Environmental Tax and the Distribution of Income with Heterogeneous Workers

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1 Envronmental Tax and the Dstrbuton of Income wth Heterogeneous Workers Mrelle Chroleu-Assoulne Pars School of Economcs - Unversty Pars 1 Panthéon-Sorbonne Centre d Econome de la Sorbonne, Bd de l Hôptal PARIS Cedex 13 Tel : Fax : emal : Mrelle.Chroleu-Assoulne@unv-pars1.fr Mouez Fodha Pars School of Economcs - Unversty Pars 1 Panthéon-Sorbonne Centre d Econome de la Sorbonne, Bd de l Hôptal PARIS Cedex 13 Tel : Fax : emal : Mouez.Fodha@unv-pars1.fr March 23, 2009 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 workers class unharmed. It conssts n an ncrease of the progressvty together wth a decrease of the at component of the wage tax. JEL class caton: D60 - D62 - E62 - H23 Key words: Envronmental tax - Overlappng generatons model - Intergeneratonal equty- Double dvdend. 1

2 Envronmental Tax and the Dstrbuton of Income wth Heterogeneous Workers 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 workers class unharmed. It conssts n an ncrease of the progressvty together wth a decrease of the at component of the wage tax. JEL class caton: D60 - D62 - E62 - H23. Keywords: Envronmental tax - Heterogenous agents - Welfare analyss - Tax progressvty. 2

3 1 Introducton One of the most publcly debated ssues about the envronmental regulaton concerns ts e ects on the poorest agents and the farness of such a polcy. Ths queston comes nowadays to lght agan because of the relatve falure observed untl now of the emssons tradng system chosen as nstrument for the 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? The economc lterature does not contrbute much to ths debate and our paper ams to ll n the exstng gap. The yet open queston Can an envronmental tax reform be desgned wthout deteroratng the economc welfare? gave brth to the huge lterature about the double dvdend. Terkla [29], Parry [22], or Poterba [26] had rst the ntuton that the recyclng of the revenue of an envronmental tax could reduce or even annhlate the gross cost of the mplementaton of an envronmental tax. 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 [13]). Baumol and Oates [1], Pearce [23] or Oates [19] 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 [4] and ther followers), Goulder [13] or Lgthart [17] 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 x producton factors or to other consumers emphaszng then the role of heterogenety. Followng ths lne, Chroleu- Assoulne and Fodha [6] and [7] studed the exstence condtons of a long term double dvdend, takng account of the dstncton between wage earners and retred consumers, by the mean of OLG models. Surprsngly enough, ths large lterature has deeply analyzed the double dvdend ssue but, n the same tme, 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 yet well known that the costs and bene ts of the envronmental polces are unequally dstrbuted among agents. The poor and the rch seem to assgn d erent degrees of prorty to envronmental protec- 3

4 ton (Baumol and Oates [1]), snce wealther ndvduals would accept to pay 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 of exstng studes are emprcal works dealng manly wth the dstrbuton of bene ts of the envronmental polces among ncome classes (Chrstansen and Ttenberg [8], Ellott et al. [11], Harrson [14], Peskns [25]), hence 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 to also be regressve. In partcular, for the French case, a tax bearng on energy or transport consumpton harms the lowest wage households three tmes more heavly than the hghest wage ones (Ruz and Trannoy [27]). Moreover, the usual recyclng of the envronmental tax revenues through a decrease n the labor tax rate could be also regressve (Metcalf [18]). 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 - 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 of 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 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 any workers class better o. We consder an overlappng generatons economy wth pollutng captal. Our model shares the mean features of Chroleu-Assoulne and Fodha [6] and [7]. As n Chao and Peck [5] or Wllams [30] or [31], 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 (OCDE [20]) and the mpact of the health of workers on labor productvty 4

