects. 3 Moreover, consderng ths case helps clarfy the qute strkng trade-offs nvolved n allocatng clmate polcy rents. In ths paper, we develop and parameterze an analytcal general-equlbrum model that syntheszes two dfferent strands n the lterature on domestc clmate polcy, one focusng on the cost-effectveness of alternatve market-based polces n a homogeneous agent framework and the other that looks at dstrbutonal effects n mult-agent models but wth no attenton to effcency. Whle some of our results such as the low cost-effectveness of cap-and-dvdend and grandfathered permts have been recognzed for some tme, our analyss offers a more complete pcture of effcency/dstrbutonal trade-offs than can be gleaned from pror lterature. 4 3 The Waxman-Markey, bll for example, devotes a porton of revenue to defct reducton. If that defct reducton would otherwse have been accomplshed by rasng margnal rates, then ths would have the same effect as lowerng margnal rates. In addton, a bll sponsored by Rep. Larson (HR 1337) would have used revenues to exempt a porton of ncome from payroll taxes. Whle ths form of recyclng would ncrease the return to labor force partcpaton t would be less effcent than cuttng margnal ncome tax rates. The latter would also ncrease effort on the job and reduce the bas towards tax-preferred spendng. CO 2 taxes whch are largely revenue neutral have been mplemented n Brtsh Columba and n Scandnavan countres, though a tax proposal for France (wth very lmted coverage) was recently ruled unconsttutonal. 4 Pror analyses by Burtraw et al. (2009), Dnan and Rogers (2002), and Parry (2004) have studed the dstrbutonal mpacts of varous optons for recyclng clmate polcy revenues through the tax system. And many papers have been wrtten on the lnkages between envronmental polces and the broader tax system and how these affect the overall costs of polcy (see, for example, Goulder et al., 1999, Fullerton and Metcalf, 2001, Bovenberg and Goulder, 2002, and Schöb, 2006, among many others). Our analyss s more than just the sum of fndngs from these two lteratures, however. Most mportantly, the effcency and dstrbutonal results come from the same model, and thus are drectly comparable. Ths model has several addtonal advantages. Unlke n most pror lterature we account for broader dstortons of the tax 2

5 Our analyss consders three boundng cases for rent allocaton and use under cap-andtrade systems. These nclude full grandfatherng of allowances; full aucton of allowances wth revenues returned n lump-sum-transfers; and full auctons wth revenues recycled n equal, proportonate cuts n margnal ncome taxes across all household groups. We also consder a dstrbuton neutral polcy where the tax and beneft system s adjusted to neutralze any dstrbutonal effects of the cap-and-trade polcy on households, leavng the overall polcy change nether progressve nor regressve. Polcymakers are more lkely to choose combnatons of the boundng cases studed here, rather than usng 100 percent of rents for one purpose alone, however the mplcatons of these combnatons are easly nferred by takng the approprate weghted averages of our boundng cases. Furthermore, although our dscusson s couched n terms of cap-and-trade, each cap-and-trade varant has an emssons tax counterpart n our analyss. 5 New revenue sources mght be used n many ways other than those studed here. These run the gamut from program enhancng measures lke clean technology programs, ncentves for energy effcency, and capacty nvestments to facltate adaptaton to clmate change, to general ncreases n publc spendng and federal defct reducton. However, t s dffcult to make general statements about the potental effcency mplcatons from these broader alternatves for revenue use, wthout specfc evdence on the beneft and costs of the spendng measures, accountng for possble market falures that they mght address. Even the effects of defct reducton are opaque, as t s unclear whether lower debt burdens for future generatons wll lead to lower taxes or more publc spendng. system beyond those n factor markets, so we can ntegrate emprcal fndngs from recent publc fnance lterature on the taxable ncome elastcty (see below). Furthermore, our dstrbutonal analyss takes nto account mplct burdens on households from the changes n deadweght loss from the broader fscal system. Moreover, we account for nflaton ndexng of the tax/beneft system, whch provdes some (albet lmted) automatc adjustment to hgher energy prces. In addton, the type of mult-agent model used here s needed to avod aggregaton bas when households face dfferent tax rates, beneft dfferently from revenue-recyclng schemes, and have dfferent behavoral responses to tax changes. Fnally, the dstrbuton-neutral approach descrbed below has not prevously been analyzed n the context of carbon polcy. 5 For example, a carbon tax wth revenues returned n lump-sum transfers to frms n proporton to ther hstorcal emssons would be equvalent to cap-and-trade wth grandfathered allowances. The tax and cap-and-trade approaches would dffer f our analyss were extended to ncorporate uncertanty over future emssons abatement costs (e.g., Pzer, 2003). 3

