Capital Income Taxation and Economic Growth in Open Economies

Transcription

1 WP/04/91 Capal Income Taxaon and Economc Growh n Open Economes Gerema Palomba

2 2004 Inernaonal Moneary Fund WP/04/91 IMF Workng Paper Fscal Affars Deparmen Capal Income Taxaon and Economc Growh n Open Economes Prepared by Gerema Palomba * Auhorzed for dsrbuon by Mchael Keen May 2004 Absrac Ths Workng Paper should no be repored as represenng he vews of he IMF. The vews expressed n hs are hose of he auhor(s) and do no necessarly represen hose of he IMF or IMF polcy. descrbe research n progress by he auhor(s) and are publshed o elc commens and o furher debae. Do reducons n capal ncome axes arac foregn capal and, a he same me, foser economc growh? Ths paper examnes he effec of capal ncome axaon on he nernaonal allocaon of capal and on economc growh n a wo-counry overlappng generaons model wh endogenous growh and nernaonally moble capal. I shows ha domesc capal axes affec boh he nernaonal allocaon of capal and he rae of economc growh and ha hese wo effecs are no necessarly he same. A counry can ncrease s share of he exsng world capal by changng s axes bu, dependng on he elascy of savng o afer-ax reurns, hs may reduce he rae of capal accumulaon and economc growh. JEL Classfcaon Numbers: F2, H2, O4 Keywords: Open economes, endogenous growh, capal ncome axaon Auhor s E-Mal Address: gpalomba@mf.org * The auhor wshes o hank Tony Aknson and Mchael Keen for her advce and commens.

3 - 2 - Conens Page I. Inroducon... 3 II. The Model... 4 A. Indvduals... 5 B. Frms... 7 C. Publc Secor D. Marke Equlbra and Accumulaon...10 III. Tax Inerdependences n Open Economes IV. The Effec of Taxaon n a Two-Counry World A. Momenary Equlbra and Inernaonal Allocaon of Capal B. Ineremporal Equlbra, Economc Growh, and Welfare C. Comparng Predcons V. Conclusons Appendx I. Two-Counry Model wh Cobb-Douglas Uly and Producon Funcons References Fgure 1. Momenary Equlbrum...15

4 -3- I. INTRODUCTION In many counres, reducons n capal ncome axes are used as a means of aracng foregn capal and foserng economc growh. In he European Unon, for example, many counres have reduced capal ncome axes. In he Uned Saes, here has recenly been consderable debae abou he need o cu corporae axaon. However, despe he lnk beween domesc axaon of capal and nernaonal accumulaon, lmed aenon has been gven o examnng how domesc ax reforms may dfferenly affec he nernaonal allocaon of capal and s accumulaon n an negraed world. The dsncon s mporan. If a reducon n capal ncome axes fosers accumulaon, hen we need o know wheher ncreases he level of capal or wheher ncreases he rae of capal accumulaon. The numercal measure of he supposed advanage may be dfferen. Unforunaely, he heorecal analyss of nernaonal axaon usually reles on shor-perod models ha focus on he effec of domesc axes on he nernaonal allocaon of a gven sock of capal and gnore long-erm accumulaon (e.g., Gordon, 1983; Zodrow and Meszkowsk, 1986; Razn and Sadka, 1991; Wldasn 1991; Wlson 1986, 1991; and Bucovesky and Wlson, 1991). Models ha consder accumulaon ypcally lm he analyss o he case of small economes (e.g., Razn and Yuen, 1993, 1999; Turnovsky, 1996; and Asea and Turnovsky, 1998) or o economes wh no economc growh (e.g. Bovenberg 1986; Sber, 1990; Ghosh 1991; and Ha and Sber, 1997). Thus, he queson remans: can ax reducons arac foregn capal and, a he same me, foser capal accumulaon, as s ofen clamed? The am of hs paper s o examne he nernaonal effecs of domesc axaon of capal on he nernaonal allocaon of capal and on accumulaon n an negraed world wh large economes. The analyss s conduced n erms of a wo-counry model of endogenous growh where capal s nernaonally moble and ax decsons n one counry affec he growh process n he oher. In so dong, he approach aken here dffers n several respecs from ha n prevous conrbuons. Frs, he nernaonal effecs of domesc axes are examned by focusng on he neremporal mplcaons on accumulaon and growh and no smply on he cross-counry allocaon of a gven sock of capal. Second, explc accoun s aken of he nerdependence beween capal mobly and growh. I s ofen recognzed ha mobly of physcal capal mples ransfers of echnology and knowledge across counres, so ha echnology splls over from one counry o ohers (Bernsen and Mohnen, 1998; and Bayoum, Coe, and Helpman, 1999). However, progress n formulang models of economc growh wh nernaonal spllovers n echnology has been lmed. The model presened n hs paper capures hese nernaonal lnks by exendng a ypcal learnng-by-dong model o he case of open economes (Berola, 1993). The basc model of growh s formally se up n he nex secon. Ths s a wo-counry Samuelson-Damond ype of model wh overlappng generaons as n Buer (1981), bu ncorporaes, n addon, he publc secor and economc growh. These aspecs have been reaed by Razn and Yuen (1996) and Lejour and Verbon (1997) n he conex of nfne-lfe-agen models. In hese models, however, me preferences lm cross-counry ax dependences wh he effec ha he Euler equaon predcs a sable long-run posve relaon beween he ne-of-ax neres rae and economc growh. As a resul, ncreases n axaon reduce (hrough lower ne reurns) he sock of domesc capal and decrease he rae of economc growh. For example, n her analyss of ax compeon n a wo-counry world, Lejour and Verbon (1997) observe ha:

5 -4-...a hgher domesc source-based capal-ncome ax wll generae a lower growh rae of wealh (p. 485) and (hrough lower ne reurns) an ouflow of capal. Thus, he effec on he nernaonal allocaon of capal and on economc growh concde. The use of he overlappng-generaons model solves hs problem. In hs model, frs-perod consumpon dffers from second-perod consumpon; hus, he ne-of-ax neres rae does no have o equal he rae of me preference. In hs seng, changes n he domesc ax raes affec he neres rae and he ndvdual savng behavor n each counry, hereby nfluencng he nernaonal allocaon of capal and economc growh n dfferen ways. Ths model s used o examne he nernaonal effecs of domesc source- and resdence-based capal axes. The analyss shows ha axes affec he nernaonal allocaon of capal, bu hs sac effec s no smply repeaed generaon afer generaon. Changes n capal ncome axes also affec he rae of growh of capal, and he sac and growh effecs do no necessarly go n he same drecon. A counry can ncrease s share of curren world capal by reducng s source-based axes bu, dependng on he elascy of savng o ne-of-ax reurns, hs may reduce s savng level, hus lowerng he rae of economc growh; hs s a case ha appears o have some emprcal suppor (e.g., Berhem, 2002). The analyss also brngs ou a second mporan pon, namely ha he oupu and he welfare effecs of a gven ax polcy do no necessarly concde. Ths s hardly surprsng bu deserves menonng because of s specfc raonale n he open-economy seng. In an open economy, a dsncon exss beween he effec of axes on domesc produc and he effec on resdens clams on ha produc, ha s he naonal ncome. Polcans are ofen concerned wh he effec of ax reforms on he rae of growh of domesc produc, bu welfare s concerned wh he naonal ncome, and he wo effecs may be dfferen. A counry can ncrease domesc producvy and he growh rae of s produc by lowerng s axes, bu hs may lower he level of domesc savng, hus reducng he clams of s czens on fuure produc and, herefore, her welfare. The res of he paper s organzed as follows. The model s formally se up n Secon II. Secons III and IV examne he nernaonal effecs of domesc source- and resdence-based capal axes. Secon V summarzes he resuls and concludes. II. THE MODEL Consder a sylzed economy conssng of wo counres ( =1, 2), eachnhabedbyasngle ndvdual or an aggregae of dencal ndvduals, as well as frms and a governmen. To provde a smple model of ndvdual savng behavor, we use an overlappng generaons model n whch ndvduals born a me lve for wo perods. The global economy, herefore, consss of wo Samuelson-Damond ype economes. The me srucure of he model s as follows. In each counry, ndvduals work only n he frs perod of lfe, supplyng nelascally her labor L and earnng a real wage rae w and a oal wage ncome w L. They consume par of hs ncome mmedaely and save he res o fnance her second-perod reremen consumpon. The savng of he young a me can be allocaed eher domescally or abroad and generaes he capal sock n he followng perod. For smplcy, ndvduals are assumed o be mmoble, bu capal s perfecly moble across counres. Once he second perod arrves, compeve frms operang n each counry combne

6 -5- nernaonally moble capal K +1 wh local labor of he young L +1 o produce a sngle homogeneous oupu. Each counry s oupu s hen eher sold as fnal consumpon or purchased by he naonal governmen and used o provde an amoun G +1 per head of publc good. 1 Governmens fnance her publc expendure hrough wo dfferen ypes of capal ncome axes. Each naonal governmen leves a proporonal source-based ax σ on ncome from capal nvesed n he counry. In many counres, hese axes apply o a large number of ax bases ncludng, corporae profs, neress and capal gans. Governmens also levy a lnear ax ρ on resdens ncome ndependenly of where ncome orgnaes; ha s, hey levy a resdence-based ax on naonal savngs. Each of hese axes may vary over me, hus each generaon faces domesc ax vecors τ +1 = ρ +1, σ As a resul of hese assumpons, he reparaed reurn o capal nvesed n counry, r,s r = 1 σ r where r denoes he margnal reurn ha frms pay o capal. The afer ax reurn accrung o naonal savngs nvesed a home and abroad s, respecvely, β = 1 ρ r = 1 ρ 1 σ r β j = 1 ρ r j = 1 ρ 1 σ j r j where, j =1, 2 and 6= j. Ths s he reurn ne-of-savng axaon o counry s resdens from capal nvesed n, respecvely, counry and j. A. Indvduals In each counry, he represenave member of he generaon born a me plans hs consumpon so as o maxmze he uly funcon 3 u c 1,c 2+1,L + m G +1 where c 1 and L denoe he frs-perod consumpon and consan labor supply, respecvely, 1 The publc good can be seen as a publcly provded prvae good, so ha scale effecs are gnored. 2 The generaon born a me s subjec o capal ncome axes on reurns maurng when old, ha s a me +1. Oher forms of axaon are, of course, preferable o hese axes whch dsor nvesmen and savng decsons. In hs seng, a ax on labor ncome, for example, s non-dsoronary as labor s nelascally suppled. However, hs s equvalen o levyng a lump-sum ax, and he purpose of he analyss s o explore decenralzed governmen behavor n he absence of lump-sum axaon. In addon, s worh nong ha n a seng wh large counres, naonal governmens may wan o use dsoronary axes even f frs-bes ools are avalable. 3 For smplcy, we assume ha here s no populaon growh and normalze oal populaon o be equal o one. Ths allows us o concenrae on he sngle represenave member of each generaon.

7 -6- wh L = L ; c 2+1 and G +1 denoe he second-perod consumpon and publc good provson, and s assumed ha he funcons u ( ) and m ( ) are srcly ncreasng, srcly quas-concave and wce connuously dfferenable, wh lm u 0 c 1 0 c 1 (c 1,c 2) = lm u 0 c 2 0 c 2 (c 1,c 2)=+, and lm m 0 (G )=+, wh publc goods enerng n a separable manner. The assumpons on G 0 publc goods are clearly srong. The addve separably of he uly funcon s unforunaely resrcve, as s he assumpon ha uly derved from publc goods s ndependen of he crcumsances of he recpens. 4 The represenave ndvdual maxmzes hs uly subjec o he lfeme consrans w L = c 1 + S S = S + S j c 2+1 = 1+ 1 ρ +1 r +1 S ρ +1 r j +1 S j where 6= j. The frs consran saes ha he frs-perod wage ncome, wl, can be consumed or saved. In urn, savng S s nvesed eher home, S, or abroad, S j. The las consran requres ha, n he second perod, he ndvdual consumes all hs wealh, ncludng prncpal and ne reurns, gven ax raes and he afer-ax domesc reurns r+1 and r+1. j The ndvdual s supposed o have perfec foresgh regardng r+1 and r+1, j and he fuure ax raes on capal ncome boh a home and abroad. Capal s nernaonally moble and, n equlbrum, s allocaed across counres so as o equae naonal afer-resdence ax reurns β +1 and β j +1 (wh, j =1, 2 and 6= j) whch mples ha r+1 1 = r+1; 2 hus, n equlbrum R +1 = 1 σ 1 +1 r 1 +1 = 1 σ 2 +1 r 2 +1 (1) where R +1 s he economy-wde reurn o capal before resdence ax and depends on boh counres source axes. As far as her asse allocaon s concerned, prvae nvesors respond o dfferences n naonal source-based axes σ +1, bu no o changes n he resdence ax raes ρ +1. In fac, he burden of resdence axaon s ndependen of where savngs are nvesed, and has no effec on he nernaonal locaon of capal. In equlbrum, he ndvdual s, herefore, ndfferen o nvesng a home (S ) or abroad S j, carng only abou he level of oal savng. We can hen consoldae prevous consrans no a sngle presen-value budge consran c 2+1 = 1+ 1 ρ+1 R+1 w L c 1 (2) The soluon o he consumer s problem of maxmzng uly subjec o (2) s sraghforward. Applyng he sandard mehod of consraned opmzaon, he frs order condon for a maxmum s u 0 c 1 ( ) =u 0 c 2 ( ) 1+ 1 ρ +1 R+1 (3) where he condons on he uly funcon u ensure ha c 1 > 0 and c 2+1 > 0. 4 For alernave assumpons abou he role of publc goods, see for example Azarads (1993).