5 (Bloom et al. [2], 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 [21], many papers emphasze the loss of productvty caused by the health e ects of polluton, e.g. Samakovls et al. [28], or Pervn et al. [24] for ar-polluton, and also Bosello et al. [3] or Hübler et al. [15] for the health e ects of clmate change. For example, accordng to Bosello et al. [3] strong heat stress causes a productvty loss of 3% and extreme heat a loss of 12%. Another source of productvty loss orgnates n the mpact of polluton on the qualty of natural resources (Gollop and Swnand [12] for the agrcultural sector). 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 correspondng 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 retred). The envronmental polcy conssts of ncreasng the Pgovan 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 such economc condtons that the double dvdend hypothess seems unrealstc. Conversely, we show that the condtons for the obtanng of a double dvdend le on 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 dependant of 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. Secton 4 gves the spec caton of the balanced tax reform. 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. 5

6 2 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. The labor tax s a very general one that could be ether a progressve or proportonal tax. We assume that N t ndvduals are born n perod t and that 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 the sze of each class s equal to q (wth P I =1 q = 1). Each agent supples one unt of labor 1 when she s young and earns a wage w t; she dvdes her labor ncome between consumpton and savngs s t. In the second perod the household consumes her savngs and the nterest she earns. 2 ]0; 1[ represents the ndvdual propensty to save. The welfare of an ndvdual born at t s measured wth the ntertemporal separable utlty functon: 2 wth c y t U c y t ; co t+1 = (1 ) ln c ;y t + ln c ;o t+1 denotng the rst-perod consumpton of the agent born at t, c o t+1 her secondperod consumpton. 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+1. As the captal s pollutng, the envronmental polcy conssts n a Pgovan tax on savngs e. The household s budget constrants wrtes: 1 t w t = c y t + (1 + e t ) s t c o t+1 = (1 + r t+1) s t (1) 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, 1 Our long term vew allows us to assume full employment. Moreover we focus on e cency double dvdend (accordng to Goulder [13]) and not on employment double dvdend. 2 We do not ntroduce any drect e ect of polluton on the households 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

7 wthn the Damond s framework (Damond [10]) wth a homothetc utlty functon: 8 c y t = (1 ) 1 t w t >< c o t+1 = (1 + r t+1) (1 + e t ) 1 t w t >: s t = 1 t (1 + e t ) w t (2) 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 deterorates 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, + = 1. 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 =1 L ;t IX wtl ;t =1 IY =1 L ;t (1 + 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 >< = 1 + 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 IY =1 q (3) wt wt 1 = 1 q 1 q 7

8 Assumpton 1: The d erent labors are ranked by growng sklls,.e. by growng wages: w t > w 1 t, q > 1 q 1 We assume that government spendng (G) s entrely nanced by current taxes. The government s budget constrant states that ts purchases must equal, at each perod, ts tax revenues generated by the polluton tax and the labor tax: IX q twt + e t =1 IX q s t = G t (4) =1 We de ne a progressvty ndex of the labor tax, such as: = 1 + a (a; ) where 1 s the at component of the tax rate, a a > 1 and a 1 = a 1 (a; 1) = 0; a > 0: (a; ) =@a > 2 a (a; ) =@a 2 = (a; ) =@ > 0 2 a (a; ) =@ 2 R 0: We consder the general case for the characterstcs of the tax progressvty. 3 For example, the desgn of progressvty ts well the characterstcs of the French tax system 2 a (a; ) =@ 2 < 0. Ths yelds! IX IX IX q w = Y = Y 1 (1 ) + a (a; ) =1 =1 =1 Assume a (a; ) = ab () wth b (1) = 0; b 0 > 0; b 00 T 0: We obtan: IX IX a (a; ) = a b () = ab =1 =1 P let B I b () > 0 whch s constant for any I < 1. =1 3 Unlke the usual spec caton of the tax progressvty n the lterature, we assume here that depends on the class of the agent and not drectly on the wage w : But as assumpton 1 mples a rankng between and w, our de nton of the tax progressvty s qualtatvely equvalent to the usual one. 8

