A Quantitative Analysis of Tax Competition v. Tax Coordination under Perfect Capital Mobility

Transcription

1 RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS School of Public Policy The Universiy of Michigan Ann Arbor, Michigan Discussion Paper No. 507 A Quaniaive Analysis of Tax Compeiion v. Tax Coordinaion under Perfec Capial Mobiliy Enrique G. Mendoza Universiy of Maryland Linda L. Tesar Universiy of Michigan April, 2003 Recen RSIE Discussion Papers are available on he World Wide Web a: hp://

2 A Quaniaive Analysis of Tax Compeiion v. Tax Coordinaion under Perfec Capial Mobiliy Enrique G. Mendoza Cener for Inernaional Economics Deparmen of Economics Universiy of Maryland and NBER College Park, MD Linda L. Tesar Deparmen of Economics Universiy of Michigan and NBER Ann Arbor, MI April 2003 Absrac Theory predics ha sraegically-deermined ax raes induce negaive exernaliies across counries in relaive prices, he wealh disribuion and ax revenue. This paper sudies he ineracion of hese exernaliies in a dynamic, general equilibrium environmen and is effecs on quaniaive oucomes of ax compeiion in one-sho games over capial income axes beween wo governmens ha se ime-invarian axes and issue deb. Sraegic payoffs correspond o welfare gains ne of he cos of ransiional dynamics in a sandard neoclassical wo-counry model wih exogenous balanced growh. The model is calibraed o European daa for he early 1980s saring from a benchmark wih symmeric counries. When counries compee over capial axes adjusing labor axes o mainain fiscal solvency, he Nash equilibrium replicaes calibraed axes, suggesing ha European axes can be he oucome of Nash compeiion. When consumpion axes are adjused o mainain fiscal solvency, compeiion riggers a race o he boom in capial axes bu his oucome is welfare-improving relaive o calibraed axes. Sensiiviy analysis shows ha compeiion can produce a race o he op in capial axes and ha he Unied Kingdom can benefi from ax compeiion wih Coninenal Europe. Surprisingly, he gains from coordinaion in all of hese experimens are small.

3 "There is clearly a pressing need o ensure a more effecive co-ordinaion of axaion policies Tackling he issue of harmful ax compeiion, which hreaens boh o reduce revenues and o disor axaion srucures, should be cenral o his process." (The Package o Tackle Harmful Tax Compeiion, ECOFIN Minisers of he European Communiy, 1997) The prioriy is o reduce he ax burden EU wide. And don even aemp o harmonize naional ax sysems across he board.he EU is already pledged o eliminae harmful ax compeiion, bu a reasonable degree of ax compeiion would no be harmful a all: i would lead o a marke-driven convergence owards lower ax raes... (The Economis, Feb. 10, 2001, p. 52, ciing Fris Bolkensein, EU Commissioner for he Inernal Marke) 1. Inroducion. Much of he open-economy macroeconomics lieraure on ax coordinaion is based on he premise ha ax compeiion is harmful and ha coordinaion of ax policy beween naional auhoriies is herefore welfare-improving (see he survey by Persson and Tabellini (1995) and he books by Frankel, Razin and Sadka (1991) and Turnovsky (1997)). Paradoxically, here have been few aemps o quanify he oucomes of ax compeiion and he magniude of he gains of ax coordinaion o assess he robusness of his premise. 1 The goal of his paper is o provide a quaniaive assessmen of ax compeiion and he benefis of ax coordinaion in a world wih rade in financial capial. Our framework for analysis is a sandard wo-counry, dynamic general equilibrium model driven by labor-augmening echnological change. We use his model o compare he cooperaive and non-cooperaive equilibria of one-sho games played by wo naional fiscal auhoriies ha se axes on facor incomes and consumpion and have access o domesic deb markes. The auhoriies are benevolen in ha hey assess he payoffs of ax sraegies by compuing he impac on households lifeime uiliy, aking ino accoun he economies ransiional dynamics along he ineremporal compeiive equilibrium pah. Sudies of inernaional ax compeiion generally emphasize hree global exernaliies of naional ax policy ha lead o sraegic behavior. The firs exernaliy is a varian of he radiional marke-power or beggar-hy-neighbor effec on relaive prices: counries engaged in ax compeiion aemp o use ax policy so as o influence he erms of rade or he world real ineres rae in heir favor. The magniude of hese relaive-price exernaliies has been shown in heory o depend on facors such as a counry s relaive size, or he degree of marke concenraion (see for example Chari and Kehoe (1990) and Kanbur and Keen (1993)). 1 A recen quaniaive sudy by Klein, Quadrini and Rios-Rull (2001) sudies opimal, ime-consisen policies in a seing wih dynamic sraegic ineracion o explain why he ax on capial income is higher in he Unied Saes han in Europe. Sorensen (1999, 2003) and Egger (1998) quanify he gains from ax coordinaion using saic models ha emphasize sraegic effecs on inernaional prices. 1