8 -7- Ths also gves us he savng behavor of he sngle generaon n each counry, S = ξ w L, 1 ρ+1 R+1 = ξ w L, β +1 (4) where, dfferenang wh respec o he varables w and β +1, we oban 0 < ξ 0 w < 1, whle he sgn of ξ 0 β s undeermned. In hs model, savng s an ncreasng funcon of wage-ncome, +1 bu he effec of he ne rae of reurn β +1 s ambguous. An ncrease n he neres rae (or a decrease n he ax raes) leads ndvduals o shf consumpon from he frs o he second perod (subsuon effec), bu also makes possble o ncrease consumpon n boh perods (ncome effec). The overall mpac of hese effecs depends on he elascy of subsuon beween consumpon n he frs and second perod of lfe. If hs elascy s greaer (smaller) han one (where one s assumed o be he expendure elascy), hen he subsuon (ncome) effec domnaes, and an ncrease n he rae of reurn β +1,oraloweraxrae,leadsoanncrease (decrease) n savng. I may be noced ha he behavor of generaon depends on boh domesc and foregn axes. I drecly depends on he domesc resdence ax rae ρ +1 and hrough he worldwde reurn o capal R, also depends on he source ax rae a home and abroad σ +1, σ j +1. A mes, may be convenen o work wh homohec uly funcons. In hs case, he opmal condons ake, n fac, a parcularly smple form wh savng beng lnear n he wage ncome: S = s 1 ρ +1 R+1 w L (5) If we furher resrc he aenon o he specal case wh Cobb-Douglas uly funcons, he facor s ( ) becomes a consan (see Appendx I). In wha follows, hese smple examples wll be useful n dscussng a numberofax-relaedssues. B. Frms In each counry, frms ac compevely, hrng local labor and renng capal o produce a sngle homogeneous oupu accordng o he aggregae ne producon echnology F (A,K,L ).Ths s a wce connuously dfferenable funcon wh decreasng reurns n capal and labor, and a local producvy facor A. 5 To model connual endogenous growh, we assume ha frms n each counry accumulae new capal and nadverenly conrbue o he producvy of capal locally nvesed by ohers. In hs sense, producon spllovers exs ha are naonal n scope, and he producvy facor may be defned as A (K ). Ths represens uncompensaed spllovers of knowledge or deas from one producer o anoher whn he same counry as for example n Arrow (1962). In an negraed world economy counres have access, however, o a larger se of knowledge and echnologes han hey have n a non-negraed envronmen. In parcular, he sock of capal avalable abroad affecs producvy a home, and nernaonal mobly of hs capal 5 I s also assumed, for convenence, ha he funcon F ( ) sasfes he Inada condons wh respec o he sock of domesc capal K.

9 -8- mples ransfers of echnology and deas, so ha echnology splls over from one counry o ohers. To capure hese cross-border echnologcal exernales, he producvy facor may be redefned as A K,K j,where 6= j (Berola, 1993). Wh hs formulaon, capal abroad affecs producvy a home and cross-counry capal flows mply nernaonal ransfers of echnology and knowledge. Ths mechansm of growh s a very smple exenson of he learnng by dong model orgnally proposed by Arrow (1962), and laer suded by Romer (1986). In addon, however, akes no accoun he fac ha domesc producon and nvesmen canno be ndependen when counres are economcally negraed. 6 The exsence of nernaonal growh exernales has recenly receved wdespread aenon. Coe and Helpman (1995), for example, analyzed he effecs of R&D spendng n OECD counres and concluded ha each counry s oal facor producvy sgnfcanly depends on foregn R&D capal. Usng a specal verson of he IMF s MULTIMOD, hese auhors (and Bayoum, 1999) calculaed ha 7 When all ndusral counres rase R&D spendng by an amoun equvalen o 1 of 1% of 2 GDP, he long-run US oupu gan s 50% hgher han n he case when only US R&D spendng rses. (Bayoum e al, 1999, p. 425) Turnng o he deals of he model, n each counry he producon funcon F (A,K,L ) s assumed o be lnearly homogeneous n he domesc sock of capal K and n he producvy facor A. In urn, he producvy facor s lnearly homogeneous n K and K j, and a he lm A 0 as K 0 or K j 0, so ha posve producvy requres a posve level of capal n boh counres. The assumpon ha he producvy facor A s lnearly homogeneous n capal socks s he naural counerpar of he ypcal AK-model of growh ha has been so wdely used n sngle counry models. In hese models, he lnear-homogeney assumpon capures he producvy spllover n naonal conex. In a wo-counry conex, however, would no be reasonable o assume ha he foregn capal smply adds o he domesc effec, hereby generang ncreasng reurns o capal. Raher, he assumpon here s ha domesc and foregn capal combne o have he same mpac on producvy as assumed n a sngle counry model. Under hese assumpons, we can wre he oupu n each counry as F Ã Ã!! A K,K j,k,l K j = f a K = H (α ) K where he consan supply of labor L has been omed, and α = Kj,wh 6= j. We hen have K a sor of open-economy verson of an AK-model where endogenous growh s susaned by a posve exernal effec of boh domesc and foregn capal socks on oal facor producvy. I s worh nong ha n hs model, he reurn o capal s consan n he aggregae, and hs s a suffcen condon for havng economc growh; however, decreasng reurns sll preval 6 For dscusson of nernaonal spllovers of knowledge, see for example Berola (1993), and Grossman and Helpman (1994). 7 For emprcal evdence of nernaonal spllovers of R&D spendng, and references o he leraure, see also Bernsen and Mohnen (1998), and Leahy and Neary (1999). K