6 We fnd that the allocaton of rents under cap-and-trade (or use of revenues under carbon taxes) can have huge effcency and dstrbutonal consequences for carbon polcy, effects that can be much larger than the drect effects of the carbon polcy tself. Wthn the range of optons we consder, the drect cost of reducng CO 2 emssons to 9% below busness-as-usual levels n the year 2020 s $9 bllon (all fgures are n year 2007 $). However, the overall welfare costs of dfferent polces, takng nto account lnkages wth the broader fscal system, ranges from negatve $6 bllon/year to $53 bllon/year. In terms of average cost of CO 2 reductons ths s a huge range from mnus $12 to almost $100 per ton. The dstrbuton of that cost ranges from hghly progressve (wth the bottom two ncome quntles bearng a negatve burden) to hghly regressve (wth the top two quntles bearng a negatve burden). There are stark trade-offs between cost-effectveness and dstrbuton n the desgn of market-based clmate control polces. A cap-and-dvdend approach makes carbon polcy more progressve at the expense of dramatcally rasng the overall cost, and conversely, usng revenue to fund a proportonal ncome tax cut lowers overall cost but leads to a regressve dstrbuton of those costs. A dstrbuton-neutralzng tax change represents a mddle ground for both effcency and dstrbutonal effects. Cap-and-trade wth grandfathered allowances performs poorly on both cost and dstrbutonal grounds, though t may reduce ndustry opposton and thus be more poltcally feasble. The rest of the paper s organzed as follows. Secton 2 develops our analytcal framework and key formulas for the effcency cost and dstrbutonal burden of dfferent polces. Secton 3 descrbes the model parameterzaton. Secton 4 presents the man quanttatve fndngs and senstvty analyss. Secton 5 offers concludng remarks. 2. Analytcal Framework A. Model Assumptons We use a long run, comparatve statc model wth multple agents, each representng an average over all households wthn a partcular ncome class. Households choose consumpton of general goods, products that are energy ntensve, products that receve favorable treatment from the tax system, and labor supply. The government prces carbon doxde (CO 2 ) emssons, through a cap-and-trade system, whch n turn drves up energy costs and product prces n 4

7 general. Rents created by clmate polcy may accrue to the prvate sector (e.g., through free allowance allocaton) or to the government. In the latter case, revenues are used to adjust the ncome tax and transfer system. () Household utlty. We dvde households nto 5 equal-szed ncome groups, ndexed by, where = 1 and 5 denote the lowest and hghest ncome quntles, respectvely. Each group s modeled as a sngle representatve household, wth the utlty functon: (1) u (X E, X F, X C, L,G PUB ) X E denotes consumpton of an aggregate of goods whose producton or use s energy ntensve (e.g., electrcty-usng durables, auto travel, home heatng fuels). X F s consumpton of goods that are favored through the broader tax system, such as employer-provded medcal nsurance or owner-occuped housng. X C s an aggregate of all other (non-energy-ntensve, non-tax-favored) goods. L s work effort, mplctly combnng labor force partcpaton rates and average hours worked on the job by households n that group. G PUB s government spendng on publc goods, whch s fxed, and s ncluded only to scale ncome tax rates to ther observed levels. u s quasconcave, twce dfferentable, decreasng n labor supply, and ncreasng n all other arguments. () Household budget constrant. The household budget constrant s gven by: (2)! p j X j = I j where j = E, F, C ndexes the three goods and p j s the market prce of good j. The tax and transfer system, reflectng state and federal personal ncome taxes, employer and employee payroll taxes, and sales taxes, mnus government transfers, s represented as a pecewse-lnear functon wth fve segments and each of the fve ncome groups fallng on a dfferent segment. For smplcty, we assume that any polcy-nduced changes n taxable ncome wll be suffcently small that no group wll move to a dfferent segment of the tax schedule. Under ths assumpton, the tax schedule group faces s equvalent to a lnear tax wth rate t and ntercept!g (whch can be found by extendng the relevant segment of the pecewse-lnear tax schedule out to a pont wth zero pre-tax ncome). Dsposable ncome (I ) conssts of taxable ncome (! ), net of taxes pad on that ncome. Ths gves 5

8 (3a) I = (1! t )" + G Taxable ncome conssts of the wage w tmes labor supply, plus lump-sum net-of-tax proft ncome π, less spendng on tax-favored goods. Proft ncome accrues to households va ther ownershp of frms and reflects any producer rents created by cap-and-trade polcy. (3b)! = w L + " # p F X F The (pre-exstng) tax system causes two sources of dstorton. Frst, t dstorts labor supply by depressng the returns to work effort. Second, t creates a bas towards tax-preferred spendng. The combned effect of carbon polces on these two dstortons can be summarzed by changes n taxable ncome. 6 () Producton, CO 2 emssons, prces and rents. All goods are produced under constant returns to scale under perfect competton (hence there are no pure profts n the absence of carbon polcy). Market prces of goods, whch mplctly ncorporate any energy costs assocated wth ther use, are determned by: (4) p j =! j p H + " j Here ρ j s the energy ntensty of good j, where! E >! C,! F ; p H s the prce of energy; and! j s a parameter representng non-energy costs. 7 The prce of energy s determned as follows (5) p H = c(z 0 0! z) + "z + p H where z s CO 2 emssons per unt of energy, c(.) s a postve, convex abatement cost functon (c(0) = 0) and a superscrpt 0 denotes the ntal value of a varable (pror to the ntroducton of carbon polcy). A reducton n z represents a swtch to lower carbon but more expensve fuels n energy producton (e.g., a swtch from coal to renewables or nuclear power). Emssons are prced at rate τ, whch reflects the allowance prce. Our assumptons also mply that emssons 6 We mplctly assume that that tax preferences do not address any market falures, and thus are purely dstortonary. 7 For smplcty ρ j s taken as fxed though relaxng ths would not affect the results, gven our parameterzaton below. 6