4 The second exernaliy operaes via a wealh-redisribuion effec. Sraegic cus in axes can be used o arac inernaionally mobile facors of producion. The payoffs assigned o sraegic ax cus reflec he welfare effecs induced by he cross-counry relocaion of mobile facors and is impac on he presen discouned value of naional income and he long-run socks of physical capial and foreign financial asses. Mendoza and Tesar (1998) and Mendoza (2002) show ha his wealh-redisribuion exernaliy is large and has significan welfare effecs in quaniaive experimens of unilaeral capial income ax cus. The hird exernaliy is a fiscal solvency exernaliy riggered by he adverse effec of ax compeiion on ax revenue, and is a byproduc of he relaive-price and wealh-redisribuion exernaliies discussed above. For example, ax compeiion may rigger a race o he boom in which governmens reduce axes on mobile facors of producion. This erodes ax revenues because (a) revenues from axes on mobile facors decline on accoun of lower ax raes (assuming hese ax raes are in he upward-slopping region of heir Laffer curves), (b) he flow of mobile facors of producion from a high-ax counry o a low-ax counry direcly reduces he ax base in he high ax counry, and (c), in general equilibrium, he relocaion of mobile facors can also lower facor paymens o immobile facors and overall facor income in he high ax counry, hus furher eroding is ax base. As ax revenue falls, governmens are forced eiher o reduce expendiures or o raise oher axes. If governmen oulays have uiliy or producion benefis, or if he alernaive axes are disorionary, his fiscal solvency exernaliy reduces welfare (see Huber (1999), Keen and Marchand (1997) and Rodrik and van Ypersele (1999)). The exising lieraure on inernaional ax compeiion ypically reas hese hree exernaliies separaely and ofen deals wih hem in simplified dynamic environmens under parial equilibrium and wih governmens running balanced budges in every period. In conras, he quaniaive analysis we conduc in his paper capures he hree inernaional exernaliies of naional ax policy simulaneously in a fully dynamic general equilibrium framework. Each counry axes a mobile facor of producion (physical capial), an immobile facor (labor) and consumpion using ime-invarian ax raes. Counries rade one-period bonds under perfec mobiliy of financial capial. This allows physical capial o relocae across counries even hough ownership shares of each counry s capial sock are no direcly raded. The inernaional mobiliy of physical capial is less han perfec, however, because capial-adjusmen coss limi he pace a which capial migraes across counries. The model also feaures domesic public deb markes so ha he fiscal auhoriies do no need o balance he primary defici each period, bu insead equae he presen value of ax revenue wih he presen value of a pre-deermined, imeinvarian amoun of governmen oulays (i.e., curren governmen purchases plus ransfer 2

5 paymens). Thus, he fiscal solvency exernaliy imposes endogenous ax adjusmens bu wih he flexibiliy o use public deb as a means o smooh he ax burden over ime. In Mendoza and Tesar (1998) we used a similar model o quanify he inernaional spillovers of ax policy caused by a unilaeral ax reform replacing a counry s ax on capial income wih a consumpion ax. In simulaions calibraed o daa for he Unied Saes and Europe, we found ha hese spillovers are very large and ha hey lead o imporan deviaions from wha similar experimens predic in closed-economy models. In a closed economy, agens face he prospec of a large and cosly ransiion period as he cu in he capial ax riggers an invesmen boom ha is financed a he expense of reduced consumpion and increased labor effor. The economy faces a radeoff beween he shor-run pain of posponing consumpion and he long-run benefi of higher oupu and higher consumpion ha resuls from more efficien axaion (see Chamley (1981) and Lucas (1990)). In a world wih open capial markes, however, he abiliy o borrow from abroad reduces he ransiion coss and shifs some of he burden of adjusmen ono he res of he world. Indeed, we found ha eliminaing he U.S. capial income ax leads o an increase in welfare for U.S. households equivalen o a 2.9 percen rise in rend consumpion and a fall in European welfare equivalen o a 1.7 percen adjusmen in rend consumpion. The negaive impac on Europe is due o a emporary increase in he world ineres rae, a large ouflow of capial from high-ax Europe o he low-ax Unied Saes, and an undesired increase in he European consumpion ax needed o preserve fiscal solvency (Europe s consumpion ax mus increase nearly 10 percenage poins). Our previous work did no consider he sraegic ineracion ha would surely resul from he inernaional exernaliies of unilaeral ax reforms ha we quanified. We did show ha an arbirary world-wide eliminaion of he capial income ax could lead o significan welfare gains in boh counries. Hence, our previous resuls suggesed ha sraegic ineracion is likely o play a cenral role in he analysis of inernaional axaion. This paper follows up on his suggesion by underaking a quaniaive analysis of he posiive and normaive effecs of ax compeiion and ax coordinaion. Our previous analysis also did no explore he possibiliy of rade offs across highlydisorionary axes. We assumed ha losses in he presen value of ax revenues resuling from unilaeral cus in capial income axes were made up by increases in consumpion axes, which in our Neoclassical seup resul in weak disorions. Hence, in his paper we aler his assumpion and explore ax compeiion games in which fiscal solvency effecs due o sraegic cus in capial income axes resul in eiher consumpion ax adjusmens or labor ax adjusmens. Mendoza (2002) showed ha in he laer case he rade off beween he wo highly-disoring facor income 3

6 axes can be quie complex because of dynamic Laffer curve consideraions. In our gameheoreic analysis, hese consideraions imply ha reacion curves are only well-defined in he region of he sraegy space of capial ax raes in which he Laffer curves generae enough ax revenue o cover he presen value of governmen oulays. Inernaional compeiion over capial income axaion is currenly a key issue for counries in he European Union. The 1997 repor by he ECOFIN Minisers of he European Communiy (The Package o Tackle Harmful Tax Compeiion), and recen aricles in he financial media (see, for example, Financial Times, May 2, 2003, p. 2) documen recen rounds of compeiive corporae income ax cus hroughou Europe. Ongoing negoiaions over muual reporing of non-residen capial income reflec similar concerns. In order o quaniaively assess he impac of ax compeiion in Europe, we calibrae our ax policy games o European daa. This approach sill allows for imporan differences in he ax srucure a he iniial saus quo, since he daa show ha he Unied Kingdom axes capial income significanly more han Coninenal Europe and he opposie holds for labor income (see Mendoza, Razin and Tesar (1994)). The quaniaive analysis sars wih a simulaion of wo perfecly symmeric counries in which he pre-ax-compeiion saus quo is calibraed o an average counry in coninenal Europe wih relaively high ax raes on labor income and relaively low axes on capial income. The aim is o sar wih a scenario in which he hree exernaliies driving sraegic ax choices are unaffeced by counry-specific differences in iniial ax srucures, governmen oulays, or iniial holdings of physical capial and foreign financial asses. We examine wo variaions on he ax compeiion game. In he firs case, he fiscal solvency exernaliy induced by sraegic choices on capial income axes forces endogenous adjusmens in labor income ax raes so as o ensure ha he presen value of ax revenue in each counry maches he presen value of heir unchanged governmen oulays. The second case preserves fiscal solvency by requiring insead adjusmens in consumpion ax raes. The resuls of hese experimens are sriking. In he firs experimen, he Nash equilibrium of he symmeric ax compeiion game wih labor axes adjusing in response o he fiscal solvency exernaliy yields capial and labor ax raes ha are remarkably close o he se of iniial ax raes. Thus, he model can accoun for he ax raes observed in Europe in he 1980s as he oucome of ax compeiion over capial income axes in a game in which he ax revenue exernaliy riggered changes in ax raes on he immobile facor, labor. This is also consisen wih he fac ha here was lile room for changes in indirec axes in Europe because of VAT harmonizaion reaies. When counries coordinae, we obain he sandard resul ha hey choose higher ax raes on capial income relaive o he Nash oucome, and hese higher axes in urn 4