10 -9- when domesc capal s consdered separaely. In addon, domesc producon depends on how capal s locaed beween he wo counres. In hs conex, prof-maxmzng compeve frms pay facors her margnal producvy r = F 0 w K k A (A,K )=r (α ) = H (α ) r (α )=ω (α ) where F 0 k A s he margnal producvy of capal for he sngle frm whch akes he producvy facor A as exogenously gven, and he dependence of he r and ω funcons derves from he propery of lnear homogeney of he producon funcon. I may be noced ha a each me he neress of capal owners (he old people) do no necessarly concde wh hose of wage earners (he young). Increases n he relave allocaon of domesc capal (he rao α ) rse, n fac, he prvae margnal produc of capal and have ambguous effecs on ha of labor, possbly decreasng, as r 0 α (α ) > 0 ω 0 α (α )=Hα 0 (α ) r 0 α (α ) 0 where H 0 α (α ) s posve, so ha he sgn of ω 0 α (α ) s ambguous. Ths creaes a poenal nergeneraonal conflc ha s of grea mporance n examnng he neremporal effecs of capal axes. A mes, s convenen o work wh he more resrcve class of Cobb-Douglas producon funcons h A Y = 1 1 ² 1 ² K ² L ϑ wh ²>0, ϑ < 1 and wh a mulplcave form for he producvy spllovers µ A = η K µ K j, j =1, 2 and 6= j where µ + µ =1 ² and µ, µ, η > 0 n boh counres so o sasfy prevous assumpons. In hs case, he naonal produc Y, he prvae reurn o capal r, and he wage rae w ake a very smple form, all beng funcons of he nernaonal allocaon of capal α = Kj, K Y K = η (L ) ϑ α µ r = F 0 k A = ²η (L ) ϑ α µ w =(1 ²) η (L ) ϑ α µ K (6) In hs smplfed case, he prvae rae of reurn s no a funcon of domesc capal K,oher han hrough α, whereas domesc produc and wage rse proporonally wh K.

11 -10- C. Publc Secor As seen earler, n each counry he governmen provdes an amoun of local publc goods G +1 o each generaon and fnances hese expendures by levyng dsoronary axes on he resdens ncome from savng and on ncome from domescally nvesed capal ρ +1, σ +1.If one un of oupu can be ransformed o one un of publc good, each governmen s revenue consran may be hen wren as G +1 = σ +1r (α +1 ) K +1 + ρ +1r +1S + ρ +1r j +1S j (7) where varables are per capa as here s no populaon growh and populaon has been normalzed o one. The frs erm on he rgh-hand sde of hs expresson denoes revenue from he source-based ax σ +1, and he oher wo erms ndcae revenue from axes on he reurn o naonal savngs a me ; hese savngs are nvesed, respecvely, a home and abroad, and yeld a reurn a me +1. As he reader may have already noced, governmen deb has been gnored. In hs model wh overlappng generaons, deb polcy would, n fac, be equvalen o levyng dfferenal lump-sum axes, and our purpose s o explore decenralzed governmen behavor n he absence of hese axes. 8 D. Marke Equlbra and Accumulaon A hs pon, we can complee he buldng blocks of hs wo-counry model of growh, and deermne he equlbra n he naonal facor markes and n he world capal marke, as well as derve he law of capal accumulaon for hs economy. Naonal facor markes equlbra There are wo facor markes n each counry, one for labor and one for capal servces. Labor s nelascally suppled by ndvduals and he supply of capal a each me s deermned by he savng decsons made n he prevous perod. Equlbrum n naonal facor markes s obaned when he wage and he renal rae on capal are such ha compeve frms wsh o use he avalable amoun of labor and capal servces. Therefore, he facor marke equlbrum condons are gven by equaons (6). I may be worh nong ha he wage w and he renal cos of capal r need no o be he same n he wo counres. World capal marke equlbra and accumulaon Equlbrum n he nernaonal marke of capal requres ha capal s allocaed across counres so ha equals naonal ne reurns (see condon (1)). Usng prevous equlbrum condons (6) for domesc reurns r +1, we have: R +1 = 1 σ +1 r (α +1 )= 1 σ j +1 r j (α +1 ) (8) 8 For dscusson of he equvalence beween governmen deb polcy and dfferenal lump-sum axaon n overlappng generaons models, see for example Damond (1973, p. 222) and Aknson and Sandmo (1980, p. 533).

12 -11- wh, j =1, 2 and 6= j. Capal marke equlbra also requre ha he oal demand for capal n each perod be equal o he supply or ha world nvesmen be equal o world savng: K +1 = K+1 + K j +1 = S + S j = (9) = ξ ω (α ) K, 1 ρ+1 R+1 + ξ j ω j (α ) K j, 1 ρ j +1 R+1 where K +1 s he oal sock of capal n he economy, and we have used he equlbrum condons (6) for w,wh, j =1, 2 and 6= j. Ths condon mples ha he oal sock of capal a me +1s equal o he oal world savng of he young nhered from he pas. I may be noced ha n each counry, he sock of capal can be greaer or smaller han domesc savng. In open economes, domesc savngs can be, n fac, nvesed boh a home and abroad, so ha he locaon of physcal capal and he value of clams on domesc and foregn capal by home resdens, namely naonal ncome, no longer concde. As n he naonal ncome accouns, we hen need o dsngush beween domesc produc produced wh he avalable capal and naonal ncome, ha s resdens clams on he world produc. We can solve prevous condon (8) for he equlbrum capal rao α +1 = Kj +1 K+1 he source-based axes σ +1, σ j +1, as a funcon of α +1 = Kj +1 K +1 = α σ +1, σ j +1, j =1, 2 and 6= j Ths s an ncreasng funcon n σ +1 and declnng n σ j +1. Subsung hs expresson n he equlbrum condon (8), we oban he equlbrum world-wde reurn o capal R +1, R +1 = R σ +1, σ j +1, j =1, 2 and 6= j Theworld-wdereurnR +1 s a declnng funcon n he source axes and s ndependen of he sock of capal. Ths specal feaure derves from our cross-counry mechansm of growh and makes he model parcularly racable. 9 A hs pon, we can derve he law of capal accumulaon n each counry. In parcular, we can subsue prevous expressons for α +1 and R +1 n condon (9) and usng he fac ha K j +1 = α +1 K +1 and he dependence on ax varables, we oban K+1 = K +1 = S + S j = h k, τ 1+α +1 1+α +1, τ j S K j +1 = α +1 K+1 = α + S j +1 = h j k, τ +1 1+α, τ j (10) 9 For an explc calculaon of he rao α +1 and he rae R +1 n he case of Cobb-Douglas producon funcons, see Appendx I.