9 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 global factor productvty. The dynamcs of polluton s descrbed by the followng equaton: P t = (1 h) P t 1 + K t 1 (5) where h s the constant rate of natural absorpton of polluton (0 < h < 1) and > 0 stands for the emsson rate of pollutants. The equlbrum condton of the captal market, meanng that the captal stock n perod t+1 s the amount saved by young ndvduals n perod t, s obtaned by substtutng the zero-pro t condton, the government s budget constrant (eq. 4) and the household s budget constrants (eq. 1) nto the equlbrum of the output good market. It wrtes: By substtutng eq. 2 and 3: K t = IX q s t 1 =1 q 1 K t = 1 + e 1 1 t 1 (1 ) ab w 1 t 1 t 1 (6) 1 Let K be the steady-state value of the captal stock, then usng eq. 3, one obtans: K = wth X = 1 1 (1 ) ab, constant for a gven tax system. Assumpton 2: X = 1 1 (1 ) ab > e XY (7) Ths assumpton ensures the exstence of a postve steady-state equlbrum. It reduces to b (~{) < 1 1 a where ~{ s the pecular workers class 4 such that b (~{) = I 1 b() I 1. Hence b (~{) s the average of the coe cents of progressvty, weghted by the shares of each workers class n the output. Assumpton 2 s then equvalent to ~{ = 1 + ab (~{) < 1. Proposton 1 Under assumptons 1 and 2, for a gven trplet of tax polcy nstruments, e ; 1 ; a, the equlbrum condtons can be summed up by Eq. (1 6). Thus, there exsts a unque steady-state equlbrum de ned by K such that:. 1 " K = 1 + e X 1 ( e) e IY h =1 q # 1 1 ( e) 4 More precsely, b (~{) I 1 b() I 1 and b (~{ 1) < I 1 b(), wth ~{ I. I 1 9

10 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, () s 0 r = 0 and F 00 K < 0, (v) lm k!0 (FK 0 :K=K) = 2 [0; 1[. Condtons () (v) ensure the exstence, uncty and stablty of the steady-state equlbrum (see de la Crox and Mchel [9] and Konsh and Perera-Tallo [16]). Usng Proposton 1 and eq. equlbrum: Y = Assumpton 3: e > 0: 1 + e X 7, one obtans the output value at the steady-state e 1 ( e) " h e IY =1 q # 1 1 ( e) It means that the drect contrbuton of captal to output () s greater than the ndrect one through polluton and productvty (e). 5 At ths steady-state equlbrum, the total stock of polluton s gven by: (8) P = h K (9) 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 1. To ensure the exstence of the new steady-state, the varatons of the labor tax components must verfy ths condton obtaned through the d erentaton of Assumpton 2: 3 Welfare analyss da d 1 < 1 B, 8d e > 0. Lke Chroleu-Assoulne and Fodha [7], 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. Ths margnal excess burden 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 5 Assumng the contrary ( < 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. 10

11 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 (1 + r) (1 + e ) dcy + dc o = 0 The ntertemporal budget constrant of household wrtes: Remember that 1 w = c y + (1 + e ) (1 + r) co c o (1 + r) = (1 ) (1 + e ) cy We use the rst-order condtons of the representatve household s program and the de nton of the compensatory ncome varaton dr: 1 dw w d 1 + b () da + dr = d^c y ^c o ths leads to: = ^co 2 dr + (1 + r) (1 + r) d e + (1 + e ) 1 + r d^co (1 + e ) ^c o (1 + r) 2 dr + ^co (1 + r) d e dr = 1 dw + w d 1 + b () da (1 + e ) ^c o (1 + r) 2 dr + ^co (1 + r) d e (10) Unlke Bovenberg and de Moj [4] and the greater part of the lterature on ths subject, t s here mpossble to dstngush an envronmental component and a non-envronmental one, because polluton and producton a ect each other. In ths paper, we are thus constraned to depart from the usual de nton of the double dvdend (Goulder [13]) 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 of the polluton level). An ncrease of the ndvdual lfe-cycle consumpton ensures a rse n the welfare: t s a su cent but not necessary condton. For example, f the propensty to save s su cently hgh (resp. low), a welfare mprovement could also be obtaned through a decrease (resp. 11

