Environmental Tax and the Distribution of Income among Heterogeneous Workers

Transcription

1 Envronmental Tax and the Dstrbuton of Income among Heterogeneous Workers Mrelle Chroleu-Assoulne, Mouez Fodha To cte ths verson: Mrelle Chroleu-Assoulne, Mouez Fodha. Envronmental Tax and the Dstrbuton of Income among Heterogeneous Workers. Annales d Econome et Statstques, 20, pp <hal > HAL Id: hal Submtted on 6 Dec 20 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Envronmental Tax and the Dstrbuton of Income among Heterogeneous Workers Annales d Econome et de Statstque, n 03-04, July-Decembre 20, pp Author Verson Chroleu-Assoulne, Mrelle Pars School of Economcs - Unversty Pars Panthéon-Sorbonne Fodha, Mouez Pars School of Economcs - Unversty Pars Panthéon-Sorbonne Abstract: Ths paper analyzes the envronmental tax polcy ssues when labor s heterogeneous. The objectve s to assess whether an envronmental tax polcy could be Pareto mprovng, when the revenue of the polluton tax s recycled by a change n the labor tax propertes. We show that, dependng on the heterogenety characterstcs of labor and on the ntal structure of the tax system, a polcy mx could be desgned n order to leave each class of workers unharmed. It conssts of an ncrease n progressvty together wth a decrease n the at rate component of the wage tax. * JEL class caton: D60 - D62 - E62 - H23. * Keywords: Envronmental tax - Heterogenous agents - Welfare analyss - Tax progressvty.

3 I. Introducton One of the most publcly debated ssues about envronmental regulaton concerns ts e ects on the poorest agents and the farness of such a polcy. Ths queston s beng rased agan because of the relatve falure observed untl now of the emssons tradng system chosen as an nstrument for the Greenhouse Gases (GHG) regulaton, whch explans the emergence of some new arguments n favor of a carbon tax. What would be the nequalty consequences of the European Carbon Tax Project or of the Clmate-Energy Contrbuton planned by the Grenelle de l envronnement n France? How could these consequences be smoothed or even elmnated? More generally, how s t possble to mplement an envronmental tax wthout nducng further nequaltes? The economc lterature does not contrbute much to ths debate and our paper ams to ll the exstng gap. The stll open queston Can an envronmental tax reform be desgned wthout negatvely a ectng the economc welfare? has gven rse to a huge lterature on the double dvdend. Terkla [984], Parry [995], or Poterba [993] rst had the ntuton that the recyclng of the revenue of an envronmental tax could reduce or even elmnate the gross cost of ts mplementaton. As governments use the revenues from polluton taxes to decrease other dstortonary taxes, envronmental taxes may lead to a double dvdend, accordng to Goulder s de nton, by mprovng the envronmental qualty and achevng a less dstortonary tax system (Goulder [995]). Baumol and Oates [988], Pearce [99] and Oates [99] suggested that these e cency gans could be a powerful argument n favor of envronmental taxaton. After some pror refutatons of the double dvdend hypothess (Bovenberg and de Mooj [994] and ther followers), Goulder [995] and Lgthart [998] showed that the exstence of the double dvdend essentally depends on the possblty of transferrng the global tax burden from the wage earners to some xed producton factors or to other consumers, thus emphaszng the role of heterogenety. Followng ths lne, Chroleu-Assoulne and Fodha [2005] and [2006] studed the exstence condtons of a long term double dvdend, takng nto account the dstncton between wage earners and retred consumers, by means of OLG models. Surprsngly enough, although ths large body of lterature has deeply analyzed the double dvdend ssue, t has neglected the dstrbuton ssue of the welfare gan, although t s usually obtaned at the expense of some groups of agents. It s well known that the costs and bene ts of envronmental polces are unequally dstrbuted among agents. The 2

4 rch and the poor seem to assgn d erent degrees of prorty to envronmental protecton (Baumol and Oates[988]), snce wealther ndvduals would accept payng for a hgher level of envronmental qualty (consdered as a normal good). Beyond ths fact, dstrbutve elements also matter when we consder how the costs of a polcy of envronmental protecton are lkely to be dstrbuted among ndvduals wth d erng ncomes. Most exstng studes are emprcal works dealng manly wth the dstrbuton of the bene ts of the envronmental polces among ncome classes (Chrstansen and Tetenberg [985], Ellott et al. [985], Harrson [995], Peskn [978]), and neglectng the cost sde of the polces. One can nfer from some emprcal studes emphaszng the regressvty of the ndrect taxes, that any envronmental polcy s lkely also to be regressve. In partcular, n the French case, a tax on energy or transport consumpton harms the lowest wage households three tmes more than the hghest wage households (Ruz and Trannoy [2008]). Moreover, the usual recyclng of the envronmental tax revenues through a decrease n the labor tax rate could also be regressve (Metcalf [999]). Ths pont s of nterest n a world n whch nequalty has assumed hgh prorty among socal ssues. Polces and programs that are perceved as unfar wll stand lttle prospect of passage even f they enhance the prospects for e cency and sustanablty. Is t then possble to desgn an envronmental polcy n order to ensure a non-decreasng welfare for each class of workers? Compared to the standard double dvdend lterature whch pursues two objectves n a second rank framework - mprove the envronment by ncreasng an envronmental tax ( rst dvdend) and the economc welfare by decreasng another dstorsve tax (second dvdend) - we add the thrd objectve of Pareto mprovement. It corresponds to an acceptablty/unanmty crteron for the polcy when agents are heterogenous. Three nstruments are consequently needed: we argue that the dstrbutve propertes of the tax polcy could be one of the nstruments of far nternalzaton of the envronmental externaltes. The am of ths paper s therefore to desgn a balanced envronmental tax reform able to correct these regressve propertes of taxes and to leave all classes of worker better o. We assume captal-ntensve sectors to be pollutng sectors. To keep thngs smple, as we deal only wth a one sector aggregate output, we assume that captal nput s the man In lne wth the double dvdend lterature, we are not seekng for the optmal tax system, whch would requre to use several nstruments n order to nternalze the externaltes. Nevertheless, accordng to our Pareto-mprovng crteron, our results gve condtons such that the economy gets closer to ts Pareto optmal equlbrum. 3

