ENVIRONMENTAL TAX POLICY AND LONG-RUN ECONOMIC GROWTH*

Transcription

1 The Jaanese Economic Review Vol. 54, No., June 003 Blackwell Oxford, JERE The Original Environmenal T. Ono Jaanese UK Aricle ublishing Economic Tax olicy Ld Associaion, Review and Long-run 00Economic Growh ENVIRONMENTAL TAX OLICY AND LONG-RUN ECONOMIC GROWTH* By TETSUO ONO Universiy of Tsukuba This aer focuses on wo comeing effecs of environmenal axaion on long-run economic growh. One is a negaive force, which hamers roducion; he oher is a osiive force, which increases he level of environmenal qualiy bequeahed o fuure generaions. The analysis shows ha here exiss a criical level of he ax ha balances one force wih he oher. If he ax is iniially se below (or above) he criical level, hen raising he ax rae is beneficial (or harmful) o economic growh. JEL Classificaion Numbers: D6, D9, H6, O, O30, Q0.. Inroducion The link beween environmenal ax olicy and economic growh is a conroversial issue. Environmenaliss argue ha a more ambiious olicy is necessary o achieve susainable develomen for he fuure. In conras, indusrialiss mainain ha such a olicy could hamer economic aciviy. This aer resens a framework ha encasulaes hese wo views and considers wheher here is a condiion under which one argumen dominaes he oher. There are many sudies on environmenal ax olicy and economic growh. Mos of hem focus on he normaive asec of ax olicies. They inroduce environmenal ax olicies as an insrumen for achieving he efficien or welfare-imroving allocaion of resources in a decenralized economy. In racice, however, environmenal ax olicy faces informaional and oliical consrains in imlemening he oimal levels of axes (Baumol and Oaes, 988; Bovenberg and Smulders, 996). An invesigaion of ax reform would be imoran for a discussion of he role of environmenal ax olicy in a real world. Therefore, in his aer I aim o examine he effecs of environmenal axaion on economic growh. The analysis ha follows is closely relaed o ha of Bovenberg and Smulders (995, 996), who consider he effec of a change in he environmenal ax rae on economic growh. In heir model, environmenal axaion ha reduces a flow of olluion has wo oosing effecs on long-run economic growh. On he one hand, a lower level of olluing inus imlies a fall in he final goods roducion, hereby huring economic growh; his is a negaive effec of environmenal axaion on economic growh. On he oher hand, a decrease in olluion imroves he qualiy of he environmen. Such an imrovemen leads o an increase in roduciviy, hereby romoing economic growh; his is a osiive effec of environmenal axaion. Thus, a osiive effec of environmenal qualiy on roduciviy is a key facor enhancing economic growh in he model of Bovenberg and Smulders (995, 996). * I would like o hank an anonymous referee for his or her insighful commens. See e.g. van der loeg and Wihagen (99); Lighar and van der loeg (994); John e al. (995); Ihori (996); Mohadi (996); Ono (996); Fisher and van Marrewijk (998); Sokey (998); Yoshida (998); Grimaud (999); Jouve e al. (000), and Ono and Maeda (00). 03 Jaanese Economic Associaion 003.