12 ncrease) of the rst-perod consumpton assocated wth an ncrease (resp. decrease) of the second-perod one. More generally, the ncrease of welfare s ver ed for any varatons of consumptons such that dc y =c y + (1 )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 harms more heavly the lowest wages. Proof. Let us compute the steady-state value of the compensatory ncome varaton for agent : dr q Y = Z 1 (1 + e ) d e (11) + (Z ) + (1 ) X + 1 (Z ) B X + b () (1 ) (1 1 d 1 ) 1 da wth Z = e 1 ( 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 q. Hence, when d 1 = da = 0, one obtans, for any envronmental tax ncrease d e > 0 : dr = Z 1 dw (1 + e ) d e > 0 then, as Z > 0, dr > 0 for every. But dr =dw hgh) and when w s smaller when s hgher (.e. also s hgher. When the envronmental polcy harms the consumers, the relatve burden s greater for the less sklled. 6 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 mpacts are ambguous, for the 6 Ths result doesn t 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. Namely, our regressvty property results from the progressvty characterstcs of the labor tax. 12

13 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. 4 The spec caton of the balanced tax reform We assume an exogenous ncrease of the polluton tax rate, mposed by the government n order to control polluton. The amount of government s purchases s assumed ex post nvarant, and the tax polcy has to mantan the amount of the tax revenues constant. Ths ncrease d e of the polluton tax rate can be accompaned by a varaton of the labor tax rates d by two potental means: an homogenous varaton of all labor tax rates (d 1 ) 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: 1 (1 ) + ab 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. 8). Any balanced tax reform s then characterzed by the followng relatonshp between d e, d 1 and da (wth dg = dq = d = 0): where = 1 (1 (1 ) d 1 + Bda = ( + ) (1 + ) X d e 1 + e (12) ) + ab + K Y 1 ( e) e Z X 0 (under assumpton 2), constant. 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 1 = ( + ) (1 + ) X d e (1 ) 1 + e = d e (13) varaton of the progressvty, wth nvarant at component of the tax rate (d 1 = 0):, da = ( + ) X d e (1 + ) B 1 + e = d e (14) 13

14 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, thus 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 > 1). 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 4: We only consder the La er-e cency case, where the sgn of the balanced tax reform multplers and s postve. Under 12, Assumpton 4 mples > 0, > 1 or <. 5 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 condton rewrtes (see Proposton 1): dk K = 1 d e 1 ( e) 1 + e + (1 ) d 1 + Bda < 0 X d e As 1 ( e) > 0, ths condton reduces to 1 + e + (1 ) d 1 + Bda X have the two cases correspondng to the two alternatve polces: > 0: We then nvarant progressvty (da = 0) : varaton of the progressvty d 1 = 0 : d e (1 ) d e > 1 + e X 14 d e 1 + e > Bd e X :

15 We obtan a rst dvdend f the multplers are not too hgh: 8 >< >: < < X (1 + e ) (1 ) X (1 + e ) B () < 1 (15) Ths means that the decrease of the labor tax (ether of the at component or of the progressvty ndex) should be not too strong n order to not jeopardze the envronmental bene t of the reform. Assumpton 5: We only consder the case where the tax polcy decreases polluton. Proposton 4 Under Assumptons (1-5), the tax polcy s e cent and reduces polluton f and only f the ntal envronmental tax rate s not too hgh: e < 1=Z. Proof. We have to examne the two cases whch verfy the tax e cency assumpton (Ass. 4). If () : 1 < ; then + < 1, > 1 : whch colldes the basc assumpton on : The 1 + envronmental bene t can never be acheved. If () : < ; then + < 1, < 1 : always ver ed. 1 + 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: 1 (1 ) + ab + 1+ e X 1 ( e) e Z X < () 1 (1 ) + ab + e 1+ e X 1 ( e) < X Z whch mples e 1+ e X 1 ( e) < X Z () ( e) < 1 1+ e () e < 1 ( e) e 15