9 prces and abatement costs wll be fully passed through nto energy prces. As dscussed below, ths assumpton s debatable, although t does not affect the key focus of our paper, whch s the trade-off between costs and dstrbutonal goals n allowance allocaton. Economy-wde CO 2 emssons, Z, are the product of the emssons ntensty of energy and energy use aggregated over all products and households: (6) Z = z "! j " X j j For smplcty, we focus on a polcy coverng CO 2 only, whch accounts for about 80 percent of total US greenhouse gases. In addton, the (energy-related domestc) CO 2 reductons, and the emssons prce, are approxmately consstent wth those projected under recent clmate legslaton. 8 Proft ncome to household group s gven by: (7)! = " #$Z! s the fracton of (economy-wde) energy captal owned by household group (mplctly, ths ncludes both retrement and non-retrement bond and stockholdngs), where! " = 1 and! s larger for hgher ncome groups.! s the porton of polcy rents that are left n the prvate sector, as opposed to accrung to the government n revenue.! = 0 represents a cap-and-trade system wth full allowance auctons.! = 1 represents a system wth 100 percent free allowance allocaton to energy frms, where entre polcy rents τz are reflected n hgher frm equty values and stockholder wealth, and such ncome s not taxed. Intermedate cases mght represent partal taxaton of allowance rents or partal auctonng of allowances. Outcomes for these cases are easly nferred by takng weghted averages of the results below. (v) Government Constrants and Polcy. The government s subject to the budget constrant & (8) G PUB = t! " # G + (1 # $)%Z & 8 Although under current legslaton frms may purchase offsets n other domestc sectors (e.g., forestry and agrculture) and n other countres we do not count those as part of the emsson reducton, nor do we nclude the deadweght losses (n other sectors or countres) assocated wth those broader reductons. A key concern wth offsets s the dffculty of verfyng whether or not these broader emsson reductons would have occurred anyway, and whether they mght be negated through ncreased emssons elsewhere (e.g., slowed deforestaton n one country mght accelerate deforestaton n other countres through a rse n global tmber prces). 7

10 Ths constrant requres that spendng on publc goods equals revenue from the ncome tax system, plus revenue from the carbon polcy. Followng the ntroducton of a carbon polcy, the ntercept terms n the tax schedule are adjusted as follows: (9) G = G 0 p + Ĝ, p =! µ j p j, µ j = j where we have normalzed all ntal product prces to unty. p s the general prce level, a weghted average of market prces where the weght µ j s the (ntal) share of economy-wde spendng (or consumpton) on good j.!! j Accordng to (9), the nomnal tax schedule s automatcally nflaton-ndexed to reflect ncreases n the general prce level (ths mples that margnal and average tax rates depend on real ncome). In addton, some schemes devote a porton of the new revenues to makng the X j 0 X j 0 polcy more progressve, whch mples an addtonal adjustment Ĝ to transfer payments. More specfcally, we consder four boundng cases for the allocaton/use of polcy rents (each defned for the same emssons reducton/emssons prce): Proportonal ncome tax cut (! = 0, Ĝ = 0 ). In ths case, all polcy rents go to the government and, after ndexng the nomnal tax schedule, all other revenue s used to fnance an equal reducton n the margnal tax rate faced by all ncome groups, that s, dt / d! = dt / d! < 0,". Cap and dvdend (! = 0,Ĝ = Ĝ > 0 ). For ths polcy, allowances under a cap-and-trade polcy are fully auctoned wth revenues (after ndexng) returned n equal lump-sum transfers to households. Grandfathered permts (! = 1, Ĝ = 0 ). Here all allowances are gven away for free and all polcy rents accrue to households through ther ownershp of frms. (Agan, we abstract from taxaton of rents). Dstrbuton-neutral (! = 0, Ĝ! 0 ). Whereas the tax change n the proportonal tax cut case entals the same change to all margnal tax rates, the dstrbuton-neutral case requres changng margnal ncome tax rates by dfferent amounts at dfferent ponts n the ncome dstrbuton, n 8

11 order to equalze the net burden as a percentage of ncome across all quntles. 9 The effcency gans from revenue recyclng are smaller n the dstrbuton-neutral case than n the case wth proportonal tax rate reductons. Ths occurs prmarly because margnal rates fall by less n ths case than n the proportonal tax cut case. Cuttng tax rates on low ncome groups leads to a relatvely large drop n tax revenue, because all hgher ncome groups also beneft from the rate reductons for the lower ncome brackets. Consequently, a tax cut dsproportonately targeted at lower ncome groups wll yeld a smaller reducton n margnal rates than would a proportonal tax cut. In all four cases we assume that any ndrect revenue losses are made up through equal, proportonate adjustments to all margnal ncome tax rates. 10 These losses stem from reductons n taxable ncome as households, for example, reduce labor supply n response to lower real wages as hgher energy prces drve up the general prce level. One noteworthy lmtaton of our analyss s that the model does not capture dstortons from taxes on captal ncome. In ths regard we mscharacterze, though perhaps only moderately, the effcency gans from, and the ncdence of, proportonal cuts n margnal ncome taxes. More generally, ncorporatng taxes on captal ncome would admt a wder range of possbltes for changes n the taxaton of personal and corporate ncome n response to recyclng revenue from allowance sales. B. Formulas for Effcency Costs and Dstrbutonal Burdens of Carbon Polces Here we go straght to the man formulas of nterest. These are general expressons for the components of the effcency costs and dstrbutonal burdens of carbon polces, and how those components vary under the allocaton/recyclng optons just descrbed. The formulas below are (reasonable) approxmatons gven the scale of emsson reductons consdered and would be 9 Ths s smlar to the approach taken n Wllams (2009a and 2009b) when consderng a dstrbuton-neutralzng tax change n other polcy contexts, but whle those papers assume a contnuous ncome dstrbuton, ths paper works wth a dscrete dstrbuton made up of fve quntles. The approach n those papers n turn draws on earler work by Kaplow (2004). 10 Alternatvely, we could assume that ndrect revenue losses are deducted from the amount of revenue returned n transfers under cap-and-trade, or the sze of the allowance gveaway under grandfathered permts, wth sgnfcant mplcatons for dstrbutonal ncdence. However, our assumpton s more n keepng wth actual polcy proposals (not least, gven the dffculty of accurately projectng ndrect revenue losses). 9