5 source of polluton (even f t s only a proxy). The key factor s that captal accumulaton favors the producton of polluton-ntensve goods. For ndustral polluton, ths s consstent wth evdence (Brown et al. [992], Gale and Mendez [998], Antweler et al. [200]). Indeed, Brown et al. [992] show that a 0% change n the Mexcan captal stock nduces a 9% ncrease n electrc utlty output. The concluson they draw s smply that electrcty generaton s hghly captal ntensve, and ths creates a strong lng between captal accumulaton and sulfur doxde polluton. In the same way, the emprcal work of Gale and Mendez [998] nvestgate the role that captal abundance may play n predctng cross-country d erences n polluton levels. It suggests a strong lnk beween factor endowments and polluton level. Fnally, Antweler et al. [200] nd that a % ncrease n a naton s captal-to-labor rato, holdng scale, ncome, and other determnants constant, leads to perhaps a one percentage pont ncrease n polluton. Our model shares the mean features of Chroleu-Assoulne and Fodha [2005] and [2006]. As n Chao and Peck [2000] or Wllams [2002] or [2003], we assume that the degradaton of envronmental qualty has a negatve mpact on the total productvty of factors. Ths assumpton s just ed by the results of an ncreasng number of emprcal studes measurng the health e ects of polluton (OECD [2008]) and the mpact of the health of workers on labor productvty (Bloom et al. [2004], n a sample consstng of both developng and ndustral countres, found that good health, proxed by lfe expectancy, has a szable, postve e ect on economc growth). Snce Ostro [983], many papers have emphaszed the loss of productvty caused by the health e ects of polluton, e.g. Samakovls et al. [2005], or Pervn et al. [2008] for ar-polluton, and also Bosello et al. [2006] or Hübler et al. [2008] for the health e ects of clmate change. For example, accordng to Bosello et al. [2006], strong heat stress causes a productvty loss of 3% and extreme heat a loss of 2%. Another source of productvty loss orgnates n the mpact of polluton on the qualty of natural resources (Gollop and Swnand [998] for the agrcultural sector) 2. We assume that the producton technology s a functon of captal and heterogeneous labor. Heterogeneous workers lve two perods (young and old) and earn wages correspond- 2 Our model adresses the spec c ssue of pollutons due to ndustral, hghly captal-ntensve sectors, that emt ne partcles, NOx or SOx. These pollutants are harmmful for the health of all agents, and especally of the workers employed by these sectors. As an anonymous referee ponted out, ths stylzed model can not descrbe the GHG case, snce the doxyde emssons have no drect e ect on the health and productvty of workers and they are due to the use of fossl energes whch can be susbstuted by carbon free nputs, such as captal or knowledge. 4

6 ng to ther skll and consequently to ther productvty. The labor tax s a very general one that could be ether a progressve or proportonal tax. Our demographc assumptons allow us to take nto account several ncome classes; ndeed, we consder () the heterogenety characterstcs of the labor market (hgh wages - sklled workers, mddle wages, low wages - non sklled workers...), () the heterogenety of the ndvdual ncome sources (wages for workers, savngs for retrees). The envronmental polcy conssts of ncreasng the envronmental tax on savngs, n a second-rank framework. We then characterze the necessary condtons for the obtanng of a double dvdend,.e. an mprovement of the envronmental qualty and an mprovement of the welfare when the revenue of the polluton tax s recycled by a change n the labor tax rates. Prevous studes show that the obtanng of a double dvdend requres economc condtons such that the double dvdend hypothess seems unrealstc. Conversely, we show that the condtons for the obtanng of a double dvdend le n the dstrbutve propertes of the labor taxes. Even when the double dvdend s not possble, the cost of the polluton regulaton can be mnmzed by a new desgnng of the progressvty of the labor tax nstead of an homogenous cut n the labor tax rates. The results are dependent on the ntal tax system. The paper s organzed as follows. Secton 2 presents the model and Secton 3 presents the welfare analyss of a tax polcy. tax reform. Secton 4 gves the spec caton of the balanced In Secton 5 we present the envronmental e ects of the tax reform and Secton 6 examnes the welfare e ects of such a reform. Secton 7 presents some emprcal llustratons and the last secton concludes. II. The Model We consder an overlappng generatons economy wth pollutng technology of producton.e. wth pollutng captal. Heterogeneous workers lve two perods (young and old) and earn wages correspondng to ther skll and consequently to ther productvty 3. We assume that N t ndvduals are born n perod t and that the populaton remans constant, so we can normalze N t to unty. Each household s characterzed by ts labor class (or skll). There are I classes of agents n the economy ( and I 2 N), and the sze of each 3 In our very stylzed model, the heterogenety of workers derves, by assumpton, from ther sklls. In our case, because the utlty functon s logarthmc, ths model s equvalent to a model wth endogenous work supply and heterogenous desutltes of work. We thank an anonymous referee to have drawn our attenton to ths equvalence. 5