2 The Jaanese Economic Review This aer focuses on he inergeneraional accumulaion of environmenal caial and subsequenly exhibis anoher osiive effec of environmenal axaion, one ha is no shown in he Bovenberg Smulders aers. To his end, I develo an overlainggeneraions model of growh and he environmen, based on he work of John and ecchenino (994) and John e al. (995). In he model resened below, he lower flow of olluion resuling from environmenal axaion leads o a higher qualiy of environmenal caial o be bequeahed o fuure generaions. These subsequen generaions can afford o inves more resources in saving for roducive caial because he higher qualiy of he environmen inheried from as generaions is equivalen o a higher level of environmenal wealh, which imlies a osiive income effec. Thus, a higher rae of axaion leads o a higher growh rae, under one condiion: inergeneraional accumulaion of environmenal caial is a key facor romoing economic growh. Having observed he inergeneraional effec of environmenal axaion, i is shown ha here exiss a criical level of he ax ha balances he osiive effecs of environmenal axaion wih is negaive effecs. If he ax is iniially se below (or above) he criical level, hen raising he ax is beneficial (or harmful) o economic growh; ha is, he argumen of environmenaliss (or indusrialiss) dominaes. This aer is organized as follows. Secion develos he model. Secion 3 deermines he range of environmenal ax rae ha ensures susained growh. Secion 4 finds he criical level of he ax ha aains he maximum growh rae. Secion 5 weighs he consequences of environmenal axaion under alernaive assumions. Secion 6 rovides concluding remarks.. The model Consider an infinie-horizon economy; ime is discree and denoed by =,,.... roducion There is a coninuum of idenical firms. They are erfecly comeiive rofi-maximizers, which roduce final good Y using he roducion funcion α α Y = à ( K ) ( L ) z, where à is a roduciviy scalar, K is he oal quaniy of roducive caial, L is he oal emloymen, z is he inensiy of olluion and α (0, ) is a consan arameer. The subscri denoes eriod. An index for each firm is no creaed since firms are assumed o be idenical. Caial dereciaes fully in he rocess of roducion. The aciviy of roducion leads o a flow of environmenally harmful emission, = Y (z ) ξ, where ξ > 0 is consan. A higher ξ imlies more emissions given he final ouu. Subsiuing his relaion ino he roducion funcion leads o ξ/ ( + ξ) α ξ/ ( + ξ) ξ( α)/( + ξ) /( + ξ) α Y = ( à ) ( K ) ( L ) ( ) = A ( K ) K α ( L ) L α ( ), Jaanese Economic Associaion

3 T. Ono: Environmenal Tax olicy and Long-Run Economic Growh where A (Ã ) ξ/(+ξ), α K αξ/( + ξ), α L ξ( α)/( + ξ) and α /( + ξ). This roducion funcion has consan reurns o scale, because α K + α L + α =. The inensive form of he roducion funcion is y = A (k ) α K ( ) α, where y Y /L, k K /L and /L. Le us assume he exernal effec of aggregae roducive caial on roduciviy as discussed in he conex of endogenous growh heory (see e.g. Romer, 986). We hus assume ha A = (A) α (K ) α K α, where A > 0 is a consan arameer. The aggregae roducive caial sock, K, eners he echnology as a consan arameer from he ersecive of curren roducers. The rofi of he firm in eriod, π, is π = A (k ) α K ( ) α w ρ k τ, where w is he wage rae, ρ is he renal rae of caial, and τ is an environmenal ax levied by he long-lived governmen. The rofi maximizaion under erfec comeiion yields he following firs-order condiions: ρ = α K Α (k ) α K ( ) α, () τ = α A (k ) α K ( ) α, () w = ( α K α )A (k ) α K ( ) α. (3) The long-lived governmen ransfers he revenue τ L = τ o individuals (described below) in a lum-sum fashion. Thus, τ = τ is a budge equaion which holds in every eriod. L. references and endowmens A new generaion is born in each eriod =,,..., and lives for wo eriods, youh and old age. There is no oulaion growh; he size of each generaion is uniy. Agens are idenical in each generaion. Agens born in eriod have references over consumion in youh, c, consumion in old age, c, and an index of he qualiy of he environmen when hey consume, E These references are reresened by he uiliy funcion U = u( c, c 3 +, E+ ), where u : R + R is he uiliy from consumion and environmenal qualiy. We assume he following. 3 Assumion : (i) u is wice coninuously differeniable on R ++. (ii) u is sricly quasiconcave on. (iii) Du(c, c, E) 0, (c, c 3 3 R ++, E) R ++. (iv) lim,, and (c, c c u( c, c, E), E) 0 =+ 3 lim c u ( c, c, E). 4 0 =+ lim E 0u3( c, c, E) =+ R ++ Following Zhang (999), we aly a simlisic echnical hyohesis wih resec o he uiliy funcion, which holds for he cases ha are logarihmic or Cobb Douglas. 3 4 There are many forms of echnologies suiable for an analysis of endogenous growh. I adoed AK echnology for simliciy of analysis. The suerscri refers o youh, and o old age. For a funcion u, denoe u i as he firs derivaive wih resec o he ih variable. 05 Jaanese Economic Associaion 003.