12 exact f demand and margnal abatement cost curves were lnear over the relevant range. Dervatons for the formulas are provded n the Appendx. () Effcency costs. The (approxmate) effcency cost of a carbon polcy that reduces aggregate CO 2 emssons by an amount!z = Z 0 " Z, wth assocated emssons prce τ, can be decomposed nto the followng four components: (10a) WC HT! WG RR + WC TI + WC INC WC HT = 1 2!"! #Z, WG ' * RR = MEB! ((1" #)$E " & %G + ),, "# WC TI = (1+ MEB)! $ t %p = (1+ MEB)! " I t # p & $ Z + %Z ), "p ' ( 2 * +, where WC INC =!(1+ MEB) " ' #$ % t (&G + ' ) =!(1+ MEB) " # I I % t $ #G I &G (10b) MEB =! t = $ "#! $ t "t "# # + $ t "t = "# 1$ t,! p = "# "(1$ t ) # "p! " t t % # 1$ t 1$! " t t % # 1$ t p I,! #, = "# I,! " = " "I # #",! I = " # I Begnnng wth (10b),! t,! p, and! I denote three dfferent taxable ncome elastctes for household defned wth respect to changes n margnal tax rates, changes n the general prce level, and changes n (taxable) household ncome, respectvely.! " s the share of household group s taxable ncome n economy-wde ncome. MEB s the margnal excess burden of taxaton, the effcency cost of rasng an extra dollar of revenue through a proportonate ncrease n margnal ncome taxes. The numerator of MEB s the effcency loss from an ncremental ncrease n the margnal ncome tax for group, aggregated over all households. The effcency loss for group s the nduced reducton n taxable ncome (reflectng both reductons n labor supply and ncreases n tax-preferred spendng) tmes the margnal tax rate. The denomnator of the MEB s the extra revenue from the tax ncrease, summed over all households. Alternatvely, the MEB can be expressed as a functon 10

13 of the weghted sum of taxable ncome elastctes (wth respect to tax rates) for dfferent household groups, wth weghts equal to the households share n economy-wde taxable ncome. Note that, accordng to the way we have defned t n (10b), behavoral responses underlyng the MEB are uncompensated. In equaton (10a), the frst component of the welfare cost, WC HT, corresponds to the Harberger trangle under the economy-wde margnal abatement cost curve. Ths curve represents the envelope of other margnal abatement cost curves for each margn of behavor for reducng emssons reducng emssons per unt of, and reducng overall consumpton of, energy-ntensve products. 11 The Harberger trangle s the same under all four polcy scenaros. The second component n (10a), WG RR, termed the revenue-recyclng effect (e.g., Goulder 1995), s the effcency gan that results to the extent that revenues are used to reduce margnal ncome taxes. Ths component s the product of the MEB and the amount of revenue recycled n ths fashon, where the latter s the polcy rents retaned by the government less what s spent on transfer payments and ndexng. The thrd welfare cost component, WC TI, s the tax-nteracton effect. In most pror work ths referred to the welfare loss from the reducton n labor supply as polcy-nduced ncreases n the general prce level reduced the real return to work effort (e.g., Goulder 1995). The welfare loss was the change n labor earnngs, multpled by the labor tax dstorton, and multpled by 1+MEB, as lost labor tax revenues must be made up through hgher (dstortonary) taxes to mantan budget balance. In these models, the change n labor earnngs depends on both the responsveness of labor supply to hgher prces, and the loss of worker surplus from the prce ncrease. The latter s (approxmately) equal to allowance rent plus the Harberger trangle under the margnal abatement cost curve, and corresponds to!(z + "Z / 2) n our formula for WC TI. However, n our case the tax-nteracton effect s measured wth respect to changes n taxable ncome, n response to hgher product prces, rather than labor earnngs, and hence t s the taxable ncome, rather than labor supply, elastcty that appears n our formula. The taxnteracton effect (as defned here) s also constant across dfferent polces. 11 These margnal cost curves all come out of the orgn gven that our model abstracts from other dstortons affectng the producton and use of energy, such as fuel taxes, automoble congeston, and non-compettve prcng of electrcty. 11