16 6 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 worker s class. Proposton 5 () The envronmental tax reform preferred by the workers of the lowest classes conssts of a decrease n the at component of the tax rate 1 () 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 to each polcy. Frst case (dr( 1 )): unform varaton of all labor tax rates (wth nvarant progressvty): da = 0 and d 1 = d e dr( 1 ) q Y = Z 1 (1 + e ) d e (Z ) X (1 ) + 1 (1 ) 1 d e Second case (dr(a) ): varaton of the progressvty (wth nvarant at component): d 1 = 0, da = b () da and da = d e dr(a) q Y = Z 1 (1 + e ) d e (Z ) X B + b () (1 ) 1 d e 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( 1 ) dr(a) for the workers of class. q Y = (Z ) X (1 ) 1 (Z ) X B 1 + b () T 0 16

17 Fgure 1: An llustraton of workers s class threshold n the French case Usng eq. 13 and 14 ( = 1 b () 1 ), we nd that ths sgn s equal to the sgn of: B B 1 = b () b () 1 Therefore the pecular average workers s 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, at the contrary, each less sklled class of workers would prefer a decrease n the at component of the wage tax, d 1 < 0 (Fgure 1 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 polcy mx could be desgned n order to leave each workers class unharmed by the envronmental tax reform : t wll consst n an ncrease of the progressvty ndex together wth a decrease of the at component of the wage tax rate. Assume that the balanced tax reform s de ned by d 1 < 0 and da = d 1 wth > 0 hence da > 0. Such a compensaton of the ncrease n the envronmental tax rate wll mply a greater decrease of 1 than above because the degree of progressvty s rased. Proposton 6 For economes such that a decrease n the mnmal wage rate doesn t suf- ce to reestablsh the welfare of some workers class, one can choose n order to ensure that all classes wll be better o wth the envronmental tax reform. 17

18 Proof. Let us precse 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 = 1 d 1 1 da = 1 d 1 = 1 1 d 1 B To ensure the exstence of the new steady-state equlbrum, we have shown above (Ass. da 2) that we need = < 1 d 1 B. Ths condton also ensures the decrease of the at component of the labor tax. The compensatory ncome varaton of the balanced mx polcy s: dr() " " q Y d e = 1 dr 1 q Y d e + (Z ) B X 1 + b () 1 B wth Z > 0; X > 0; constants. B 1 1 Z 1 ## (1 + e ) - dr() S 0; 8 = 1; :::I: - dr () s not monotonous n b (), nor n, 8. - If dr( 1 ) < 0; 8 = 1; :::I, all classes wll be better o even wth = 0: If 9; dr( 1 ) > 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() One can choose > 0 n order to nullfy dr { () : t ensures that all classes wll be better o (ther compensatory ncome varaton are all negatve or null). Z 1 1 ab ({) h (1 + = e 1 1 ab ({) (Z ) ) " B 1 1 Z 1 1 ab ({) (1 + e ) (1 ) X + 1 (Z ) B X (1 1 ab ({)) b ({) # Ths polcy mx ams to reduce the preexstng 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. 18

19 Fgure 2: An llustraton of the polcy-mx crteron It may be useful to sum up now 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() < 1=). 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. The heterogenety characterstcs of the economy and the progressvty of the labor tax allow to obtan more revenues from the envronmental polcy. The decrease of the at 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 Paretomprovement crteron. Observe that even f the productvty s nsenstve to polluton (e = 0) and/or f the polluton a ects the households welfare n an addtve way, our results are stll robust and contrbute to the standard lterature. 19