13 -12- where τ +1 = ρ +1, σ +1 s he vecor of ax raes n each counry, and k = K,K j s he vecor or nhered socks of capal n boh counres wh, j =1, 2 and 6= j. These equaons gve us he law of capal accumulaon and he dependency on ax polcy. In each counry, he sock of capal a me +1s a funcon of he nhered socks of capal n boh counres, he vecor k, as hey boh nfluence domesc facor prces, and of governmens ax decsons τ +1, τ j +1. I may be noced ha he sock of capal n each counry depends on boh counres domesc ax raes. As a resul, changes n one counry s ax raes nfluence capal accumulaon boh a home and abroad. Clearly, he model does no, whou furher resrcons on he uly and producon funcons, guaranee eher exsence or unqueness of an equlbrum accumulaon pah for hs economy. In wha follows, we assume ha a unque equlbrum wh posve capal exss, and Appendx I presens a Cobb-Douglas verson of hs model where an equlbrum does exs. 10 III. TAX INTERDEPENDENCIES IN OPEN ECONOMIES The analyss of prevous secons suggess ha here are a number of dfferen channels hrough whch domesc axaon of capal exers nernaonal effecs. Frs, domesc axes affec he nernaonal allocaon of he exsng sock of world capal. Ths effec has long been a he cener of publc debae and of he leraure on nernaonal axaon (for a recen survey, see Wlson 1991). Ths s no, however, he only effec. Second, domesc axes affec nernaonal growh and how capal accumulaes over me. A counry can nfluence, for example, he level of savng boh a home and abroad by changng s capal ncome axes, hence affecng he nernaonal rae of capal accumulaon and economc growh. As he analyss wll show, hs growh effec may well dffer from he sac effec on he nernaonal allocaon of capal, so ha he sac argumen canno be smply repeaed generaon afer generaon. Thrd, he analyss suggess ha an mporan dsncon exss beween he effec of axes on domesc produc and he effec on naonal ncome, namely he clams of resdens on he world produc. Ths dsncon s mporan. Polcans seem ofen concerned wh domesc produc, and welcome low axes as a means of achevng hgher raes of economc growh. Economss, on he oher hand, are more neresed n he welfare effecs of axaon, and welfare s concerned wh naonal ncome. Alhough boh growh and welfare may be legmae performance crera, he dsncon s mporan as he wo crera may lead o very dfferen conclusons as o he effec of axes. Fnally, domesc axaon of capal has mporan nernaonal dsrbuonal effecs. Changes n naonal axes n one counry nfluence he welfare of ndvduals boh a home and abroad hrough changes n he nernaonal allocaon of capal α, hus n facor prces. For example, a hgher domesc source-based ax n counry leads o a relavely smaller sock of home capal (he 10 For dscusson of he exsence and unqueness of equlbra n overlappng generaons models, and reference o he leraure, see Blanchard and Fsher (1989), and Azarads (1993). For applcaons o models wh open economes and o models wh endogenous growh, see also Buer (1981), and Buer and Klezer (1992).

14 -13- rao α decreases), and suppose ha hs also nduces an ncrease n he level of naonal wages snce, for nsance, ω 0 α (α ) < 0. As a resul, he welfare of he young people currenly alve a home rses. A he same me, he ax also affecs he welfare n he foregn counry. In fac, decreases he welfare of young abroad snce he ax-generaed capal nflow lowers her wages. The welfare effecs of a ax change may be complex. I s o some of hese ssues ha we now urn. IV. THE EFFECT OF TAXATION IN A TWO-COUNTRY WORLD In hs secon, we consder he nernaonal effecs of domesc ax polces. In parcular, we consder wo ssues: he mpac of domesc axes on he nernaonal allocaon of capal and he mpac on he rae of economc growh boh a home and abroad. These ssues have been a he cenre of he publc debae on capal ncome axaon, bu hey are ofen confused. The dsncon s, however, mporan. If s argued ha a reducon n capal ncome axes fosers accumulaon, hen we need o know wheher ncreases he level of capal or wheher rases he rae of capal accumulaon. The numercal measure of he supposed advanage may be very dfferen and so s he assessmen of he proposed ax reducon. In order o provde a rgorous dscusson of hese quesons, we nroduce wo conceps of equlbra: he sac or momenary equlbrum, and he dynamc or neremporal equlbrum. A. Momenary Equlbra and Inernaonal Allocaon of Capal The effec of domesc axes on he nernaonal allocaon of capal has been he subjec of much aenon n he leraure on capal axaon, and s from hs ssue ha we sar our dscusson. To examne hs effec, we need o nroduce he concep of sngle-perod or momenary equlbrum. Ths s defned as an nernaonal allocaon of capal ha, gven ax raes, mples equlbrum n boh counres naonal markes. I may hen be characerzed by a se of prces {w,r } and consumpon-savngs allocaons such ha, n each counry, frms maxmze profs, agens maxmze uly, and governmens sasfy her budge consrans. The exac equlbrum clearly depends on he exsng naonal fscal polces {ρ, σ,g }, and on he aggregae sock of capal, K, nhered a he begnnng of he perod. A each me, he momenary equlbrum can, herefore, be fully descrbed as a funcon of he curren naonal polces and he nhered sock of capal. The momenary equlbrum can be used o deermne he nernaonal allocaon of capal a each nsan and he dependence of ax raes. In parcular, n equlbrum he aggregae sock of capal K mus be locaed beween he wo counres, so ha K = K + K j and Kj = α σ K, σ j (as derved from he arbrage condon (8)) wh, j =1, 2 and 6= j. These condons provde a sysem of equaons ha can be solved for he equlbrum amoun of capal n each counry, K, as a funcon of he vecor of source-based axes σ, σ j, gven he sock of capal, K. A each me, we hen have ha K = d σ, σj, K, j =1, 2 and 6= j A each nsan, he equlbrum allocaons of capal K,K j depends on he source-based

15 -14- ax raes σ and σ j, bu no on resdence axaon. Resdence axes do no, n fac, dscrmnae resdens nvesmen across dfferen counres. Changes n resdence axes do, of course, affec he ndvdual savng behavor and he fuure nhered sock of capal, bu a each nsan hey leave he momenary equlbrum, and he nernaonal allocaon of he exsng sock of capal, unchanged. Wha does hs ell us abou he effec of domesc axes on he allocaon of capal? Dfferenang prevous condon (8) usng equaons (6) for r (α +1 ), wh, j =1, 2 and 6= j, and evaluang he expresson for he smples case of symmerc counres, we oban ha a each me, dk j dσ = dk dσ F 0 k = 2(1 σ ) as from he properes of producon funcons, A ³ F 0 k A 0 k ³ 0 F 0 k A < 0. k > 0, j =1, 2 6= j In equlbrum, he amoun of capal n each counry s a declnng funcon of he domesc source ax, bu an ncreasng funcon of he oher counry s ax rae. In hs seng, each counry should hen be concerned ha ncreases n domesc source axes lead o an ouflow of capal o foregn counres. I s hs exernaly ha has receved much aenon n he leraure on nernaonal capal axaon. To ge a beer undersandng of he nernaonal effec of domesc axes, may be useful o work ou a specfc example wh Cobb-Douglas producon funcons. In hs case, he equlbrum allocaon of capal n each counry akes a very smple form. 11 In hs smple example, he nernaonal allocaon of capal and he effec of axes can be llusraed n fgure 1. In hs fgure, boh counres ne raes of reurn are ploed ogeher as a funcon of he varable χ = K1, where 0 χ 1. The capal marke s n equlbrum when K r 1 = r 2, ha s a he nersecon pon I where condon (8) holds. 11 For a verson of ³ hs model wh Cobb-Douglas funcons, see Appendx I. In hs case, r 1 = ²η 1 (L 1 ) ϑ µ ³ 1 χ (1 σ 1 χ ) and r 2 = ²η 2 (L 2 ) ϑ µ χ (1 σ 2 1 χ ) where χ = K1. K