14 Our expresson for WC TI embeds a number of smplfyng assumptons that mght, to some degree, be open to queston (see the Appendx). One s that we assume all goods are equal substtutes for lesure and therefore not deservng of any Ramsey tax or subsdy from an optmal tax perspectve. In the absence of evdence to the contrary however, ths seems a reasonable, neutral assumpton. Another smplfcaton s that complance costs are fully passed forward nto hgher prces. To the extent, for example, that complance costs come at the expense of nframargnal rent earned on base load power generaton, the prce effect and tax-nteracton effect wll be weaker. 12 In short, the reader should bear n mnd that the absolute value of the taxnteracton effect s dffcult to pn down accurately, though ths s not relevant for the cost/dstrbutonal tradeoffs nvolved n allocatng cap-and-trade rents, whch s the man focus of our paper. The fnal component of welfare cost, WC INC, reflects effcency losses from the reducton n taxable ncome n response to hgher lump-sum ncome through hgher government transfers and/or proft ncome. Ths largely reflects a reducton n labor supply as households take more lesure, whch s a normal good. () Dstrbutonal burden. The dstrbutonal burden of the emssons prcng polcy on household group, relatve to ncome, s farly straghtforward and can be approxmated by (see the Appendx for dervatons): (11) "!p 0 0 j X j +!G + " j I 0 I 0 +!t " I 0 The frst terms reflects the (frst order) consumer surplus loss from the nduced ncrease n energy prces. The second term pcks up possble benefts from dvdends and rent ncome through stock ownershp under grandfathered permts. And the thrd term reflects gans from reductons n margnal tax rates. The effcency consequences from the revenue-recyclng, taxnteracton, and ncome effect on labor supply are all ncluded n the dstrbutonal analyss, through overall changes n margnal ncome tax rates, n the thrd term. We omt the Harberger 12 The prce pass through may also be mperfect n states that retan cost-of-servce regulaton for power generaton n ths case, utltes recevng free allowance allocatons cannot pass forward the opportunty cost of such allowances n hgher generaton prces. See Parry (2005) for more dscusson of these ssues. 12

15 trangle from the dstrbutonal analyss, as ths s small relatve to the frst order loss of surplus to households from hgher energy prces. 3. Parameterzaton of the Model Our baselne parameter assumptons are summarzed n Table 1. We focus on projectons for year All monetary fgures are expressed n year 2008 dollars (or thereabouts). Income dstrbuton. To obtan the ncome dstrbuton we use data from the Consumer Expendture Survey (CEX) for years 2007 and 2008, for households that completed ther year n the survey panel durng As s standard n ncdence analyss we dvde households nto quntles n two dfferent ways: based on ther pre-tax annual ncome and based on ther total consumpton. 14 To the extent that households are able to smooth consumpton over tme, the consumpton-based measure wll more accurately reflect lfetme ncome. Dstrbutonal dfferences are more muted when measured based on consumpton quntles than based on ncome quntles. Under ether measure, quntle 1 s the lowest 20 percent of ncome earners, quntle 2 the next lowest 20 percent, and so on. For smplcty, we assume the real ncome and real consumpton of each household group grows at the same 1.5 percent annual rate out to In 2020, ncome per household vares from $11,307 for the lowest ncome quntle to $181,626 for the top quntle, and consumpton vares from $19,253 for the lowest consumpton quntle to $126,173 for the hghest (Table 1). Budget shares for energy-ntensve goods. In the analytcal model, goods are ether energyntensve or non-energy ntensve. In the real world and n the data, goods vary wdely n ther energy (and thus carbon) ntensty. One could smply dvde goods nto energy-ntensve and non-energy-ntensve categores and assgn all energy-ntensve goods the same emboded carbon 13 The CEX uses a rotatng panel desgn: each calendar quarter, one fourth of the households n the sample are rotated out, so each household appears n the data for four quarters. To obtan a full year of data on each household that completed ts tme n the panel durng 2008 therefore requres usng data from both 2007 and Because ncome n the CEX s known to be poorly measured for low-ncome households, t s customary for ncdence studes to drop some very low-ncome households to mnmze the effects of that measurement problem. We follow the same approach as Granger and Kolstad (2010), droppng households wth reported ncome below $7,500, but not alterng the quntle cutoff levels of ncome and expendture as a result of droppng those households. 13

16 content and all non-energy-ntensve goods a lower or zero emboded carbon content. But gven the wde varaton n emboded carbon across goods, ths could ntroduce substantal naccuracy when measurng the dstrbutonal burden of a carbon tax. Instead, we estmate the total carbon emboded n all of the goods a household consumes, and then defne the consumpton of energy-ntensve goods n the model to be proportonal to that total. In effect, ths treats consumng a partcular good from the CEX as consumng some of the energy-ntensve good and some of the non-energy-ntensve good, wth the relatve proportons beng determned by the emboded carbon content of that good. We take the estmates of emboded carbon for goods n the CEX from Hassett et al. (2007), who calculate those estmates based on nput-output tables from the US Bureau of Economc Analyss. Stock ownershp. We calculate stock ownershp by aggregatng for each quntle the value of estmated market value of all stocks, bonds, mutual funds, and other such securtes reported by each household n the CEX. Accordng to ths calculaton, the top-ncome quntle owned 59.8 percent of stockholdngs, whle the lowest ncome quntle owned 2.6 percent. Stock ownershp shares are assumed to be the same n 2020 as n Household tax rates and transfers. Margnal and average rates of federal and state ncome taxes (accountng for the earned ncome tax credt and chld tax credts), and sales taxes, were obtaned by runnng each household from the CEX data for through the NBER s TAXSIM model, usng the tax laws for those years, and then aggregatng for each quntle. 16 We add to these employer and employee payroll taxes (based on statutory rates) to obtan the overall ncome tax rates (assumed to apply n 2020) shown n Table 1. Margnal tax rates vary from 0.17 for the bottom ncome quntle to 0.41 for the top ncome quntle and average (weghted by taxable ncome) Ideally, we would use nformaton on the pattern of stock ownershp across energy-ntensve frms (rather than all frms) to gauge the dstrbuton of rent ncome under grandfathered permts. However, ths s dffcult to obtan gven that most stocks are owned ndrectly through large nvestment frms. 16 These years pre-date the federal ncome tax cuts of 2001 and 2003, and thus wll approxmate the taxes that wll apply f those tax cuts are allowed to expre (whch seems ncreasngly lkely over tme, gven budgetary pressures). We feel ths provdes a better approxmaton to the tax laws n 2020 than would usng the 2008 tax laws. To the extent that ths over- or underestmates margnal tax rates n 2020, the magntudes of the revenue-recyclng and taxnteracton effects wll also be over- or underestmated. 14