4 The Jaanese Economic Review Assumion : The elasiciy arameer η i Eu 3 /c i u i > 0, i =,, is consan. 5 Young agens are each endowed wih one uni of labour, which hey suly o firms inelasically. They divide heir wage, w, beween consumion in youh, c, savings for consumion in old age, s, and invesmen in he environmen, m. In old age, agens suly heir savings o firms and earn he gross reurn R +. Thus, he budge equaion in youh and old age are c + s + m = w and c+ = R+ s + τ L L +,, resecively, where τ + is a lum-sum ransfer from he governmen. Environmenal qualiy is an inergeneraionally bequeahed good ha is reduced by emissions caused by firms,, bu can be imroved by mainenance invesmen, m. This mechanism is exressed by E + = E β + γ m, where β > 0 is a arameer ha evaluaes he effec of emissions on environmenal qualiy, and γ > 0 is a arameer ha reresens he efficiency of environmenal mainenance. The second erm on he righ-hand side, β, is an environmenally harmful exernaliy caused by firms. The formula o derive an environmenal equaion is based on John and ecchenino (994) and John e al. (995), bu differs from heirs on he following wo oins. Firs, boh aers define E as an index ha can ake on osiive and negaive values. A value of zero is he qualiy of environmen in he absence of human inervenion. On he oher hand, Assumion ensures ha an index, E, akes on only he osiive values; a value of E > 0 is he naural qualiy of he environmen. The environmenal qualiy remains a he naural level E if here is no human inervenion: = 0 and m = 0 for all. Second, John and ecchenino (994) and John e al. (995) assume ha he source of environmenal deerioraion is consumion by as generaions: E + = E βc + γ m. They ado his formula o focus on consumion exernaliy across generaions. In conras, his aer assumes ha firms cause he flow of environmenally harmful emissions during he rocess of roducion. I have adoed his formula o consider he regulaion of emissions by imlemening an environmenal ax. Following John and ecchenino (994) and John e al. (995), i is assumed ha a shor-lived governmen reresening he young chooses he mainenance invesmen m and savings s o maximize he uiliy of generaion on he condiion ha he old are no made worse off by his decision. 6 Given he wage, w, he reurn on savings, R +, environmenal qualiy a he beginning of eriod, E, he quaniy of emissions by firms,, and he lum-sum ransfer in old age, L τ +, he lifeime choice roblem of a reresenaive agen in generaion is max uc (, c+, E+ ) c {, s, m } 5 6 Noe ha, under Assumion, he savings funcion is indeenden of he reurn on savings; here is no subsiuion effec. The funcion U = (/η ) ln c + (/η ) ln c + ln E is an examle of he uiliy funcion ha saisfies Assumion. The role of his assumion will be discussed in Secion 5. Noe he difference beween shor-lived and long-lived governmens. The former chooses mainenance invesmen m given he environmenal ax on firms. The laer levies he environmenal ax τ on firms and ransfers he ax revenue o old agens in every eriod. Jaanese Economic Associaion

5 subjec o T. Ono: Environmenal Tax olicy and Long-Run Economic Growh c + s + m = w c, = R s + τ, + + L + (4) (5) E + = E β + γ m, (6), s, m 0. The firs-order condiions of he roblem above are (4) (6) and c E + γη c (equaliy holds if m > 0), (7) R + E + γη (equaliy holds if m > 0). (8) c + Inequaliy (7) saes ha, in he case of m > 0, a generaion chooses consumion when young o equae he marginal rae of subsiuion beween consumion in youh and environmenal qualiy in old age wih he marginal rae of ransformaion γ. A he uiliy maximum, a decrease in uiliy resuling from falling consumion during youh is equal o an increase in uiliy resuling from an increase in mainenance effor, γ. Inequaliy (8) saes ha, in he case of m > 0, a generaion chooses savings o equae he marginal rae of subsiuion beween consumion in old age and environmenal qualiy in old age wih he marginal rae of ransformaion, γ /R +. A he uiliy maximum, a decrease in uiliy resuling from falling consumion during old age, R +, is equal o an increase in uiliy resuling from an increase in mainenance invesmen, γ. In eriod, here are boh young agens of generaion and iniial old agens of generaion 0. Each iniial old agen is endowed wih k unis of roducive caial, and L earns he reurn R k and he lum-sum ransfer τ. The uiliy of an iniial old agen is U = v ( c, E), where he funcion v is increasing in each argumen and he iniial condiion E is given. 3. Equilibrium This secion characerizes he equilibrium ah, and hen shows he necessary and sufficien condiion for he exisence of he susained growh under which caial, environmenal qualiy and consumion grow a a consan rae over ime. Definiion: An equilibrium is a sequence { c, c, s, m, E, w, ρ, R,, k} = such ha (i) firms maximize rofis; (ii) shor-lived governmens maximize uiliy; and (iii) markes clear, given he iniial condiion {k, E }. The firs-order condiions of rofi maximizaion are () (3), and he firs-order condiions of uiliy maximizaion are (4) (8). Given ha L = for all, k K /L = K. Wih A = A α (K ) α K α = A α (k ) α K α, () is rewrien as τ = α A α (k ) α ( ) α, or = (α /τ ) /( α ) Ak (k ; τ ). (9) 07 Jaanese Economic Associaion 003.