7 suppor slighly lower labor ax raes. However, despie he large differences beween ax policy and real allocaions under ax compeiion and coordinaion, he welfare gain of coordinaion is under 0.26 percen in erms of a compensaing variaion in lifeime consumpion. In he case in which he fiscal solvency exernaliy works hrough adjusmens in he consumpion ax, he resuls are markedly differen. Tax compeiion riggers a race o he boom in capial income ax raes, and he consumpion ax raes in each counry increase by 8 percen o mainain fiscal solvency. However, as he opening quoe from Fris Bolkensein suggesed, boh counries gain from ax compeiion (relaive o he saus quo) as he more disorionary capial income ax is replaced by higher consumpion axes. The gains from coordinaion are even smaller han in he previous game as he gain in welfare relaive o he Nash oucome is abou 0.04 a percenage poin. We hen move on o a scenario calibraed o capure ax compeiion beween he Unied Kingdom and Coninenal Europe (which incorporaes observed differences in iniial ax raes and ransfer paymens). We find ha ax compeiion is immiserizing for Europe and welfareimproving for he UK when labor axes mus be used o mainain fiscal solvency. The UK sars he game wih a lower labor income ax rae and a higher capial income ax rae. Tax compeiion resuls in a lower capial income ax in he UK and capial relocaes from Coninenal Europe o he UK. The ax base in Europe erodes and herefore Europe mus increase boh capial and labor income ax raes o mainain fiscal solvency. The gains from coordinaion are small for boh he UK and Europe, and do no allow Europe o recoup is losses from ax compeiion. In he ax compeiion game wih adjusmen in he consumpion ax, we again observe he race-o-heboom in capial income axes and boh paries gain from compeiion. Coordinaion again yields only iny welfare gains over he Nash oucome. We conduc sensiiviy analysis how our resuls vary wih changes in iniial deb levels, labor supply elasiciy, and capial adjusmen coss. The ax raes ha emerge from ax compeiion are quie differen from our benchmark case, and in some insances i is possible for counries o engage in a race o he op in capial income axaion. However, he finding ha he gains from ax coordinaion are small is robus o he sensiiviy analysis, ranging from 0.01 o 0.5 percen of rend consumpion. Based on hese findings we conclude ha he srucure of ax raes observed in Europe is consisen wih he pressures induced by ax compeiion, and ha, given he small incremenal gains from ax compeiion, i is no surprising ha ax policy coordinaion has proven o be an elusive goal. The paper proceeds as follows. Secion 2 presens he srucure of he model, defines he model s compeiive equilibrium, and develops he inuiion behind he hree inernaional 5

8 exernaliies of unilaeral ax policy. Secion 3 defines he ax compeiion environmen by providing explici definiions for he pre-ax-compeiion equilibrium, he ax sraegy space, he Nash equilibrium of ax compeiion, and he cooperaive equilibrium. Secion 4 calibraes he model o European daa. Secion 5 repors he resuls from he ax compeiion experimens and Secion 6 concludes. 2. A Two-Counry World Economy wih Disorionary Taxes We sudy inernaional ax compeiion using a sandard wo-counry, neoclassical balanced-growh model. The model is a deerminisic version of he ypical wo-counry realbusiness-cycle model o which we inroduce fiscal policy following he seup developed by Mendoza and Tesar (1998). Each counry is inhabied by idenical, infiniely-lived individuals. Boh counries produce a single radable commodiy using capial and labor as inpus, and rade his good and real one-period bonds issued by he privae secor. All markes for goods, facors of producion and financial asses are perfecly compeiive. To help isolae he effecs of he inernaional exernaliies of ax policy and heir impac on ax compeiion, we assume ha counries are fully symmeric in echnology and preferences. Therefore, he model will be characerized using home-counry equaions. Laer, foreign variables will be denoed wih an aserisk (*). The specificaion of preferences and echnology is consisen wih he well-known condiions required o suppor exogenous balanced growh driven by labor-augmening echnological change. Accordingly, we assume ha long-run growh is driven by laboraugmening echnological change a rae γ. All variables, excep leisure and labor inpu, are made saionary by dividing hrough by γ and he saionary variables are wrien in lower case. We focus on he compeiive equilibrium of he derended model wihou loss of generaliy. The assumpion ha long-run growh is exogenous implies ha he exernaliies of ax policy and ax compeiion are modeled absracing from any effecs of axes on economic growh over he long run. This may seem a odds wih qualiaive predicions of a large class of endogenous growh models, bu i is in line wih heir quaniaive predicions and wih he evidence indicaing ha long-run growh seems largely independen of he variaions of ax raes observed in he daa (see Lucas (1990) and Mendoza, Milesi-Ferrei and Asea (1997)). Noe in addiion ha even wihou growh effecs, he welfare implicaions of ax policies ha resul from efficiency gains or losses in exogenous-growh models are generally quie large (see Lucas (1990), Cooley and Hansen (1992) and Mendoza and Tesar (1998)). 6