17 Taxable ncome elastctes. Durng the last decade, a substantal number of papers have estmated the elastcty of taxable ncome wth respect to tax rates, both for the economy as a whole, and for hgh-ncome taxpayers. Although ntal estmates of ths elastcty were qute large (e.g., Feldsten 1999), more recent estmates are consderably smaller, n part reflectng better data and mproved methods of controllng for non-tax factors affectng changes n taxable ncome. Based on a careful revew of evdence for the Unted States and other countres, Saez et al. (2009) put the taxable ncome elastcty (for the economy as a whole) at 0.12 to 0.40, wth more estmates closer to the top end of ths range than the bottom. 17 Although we assume that all taxpayers have the same labor supply elastcty, hgher ncome taxpayers tend to have more scope for explotng tax preferences, so they tend to have hgher taxable ncome elastctes. We assume taxable ncome elastctes wth respect to tax rates vary between 0.2 for the low ncome quntle and 0.35 for the top ncome quntle, as shown n Table 1, where (weghtng by household shares n taxable ncome) the average elastcty s An ncrease n the general prce level (n response to carbon polcy) has a comparable effect on labor supply to a reducton n the real household wage that s, households substtute lesure for work, though ths s partly offset by an ncome effect n the opposte drecton. The effect on tax-preferred spendng should be small snce the prce of ordnary spendng does not change relatve to the prce of tax-favored spendng. 18 For the same reason, the change n taxable ncome n response to hgher lump-sum payments should be smlar to the change n labor earnngs. We therefore use standard values for the uncompensated labor supply elastcty, and ncome elastcty of labor supply, namely 0.15 and -0.2 (e.g., Blundell and MaCurdy, 1999), as proxes for! p and! I for all households. 17 One caveat here s that there s a slght msmatch between our representaton of the taxable ncome elastcty and emprcal estmates of that elastcty. In our model, ths elastcty reflects tax-nduced reductons n labor supply and shftng to tax-preferred consumpton, whereas emprcal studes summarze a broader range of responses ncludng shftng to tax-sheltered savng. Ths msmatch (whch we beleve s not too mportant for our purposes) s due to our characterzng the ncome tax system as a tax on labor alone, rather than a tax on both labor and captal ncome. 18 That s, although tax-preferred spendng wll fall n response to hgher energy prces the resultng effcency gan (due to offsettng the tax subsdy) s modest relatve to the effcency loss from the reducton n labor supply. Ths s because the market for tax-preferred spendng s small (about percent) relatve to the labor market. 15

18 Emssons reductons and prces. These are based on a polcy smulaton of representatve clmate blls reported n Krupnck et al. (2010) usng a varant of the Energy Informaton Admnstraton s Natonal Energy Modelng System (NEMS). NEMS s a dynamc, economcengneerng model of the economy, wth consderable detal on a wde spectrum of exstng and emergng technologes across the energy system. Its projectons are wdely used by other energy modelng groups. Wthout clmate polcy, ths model projects CO 2 emssons to be about 6 bllon metrc tons n The electrcty and transport sectors account for about 40 and 33 percent of these emssons respectvely, and other sources (.e., non electrcty emssons from the ndustral, commercal, and resdental sectors) account for the remanng 27 percent. Wth clmate polcy, energy-related CO 2 emssons are reduced by about 9 percent below busness-as-usual levels n 2020, or by 0.54 bllon tons, and the allowance prce s $33 per ton of CO 2 n current dollars (Krupnck et al. 2010). 19 Thus, the Harberger trangle, WC HT, s about $9 bllon and polcy rents, τz, are about $180 bllon. The carbon polcy ncreases energy prces n our model by 7.9 percent or the general prce level by 0.5 percent. 4. Results A. Cost Comparson Fgure 1 shows the overall cost of mposng a carbon polcy wth an allowance prce of $33 per ton of CO 2, under each of the four optons for the use of allowance rents: a proportonal ncome tax cut, lump sum rebates to households, free allocaton of permts to frms, and a dstrbuton-neutralzng tax cut. For ths last opton, the cost vares substantally based on whether the tax cut neutralzes dstrbutonal effects across ncome quntles or across consumpton quntles, so these are presented separately. Note that Fgure 1 provdes just an estmate of polcy costs: t does not ncorporate any estmates of the clmate benefts from lower CO 2 emssons. For each case, the fgure also shows the four components of welfare cost: the Harberger trangle term (the partal-equlbrum cost, gnorng any nteractons wth the tax system); the 19 Ths polcy run nvolves a more aggressve emsson reducton target, but allows domestc and nternatonal offsets (under an ntermedate assumpton about the avalablty of such offsets). Here we assume that the same emssons prce projected by ths run s mposed, but s appled only to CO 2 wth no offsets. In ether case, the reducton n domestc, energy-related CO 2 should be essentally the same. 16