7 class s equal to q (wth P I = q = ). Each agent supples one unt of labor 4 when she s young and earns a wage w t; she dvdes her labor ncome between consumpton and savngs s t. The sub-optmal ntal tax system s composed by an ncome tax and an envronmental tax ntended to nance the publc expendtures G: The ncome (or labor) tax s a very general one that could be ether a progressve or proportonal tax as the labor tax rate s 2 [0; [. In the second perod the household consumes her savngs and the nterest she earns. The welfare of an ndvdual born at t s measured wth the ntertemporal separable utlty functon 5 : wth c y t U c y t ; co t+ = ( ) ln c ;y t + ln c ;o t+ denotng the rst-perod consumpton of the agent born at t, c o t+ her secondperod consumpton. 2 ]0; [ represents the ndvdual propensty to save. The two nstantaneous components of the utlty functon obvously exhbt the usual propertes: they are ncreasng n ther argument, strctly concave and satsfy the Inada condtons. The real nterest rate s r t+. As the captal s pollutng, the envronmental polcy conssts n a tax on savngs e 2 [0; [. The household s budget constrants wrtes: t w t = c y t + ( + e t ) s t c o t+ = ( + r t+) s t () The household s problem s to choose her consumpton path to maxmze her lfetme utlty subject to the ntertemporal budget constrant. Ths yelds the optmal consumpton and savngs path of the representatve household, wthn the Damond framework (Damond [965]) wth a homothetc utlty functon: 8 c y t = ( ) t w t >< c o t+ = ( + r t+) ( + e t ) t w t (2) >: s t = t ( + e t ) w t 4 Our long term vew allows us to assume full employment. Moreover, we focus on the e cency double dvdend (accordng to Goulder [995]) and not on the employment double dvdend. 5 We do not ntroduce any drect e ect of polluton on the household s welfare, but only the ndrect one through the consequences on productvty of the degradaton of envronmental qualty (see below). Indeed the drect e ect would have no mpact on the welfare dstrbuton among heterogenous agents whle the ndrect one a ects the wage gaps, because agents do not d er here by ther preferences. 6

8 The producton sector conssts of many rms, each of them beng characterzed by the same Cobb-Douglas producton functon F () wth constant returns to scale. They use d erent knds of labor (hgh wages - sklled workers, mddle wages, low wages - non sklled workers) and the total productvty of factors A (P t ) s negatvely a ected by polluton P t because polluton degrades the health of workers or the qualty of natural resources (A (P ) = P e wth e > 0): Y t = A (P t ) F (K t ; L ;t ) = A (P t ) K t where > 0 and 0 stand for the shares of the nput factors n producton, + =. The maxmzaton problem of the representatve rm s (takng the output prce as numerare): Max K;fL g t = A (P t ) K t IY = L ;t IX wtl ;t = IY = L ;t ( + r t ) K t wth t the current net revenue, w t the real wage rate of class of workers. The deprecaton rate of captal s equal to unty. Snce markets are compettve, captal and labor earn ther margnal products: 8 Y t >< = + r t >: K t Y t L ;t = w t Ths yelds, at the equlbrum of the labor markets: The rato of wages s (usng 3): Y t = A (P t ) K t wt wt IY = = q q (3) q (4) Assumpton : The d erent labor classes are ranked by growng sklls,.e. by growng wages: w t > w t, q > q 7

9 We assume that government spendng (G) s entrely nanced by current taxes. The government s budget constrant states that, at each perod, ts purchases must be equal to ts tax revenues generated by the polluton tax and the labor tax: IX q twt + e t = IX q s t = G t (5) = We de ne a progressvty ndex of the labor tax, a = ab(), such as: = + a = + ab () where s the at component of the tax rate and a s a postve parameter. Assume b() = 0 and b(+) > b() 8 > : We consder the general case for the characterstcs of the tax progressvty 6. For example, the desgn of progressvty ts well the characterstcs of the French tax system when b( + 2) b( + ) < b( + ) b(): Ths yelds! IX IX IX q w = Y = Y ( ) + a b() = = = P Let us de ne B I as the sum I b (). B I > 0 s constant for any gven I and = progressvty characterstcs fb()g I. The polluton ow s due to the captal stock, and we assume that the welfare s a ected by the stock of polluton only through ts e ect on the total factor productvty. The dynamcs of polluton are descrbed by the followng equaton: P t = ( h) P t + K t (6) where h s the constant rate of natural absorpton of polluton (0 < h < ) and > 0 stands for the emsson rate of pollutants. The equlbrum condton of the captal market, meanng that the captal stock n perod t+ s the amount saved by young ndvduals n perod t, s obtaned by substtutng 6 Unlke the usual spec caton of the tax progressvty n the lterature, we assume here that depends on the class of the agent and do not depend drectly on the wage w : As assumpton mples a rankng between and w, our de nton of the tax progressvty s nearly, but not exactly equvalent to the usual one, snce t reles here on an ordnal concept rather than on a cardnal one, as usual. 8