9 Households The represenaive household in he home counry maximizes an isoelasic lifeime uiliy funcion over consumpion, c, and leisure, : = 0 a ( c ) 1 σ 1 σ β (1 γ ) +, σ > 1, a > 0, 0 < β < 1. (1) 1 σ In his expression, β is he household s subjecive discoun facor, 1/σ is he ineremporal elasiciy of subsiuion in consumpion, and a is a coefficien ha governs he ineremporal elasiciy of labor supply for a given value of σ. Noe ha he saionary ransformaion of he model implies an effecive discoun facor given by β(1+γ ) 1-σ insead of β. The household maximizes (1) subjec o he sequence of period budge consrains: 2 g η x (1 + τ C ) c + (1 + γ ) ( k+ 1 + q b+ 1 + q d + 1) + z 1 k = 2 k (1 τ ) wl + (1 τ )( r δ ) k + b + d + e L K (2) for = 0,...,, given he iniial condiions k0>0, b 0, and d 0. The household akes as given governmen-deermined ax raes on consumpion, labor income and capial income, denoed τ C, τ L, andτ K, respecively, and lump-sum governmen ransfer or enilemen paymens, denoed by e. The household also akes he facor paymen raes o labor, w and capial, r, and he prices of governmen bonds and foreign bonds, q g and q as given (for simpliciy, inernaional and governmen bonds are represened as discouned bonds, so he gross real raes of reurn on hese bonds are R /(1/q ) and R g /(1/q g ) respecively). The lef-hand-side of (2) measures household expendiures. These include purchases of consumpion goods inclusive of he indirec ax, new capial goods, k +1, privae inernaional bonds, b +1, and domesic governmen bonds d +1. The price of capial and he price of consumer goods differ because invesmen incurs quadraic capial-adjusmen coss as a funcion of he raio of ne invesmen (x ) o exising capial (k ). The coefficien η deermines he speed of adjusmen of he capial sock, while z is se equal o he long-run invesmen-capial raio o ensure ha a seady sae he capial adjusmen cos is zero. Ne invesmen adjused for exogenous echnological progress is defined as x / (1+γ)k +1 -(1-δ)k, where δ is he rae of depreciaion of he capial sock. The righ-hand side of (2) shows he household's afer-ax income, which includes paymens on labor and capial rened ou o firms, he payoffs on domesic public bonds and foreign bonds, and governmen ransfers. Implici in his expression are he assumpions ha he 7

10 capial income ax is based on he residence principle and he ax code provides for a depreciaion allowance. Also implici is he assumpion ha bond paymens are ax-free (Mendoza and Tesar (1998) examined he implicaions of relaxing his assumpion and found ha i can have imporan effecs on he quaniaive predicions of he model). According o equaion (2), domesic physical capial and public deb are owned enirely by domesic households. This assumpion of exreme home bias in he holdings of hese asses is required for he model o suppor compeiive equilibria in which inernaional rade in privae bonds and residence-based axaion co-exis wih differen counry-specific ax raes on domesic capial income. As we show in Mendoza and Tesar (1998), his is no possible if shares on physical capial and/or governmen bonds are freely raded across counries (see also Frenkel e al. (1991)). Oher forms of financial-marke segmenaion, such as rading coss or shor-selling consrains, could be inroduced for he same purpose, bu so far hey have proven inadequae o solve he high degree of home bias observed in he daa and hey would complicae he model significanly. 2 Households also face a sandard no-ponzi-game resricion. This resricion, ogeher wih (2) implies ha he presen value of household income mus equal ha of expendiures plus any iniial asse holdings. Households allocae heir ime beween labor and leisure subjec o he ime consrain: + L = 1 (3) where we normalize he oal number of hours o uniy. Labor is immobile across counries. Firms Firms employ labor and capial so as o maximize profis, aking facor prices as given. The producion funcion is Cobb-Douglas: Fk L k L 1 (, ) = α α, 0< α < 1. where α is he labor income share. Since firms operae under perfec compeiion, hey earn zero profis in equilibrium and facor demands are given by sandard marginal produciviy condiions. Wihou loss of generaliy, all corporae axes are viewed as included in he capial income ax levied on households. (4) 2 The assumpions of exreme home bias and residence-based axaion could be replaced wih source-based axaion and his would resul in similar saving and invesmen opimaliy condiions ha would suppor compeiive equilibria wih differen capial income ax raes across counries. However, acual ax sysems are a mixure of residence- and source-based sysems. Frenkel e al. (1991) show ha personal income axes across OECD counries are mainly residence based, while corporae income axes are source based in principle bu supplemened by reaies ha allow for credis or deducions so as o approximae residencebased axaion. 8

11 The Public Secor Fiscal policy in each counry has hree componens: firs, a predeermined sequence of governmen oulays made up of unproducive expendiures and enilemen paymens, (g +e ) for =0,..., ; second, a se of ime-invarian ax raes τ =(τc, τ L, τ K ); and hird, a sequence of public bond issues, d, for =0,...,. The period governmen budge consrain is given by: g ( g e) d τ cc τ Lw L τ K ( r δ ) k (1 γ ) q d = (5) The lef-hand-side of equaion (5) measures uses of governmen income (i.e. goods purchases, enilemen paymens, and deb paymens). The righ-hand-side measures sources of governmen income: ax revenue and he proceedings from sales of newly-issued bonds (adjused o conform wih he saionary ransformaion of he model). Governmen purchases, enilemen paymens, and ax raes are he insrumens of fiscal policy. Thus, a primary fiscal defici or surplus a dae (i.e., a gap beween goods purchases, enilemen paymens and ax revenue) is offse by an endogenous change in public deb (ne of ineres and principal on exising deb). However, since he governmen also faces a no-ponzi-game consrain, he ineremporal governmen budge consrain requires ha he presen value of governmen expendiures plus enilemen paymens mus equal he presen value of ax revenue ne of paymens on iniial public deb. 3 Hence, given is ax and expendiure policies and is iniial bond posiion, he governmen is consrained o choosing a ime pah of public bond issues ha saisfies is ineremporal budge consrain. Public deb is "Ricardian" in he sense ha, given d 0 and he policy choices on governmen purchases, enilemen paymens, and ax raes, he compeiive equilibrium can be represened eiher wih he pah of public bonds dicaed by (5) or wih a hypoheical sequence of lump-sum axes (subsidies), T, se o an amoun equal o he primary fiscal defici (surplus) each period: ( ) T = τ c + τ w L + τ ( r δ) k g + e (6) C L K For simpliciy, he numerical analysis is conduced using his Ricardian represenaion of he governmen budge consrain. Wih his change, he budge consrain for households becomes: 2 η x (1 + τ C) c + (1 + γ ) ( k+ 1 + qb+ 1) + z 1 k = 2 k (1 τ ) wl + (1 τ )( r δ ) k + b + e + T L K (7) 3 Noe ha (2), (5), and he no-ponzi-game consrains on households and governmen imply ha he presen value of he rade balance equals b 0. 9