16 -15- r 1 r 2 I 0 χ I χ I 1 χ Fgure 1. Momenary Equlbrum As shown n he fgure, any ncrease n he domesc source ax rae (e.g., n counry 1) shfs he ne-reurn curve of he counry downwards (he dashed lne). Ths leads o an nernaonal reallocaon of capal wh a lower domesc capal sock and a hgher level of capal n he oher counry (.e. a smaller χ). In equlbrum, he nernaonal neres rae also falls as a resul of he hgher source-based ax rae. Ths cross-counry capal flow effec can be nerpreed as a one-perod or sac fscal exernaly of domesc polcy and has been ofen dscussed n he leraure on nernaonal capal axaon. Ths example brngs ou an mporan pon: ha he capal relocaon effec s a pure sac or sngle-perod effec and does no depend on capal accumulaon and economc growh. To llusrae hs pon, consder he case wh Cobb-Douglas producon funcons wh no exernales and no economc growh (so ha µ = µ =0and 0 <²<1). As n he prevous case, an nernaonal equlbrum exss. In hs equlbrum, changes n domesc ax raes lead, agan, o a reallocaon of capal n favor of he ax-reducng counry. 12 I s no, of course, suggesed ha economc growh s unmporan; however, an mporan dsncon exss beween he effec of domesc axes on he nernaonal allocaon of he curren capal, whch s sac, and he mpac on economc growh, whch s dynamc. I s he sac relocaon effec whch has receved much aenon n he debae on capal axaon, bu hs s no he only effec we should consder. A ax change also affecs he growh process and he fuure sock of capal a any nsan. Indeed, he sac analyss canno be smply repeaed generaon afer generaon, and s o hs dynamc effec ha we now urn. 12 In hs case, he ne reurn o capal n each counry may be wren as r 1 = ³ 1 ²and ³ (1 σ 1 ) ²η 1 (L 1 ) K ² 1 1 χ r 2 =(1 σ 2 ) ²η 2 (L 2 ) K ² χ 1 ² and we can draw a dagram analogous o ha of Fgure 1 where he naonal ne reurn curves agan decrease, crossng he vercal lnes a a posve value above zero.

17 -16- B. Ineremporal Equlbra, Economc Growh, and Welfare Much of he polcal rheorc abou capal ax reforms has cenered round he effecs on economc growh; bu, how exacly do domesc axes nfluence growh n an negraed economy? To consder hs, we need o nroduce he concep of neremporal equlbrum. Ths can be defned as ha sequence of momenary equlbra n whch naonal consumpon profles seadly grow from generaon o generaon, gven he sequence of prevalng fscal polces {ρ, σ,g } =0 n each counry. To smplfy he analyss, le us focus he aenon on he growh rae of domesc produc, and le us assume for convenence ha naonal polces are consan. In hs case, we can use he propery of lnear homogeney of producon echnologes and wre each counry s produc as a funcon of he capal rao α and of a sngle counry s sock of capal; we have, for example, ha Y 1 Y 2 = F 1 (A 1 (K 1,K2 ),K1 )=H 1 (α) K 1 = F 2 (A 2 (K 1,K 2 ),K 2 )=H 2 (α) K 1 where, he nelasc supply of labor has been omed, and he capal rao α σ, σ j s consan because of consan ax polces. The domesc produc n he wo counres hus grows a a common rae. However, should be noced ha he clams on ha produc,.e. he naonal ncome, may grow a dfferen raes as hese depend on domesc savngs. For example, one counry may save more han he oher, so ha wll come o own an ncreasng share of he enre world produc. Thus, domesc produc and naonal ncome do no necessarly grow a he same rae. From prevous expressons, also follows ha domesc ax polces may affec boh he world-wde growh rae and he dsrbuon of producon across counres by changng he rao α because growh and dsrbuon depend on how capal s nernaonally allocaed; however, ax polcy canno generae dfferences n he counres raes of growh of domesc produc. A hs pon, we can examne he effec of domesc axes on he rae of economc growh n hs wo-counry economy. To hs purpose, we can focus on a sngle counry snce he oher s characerzed by dencal dynamcs. In parcular, prevous accumulaon equaons (10) gve us he law of moon of capal n each counry, K +1 = h K,Kj, τ, τ j, j =1, 2 6= j where τ =(ρ, σ ) and τ j =(ρ j, σ j ), and we have dropped he me ndex for he ax raes as hese are consan. Ths equaon descrbes a relaonshp beween he domesc sock of capal K+1 and K a dfferen mes, gven he vecors of ax raes τ and τ j and he fac ha he nhered sock of capal n he oher counry can be wren n erm of he domesc sock of capal as K j = αk. Therefore, wh well behaved uly funcons, he dynamcs can, evenually, be expressed as K+1 =(1+g ) K =1, 2 (11) where g = g (τ, τ j ) s consan (for an example see appendx I). Equaon (11) gves us he rae of economc growh n each counry, and n he enre economy, as a funcon of domesc and foregn ax raes. Thus, he growh rae n each counry s no funcon of domescfscal decsons only: he ax raes of he oher counry also affec he domesc growh