10 the zero-pro t condton, the government s budget constrant (eq. 5) and the household s budget constrants (eq. ) nto the equlbrum of the output good market. It wrtes: K t = IX q s t = By substtutng eq. 2: K t = + e t q t ( ) abi w t (7) and usng eq. 3, we nally obtan: K t = + e t t ( ) abi Yt (8) The steady-state A steady state equlbrum s an allocaton where captal and polluton are statonary,.e. K and P are such that (usng eq. 6 and by substtuton of eq. 4 n eq. 8): " K IY = + e XA (P ) = q # (9) P = h K (0) wth X = ( ) ab I, constant for a gven tax system. It s easy to verfy that X s always strctly postve, whch ensures the exstence of a postve steady-state equlbrum. X > 0 reduces to b (~{) < a where ~{ s the partcular class of worker 7 such that b (~{) = I b() I. Hence b (~{) s the average of the coe cents of progressvty, weghted by the shares of each class of worker n the output. X > 0 s then equvalent to ~{ = + ab (~{) <, meanng that the revenue of ths partcular class s not totally con scated. Ths s always ver ed snce we assumed that < 8. The followng proposton characterzes the steady state of ths model. 7 More precsely, b (~{) I b() I and b (~{ ) < I b(), wth ~{ I. I 9

11 Proposton For gven ntal condtons fk 0 ; K ; P g and for a gven trplet of tax polcy nstruments, e ; ; a, the equlbrum condtons can be summed up by eq. (2) ; (3) ; (5) ; (6) ; (8). Thus, there exsts a locally stable steady-state de ned by (K ; P ) such that: K = P = h + e X + e X ( e) ( e) " h e " h IY = e q IY = # ( e) q # ( e) Proof. See above for the de nton of the captal market equlbrum. Moreover, () the utlty functon s homothetc, () the utlty and the producton functons verfy the Inada condtons, () F 00 K < 0, (v) lm K!0 (FK 0 :K=F (K)) 2 [0; [. Condtons () () (v) ensure the exstence of the steady-state equlbrum (see de la Crox and Mchel [2002] and Konsh and Perera-Tallo [997]). Concernng local stablty, we show that the steady state assocated wth the dynamc system, (6; 8), s a snk (see Appendx). Usng Proposton and eq. equlbrum: Y = Assumpton 2: e > 0: + e X 9, one obtans the output value at the steady-state e ( e) " h e IY = q # ( e) It means that the drect contrbuton of captal to output () s greater than the ndrect one through polluton and productvty (e) 8. In the rest of the paper, we wll only consder the consequences of varatons of the tax rates on the steady-state equlbrum de ned n Proposton. The exstence of the new steady-state s ensured f and only f X remans postve,.e. ~{ + d ~{ <. Notce that X may reman postve even f some hgh wages classes bear a tax rate equal or greater than unty. A su cent condton to ensure the postvty of X after the tax reform s that dx > 0,.e. that the varatons of the labor tax components verfy III. Welfare Analyss (2) da < d B I, 8d e > 0. 8 The reverse ( < e) would smplfy the analyss but ths case would be of neglgble economc nterest because any rse n e would result n a decrease of K allowng an ncrease of Y. 0

12 Lke Chroleu-Assoulne and Fodha [2006], we examne here the welfare e ects of the tax change for a generaton durng ts lfe-cycle, once the nal steady-state equlbrum s reached. In ths secton, the welfare ssue s thus a long term one. One can measure the welfare e ects of small tax changes by the margnal excess burden. It corresponds to the addtonal ncome that needs to be provded to the representatve household to keep her utlty at ts ntal level: ths s the compensatory ncome varaton, denoted dr. It stands for the excess welfare loss of the consumers over and above the tax revenues collected by the government and can be nterpreted as the hdden costs of nancng publc spendng: a postve value for the margnal excess burden ndcates a loss n welfare after the tax reform. Let us determne the compensatory ncome varaton whch, after the tax reform, would leave the level of lfe-cycle utlty unchanged (du y dcy o dco = 0 ( + r) ( + e ) dcy + dc o = 0 The ntertemporal budget constrant of household wrtes: Remember that w = c y + ( + e ) ( + r) co c o ( + r) = ( ) ( + e ) cy We use the rst-order condtons of the representatve household s program and the de nton of the compensatory ncome varaton dr: dw w d + b () da + dr = d^c y ^c o ths leads to: = ^co 2 dr + ( + r) ( + r) d e + ( + e ) + r d^co ( + e ) ^c o ( + r) 2 dr + ^co ( + r) d e dr = dw + w d + b () da ( + e ) ^c o ( + r) 2 dr + ^co ( + r) d e (3) Unlke Bovenberg and de Moj [994] and the greater part of the lterature on ths subject, t s here mpossble to dstngush an envronmental component and a nonenvronmental one, because polluton and producton a ect each other. In ths paper, we