12 Compeiive Equilibrium A compeiive equilibrium for his wo-counry world economy is defined by sequences of prices [r, r *, q, w, w * ] and allocaions [k +1, k * +1, b +1, b * +1,x, x *,L, L *,,, c, c *,T, T * ] * for =0,, such ha: (a) households in each counry maximize uiliy subjec o heir corresponding budge consrains, ime consrains and no-ponzi-game consrains, aking as given pre-ax prices and facor renal raes, he values of all fiscal policy variables, and dae-0 holdings of capial and foreign bonds, (b) firms maximize profis subjec o he Cobb-Douglas echnologies aking as given pre-ax facor prices, (c) he governmen budge consrains hold for given ax raes and exogenous sequences of governmen purchases and enilemens, and (d) he following marke-clearing condiions for he global markes of goods and bonds hold: 1 α ( ) ( ) 1 α α * * * * α k L + k L = 2 2 * * * η x * η x * * * , * k 2 k c c x z k x z k g g (8) b + b = 0 (9) * The Three Inernaional Exernalies of Naional Tax Policy The inernaional exernaliies of ax policy operaing in he model can be undersood by sudying he implicaions of he ax disorions on saving, invesmen and labor supply. This issue is covered in deail in Mendoza and Tesar (1998). We provide here a condensed descripion o make more room for he analysis of ax compeiion. One of he main driving forces of inernaional ax policy exernaliies in he model is he arbirage of afer-ax real reurns o physical capial ha is obained hrough cross-counry rade in one-period privae bonds. The opimaliy condiions for capial and bond allocaions in he wo counries (simplified here o ignore capial-adjusmen coss) imply: (1 + γ ) u1 ( c, L) β u ( c, L ) = (1 τ )[ F ( K, N ) δ ] + 1 = R (10) k (1 + γ ) u1 ( c *, L * ) β u ( c *, L * ) = (1 τ * )[ F ( K *, N * ) δ ] + 1 = R (11) k Bond rading ensures ha he ineremporal marginal rae of subsiuion in consumpion in each counry equals he common real rae of reurn on bonds. In urn, households in each counry se opimal invesmen in heir counry s capial so ha he afer-ax ne reurn on capial equals he reurn on inernaional bonds. Thus, afer-ax reurns on capial are equalized across counries. 10

13 Consider a unilaeral cu in he home capial income ax rae. The home counry afer-ax reurn on capial increases relaive o he foreign counry. This efficiency gain leads home agens o borrow from abroad o spread he resuling increase in wealh across consumpion in all periods and o offse he shor-run burden of increased invesmen as he economy evolves oward a higher capial sock. This shor-run accumulaion of deb leads hem o service a larger sock of foreign deb in he new long-run equilibrium. In Mendoza and Tesar (1998) we labeled he iniial inflow of foreign goods o he home counry implied by he deb build-up he smoohing effec, and he long-run ouflow implied by he increased long-run deb service he incomeredisribuion effec. The increased borrowing by he domesic economy pus pressure on he world ineres rae o increase, bu he increase can only be emporary because in he long run he model s balanced growh resricions pin down he long-run real ineres rae independenly of he ax srucure. In paricular, he gross long-run real ineres rae is given by R=β -1 -γσ. However, we show in Mendoza and Tesar (1998) ha even hough he ineres rae hike is only emporary and quaniaively small, i can rigger large reallocaions of capial across counries and large adjusmens in consumpion (which in urn can have sizable welfare effecs). In his example of a unilaeral home capial income ax cu, he inernaional exernaliy operaing via he ineremporal relaive price of consumpion is refleced in he ransiory ineres rae hike discussed above. Moreover, since equilibrium facor prices depend on labor and capial allocaions, which are alered by he ax cu, here are also price exernaliies working hrough changes in wages and he renal rae of capial in each counry. The wealh redisribuion effec resuls from changes in he presen value of facor income induced by he reallocaion of capial across counries and he changes in he dynamics of capial and labor allocaed o producion. Changes in prices, facor incomes and he disribuion of wealh in urn have an impac on he ax base in he wo counries. Since we assume ha governmen oulays are consan, he decline in he foreign counry s presen value of ax revenue induced by he price and wealh exernaliies means ha he foreign labor income and/or consumpion axes mus increase o bring he presen value of ax revenue back ino balance wih he presen value of governmen oulays. These changes in consumpion or labor axes abroad are disorionary because hey drive he radiional wedge beween he marginal rae of subsiuion in consumpion and leisure and he pre-ax real wage. Labor and consumpion axes have symmeric disorionary effecs on accoun of his wedge, bu hey are no equivalen because labor is no he sole source of facor income 11