19 revenue-recyclng effect (the gan from usng allowance rents to fnance tax rate cuts); the taxnteracton effect (the general-equlbrum loss resultng when hgher energy prces dscourage labor supply); and the ncome effect on labor supply (a further general-equlbrum loss as the ncome effect from the dstrbuton of polcy rents further dscourages labor supply). The Harberger trangle s the same across all the polcy smulatons ($8.9 bllon a year n 2020) as s the tax-nteracton effect ($25.0 bllon). However, the revenue-recyclng effect, n partcular, dffers across polces, as does the ncome effect on labor supply. When allowance rents are used to fnance a proportonal ncome tax cut, the overall cost of the polcy s -$6.4 bllon/year. Ths case yelds a strong double dvdend (Goulder, 1995): even gnorng the benefts of reduced carbon emssons, the cost of the polcy s stll negatve. As dscussed n Parry and Bento (2000), when certan categores of spendng are tax-favored, the gans from the revenue-recyclng effect are magnfed (relatve to a case wthout such tax preferences), but the losses from the tax-nteracton effect are approxmately unaffected. As a result, the revenue-recyclng effect (a gan of $41.3 bllon) exceeds the tax-nteracton effect, and by enough to more than offset the Harberger trangle. Ths qualtatve result s dfferent than n earler lterature that focused only on the labor market dstorton caused by the tax system (e.g., Goulder, 1995). In the latter models, the revenue-recyclng effect typcally falls short of the tax-nteracton effect and the overall costs of auctoned cap-and-trade systems (or carbon taxes) s postve, and exceeds the Harberger trangle. 20 The welfare cost of the cap-and-trade polcy s much hgher under ether the cap-anddvdend or free permt allocaton cases: under each of these optons the cost s roughly $50 bllon a year n By gvng away the permt rents, these two optons gve up the large gan from the revenue-recyclng effect ($41.3 bllon). In addton they produce a smaller, but stll sgnfcant, loss of $6.4 bllon (under cap-and-dvdend) or $11.6 bllon per year (under grandfathered permts) because the resultng lump-sum ncome to households reduces labor supply. Ths effect s stronger for the grandfathered permt case as hgher ncome households who face hgher margnal ncome tax rates receve a dsproportonately larger share of the polcy rents n ths case. The overall welfare cost of the cap-and-dvdend and grandfathered permt polces s over fve tmes the Harberger trangle, underscorng the bas n cost analyses 20 Smlarly, f tax preferences were entrely justfed by market falures then the revenue-recyclng effect would be smaller. In ths case, the overall cost of our proportonal tax cut case would be postve (roughly $15 bllon). 17

20 that omt nteractons wth the broader tax system. 21 Dvdng total costs by the CO 2 reducton (0.54 bllon tons) the average cost per ton reduced s around $90 under cap-and-trade, compared wth mnus $12 n the proportonal tax reducton case. Inflaton-ndexng of taxes and transfers n the above polcy cases requres revenue outlays of $30 bllon/year n 2020, or one-sxth of the polcy rents. The mpled ncrease n margnal tax rates to cover ths revenue loss adds $7.4 bllon/year to overall welfare costs. In the proportonal ncome tax case ths cost leads to a smaller overall gan from the revenue-recyclng effect, whle n the grandfathered permt and cap-and-dvdend cases (whch gve away the entre $180 bllon of polcy rents) t s reflected n a negatve revenue-recyclng effect. 22 The overall cost of the dstrbuton-neutral optons fall between the cost under the proportonal tax cut and the cost under the cap-and-dvdend polcy welfare costs are $9.9 and $22.6 bllon n the consumpton-based and annual ncome-based cases for measurng nequalty, respectvely. The dstrbuton-neutralzng tax change lowers tax rates rather than provdng a lump-sum transfer, so t generates a gan from the revenue-recyclng effect, whch causes the overall cost to be substantally lower than the overall cost under the cap-and-dvdend and grandfathered permts. However, because the tax cuts are larger for lower-ncome households (to offset the regressve ncdence of hgher energy prces), the margnal tax rate reductons and correspondng effcency gans from revenue recyclng are smaller than n the proportonal tax cut case. Ths effect s even more pronounced when nequalty s measured usng annual ncome rather than consumpton. In the former case, hgher energy prces are more regressve, requrng 21 These results mplctly assume that none of the permt rents are taxed under ether polcy opton. Ths s very lkely to be true n the cap-and-dvdend case. However, n the free permt allocaton case, the permt rents could well be taxed, at least n part. To the extent that these rents accrue to stocks held n taxable accounts (as opposed to retrement or other tax-sheltered accounts), they wll be subject to tax. Under ether polcy opton, f the rents are taxed, then the overall cost wll be a lnear combnaton of the cost under that polcy opton (whch assumes that none of the rents are taxed) and the cost under the proportonal tax cut (whch s equvalent to a case n whch all of the permt rents are taxed at a rate of 100 percent). 22 Note that because the tax system s ndexed such that tax rates depend on real ncome, the overall results both for effcency and dstrbuton do not depend on the partcular normalzaton used for prces (.e., the choce of numerare). However, the decomposton of those results nto nflaton ndexng and other components does depend on the prce normalzaton. We use a prce normalzaton that holds the pre-tax wage constant, so a rse n the prce of consumer goods relatve to labor shows up as an ncrease n the overall prce level, whch produces the nflaton ndexng results shown here. If nstead we were to use a normalzaton that holds the prce of consumer goods constant, that same relatve prce change would show up as a reducton n the pre-tax wage. In ths case, there would be no revenue cost for nflaton ndexng, but nstead there would be a reducton n ncome tax revenue resultng from the lower wages. Thus, the overall effect would be the same, but the decomposton of that effect between nflaton ndexng and other effects on revenue would dffer. 18