6 The Jaanese Economic Review By subsiuing (9) ino () and (3), he renal rice can be exressed as a funcion of τ, and he wage rae as a funcion of k and τ : ρ = α K (α /τ ) α /( α ) A ρ(τ ), (0) w = ( α K α )(α /τ ) α /( α ) Ak w(k ;τ ). () A marke-clearing condiion for roducive caial is s L = K +, which indicaes ha he oal savings by young agens of generaion, s L, mus equal heir own addiion o he fuure sock of roducive caial, K +. Given ha L = for all, his condiion is rewrien as s = k +. () Because he marke for roducive caial is comeiive, we have an arbirage condiion of he firm: ρ = R = R(τ ),. (3) is char- Given {k, E }, an equilibrium allocaion { c, c, s, m, E, w,, R,, k} acerized by (4) (3). Summarizing hese condiions, we obain: E + γη c (equaliy holds if m > 0), ; (4) R(τ )E + γη (equaliy holds if m > 0), ; (5) c c + c + ρ = + k + + m = w(k ; τ ), ; (6) = R(τ )k + + τ (k + ; τ ), ; (7) E + = E β(k ; τ ) + γ m,. (8) Exressions (4) (8) characerize he equilibrium sequence { c, c, m, E, k} =, given {k, E }. In wha follows, he focus is on he equilibrium ah wih m > 0; (4) and (5) hold wih equaliy. If successive generaions choose no o inves in he environmen, caial accumulaion occurs, whereas he qualiy of he environmen decreases coninuously in he fuure because of boh he accumulaion of emissions and he lack of mainenance invesmen. A some eriod, agens born in his eriod will find i worhwhile o inves in he environmen. The equilibrium ah of generaions wih osiive mainenance may dislay caial accumulaion and imrovemen in he qualiy of he environmen ino he fuure. We herefore focus on he equilibrium ah wih m > 0. 7 Summarizing (4) (8), we obain he scalar sysem of {k } under osiive mainenance: 7 See John and ecchenino (994) for he deailed characerizaion of he equilibrium ah, including he case of m = 0. Jaanese Economic Associaion

7 T. Ono: Environmenal Tax olicy and Long-Run Economic Growh FIGURE. k + ( + / K) + ( / ) A K G( ) = /( α η α α α τ ) [( α α ) τ / α β/ γ] τ, (9) k η where η η (/η + )( + α /α K ) + > 0 (see Aendix for he deailed calculaion). Equaion (9) characerizes he equilibrium ah wih m > 0. We also have 8 k+ E+ c+ c = = = (0) k E c c. The funcion G(τ ) shows he gross raes of growh in caial, environmenal qualiy and consumion. Thus, he (ne) growh rae is defined as g(τ ) G(τ ). () The rae is linearly relaed o roducive caial (k) because of he assumion of AK echnology. If g(τ ) 0 he economy dislays susainable develomen; ha is, roducive caial, environmenal qualiy and consumion remain consan (if g(τ ) = 0) or grow over ime (if g(τ ) > 0). On he oher hand, if g(τ ) < 0 he economy canno be susained. We herefore focus on he case of g(τ ) 0 in he following analysis. roosiion : Suose ha he following inequaliy holds: α α β η α α α [ A( αk α)( α)] A + +. α γ η αk () Then here exis wo criical values of τ, ] and 7, where 0 < ] < 7 <, such ha g(τ ) 0 for τ [], 7 ]. roof: From (9) and (), g(τ ) 0 is equivalen o where 3 η ( + α /α K )/η +. /( ) ( α / τ ) α A [( α α ) τ / α β/ γ] 3, K 8 See Aendix for deailed calculaion. 09 Jaanese Economic Associaion 003.