14 and capial and labor income are no axed a he same raes. 4 Moreover, around he calibraed values of he ax raes we work wih laer, labor and consumpion axes have very differen effecs on ax revenue, welfare and household income. In paricular, he increase in he labor ax needed o replace he loss in he presen value of ax revenue due o a reducion in he capial income ax involves greaer disorions han hose caused by he consumpion ax. 3. Pre-Tax Compeiion Equilibrium and Tax Compeiion Framework The sraegic ineracion beween he wo counries fiscal auhoriies akes place saring from a pre-ax-compeiion saionary equilibrium. This pre-ax-compeiion equilibrium is deermined by assigning values o he model s preference, echnology and fiscal policy parameers and solving for seady-sae allocaions along he long-run balanced-growh pah (he equaions describing he balanced-growh saionary equilibrium of he home counry are provided in Appendix A). Wih regard o fiscal policy, his calibraion exercise specifies a pair of iniial ax srucures τ = [ τ, τ, τ ] and τ* [ τ *, τ *, τ ] c L k = *, and ime-invarian levels of c L k ransfer paymens and governmen purchases in each counry [g,e] and [g*,e*]. The soluion o he saionary equilibrium yields a soluion for he primary fiscal balances T and T*, which represen he deb service of he seady-sae socks of public deb in each counry. Once he prices and allocaions of he pre-ax compeiion equilibrium are deermined, we calculae he payoff ha each counry receives under a paricular choice of capial ax sraegies played by each counry s fiscal auhoriy. These payoffs correspond o he welfare gain or loss ha each counry sands o make a he compeiive equilibrium suppored by he chosen capial ax raes and he endogenous labor or consumpion axes needed o saisfy he ineremporal governmen budge consrains. Welfare gains are compued as percen variaions in consumpion a all daes ha render households indifferen beween he pre-ax-compeiion levels of lifeime uiliy and he lifeime uiliy derived under he compeiive equilibrium of he new ax raes. The welfare calculaions ake ino accoun he ransiional dynamics ha he wo counries follow in moving from he pre-ax-compeiion equilibrium o he new long-run equilibrium implied by he new se of ax raes. 5 Boh he ransiional dynamics and he new long-run equilibrium need o be solved simulaneously because models of he class we sudy here display dependency on iniial condiions in he long-run allocaions of foreign bonds, and because 4 See Frenkel e al. (1991) for deails on direc versus indirec axaion equivalences. The equivalence in our model would also require an inelasic capial sock because oherwise he common labor-capial ax ha could yield a leisure-consumpion disorion idenical o ha of a given consumpion ax would imply a differen disorion on he invesmen margin. 12

15 of he endogenous adjusmen in eiher he labor or he consumpion ax needed o preserve fiscal solvency. We employ he soluion mehod proposed in Mendoza and Tesar (1998), which akes care of hese wo issues by ensuring ha he ax raes in each counry and he dynamics of foreign asses saisfy he presen-value consrains of privae agens and he governmen in boh counries. The relaionship beween he endogenous ax adjusmens needed o preserve fiscal solvency and he ineremporal governmen budge consrains can be characerized as follows. A a compeiive equilibrium, he home counry s ineremporal governmen budge consrain can be expressed as: = 0 τ = 0 1 * Rτ ( ττ, ) ( g+ e) = (15) 1 * Rτ r k w N c = 0 τ = 0 * * * * * ( ττ, ) τk ( ( ττ, ) δ) ( ττ, ) + τl ( ττ, ) ( ττ, ) + τc ( ττ, ) The lef-hand-side of (15) is he presen value of he consan sream of governmen oulays g+e. * (, ) 0 In his presen value calculaion, R ττ is he ineremporal sequence of equilibrium world real ineres raes ha perain o a compeiive equilibrium for given vecors of ax policy (τ,τ*). The righ-hand-side of (15) is he presen value of ax revenues. The sequences of equilibrium facor prices and allocaions ha deermine he flow of ax revenues (r, k,, w, N, and c ) are also compeiive equilibrium prices and allocaion for he same wo ax vecors. In principle, for given capial income axes (τ K,τ K *), he home-counry governmen could saisfy he above consrain (i.e., mainain ineremporal fiscal solvency) wih any combinaion of τ C and τ L ha solves equaion (15). However, he equaion canno be solved in closed form for hese endogenous ax adjusmens because he equilibrium prices and allocaions in boh sides of (15) vary wih he ax raes on facor incomes and consumpion. For racabiliy, we narrow he analysis o ax compeiion experimens ha adop one of hese wo rules o mainain fiscal solvency: adjus consumpion axes only (keeping labor ax raes consan) or adjus labor axes only (keeping consumpion axes consan). These fiscal solvency rules are known o boh governmens and boh governmens are assumed o be credibly commied o follow hem. The fiscal solvency rule ha adjuss he labor ax is a beer proxy for he curren siuaion in he European Union, where he high degree of VAT harmonizaion aained by inernaional reaies limis he possibiliy of adjusing indirec ax raes. 8 We consider only ime-invarian changes in ax policy. In he closed-economy conex, Lucas (1990) and Cooley and Hansen (1992) show ha he welfare gains from ax reform wih ime-invarian ax raes dwarf he addiional gains from allowing ime-variaion in ax raes. 13