20 Fgure 3: The wage tax rates 7 The French Case: A Smple Emprcal Illustraton In order to llustrate the economc and welfare consequences of the envronmental polcymx, 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. More n detal, we compute for d erent realstc values of the values of the dr( 1 ) ; dr (a) and dr () : The ntal tax system s supposed to be de ned by the followng values: e = 0:01; 1 = 0:1 and a = 0:1: 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 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 many West European cases. More precsely, the wage tax rate wrtes = 1 + ab () wth b () = ln : We have consdered 7 cases: = (0:01; 0:1; 0:5; 1; 1:5; 2; 3), see Fg. 3. In partcular, the French case corresponds to = 1:5: 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; = 10; h = 0:3. Nevertheless, our results 20

21 Class (I = 10) q 0:1 0:1 0:1 0:1 0:1 0:1 0:1 0:1 0:1 0:1 0:01 0:02 0:03 0:04 0:05 0:06 0:07 0:1 0:12 0:15 w =w Table 1: Labor market characterstcs Prog. Case: :01 0:1 0:5 1 1: :1 0:11?? 0:26 0:23 Tax ne cency Table 2: The Polcy Mx are robust to any changes n the values of these parameters. Table 1 presents the labor market characterstcs. We assume an equ-dstrbuton of the workers among the classes, such that q = 0:1; 8 and I = 10; 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 15 for the hghest class. We have numercally computed the value of requred by the polcy mx accordng to the d erent cases of progressvty (see Table 2). Concernng the low progressvty cases = 0:01 (resp. 0:1); the consequences on welfare of the alternatve polces, measured by dr ( 1 ) 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 0:1 (resp. 0:11). Therefore, even the rst class would bene t from the envronmental tax polcy. The ncrease of the welfare of the upper classes wll be reduced, but stll hgh, comparatvely to the lower classes. For some ntermedate levels of the labor tax rate ( = 0:5 and 1), t s mpossble to de ne a polcy compatble wth the Pareto-mprovement crteron. 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 = 1:5 (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 to all the agents. The envronmental tax polcy s 21

22 then Pareto-mprovng and acceptable. 8 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 le 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 wages prefer an envronmental tax reform balanced by a decrease of the at component but the hgh wages 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 an homogenous cut n the labor tax rates. We conclude that the dstrbutve propertes of the tax polcy could be one of the nstruments of nternalzaton of the ntergeneratonal externaltes. To a certan extent, our paper underlnes the gap between economc e cency and vertcal equty and llustrates the problem of the aggregaton of postve and negatve compensatory varatons: the usual way 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. References [1] W.J. Baumol and W.E. Oates, The Theory of Envronmental Polcy, Cambrdge Unversty Press, 2nd edton, (1988). [2] D.E. Bloom, D. Cannng and J. Sevlla, The E ects of Health on Economc Growth: A Producton Functon Approach, World Development, 32, 1-13 (2004). [3] F. Bosello, R. Roson and R.S.J. Tol, Economy-wde Estmates of the Implcatons of Clmate Change: Human Health, Ecologcal Economcs, 58, (2006). 22