18 -17- rae,muchnhesamewayasanexernaly. 13 In fac, domesc axes creae an neremporal or growh exernaly. The man neres of hs model ress precsely n hese neremporal ransmsson effecs. Unforunaely, prevous equaons do no allow us o drecly examne he growh effecs of domesc axes snce he funconal forms of he problem are unknown. 14 To ge a beer undersandng of he effecs of domesc axes on nernaonal growh, s useful o work ou a specfc example. We may consder for smplcy counres ha are symmerc bu for her ax polcy, use he Cobb-Douglas echnologes descrbed above, and nroduce homohec uly funcons. 15 For hs class of uly funcons, he ndvdual opmaly condons ake, n fac, a very smple form wh he savng n each counry dependng on he sock of domesc capal (equaon (5)), S = s β +1 (1 ²) η L 1+ϑ α µ K S j = s β µ j +1 (1 ²) ηj L j 1+ϑ 1 α where β +1 =(1 ρ ) R +1. Subsung hese expressons n (10),K+1 = S +Sj 1+α +1, we oban a very smple expresson for he rae of economc growh K +1 K =1+g =(1 ²) s β +1 (L) 1+ϑ µ αk µ α µ + α 1 µ 1+α where, for convenence, he erms η, η j have been normalzed o be equal o one, and L = L j = L. 16 Armed wh hs smple example, we can now examne he nernaonal effecs of naonal axaon on economc growh, and we sar consderng he mpac of resdence axaon. From 13 I may be noced ha n hs model wh perfec capal mobly here are no ransonal dynamcs, and he economy s always a s balanced growh pah. However, as noed n prevous secons, he exsence and unqueness of a balanced accumulaon pah wh posve economc growh are no guaraneed. In wha follows, we assume ha a unque equlbrum for any gven se of ax raes exss, and Appendx I provdes an example wh Cobb-Douglas uly and producon funcons where a unque equlbrum exss ndeed. 14 We may noce ha, n hs model, changes n domesc axes have srong nernaonal effecs. Specfcally, changes n one counry s axes has as srong an effec on domesc growh as on foregn growh. Ths undesrable feaure of hs model derves from he fac ha he model has no ransonal dynamcs and perfec mobly of capal. Inroducng hese dynamcs an mperfec capal mobly would lead o counry dfferenaed effecs. However, he purpose of he analyss s o examne he effecs of domesc ax polces along he balanced growh pah, and he absence of ransonal dynamcs grealy smplfes hs ask. 15 I s worh nong ha for a seady sae o exs, preferences mus be homohec; see for example Buer and Klezer (1992). 16 For a smplfed verson of hs model wh Cobb-Douglas uly and producon funcons, see appendx I. In hs example, condons on he parameers of he model can be found such ha a posve long-run growh rae for he economy ndeed exss (see Appendx I). (12)

19 -18- equaon (12), we can observe ha resdence axes have no effecs on he nernaonal allocaon of capal α as α (σ, σ j ), bu hey do affec he rae of growh hrough changes n he savng propensy facor s β +1. In parcular, an ncrease n resdence axes has a zero, posve or negave mpac on he naonal (as well as foregn and nernaonal) rae of growh, dependng on wheher he elascy of subsuon a home s equal, smaller or greaer han one (where one s he value of he expendure elascy for homohec uly funcons). A clear dsncon exss beween he sac effec of resdence axes on he nernaonal allocaon of capal and he dynamc effec on economc growh. We conclude ha resdence axes do no affec he nernaonal allocaon of capal, bu hey may rase or lower capal accumulaon; n fac, hey are no necessarly harmful o economc growh. Hgher resdence axes change he savng behavor of generaons and, f he elascy of subsuon s, for example, smaller han one, hen hey evenually boos economc growh. Ths resul has long been known n he heorecal leraure on savng behavor and a large volume of emprcal work suggess ha elasces of subsuon are ndeed generally less han uny. Thus, he emprcal possbly exss ha ncreases n resdence axaon do lead o faser growh, whle leavng he nernaonal allocaon of capal unchanged. 17 The effec of changes n he source-based ax raes, σ,aremorecomplexoexamne.asclear from prevous equaon (12), source axes affec he growh hrough wo channels. They nfluence he propensy o save s ( ), as well as he nernaonal allocaon of capal, α ( ), hus leadng o ambguous effecs on he rae of growh. Some defne conclusons can be, however, reached f we resrc furher he aenon o he specal case of Cobb-Douglas uly funcons. In hs case, s ( ) becomes a consan, and naonal growh raes ake a very smple form, K+1 µ α K =1+g = s (1 ²)(L) 1+ϑ µ + α 1 µ 1+α µ 1 j 2 (1 σ where α µ = ) wh, j =1, 2 and 6= j (see appendx I). Under hs assumpon, he (1 σ ) rae of growh g s hus ndependen of he resdence-based ax raes ρ, bu depends on source axaon hrough he rao α (σ, σ j ). In hs specal case, here s a naonal ax (or subsdy) rae σ whch, gven he parameers of he model, maxmzes he rae of economc growh. 18 Clearly, here s a non-monoonc relaon beween source-based axes and he rae of economc growh, and hs akes he form of a Laffer curve-ype relaon. Ths relaon s he resul of he specal cross-counry growh 17 A large volume of emprcal work whch seeks o deermne he effecs of capal axaon on personal savngs and economc growh exss whch suggess he possbly of low elascy of subsuon. For dscusson of hs evdence, and references o he leraure, see for example Aknson and Sglz (1980), (Hall, 1988), Uhlg and Yanagawa (1996), and Bernhem (2002). 18 For example, he erm n he bracke s maxmzed a α =1.Fromhedefnon of α, hen follows ha, he growh rae s maxmum when σ 1 = σ 2. These may be eher axes (posve) or subsdes (negave), dependng of he exac parameerzaon of he model.

20 -19- mechansm A K,K j. Wh hs mechansm, only one nernaonal allocaon of capal exss ha maxmzes growh exernales, and hs can only be acheved wh specfc naonal source ax raes. Ths specal case brngs ou he mporan pon ha lower source axes ncrease he sock of domesc capal bu hey do no necessarly rase he rae of economc growh. Growh depends, n fac, on how capal s allocaed across counres. For example, any change away from he growh maxmzng ax rae, even lower axes or hgher subsdes, ncreases he domesc share of he exsng sock of world capal, bu reduces he rae of growh boh a home and abroad. Clearly, an mporan dsncon exss beween he sac effec of domesc source axes on he nernaonal allocaon of capal and he dynamc effec on he rae of growh, and hese effecs may well dffer. Ths smple example also serves o show ha he effec of a ax change on domesc produc may be dfferen from he effec on naonal ncome, namely welfare. Ths can be seen wh a smple example. Suppose ha he despe he assumpon of symmerc counres, counry leves a lower source ax han counry j. In hs case, an ncrease n counry s source ax would rase he rae of growh of domesc produc bu, under specfc parameerzaon of he model, wll also lower domesc savng, hence reducng he naonal ncome. 19 Clearly, he supposed advanage of a ax change vares wh he performance creron we adop, n hs case domesc produc and welfare (naonal ncome). Consderable crcumspecon s hen necessary n assessng he effec of a ax polcy n a dynamc model. C. Comparng Predcons The predcons of he model descrbed here may be compared wh hose ohers have reached n nfne-lfe Ramsey models. In her analyss of publc fnance and economc growh, for example, Barro and Sala-I-Marn consder a Ramsey model wh dfferen mechansms of growh, and conclude: Pung he resuls ogeher, he mplcaon s ha he models predc posvely correlaed movemens n r (he ne rae of reurn) andγ (he rae of economc growh). (Barro and Sala-I-Marn, 1992, p. 655) hus, capal axes reduce ne reurns and he rae of growh. They examne a closed economy, bu he same resul apples o he case of open economes wh nernaonally moble capal. Lejour and Verbon (1997), for example, use a Ramsey accumulaon model o nvesgae he ssue of ax compeon n a wo-counry world, and observe So, a hgher domesc source-based capal-ncome ax wll generae a lower growh rae of wealh,... (Lejour and Verbon, 1997, p. 485) Thus, he effec of domesc axes on he nernaonal allocaon of capal and on economc 19 Ths resul holds, for example, under he assumpon ha µ =0.5and s (1 ²)(L) 1+ϑ > 1+α α µ +α1 µ, whch s also a suffcen condon for growh o be posve (see appendx I). Oher parameersaons can also be found.