16 In his environmen of inernaional ax compeiion, a sraegic decision rule for each counry s capial income ax rae given he oher counry s capial ax rae is obained as follows. The governmen of each counry chooses is capial income ax rae so as o maximize he payoff o ha counry s residens aking as given he oher counry s capial income ax and subjec o he consrains ha: (a) he implied allocaions and prices for a global ax srucure τ=(τ K,τ L,τ C ) and τ*=(τ K *,τ L *,τ C *) are a compeiive equilibrium, and (b) he labor or consumpion axes in boh counries adjus so ha he ineremporal governmen budge consrains of he wo counries hold. In he numerical soluions of he ax compeiion games, each counry can choose is capial income ax rae from values in discree grids: τk K { τk,1 τk,2... τk, M} {,1,2..., } * * * * * K K K K K M Ψ = < < < and τ Ψ = τ < τ < < τ. Hence he ax sraegy space is defined by he se of MxN capial income ax rae pairs (τ K,τ K *) in Ψ k xψ * k. For each of hese pairs, we compue prices and allocaions ha saisfy condiions (a) and (b) and he associaed welfare payoffs. Condiion (b) implies endogenous adjusmens in eiher (τ L,τ L *) or (τ C,,τ C *) so as o ensure ha he presen value of governmen oulays equals he presen value of ax revenue in each counry. When he consumpion (labor) axes are used o mainain fiscal solvency he labor (consumpion) axes are held consan a heir pre-ax-compeiion values. The payoff funcion for he domesic counry s sraegic choice of capial income ax given a foreign capial income ax is denoed by V(τ K τ K *). The corresponding foreign payoff funcion is denoed by V*( τ K * τ K ). Hence, he home counry reacion curve τ K (τ K *) is given by τ K = argmax τk V(τ K τ K *) and he foreign reacion curve τ K * (τ K ) is given by τ K * = argmax τk* V(τ K * τ K ). Two imporan caveas wih regard o he above characerizaion of opimal ax sraegies are worh noing. Firs, here can be muliple soluions ha saisfy condiions (a) and (b) because of he Laffer-curve effecs of disorionary axes. For a given pair (τ K,τ K *) in Ψ k xψ * k, bell-shaped ineremporal Laffer curves relaing he presen value of ax revenues o labor or consumpion ax raes imply ha here can be up o four combinaions of foreign and domesic labor or consumpion ax raes ha produce presen values of ax revenues equal o he presen values of governmen oulays (wih he labor or consumpion ax of each counry se in he efficien or he inefficien side of he corresponding Laffer curve). In his case, we assume ha he oucome ha Pareo-dominaes he ohers prevails. This oucome will keep he endogenous labor or consumpion axes of boh counries in he upward-sloping porion of he Laffer curve. The same 14

17 oucome would obain if we assume ha counries play a his poin a game over he consumpion or labor ax raes, for given capial axes. The Nash equilibrium would se he consumpion or labor ax raes o he efficien side of he Laffer curve. The second cavea relaes o he possibiliy ha soluions saisfying condiions (a) and (b) may no exis. This is possible because he inernaional exernaliies of unilaeral capial income ax cus in one counry cause a downward shif in he oher counry s ineremporal Laffer curve. As a resul, i is possible ha a given pair (τ K,τ K *) in Ψ k xψ * k does no have a soluion ha can saisfy (b). This will occur when he ineremporal Laffer curve in a leas one of he wo counries lies below he presen value of governmen oulays for all values of he counry s labor or consumpion ax raes. Hence, he reacion curves are well-defined only for pairs (τ K,τ K *) in Ψ k xψ * k for which a soluion ha saisfies (a) and (b) exiss, and hey are disconinuous oherwise. A Nash equilibrium for he capial-income-ax compeiion game is defined by a pair of capial income ax raes (τ N K,τ K * N ) and he associaed payoffs V(τ N K τ K * N ) and V*(τ K * N τ N K ) such ha: (a) τ N K maximizes V(τ N K τ K * N ) given τ K * N, (b) τ K * N maximizes V*(τ K * N τ N K ) given τ N K, (c) he payoffs are suppored by he prices and allocaions corresponding o he compeiive equilibrium for (τ N K,τ K * N ), and (d) he fiscal solvency rules of boh counries (seing eiher (τ C,τ C *) or (τ L,τ L *)) are saisfied. Thus, he Nash equilibrium saisfies τ N K = τ K (τ K * N ) and τ N* K = τ * K (τ N K ) (i.e., he Nash equilibrium is a he inersecion of he reacion curves). A cooperaive equilibrium is defined as a pair (τ C K,τ K * C ) ha maximizes he weighed sum of counry payoffs, λv(τ K τ K *) + (1-λ)V*(τ K * τ K ) for any λ [0,1] subjec o he consrain ha each counry is a leas as well off as in he Nash equilibrium: V(τ C K τ K * C ) V(τK N τ K * N ) and V*(τ K * C τ C K ) V*(τK* N τ N K ). Thus, here can be several cooperaive equilibria suppored by differen λ s and he se of all cooperaive equilibria deermines he core of he players conrac curve. Cooperaive equilibria are sill ax-disored compeiive equilibria because cooperaion undoes he effecs of he inernaional ax exernaliies bu no hose of domesic ax disorions. I is imporan o noe ha he ax compeiion games modeled here are one-sho games in which ax auhoriies mee once a dae =0. We implicily assume ha here is an insiuional arrangemen (such as an inernaional ax reay) ha operaes as a credible commimen mechanism prevening counries from deviaing in he fuure from he oucome of he dae-0 game. Sill, even hough he game is played once, he oucome of he game is influenced by hree key dynamic feaures. Firs, he payoffs are dynamic because hey capure he equilibrium dynamics ha ake he world economy from he pre-ax-compeiion equilibrium o he equilibrium deermined by he new ax raes. Second, implici in he deerminaion of he payoffs are he ineremporal effecs of he hree inernaional exernaliies of ax policy ha we reviewed 15

18 earlier. Third, he payoffs also consider ha governmens in each counry access heir corresponding domesic public deb markes in order o smooh ineremporally he impac of he fiscal solvency exernaliy on he seing of axes on consumpion or labor. We acknowledge ha a limiaion of he analysis of one-sho games is ha i canno address he ime-inconsisency problems ha regularly arise in he class of one-sho policy games like he ones sudied here. I is ineresing o noe, however, ha Klein, Quadrini and Rios-Rull (2001)) found ha when ime-inconsisency is aken ino accoun, sraegic ineracion amongs wo naional ax auhoriies resuls in equilibrium sraegies ha feaure large adjusmens in capial income axes in he firs period followed by nearly ime-invarian axes. 4. Pre-Tax Compeiion Calibraion We consruc he pre-ax compeiion calibraion so ha he seady-sae, balanced-growh equilibrium of a version of he model wih wo idenical counries maches key feaures of macroeconomic and fiscal policy daa for he hree large economies of coninenal Europe (or he C3 ), France, Ialy and Germany. The C3 have similar macroeconomic feaures and also share similar ax srucures. Laer we also consider daa for he Unied Kingdom o inroduce asymmery in iniial ax srucures. Since our goal is o characerize he oucome of ax compeiion under perfec inernaional capial mobiliy, we calibrae he model using daa for he early 1980s when barriers o capial mobiliy across Europe were largely being dismanled. 6 The calibraed values of echnology and preference parameers, ax raes and governmen expendiure shares used in he pre-ax-compeiion calibraion are lised in Table 1. Figures 1 hrough 3 plo he ime series of capial, labor and consumpion axes in he C3 and he UK over he period. These ax raes are updaed esimaes of he effecive ax raes proposed by Mendoza, Razin and Tesar (1994). Figure 1 shows ha capial income axes have remained fairly consan since he early 1980s, hovering around percen, wih a significan increase in he capial ax rae in Ialy in he early 1990s. Sill, he capial ax raes of France, Germany and Ialy have remained consisenly below he capial income axes in he UK. On he oher hand, labor income axes in he C3 (see Figure 2) have seadily risen since he 1960s and are significanly higher han labor income ax raes in he UK. Consumpion axes used o differ significanly across all European counries, bu he susained effors a indirec ax harmonizaion have resuled in significan convergence in effecive consumpion ax raes across he C3 and he UK over he course of he 1990s. For he purposes of he pre-ax compeiion calibraion, we ake he average of each of capial income, labor income and consumpion ax raes across he C3 in 1980 (26.5, 37.4 and 16.6, respecively). 16