13 are thus constraned to depart from the usual de nton of the double dvdend (Goulder [995]) because of ths non-separablty: a double dvdend wll be characterzed by the smultaneous decrease of polluton (whch stands for the usual rst dvdend) and ncrease of economc welfare (whch depends here also on the polluton level). The ncrease of welfare s ver ed for any varatons of consumptons such that dc y =c y + ( )dc o =c o > 0. Ths property plays an mportant role n our results. The rst dvdend requres a decrease of the captal stock nducng a decrease of the output, but ths does not prevent the obtanng of the economc dvdend. Ths orgnates n the opposte mpacts of dk on w and r: dw=dk > 0 and dr=dk < 0. Proposton 2 The ncrease of the envronmental tax s regressve.e. t more heavly penalses the lowest wage-earners. Proof. Let us compute the steady-state value of the compensatory ncome varaton for agent : dr q Y = Z ( + e ) d e (4) + (Z ) + (Z ) B I X + ( ) X + b () ( ) ( d ) da wth Z = e ( e) > 0. Notce that from the optmalty condtons of the rm (eq. 3) and the equlbrum condton of the labor market, we have Y = w. Hence, when d = da = 0, one obtans, for q any envronmental tax ncrease d e > 0 : dr w = Z ( + e ) d e > 0 then, as Z > 0, dr > 0 for every. But dr =w s smaller when s hgher (.e. s also hgh) and when w s hgher. When the envronmental polcy harms the consumers, the relatve burden s greater for the less sklled 9. 9 Ths result does not rely on the usual channels causng the regressvty of an envronmental tax. Indeed, as preferences are dentcal among agents, ther savngs rate and ther budget share for pollutng goods are the same. Our regressvty property results from the progressvty characterstcs of the labor tax. 2

14 The consequences of the ncrease of the envronmental tax e are clearly harmful for all the agents as t mples a decrease of the second-perod consumpton wthout any postve e ect on the rst-perod one. Concernng the labor tax, ts mpact s ambguous, for the at component as well as for the progressvty ndex. Ths s because the decrease of the ncome of the agents could be compensated by an ncrease of the nterest rate rasng the consumpton of the old agents. Ths latter e ect ncreases wth. IV. The Spec caton of the Balanced Tax Reform We assume an exogenous ncrease of the envronmental tax rate, mposed by the government n order to control polluton. The amount of government spendng s assumed ex post nvarant, and the tax polcy has to mantan the amount of the tax revenues constant 0. Ths ncrease d e of the envronmental tax rate can be accompaned by a varaton of the labor tax rates d by two potental means: a homogenous varaton of all labor tax rates through the at rate component (d ) or a varaton n the progressvty of the labor tax (da through a varaton of a). At the steady-state equlbrum, the government s budget constrant s: ( ) + ab I Y + e K = G The lnk between the varatons of the polluton tax and of the characterstcs of the labor tax s obtaned through the d erentaton of ths constrant, whch s qute drect (usng eq. 2). Any balanced tax reform s then characterzed by the followng relatonshp between d e, d and da (wth dg = dq = d = 0): where = ( ( ) d + B I da = ( + ) ( + ) X d e + e (5) ) + ab I + K Y ( e) e Z X 0 (wth X > 0), constant. 0 As notced prevously, ths tax reform does not consttute the optmal one. Seekng for optmalty would requre to take nto account the ntergeneratonal externalty on captal accumulaton (dynamc e cency) and the envronmental externalty. These two externaltes would be corrected by the use of our two taxes. Concernng the dstrbuton of welfare among the agents, we have to consder ntergeneratonal and ntrageneratonal characterstcs. Intergeneratonal optmalty consderatons turn to the very general debate about the choce of the dscount rate. But n our very smple model, the heterogenety of workers s not an externalty and would not deserve any correcton. Intrageneratonal welfare would be the sum of the welfare of each class weghted by ts sze. 3

15 We wll study two polar cases for balancng ths envronmental tax reform: unform varaton of all labor tax rates, wth nvarant progressvty (da = 0): d = ( + ) ( + ) X d e ( ) + e = d e (6) varaton of the progressvty, wth nvarant at rate component of the tax rate (d = 0): da = ( + ) X d e ( + ) B I + e = d e (7) Proposton 3 The sgn of the balanced tax reform multplers and s a pror undetermned and depends on the ntal tax rates and on the values of the varous elastctes. Proof. () The numerator measures the e ect of the change n polluton tax rate on ts revenue. There are both a value e ect (the tax revenue ncreases wth the tax rate, for unchanged stock of captal), summed up by, and a tax base e ect (the stock of captal decreases, and so does the output; as the tax rate ncreases, so the tax base erodes), condtoned by, whch work n opposte ways. As a result, ths term mght be postve (f > ) or negatve. () The denomnator measures the e ect of the change n labor tax rate on ts revenue. There are also both a value e ect proportonal to (the tax revenue ncreases wth the tax rate, for unchanged wages) and a tax base e ect (the wages decrease as the tax rate ncreases, thus the tax base erodes) whch work n opposte ways. As a result, ths term too mght be postve or negatve (f > ). As the sgns of the numerator and of the denomnator are undetermned, the sgn of the necessary change n the labor tax components s also undetermned. Assumpton 3: We only consder the La er-e cency case, where the sgn of the balanced tax reform multplers and s postve. Under eq. 5, Assumpton 3 mples + + > 0, > or <. V. The Envronmental E ects of the Tax Reform As steady-state polluton depends only on steady-state captal, we nd straghtforward that the rst dvdend (:e: a decrease of polluton) s reached f dp = h dk < 0: Ths 4