21 -20- growh concde. The man reason hese conclusons are dfferen from ours s ha hey draw on nfne-lved Ramsey models of accumulaon. In hese models, me preferences lm opporunes for cross-counry ax and growh dependences. 20 Suppose, for example, ha each naonal economy conssed of Ramsey nfne-lved opmzng ndvduals who maxmze he nfne sream of her uly dscouned by her raes of me preference. In hs case, he long-run equlbrum sock of capal n each counry s gven by he so-called modfed golden rule (see for example n Blanchard and Fsher, 1989, p. 57). Ths requres ha, n he saonary sae, he ne-of-ax neres rae n each counry equals he rae of me preference of ndvduals or, n erms of prevous noaon, ha n each counry, β = 1 ρ 1 σ r = θ =1, 2 where θ s he ndvdual rae of me preference whch s assumed o be consan and equal n he wo counres. 21 From hs rule, s clear ha n Ramsey-lke models, domesc axes have no long-run nernaonal effec. In hese models, changes n he domesc source-based ax σ affec he ne-of-ax reurn o home capal, and cause capal o move across borders, bu hs s a shor-erm effec. The long-run equlbrum level of capal abroad s gven, n fac, by he modfed golden rule ha remans unchanged; hus, he equlbrum long-run level of capal s no affeced by changes n he foregn ax raes. The resdence-based ax rae ρ does no nfluence he nernaonal allocaon of capal eher, snce he burden of resdence axaon s ndependen of where savngs are nvesed. I follows ha n he Ramsey-ype models domesc ax polces have no long-run nernaonal effec. 22 In he prevous model wh overlappng generaons, hs problem does no emerge. In ha model, frs-perod consumpon dffers from second-perod consumpon, hus he ne-of-ax neres rae does no have o equal he rae of me preference. In hs seng, changes n he domesc ax raes affec he neres rae and he ndvdual savng behavor n each counry, hereby nfluencng he nernaonal allocaon of capal and economc growh. Dependng on he ndvdual savng funcons, a ax change has dfferen effecs on he rae of growh, and hese effecs do no necessarly correspond o he mpac on he nernaonal allocaon of capal. V. CONCLUSIONS The model presened n hs paper has shown how we can analyze he mpac of domesc axes on capal ncome n a conex closer o wha s observed n he real world. I consders 20 Specfcally, n hese models, he Euler equaon predcs a sable long-run posve relaon beween he ne neres rae and economc growh; hus ncreases n axaon reduce he sock of domesc capal and also decrease he rae of growh. 21 For dscusson of he nfne-lved agen model, and references o he leraure, see for example Blanchard and Fscher (1989). For specfc applcaons o he case of open economes, see also Lejour and Verbon (1998). 22 There wll, however, be adjusmens along he dynamcs beween saonary saes as world savngs adjus o new ax raes.

22 -21- large counres, nernaonal capal mobly, economc growh, and generaonal savngs as hese aspecs are necessary when examnng he mplcaons of domesc capal axes n an negraed world economy. In dong so, he paper also explores he basc mplcaons of usng he overlappng-generaons approach o examnng he problem of capal ncome axaon n open economes. The paper shows ha he nernaonal effecs of domesc axes on capal ncome are less sraghforward han s ofen supposed. We need o dsngush beween he effec of domesc axes on he nernaonal allocaon of capal and her mpac on he rae of economc growh. I s rue, for example, ha ncreasng domesc source axes reduces he sock of domesc capal. Bu domesc axaon also nfluences capal accumulaon (hrough savng), and he wo effecs are no necessarly smlar. Ths concluson clearly dffers from he resul one can derve n nfne-lved-agen models. An mporan dsncon also exss beween he growh and welfare effecs of capal axaon. A ax change could ncrease he growh rae of domesc produc, bu could lower naonal ncome whch s relaed o resdens welfare. Indeed, he assessmen of a ax polcy crcally depends on he evaluaon creron adoped. These nernaonal ax nerdependences pose suble problems of polcy desgn o naonal governmens. Governmens may use axes on capal ncome boh o compee for he exsng sock of world capal and o affec he rae of capal accumulaon over me, and he choce of he ax polcy depends on he governmen s objecve. A polcy ha ncreases he domesc share of curren capal may no ncrease he growh rae of ha capal n he fuure. Clearly, hs poses suble ssues as o he bes way of axng capal and he naure of Pareo-opmal ax raes.

23 -22- APPENDIX I I. TWO-COUNTRY MODEL WITH COBB-DOUGLAS UTILITY AND PRODUCTION FUNCTIONS Ths appendx presens a smplfed verson of our wo-counry model of growh wh Cobb- Douglas uly and producon funcons. Ths was used n Secon 4 o examne he effec of axes on capal ncome. In presenng hs smplfed model, we frs examne he opmzng behavor of consumers and frms, hen consder he equlbrum n he world capal marke and he law of capal accumulaon for he wo-counry economy. A. Consumers The represenave consumer n each counry has a Cobb-Douglas uly funcon u = a log c 1 +(1 a)logc b log T L + γ log G +1 where he me endowmen T, he labor supply L, and he publc good provson G +1 are gven wh L = L,sohaconsumpondecsonsc 1 and c 2+1 are he only choce varables. The consumer chooses lfeme consumpon c 1 and c 2+1 so as o maxmze hs uly subjec o he presen value budge consran c 2+1 = 1+ 1 ρ+1 R+1 w L c 1 In hs specal case, he soluon o he consumer s maxmzaon problem akes a very smple form. Applyng he sandard mehod of consraned opmzaon, we oban: c 1 = awl =(1 s) wl S = (1 a) wl = swl c 2+1 = 1+ 1 ρ +1 R+1 sw L where s =1 a s he propensy o save wage ncome. I may be noced ha, n hs specal case, savng s lnear n he wage ncome. We assume for convenence ha here s no populaon growh and normalze oal populaon o one. Thus, ndvdual and aggregae decsons concde. B. Frms A any me, compeve frmsneachcounry produce a homogenous oupu Y a consan reurn Cobb-Douglas producon funcon n capal and labor accordng o Y = h A 1 1 ² 1 ² K ² L ϑ wh ²>0, ϑ < 1 and =1, 2 wh a producvy facor A = η K µ K j µ, j =1, 2 and 6= j