8 The Jaanese Economic Review Mulilying boh sides of his inequaliy by (τ ) /( α ) and rearranging, we have /( α ) /( ) ( α ) α A [( α α ) τ / α β/ γ] 3 ( τ ), K or α H ( ) ( ) /( α ) A( ) H ( ) ( ) / ( α τ α α α τ τ τ ) β( α ) / ( α 3 + ) A/ γ. K The lef-hand side of he above inequaliy is denoed by H (τ ), and he righ-hand side by H (τ ). As deiced in Figure, H (τ ) is a sraigh line crossing he origin, whereas H (τ ) is a convex curve wih an inerce β(α ) /( α ) A/γ > 0. Thus, here exiss τ (0, ) such ha g(τ ) 0 if and only if here exiss τ (0, ) ha saisfies H (τ ) H (τ ). The ask is o seek he range of τ ha saisfies H (τ ) H (τ ). Le 4 denoe he ax rae saisfying H (τ ) = H (τ ); a τ =, he sloe of H (τ ) is equivalen o he sloe of H (τ ). By direc calculaion, we obain A( αk α)( α) = α 3 ( α )/ α. There exiss τ (0, ) such ha H (τ ) H (τ ) if and only if H ( ) H ( ). The inequaliy H ( ) H ( ) is equivalen o (). If () holds wih a sric inequaliy, here exis wo values, ] and 7, where ] < 7 such ha H (τ ) = H (τ ) holds a τ = 7 and ], and H (τ ) > H (τ ) holds a τ (], 7 ). Under (), he inequaliy g(τ ) 0 holds when he ax rae saisfies τ [], 7 ]. The economy dislays susainable develomen where roducive caial, environmenal qualiy and consumion remain consan if τ = ] or 7, and where hey grow over ime if τ (], 7 ). If τ [], 7 ], he economy canno aain he susained growh. An environmenal ax has boh osiive and negaive income effecs on economic growh. To see hese effecs, consider he consrains of generaion in equilibrium, (6), (7) and (8), which are reduced o c c+ τ k ( + ; τ ) + + E w k E k + = ( ; τ ) + + [ β ( ; τ )]. R( τ ) γ R( τ ) γ Wih regard o he righ-hand side, he firs erm is wage income and he second erm is a lum-sum ransfer in old age evaluaed in erms of he rivae good in youh. These wo values are rivae good asses. The hird erm, [E β(k ; τ )]/γ, is he environmenal qualiy bequeahed from he revious generaion evaluaed in erms of he rivae good in youh: his is an environmenal asse. A higher ax leads o a smaller amoun of emissions; he hird erm on he righ-hand side becomes large. Generaion receives a higher qualiy of he environmen when i is born, which imlies a osiive income effec. I can choose more savings ha enhance caial accumulaion. On he oher hand, a higher ax imoses a heavier burden on he firms. They can ay lower wages o workers and lower axes o he governmen; he firs and he second erms become small. This negaive income effec leads o a decrease in mainenance invesmen and savings, hereby lowering levels of environmenal qualiy and caial. When he ax rae is oo low, such ha τ < ], he firms emi oo much olluion, so ha generaion receives a lower level of environmenal caial. This negaive income effec revens he economy from aaining susainable Jaanese Economic Associaion

9 T. Ono: Environmenal Tax olicy and Long-Run Economic Growh FIGURE. develomen. When he ax rae is oo high, such ha τ > 7, he firms have a heavy ax burden, so ha he level of rivae asses falls. This negaive income effec hinders susainable develomen. To obain susainable develomen, herefore, he long-lived governmen mus levy a moderae ax rae, i.e. τ (], 7 ). 4. Maximum rae of economic growh This secion aims o deermine he ax rae ha achieves he maximum rae of economic growh. roosiion : The growh rae g(τ ) aains he maximum a τ = τ * where τ * β ( ], 7 ). ( α α ) γ K (3) roof: From (9) and (), we have g ( τ ) = /( α ) ( α/ τ ) A( αk α) /( α ( ) ) β τ η( α ) τ γ( α α ) K τ. Thus, for τ (], 7 ), g (τ ) 0 holds if and only if τ τ *, imlying ha he growh rae is maximized a τ = τ *. The relaion τ * (],7 ) holds if H (τ *) > H (τ *) where he funcion H i (τ ) is defined in he roof of roosiion. By direc calculaion, i is shown ha H (τ *) > H (τ *) is equivalen o (). Thus, τ * (], 7 ) holds under (). Figure deics he relaion beween an environmenal ax rae and a rae of economic growh, and Figures 3 and 4 show numerical examles. 9 When he ax rae is iniially se 9 The mehod of deriving Figures 3 and 4 will be exlained below. Jaanese Economic Associaion 003.