16 condton rewrtes (see Proposton ): dk K = d e ( e) + e + ( ) d + B I da < 0 X d e As ( e) > 0, ths condton reduces to + e + ( ) d + B I da X have the two cases correspondng to the two alternatve polces: > 0: We then nvarant progressvty (da = 0) : varaton of the progressvty d = 0 : d e ( ) d e > + e X d e + e > B Id e X : We obtan a rst dvdend f the multplers are not too hgh: 8 >< >: < X ( + e ) ( ) X < ( + e ) B I () + + < (8) Ths means that the decrease of the labor tax (ether of the at rate component or of the progressvty ndex) should be not too great n order not to jeopardze the envronmental bene t of the reform. Assumpton 4: We only consder the case where the tax polcy decreases polluton. Proposton 4 Under Assumptons (-4), the tax polcy s e cent and reduces polluton f and only f the ntal envronmental tax rate s not too hgh: e < =Z. Proof. We have to examne the two cases whch verfy the tax e cency assumpton (Ass. 3). If () : < ; then + <, > : whch con cts wth the basc assumpton on + : The envronmental bene t can never be acheved. If () : < ; then + <, < : always ver ed. + Fnally, such that to reach the rst dvdend under the tax e cency assumpton, one needs to mpose < ; whch s a necessary and su cent condton. Ths condton s met f and only f: ( ) + ab I + + e X ( e) e Z X <, ( ) + ab I + e + e X ( e) < X Z 5

17 whch mples e + e X ( e) < X Z, ( e) < + e, e < ( e) e QED. VI. The Welfare E ects of the Tax Reform As each polcy does not a ect all classes equally, one can wonder whch one wll be preferred by each class of worker. Proposton 5 () The envronmental tax reform preferred by the workers of the lowest classes conssts of a decrease n the at rate component of the tax rate () but the one preferred by the workers of the hghest classes conssts of a decrease n the progressvty of the wage tax rate. Proof. Let us compare the compensatory ncome varatons assocated wth each polcy. Frst case (dr( )): unform varaton of all labor tax rates (wth nvarant progressvty): da = 0 and d = d e dr( ) q Y = Z ( + e ) d e (Z ) X ( ) + ( ) d e Second case (dr(a) ): varaton of the progressvty (wth nvarant at rate component): d = 0, da = b () da and da = d e dr(a) q Y = Z ( + e ) d e (Z ) X B I + b () ( ) d e 6

18 Agents prefer da < 0 0 % b() Agents prefer < 0 Fgure : An Illustraton of Workers Class Threshold n the French Case The sgns of these compensatory ncome varatons depend on the values of the characterstcs of the economy (, e, b(), ) and of the ntal tax rates ( e,, a). We now compare the relatve e ects on welfare of the two tax polces. Consequently, we have to determne the sgn of = dr( ) dr(a) for the workers of class. q Y = (Z ) X ( ) (Z ) + + X B I + b () T 0 Usng eq. 6 and 7 ( = B I ), we nd that ths sgn s equal to the sgn of: b () B I = b () b () Therefore the partcular average workers class ~{ de ned above s nd erent between both polces ( ~{ = 0). Each class of workers of a hgher skll would prefer a decrease n the progressvty ndex, da < 0, and, conversely, each less sklled class of workers would prefer a decrease n the at rate component of the wage tax, d < 0 (Fgure correspondng to the French case of a progressve labor tax). The result above suggests that, n the case where some workers classes would be sufferng from a deteroraton of ther welfare after the above tax reforms, an approprate In order to smplfy the graphcs (especally Fgure 3), we have chosen to plot gures as f all functons were contnuously de ned over a great number of workers classes. 7

19 polcy mx could be desgned n order to leave each workers class unharmed by the envronmental tax reform : t would consst n an ncrease of the progressvty ndex together wth a decrease of the at rate component of the wage tax rate. Assume that the balanced tax reform s de ned by d < 0 and da = d wth > 0 hence da > 0. Such a compensaton for the ncrease n the envronmental tax rate wll mply a greater decrease of than above because the degree of progressvty s rased. Proposton 6 For economes where a decrease n the mnmal wage rate does not su ce to re-establsh the welfare of some class of worker, one can choose n order to ensure that all classes wll be better o wth the envronmental tax reform. Proof. Let us specfy the lnk mpled by such a polcy between the ncrease n the envronmental tax rate and the decrease n the at component of the wage tax. d e = d da = d = d To ensure the exstence of the new steady-state equlbrum, we have shown above (Ass. da 2) that we need = < d B I. Ths condton also ensures the decrease of the at rate component of the labor tax. The compensatory ncome varaton of the balanced mx polcy s: dr() " " q Y d e = dr q Y d e + B I wth Z > 0; X > 0; constants. B I (Z ) B I X + b () B I Z ## ( + e ) - dr() S 0; 8 = ; :::I: - dr () s not monotonous n b (), nor n, 8. - If dr( ) < 0; 8 = ; :::I, all classes wll be better o even wth = 0: If 9; dr( ) > 0; as the functon dr () s bound for each, there s one { whch maxmzes t (see Fg. 2 for a smple llustraton): h { = INT arg max dr() 8