23 [4] A.L. Bovenberg and R.A. de Mooj, Envronmental Leves and Dstortonary Taxaton, Amercan Economc Revew, 84 (4), (1994). [5] H.-p. Chao and S. Peck, Greenhouse Gas Abatement: How Much? and Who Pays?, Resource and Energy Economcs, 22, 1-20 (2000). [6] M. Chroleu-Assoulne and M. Fodha, Double Dvdend wth Involuntary Unemployment: E cency and Intergeneratonal Equty, Envronmental and Resource Economcs, 31(4), (2005). [7] M. Chroleu-Assoulne and M. Fodha, Double Dvdend Hypothess, Golden Rule and Welfare Dstrbuton, Journal of Envronmental Economcs and Management, 51(3), (2006). [8] GB. Chrstansen and TH. Ttenberg, Dstrbutonal and Macroeconomc Aspects of Envronmental Polcy, n A Kneese and J. Sweeney, eds. Handbook of Natural Resource and Energy Economcs, Amsterdam, (1985). [9] D. de la Crox and Ph. Mchel, A Theory of Economc Growth: Dynamcs and Polcy n Overlappng Generatons, Cambrdge Unversty Press (2002). [10] P.A. Damond, Natonal Debt n a Neoclasscal Model, Amercan Economc Revew, 55, (1965). [11] DB. Ellott and JC. Mllan, Toward a Theory of Statutory Evoluton: The federalzaton of Envronmental Law, Journal of Law, Economcs, and Organzaton, (1985). [12] F.M. Gollop and G.P. Swnand, From Total Factor to Total Resource Productvty: An Applcaton to Agrculture, Amercan Journal of Agrcultural Economcs, 80, (1998). [13] L.H. Goulder, Envronmental Taxaton and the Double Dvdend : A Reader s Gude, Internatonal Tax and Publc Fnance, 2, (1995). [14] D. Jr. Harrson, The Dstrbutve E ects of Economc Instruments for Envronmental Polcy, Pars, OECD, (1994). 23

24 [15] M. Hübler, G. Klepper and S. Peterson, Costs of Clmate Change - The E ects of Rsng Temperatures on Health and Productvty, Ecologcal Economcs, 68, (2008). [16] H. Konsh and F. Perera-Tallo, Exstence of steady-state equlbrum n an overlappng-generatons model wth producton, Economc Theory, 9, (1997). [17] J.E. Lgthart, The Macroeconomc E ects of Envronmental Taxes : A Closer Look at the Feasblty of Wn-Wn Outcomes, Workng Paper of the Internatonal Monetary Fund, Washngton, (1998). [18] G.E. Metcalf, A Dstrbutonal Analyss of Green Tax Reforms, Natonal Tax Journal, 52 (4), (1999). [19] W.E. Oates, Polluton Charges As a Source of Publc Revenues, Resources of the Future Dscusson Paper, QE92-05, (1991). [20] OECD, Costs of Inacton on Key Envronmental Challenges, Pars, (2008). [21] B.D. Ostro, The E ects of Ar Polluton on Work Loss and Morbdty, Journal of Envronmental Economcs and Management, 10, , (1983). [22] I.W.H. Parry, Polluton Taxes and Revenue Recyclng, Journal of Envronmental Economcs and Management, 29 (3), (1995). [23] D.W. Pearce, The Role of Carbon Taxes n Adjustng To Global Warmng, The Economc Journal, 101, (1991). [24] T. Pervn, U.-G. Gerdtham and C.Hampus Lytkens, Socetal Costs of Ar Polluton- Related Health Hazards: A Revew of Methods and Results, Cost E ectveness and Resource Allocaton, 6 (19), (2008). [25] H. Peskns, Envronmental Polcy and the Dstrbuton of Bene ts and Costs, n R. Portney, ed. Current Issues n U.S. Envronmental Polcy, J. Hopkns Unversty Press for Resources for the Future, (1978). [26] J.M. Poterba, Global Warmng Polcy: A Publc Fnance Perspectve, Journal of Economc Perspectves, 7 (4), (1993). 24

25 [27] N. Ruz and A. Trannoy, Le caractère régressf des taxes ndrectes : les ensegnements d un modèle de mcrosmulaton, Econome et Statstque, 413, (2008). [28] E. Samakovls, A. Huhtala, T. Bellander and M. Svartengren, Valung Health Effects of Ar Polluton - Focus on Concentraton-response Functons, Journal of Urban Economcs, 58, (2005). [29] D. Terkla, The E cency Value of E uent Tax Revenues, Journal of Envronmental Economcs and Management, 11, (1984). [30] R.C. Wllams III, Envronmental Tax Interactons when Polluton A ects Health or Productvty, Journal of Envronmental Economcs and Management, 44, (2002). [31] R.C. Wllams III,, Health E ects and Optmal Envronmental Taxes, Journal of Publc Economcs, 87(2), (2003). 25

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