10 The Jaanese Economic Review FIGURE 3. The figures describe he relaion beween he environmenal ax and he growh rae er eriod. The horizonal axis is he environmenal ax and he verical axis is he growh rae er eriod. The solid, dashed and doed lines corresond o he cases of γ/β = 0, 0 and 30, resecively. FIGURE 4. The figures describe he relaion beween he environmenal ax and he growh rae er year. The horizonal axis is he environmenal ax and he verical axis is he growh rae er year. The solid, dashed and doed lines corresond o he cases of γ/β = 0, 0 and 30, resecively. Jaanese Economic Associaion 003.

11 T. Ono: Environmenal Tax olicy and Long-Run Economic Growh below he criical level, raising he ax leads o a higher growh rae; he argumen of environmenaliss is effecive in his case. On he oher hand, when he ax rae is iniially se above he criical level, raising he ax lowers he growh rae; he argumen of indusrialiss is oeraive in his case. Therefore, wheher environmenaliss or indusrialiss are correc deends on wheher he ax is iniially se below or above he criical level, τ *. The ax rae ha achieves he maximum growh rae is high (low) if β is high (low) and γ is low (high). When β is higher and γ is lower, emissions have a greaer effec on he environmen while he environmenal mainenance has a lesser effec. Thus, he long-lived governmen needs o levy a higher rae of ax o conrol environmenal deerioraion. On he oher hand, when β is low and γ is high, he oosie argumen holds. The maximum rae of economic growh, g*, is measured by subsiuing τ = τ * ino (9): g* g( τ *) = α A( + + )( K ) /( α αγ η α α α ) αk β η α /( α ) The maximum growh rae is higher when he degree of he effec of emissions, β, is small and he degree of he effec of environmenal mainenance, γ, is high. A lower β imlies a lesser exernal effec of emissions on environmenal qualiy, while a higher γ means a greaer effec of environmenal mainenance on he environmen. These condiions imly ha fuure generaions can inheri a higher qualiy of he environmen from as generaions, which imlies a osiive income effec on savings and environmenal mainenance. Thus, a lower β and a higher γ lead o higher growh raes of roducive caial and environmenal qualiy. Figure 3 (4) deics he numerical examles of he relaion beween environmenal ax and he growh rae er eriod (er year) under several alernaive values of γ/β. 0 As for he oher arameer values, we assume η = η = and A = 6. Since here is lile evidence on he values of arameers abou references (η and η ) and he roduciviy including exernal effec of caial (A), we choose hese values in order o roduce lausible growh raes. From he figures, we can find ha, given he ax, he economy wih a higher efficiency of environmenal reservaion (i.e. a higher γ/β ) can aain a higher rae of economic growh. In closing his secion, I mus briefly menion he welfare imlicaions of he criical level of such a ax. Each generaion achieves he highes level of uiliy a he ax rae τ * along he equilibrium ah under osiive mainenance. Equaion (0) verifies his resul. A he ax rae τ * he economy dislays he highes growh raes of consumion and environmenal qualiy; ha is, each generaion under osiive mainenance can aain is highes levels of consumion and environmenal qualiy. Therefore, he ax rae τ * roduces a areo-suerior oucome o he oher ax raes, under he condiion ha he long-lived governmen levies an environmenal ax on firms. (4) 0 A eriod is assumed o be 5 years, roughly equal o he ime san of a generaion. Readers would susec ha, in he numerical examles resened in Figures 3 and 4, he value of β is exremely low relaive o ha of γ. This is because realisic values of hese arameers are hard o find. This aer ados several alernaive values of γ/β in order o derive lausible growh raes. 3 Jaanese Economic Associaion 003.