20 dr = µ =3 =2 =4 =5 =6 =7 Fgure 2: An Illustraton of the Polcy-Mx Crteron One can choose > 0 n order to nullfy dr { () : t ensures that all classes wll be better o (ther compensatory ncome varatons are all negatve or null). Z ab ({) h ( + e ab ({) (Z ) ) = " B I Z ab ({) ( + e ) ( ) X + (Z ) B I X ( ab ({)) b ({) # Ths polcy mx ams to reduce the pre-exstng dstortons of the tax system, n a second-best world, but not to reach an optmal outcome. Therefore comes from our Pareto-mprovng crteron but not from any optmalty crteron. It may be useful now to sum up the man mechansms at work. The prmary consequence of the envronmental polcy s the decrease of the polluton allowed by the decrease of the captal stock whch also mples a reducton of the output. The cost of ths envronmental bene t conssts n a fall n the gross wages of all agents. Nevertheless, for some groups of agents, ths declne of the gross wages may be slowed by a decrease of ther labor tax rate (for any group such that b() < =). The harmful e ect of the fall n net wages on the total lfe-cycle consumpton can be somehow counterbalanced by the drop n the captal stock, mplyng a rse of the nterest rate whch bene ts the second-perod consumpton. 9

21 The heterogenety characterstcs of the economy and the progressvty of the labor tax allow the government to obtan more revenues from the envronmental polcy. The decrease of the at rate component can be greater wthout compromsng the envronmental bene t. Moreover, t enables the redstrbuton of welfare between the agents n order to ful ll our Pareto-mprovement crteron. Observe that even f the productvty s nsenstve to polluton (e = 0) and/or f the polluton would a ect the household s welfare n an addtve way, our results would stll be robust and contrbute to the standard lterature. VII. The French Case: A Smple Emprcal Illustraton In order to llustrate the economc and welfare consequences of the envronmental polcy-mx, we choose some realstc values for the parameters of our theoretcal model. Then, under these parameters con guraton, we compute the varatons of compensatory ncome wth respect to the class of agents : Actually, we want to test the senstvty of wth respect to the ntal level of the labor tax rates. In more detal, we compute the values of the dr( ) ; dr (a) and dr () for d erent realstc values of : The ntal tax system s supposed to be de ned by the followng values: e = 0:0; = 0: and a = 0:: Concernng the envronmental tax rate, t corresponds closely to the budget of the French Envronment and Energy Management Agency (ADEME) whch s entrely nanced by envronmental tax revenues. The at rate component of the labor tax s the average ncome tax bearng on the rst decle of taxable households. The desgn of the progressvty ndex s very general and ts well wth many West European cases. More precsely, the wage tax rate wrtes = + ab () wth b () = ln : We have consdered 7 cases: = (0:0; 0:; 0:5; ; :5; 2; 3), see Fg. 3. In partcular, the French case corresponds to = :5: The share of captal n total output s very common for developed countres ( = 0:35) and we assume no partcular preferences for the future ( = 0:5). The envronmental parameters are not easy to de ne. We xed these values to some reasonable levels for ths lterature: e = 0:05; = 0; h = 0:3. Nevertheless, our results are robust to any changes n the values of these parameters. 20

22 Tax Fgure 3: The Wage Tax Rates Table I. Labor Market Characterstcs Class (I = 0) q 0: 0: 0: 0: 0: 0: 0: 0: 0: 0: 0:0 0:02 0:03 0:04 0:05 0:06 0:07 0: 0:2 0:5 w =w Table I. presents the labor market characterstcs. We assume an equ-dstrbuton of the workers among the classes, such that q = 0:; 8 and I = 0; hence each represents a decle of the correspondng class. We calbrated the shares n total output for workers of class ( ) such that the ratos of wages t the French data. Ths rato s equal to 5 for the hghest class. Table II. The Polcy Mx Prog. Case: :0 0: 0:5 : : 0:?? 0:26 0:23 Tax ne cency We have numercally computed the value of requred by the polcy mx accordng to the d erent cases of progressvty (see Table II.). Concernng the low progressvty cases = 0:0 (resp. 0:); the consequences on welfare of the alternatve polces, measured by dr( ) and dr (a), show that the rst class would be damaged by the polces, the second class s una ected, and all the other classes would be better o. These polces are not Pareto mprovng. But, f the government can combne varatons of the two parts of the labor tax rate and desgn a polcy-mx system, he has to x to 0: (resp. 0:). Therefore, 2