21 an even greater concentraton of tax cuts among lower ncome households. Thus, the revenuerecyclng gans are $15.8 bllon n ths case, compared wth $25.7 bllon when nequalty s measured usng the consumpton approach. B. Dstrbutonal Effects Fgures 2 and 3 summarze the dstrbutonal burdens of the dfferent polces across ncome quntles, based on ncome and consumpton quntles, respectvely. Burdens are expressed as a percent of household ncome. In addton, the net burden s decomposed nto the burden of the hgher energy prces caused by the cap-and-trade program; the gan to households resultng from nflaton-ndexng of the tax and transfer system; any gan from reductons n margnal ncome tax rates; and possble gans from permt rents or lump-sum dvdends. 23 All polces mpose the same pattern of burdens across households due to hgher energy prces. Ths burden component falls wth ncome for example, the bottom quntle bears a burden of 6.0 percent when nequalty s measured on an ncome bass, fallng steadly to 1.2 percent for the top quntle. Lower ncome groups spend a greater fracton of ther ncome on energy-ntensve consumpton. One reason for ths s that energy-ntensve goods make up a slghtly larger share of spendng for lower-ncome households. Another s that lower-ncome households spend a larger fracton of ther ncome due to lower or even negatve savng rates (on average lower ncome households spend more than ther ncome). Dvdng households nto consumpton quntles rather than ncome quntles greatly reduces ths second effect, and hence the dstrbutonal burden s consderably less regressve when measured based on consumpton quntles. In ths case, the bottom quntle bears a burden of 3.3 percent whle the top quntle bears a burden of 1.5 percent. Inflaton-ndexng of the tax and transfer system provdes an automatc offset for part of the burden of the polcy and agan the pattern of ths gan across households s the same across polcy scenaros. As the prces of energy-ntensve goods rse, nflaton-ndexng causes an ncrease n transfers (or decrease n taxes pad, for ndexng of tax brackets and other elements of the tax system). Averaged across all households, the beneft from nflaton ndexng s about The results dscussed below are broadly consstent wth those n Burtraw et al. (2009) who look at the ncdence of federal cap-and-trade polces under alternatve revenue uses usng a model wth consderable dsaggregaton by households and regon. 19

22 percent of ncome, or about one-seventh of the average burden from hgher energy prces (1.9 percent). The porton of the burden of energy prces offset by nflaton ndexng vares relatvely lttle across ncome quntles for example, t offsets roughly one-seventh of the burden for the bottom quntle, about one-ffth for the mddle, and one-eleventh for the top quntle. 24 For the proportonal ncome tax case (Fgures 2a and 3a), by defnton the gans from the tax cut are the same for each quntle, roughly 1.7 percent of ncome for each group. The overall net burden under ths polcy as a percentage of ncome s hghest for the bottom quntle and falls steadly as one moves up the ncome dstrbuton, gven that revenue-recyclng does nothng to offset the regressve effect of hgher energy prces. For ncome-based quntles the net burden vares between 3.5 and mnus 0.6 percent across the lowest and hghest quntles, whle for consumpton-based quntles t vares from 1.2 to mnus 0.3 percent. For the cap-and-dvdend polcy (Fgures 2b and 3b) the dstrbuton of the polcy dvdend s hghly progressve, gven that all households receve the same absolute cash rebate. As a result, even though the overall cost of ths polcy s much hgher than n the proportonal ncome tax cut case, the bottom three quntles experence smaller net burdens under cap-anddvdend. In fact, the bottom two quntles actually have a negatve net burden (under ether ncome- or consumpton-based quntles). Ths llustrates the stark tradeoff between effcency and dstrbuton: lower-ncome groups are much better off under cap-and-dvdend than they are under a proportonal ncome tax cut, but the overall welfare cost of the polcy s dramatcally hgher. The polcy wth free allowance allocaton to frms (Fgures 2c and 3c) does nothng to offset the regressve effect of hgher energy prces n fact the dstrbuton of rent ncome s tself regressve, for the most part, gven that for better off households captal s typcally a larger share of ther ncome. Comparng ths case to ether the proportonal ncome tax cut or the capand-dvdend case reveals no tradeoff between effcency and dstrbuton. Freely allocatng permts to frms results n a smlarly regressve dstrbuton of net burden to the proportonal ncome tax case, but a much hgher overall cost because t fals to explot the revenue-recyclng effect. In fact, every ncome quntle s better off under the proportonal ncome tax cut than 24 For reasons analogous to those dscussed n footnote 22, above, the net burden on each quntle s ndependent of the choce of prce normalzaton. But the decomposton of that net burden nto nflaton ndexng and other components does depend on the normalzaton. 20