12 5. Discussion The Jaanese Economic Review The resul in roosiion deends heavily on he following wo assumions: (i) he disincion beween he shor-lived and he long-lived governmens, and (ii) he secific form of he uiliy funcion saisfying Assumion. This secion briefly considers how he modificaion of hese assumions would change he resul. A more realisic assumion abou he fiscal behaviour of he governmen is ha, under a given rae of ax, he governmen sends he ax revenue, τ, o finance environmenal invesmen, m. The governmen budge consrain is m = τ. This alernaive assumion, similar o ha in Barro (990), who considers he relaion beween ax and growh, imlies ha here is no disincion beween he shor-lived and long-lived governmens. In his case, each individual chooses his or her savings given environmenal invesmen by he governmen, m. The individual s roblem is o choose he level of saving, s, o maximize his or her uiliy subjec o he budge consrains uc (, c+, E+ ) c + s = w and c+ = R+ s, given m. Under Assumion, he saving funcion is s = η w /(η + η ). Thus, given he iniial endowmens {k, E }, he equilibrium sequence { k, E} = is characerized by he following wo equaions: η η α k+ = w( k; τ ) ( αk α) Ak ; η + η η + η τ E = E β( k ; τ ) + γτ k ( ; τ ). + α /( α ) The firs equaion is he caial-marke-clearing condiion, and he second is he environmenal equaion. Equaion (5) shows ha he growh rae of caial is decreasing in environmenal ax; ha is, he ax is always harmful o economic growh. This is a differen resul from ha in roosiion. By making an alernaive assumion abou he fiscal behaviour of he governmen, he inergeneraional disribuion effec hrough he environmen is eliminaed from he economy. Thus, he disincion beween he shor-lived and he long-lived governmens lays a key role in deriving he resul in roosiion. Anoher ossible modificaion is he generalizaion of he uiliy funcion. Under Assumion, he saving funcion is indeenden of he real ineres rae. This indeendence leads o a simle relaion beween environmenal ax and he growh rae shown in roosiion. If we assume a more general form of he uiliy funcion, here could aear o have an addiional effec of he ax hrough he ineres rae, yielding an addiional imac on economic growh. For examle, consider he following uiliy funcion, ofen used in he conex of economic growh: U θ ( c ) θ ( c + ) ( E + ) = + + θ π, µ θ θ θ where θ > 0 and θ, π > 0 is a discoun facor and µ > 0 is a arameer of environmenal awareness. The saving funcion derived from he above uiliy funcion deends on he real ineres rae. Afer some calculaion, he growh rae is (5) If θ =, he uiliy funcion is U = ln c + π (ln c+ + µ ln E+ ), yielding he saving funcion indeenden of he real ineres rae. Jaanese Economic Associaion

13 g( τ ) = T. Ono: Environmenal Tax olicy and Long-Run Economic Growh αk + α α K α γµ γ( αk α) γµ β τ + α K R( τ ) α R( τ ) α K + α / θ γ µ ( + γγπµ ( ) ) + α µ R( τ ) K / θ / θ K / θ. The ax has effecs on he growh rae in hree direcions. The firs wo aear in he numeraor; boh of hem are also found in he analysis of he revious secion (see he numeraor in (9)). The hird effec, which could no be found in he revious secion, aears in he denominaor. This new effec is derived by assuming he above uiliy funcion. Since R(τ ) is decreasing in τ, his effec has a osiive (negaive) imlicaion for he growh rae if θ < (>). 6. Concluding remarks This aer has considered he imac of environmenal axaion on long-run economic growh. On he basis of he overlaing-generaions model of growh and he environmen, we have found wo comeing forces ha he ax exers on economic growh. One is a negaive force, which hamers economic growh; he oher is a osiive force, which increases he level of environmenal qualiy bequeahed o fuure generaions. Thus, here exiss a criical level of he environmenal ax ha balances hese forces. If he ax is iniially se below (or above) he criical level, hen raising he ax is beneficial (or harmful) o economic growh. Environmenal axaion is no necessarily harmful o economic growh. Mos of he sudies on environmenal axaion and economic growh have been conduced by normaive analysis; ha is, hey examine oimal ax olicies ha inernalize environmenal exernaliies and aain efficien resource allocaion in a decenralized economy. In racice, however, environmenal ax olicy faces severe informaional and oliical consrains in seing he oimal level of such a ax. For examle, norhern Euroean counries (Denmark, Finland, he Neherlands, Norway and Sweden) have inroduced an emissions ax, bu i has been remarked ha he ax rae is no high enough o inernalize he exernaliies of environmenally harmful emissions. Accordingly, I have analysed he imac of raising an environmenal ax on long-run economic growh. The analysis in his aer should herefore conribue o he olicy debae on environmenal axaion and economic growh in norhern Euroean counries as well as in oher counries, such as Jaan, ha lan o inroduce environmenal axaion. Aendix We firs derive he scalar sysem of k under osiive mainenance, (9). From (6) and (7), we obain he life-cycle budge equaion: c c + τ ( k ; τ ) + m w k = ( ; τ ). R( τ ) + + By subsiuing he environmenal equaion (8) ino he above equaion and relacing m, we have 5 Jaanese Economic Associaion 003.