23 even the rst class would bene t from the envronmental tax polcy. The ncrease n the welfare of the upper classes wll be reduced, but s stll hgh, comparatvely to the lower classes. For some ntermedate levels of the labor tax rate ( = 0:5 and ), t s mpossble to de ne a polcy compatble wth the Pareto-mprovement crteron. Ths con guraton could be explaned by the ntal characterstcs of the tax system. For these cases, the ntal values are e cent, close to ther optmal level. Hence, some agents would su er a bg decrease n ther revenues that could not be compensated by the small gans of the agents who bene t from the tax polcy. When the progressvty part of the labor tax rate s too hgh ( = 3), the tax system s obvously characterzed by the ne cency propertes. Fnally, for some reasonable values of the progressvty ndex = :5 (resp. 2), close to the French economc data, the alternatve polces are unambguously harmful for all the classes of workers. But, by xng to 0:26 (resp. 0:23), the envronmental polcy would bene t all the agents. The envronmental tax polcy s then Pareto-mprovng and acceptable. VIII. Concluson In ths paper, we have shown that a budget-neutral envronmental tax reform may result n a double dvdend (de ned as a decrease n polluton and an ncrease n the global economc welfare), even when the economy s characterzed by heterogenous agents (old and young) and many worker classes (heterogenous labor). We have also emphaszed that the condtons for the obtanng of a double dvdend depend on the dstrbutve propertes of the labor taxes. Hence, we have shown that () an ncrease of the envronmental tax deterorates the welfare of all and s regressve, () the low pad workers prefer an envronmental tax reform balanced by a decrease n the at rate component but the hgh pad workers prefer a decrease of the progressvty. Even when the double dvdend s not possble, the cost of the polluton regulaton can be mnmzed by a new desgnng of the progressvty of the labor tax nstead of a homogenous cut n the labor tax rates. We conclude that the dstrbutve propertes of the tax polcy could be one of the nstruments of far nternalzaton of the ntergeneratonal externaltes. To a certan extent, our paper hghlghts the gap between economc e cency and vertcal equty and llustrates the problem of the aggregaton of postve and negatve 22

24 compensatory varatons: the usual method of aggregaton gves a hgher weght to the wealthest classes and ntroduces a bas when assessng the desrablty or the acceptablty of any envronmental tax reform. Aknowledgements Ths paper bene ts from the nancal support of the French Natonal Research Agency (Grant ANR-09-BLAN ). We would lke to thank two anonymous referees for precous suggestons. We would lke to thank also partcpants to the 2008 AFSE Thematc Meetng n Envronmental and Resource Economcs, Toulouse (France), June 2008 and partcpants to the Envronmental Economcs Workshop, Corte (France), September Correspondence Detals Mrelle Chroleu-Assoulne (correspondng author) Pars School of Economcs - Unversty Pars Panthéon-Sorbonne Centre d Econome de la Sorbonne, 06-2 Bd de l Hôptal PARIS Cedex 3 Tel : Fax : emal : Mrelle.Chroleu-Assoulne@unv-pars.fr Mouez Fodha Pars School of Economcs - Unversty Pars Panthéon-Sorbonne Centre d Econome de la Sorbonne, 06-2 Bd de l Hôptal PARIS Cedex 3 Tel : Fax : emal : Mouez.Fodha@unv-pars.fr Appendx Proof of local stablty (Proposton ) To prove the local stablty part of the proposton, we lnearze the dynamc system (6; 8) around the steady state. The lnear approxmaton can be wrtten n matrx form 23

25 as: 2 where = K t+ P t+ x t+ z t+ K P x z = K t P t x t z t K P x z 0 e ( h) ( K h)p +K e ( K h)p +K h z t+ = K t : The characterstc polynomal of s h P () = (P (h(2 h) ( h) ) K( h+))+p ( h(2 h))+k(( h)+e) P ( h)+k ; x t+ = P t and We know that P =K = =h: So, we have the followng propertes P (0) = 0; P () = h > 0 and P ( ) = ((2 h)(+)+he) > 0: ( h)+ h ( h)+ For su cent condtons to local stablty, we need that the modulus of each egenvalue ( +e) h to be lower than one. We can decompose the characterstc polynomal nto two parts: P () = P () :P 2 (), wth P () = 2. Bascally, the characterstc polynomal has two egenvalues equal to = 2 = 0: Then we have to study the second part of P ().e. P 2 () = 2 (P (h(2 h) ( h) ) K( h+))+p ( h(2 h))+k(( h)+e) + P ( h)+k : We already know that P () > 0 and P ( ) > 0; whch nduce that P 2 () > 0 and P ( h(2 h))+k(( h)+e) P 2 ( ) > 0: Regardng P 2 (0) = P ( h)+k = ( h(2 h))+(( h)+e) h = h ( h)+ ( h) + he > 0: We now need P 2 (0) < whch turns to ( h) + he < ; that s always true under Assumpton 2. Hence, the steady state equlbrum (K ; P ) s locally stable. References Antweler, Werner, Bran R. Copeland, and M.Scott Taylor (200): Is free Trade Good for the Envronment, Amercan Economc Revew, 9(4), p [4] Baumol, Wllam J. and Wallace E. Oates (988): The Theory of Envronmental Polcy. Cambrdge Unversty Press, 2nd edton,. [2,3] Bloom, Davd E., Davd Cannng, and Jaypee Sevlla (2004): The E ects of Health on Economc Growth: A Producton Functon Approach, World Development, 32(), p. -3. [4] Bosello, Francesco, Roberto Roson, and Rchard S.J. Tol (2006): Economy-wde Estmates of the Implcatons of Clmate Change: Human Health, Ecologcal Economcs, 24

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