14 The Jaanese Economic Review c Exressions (4) and (5) lead o c τ ( k ; τ ) R( τ ) + [ E + E + β( k ; τ )] = w( k; τ ). γ c η c η R( τ ). = + (A) (A) We can relace c and c + wih k + by using (7) and (A): η R τ k R τ k τ k τ E E β k τ w k τ ηr( τ ) [ ( ) ( ; )] ( ) [ + + ( ; )] = ( ; ) R( τ ) γ Given ha (5) and (7) lead o we relace E + (E ) in (A3) wih k + (k ): By subsiuing (0), () and (3) ino he above equaion and rearranging, we obain (9). We nex derive he relaion (0). From (7), consumion in old age is from (9), (0) and (3). Thus, we have c+ / c = k+ / k. Under osiive mainenance, we also have E+ / E = c+ / c = k+ / k from (5), and c/ c = E+ / E = k+ / k from (4). We herefore obain (0). Final version acceed 4 February 00. E γη = R k k + R( ) [ ( τ ) τ τ ( ; τ )], η R τ k γη R τ k τ k τ R τ k τ k τ ηr( τ ) [ ( ) ( ; )] ( ) R( τ ) γ R( τ ) [ ( ) + + ( + ; )] γη R τ k R( τ ) [ ( ) + τ k ( ; τ )] + βk ( ; τ ) wk ( ; τ ). = /( ) /( ) c+ = R k+ + k+ = K Ak + ( τ ) τ ( ; τ ) α α α α τ α α + ; τ τ (A3) REFERENCES Barro, R. J. (990) Governmen Sending in a Simle Model of Endogenous Growh, Journal of oliical Economy, Vol. 98,. S03 5. Baumol, W. and W. Oaes (988) The Theory of Environmenal olicy, Cambridge: Cambridge Universiy ress. Jaanese Economic Associaion

15 T. Ono: Environmenal Tax olicy and Long-Run Economic Growh Bovenberg, A. L. and S. A. Smulders (995) Environmenal Qualiy and olluion-augmening Technological Change in a Two-Secor Endogenous Growh Model, Journal of ublic Economics, Vol. 57, and (996) Transiional Imacs of Environmenal olicy in an Endogenous Growh Model, Inernaional Economic Review, Vol. 37, Fisher, E. and C. van Marrewijk (998) olluion and Economic Growh, Journal of Inernaional Trade and Economic Develomen, Vol. 7, Grimaud, A. (999) olluion ermis and Susainable Growh in a Schumeerian Model, Journal of Environmenal Economics and Managemen, Vol. 38, Ihori, T. (996) Environmenal Exernaliies, Growh and Consumion Taxes, Universiy of Tokyo Discussion aer 96-F-0. John, A. and R. ecchenino (994) An Overlaing Generaions Model of Growh and he Environmen, Economic Journal, Vol. 04, John, A., R. ecchenino, D. Schimmelfennig and S. Schref (995) Shor-lived Agens and he Long-lived Environmen, Journal of ublic Economics, Vol. 58, Jouve,.-A.,. Michel and J.-. Vidal (000) Inergeneraional Alruism and he Environmen, Scandinavian Journal of Economics, Vol. 0, Lighar, J. and F. van der loeg (994) olluion, he Cos of ublic Funds and Endogenous Growh, Economics Leers, Vol. 46, Mohadi, H. (996) Environmen, Growh and Oimal olicy Design, Journal of ublic Economics, Vol. 63, Ono, T. (996) Oimal Tax Schemes and he Environmenal Exernaliy, Economics Leers, Vol. 53, and Y. Maeda (00) areo-imroving Environmenal olicies in an Overlaing Generaions Model, Jaanese Economic Review, Vol. 53,. 5. van der loeg, F. and C. Wihagen (99) olluion Conrol and he Ramsey roblem, Environmenal and Resource Economics, Vol., Romer,. (986) Increasing Reurns and Long-run Growh, Journal of oliical Economy, Vol. 94, Sokey, N. L. (998) Are There Limis o Growh?, Inernaional Economic Review, Vol. 39,. 3. Yoshida, M. (998) Nash Equilibrium Dynamics of Environmenal and Human Caial, Inernaional Tax and ublic Finance, Vol. 5, Zhang, J. (999) Environmenal Susainabiliy, Nonlinear Dynamics, and Chaos, Economic Theory, Vol. 4, Jaanese Economic Associaion 003.