19 Governmen expendiure shares have remained fairly seady since The sample averages for France, Germany and Ialy range beween 17 and 24 percen. We use a value of g/y =0.18 for he calibraion. The values of preference and echnology parameers lised a he op of Table 1 are aken from Mendoza and Tesar (1998). The pos-wwii average growh rae of GDP in he OECD is 1.56 per cen per annum, bu since a period in he model is defined o be one quarer we se γ = The ineremporal elasiciy of subsiuion is se a ½, which implies σ = 2. Naional accouns daa on he share of labor in GDP implies a value of α = Given hese hree parameer values, he C3 average of he invesmen-oupu raio in 1996 (adjused o exclude public invesmen), which is x/y = 0.24, and he value of τ K, he seady sae condiions (A.1) and (A.2) in he Appendix yield a value for he depreciaion rae of δ = per quarer and a value for he subjecive discoun facor of β = The seady-sae real ineres rae hen follows from he balanced-growh condiion R =β -1 -γσ, so he implied real ineres rae is 6.1 per cen per annum (1.46 percen quarerly). Seady sae condiions (A.3)-(A.5), ogeher wih g/y, x/y, τ C, τ L, a calibraed seady-sae labor supply allocaion of 0.2, and he assumpion ha in he symmeric pre-ax compeiion seady sae he share of ne expors in GDP is zero in boh counries, yield a value for he exponen of leisure in uiliy of a = and soluions for he seady-sae oupu shares of consumpion and foreign asse holdings. The parameers of he adjusmen cos funcion are se o η = 10 and z = γ+δ. The boom panel of Table 1 shows ha he model s pre-ax compeiion seady sae does well a mimicking he GDP shares of key macroeconomic aggregaes observed in European daa. The calibraion forces he model o reproduce he GDP shares of governmen expendiures and invesmen, and he rade balance is se equal o zero by he symmery assumpion. However, he consumpion, ax revenue and ne ransfers shares are produced endogenously. The model generaes slighly higher consumpion-gdp and ax revenue-gdp raios han is observed in he daa (58 v. 57 percen and 38 percen v. 37 percen respecively). 7 The raio of ransfers o oupu (e/y) is roughly he same as he average of he observed ransfers-gdp raios for France, Ialy and Germany in The 1985 average of ne ransfers (including subsidies and paymens semming from welfare, healhcare and oher enilemen programs) as a share of GDP in he C3 was 24 percen of GDP. Any remainder afer he level of ransfer paymens is subraced from he 6 We are graeful o Peer Birch Sorensen for suggesing ha we place our analysis in his conex. 7 Tax revenue as a share of GDP was fairly sable during he period in France and he UK bu i rose sharply in Germany and Ialy, reflecing largely he process of deb reducion underaken in hese counries o reach he Maasrich guidelines. The average for he C3 in 1985 ax was 37 percen. 17

20 primary defici (i.e., he gap beween he levels of ax revenue and curren expendiures) represens ineres paymens on he seady-sae level of public deb (i.e., he Ricardian ransfers described in Secion 2). We keep he level of governmen expendiures and enilemen paymens consan hroughou all he ax compeiion calculaions. 5. Quaniaive Oucomes of Tax Compeiion and Tax Coordinaion a. Tax Compeiion wih Symmeric Counries The firs ax compeiion game we consider is based on he calibraion o wo symmeric European counries described in Secion 4 and i assumes ha counries adjus labor ax raes o mainain fiscal solvency. We believe his is an ineresing saring poin for hree reasons. Firs, in our framework, he consumpion ax is close o a non-disorionary ax so ha replacing he revenue los from he reducion in he capial ax wih an increase in he consumpion ax is fairly painless. In realiy, however, governmens are likely o face more painful rade-offs by eiher cuing governmen expendiures ha have some uiliy or producion benefis or by raising anoher ax ha has more disorionary effecs. Second, much of he focus of he lieraure on ax compeiion (and cerainly a concern of European policymakers) is ha wih increased capial mobiliy, he burden of axaion has shifed from capial ono labor. This experimen looks direcly a he rade-off beween capial and labor income axes. Third, from a pracical sandpoin, a grea deal of effor has gone ino harmonizing indirec axes in Europe. I seems unlikely ha policymakers would undo he process of harmonizaion in indirec axes bu would insead use oher insrumens o mainain fiscal balance. Secion A.1. of Table 2 shows he capial and labor axes and he welfare gains when counries play Nash and when hey cooperae. Figure 4 shows he reacion curves of each counry and he core of he conrac curve under cooperaion. Srikingly, he Nash equilibrium yields ax raes on capial and labor ha are almos idenical o he ax raes in he pre-ax compeiion equilibrium! This suggess ha he ax raes observed in Europe a he ime in which barriers o capial mobiliy were removed can be raionalized as he oucome of ax compeiion beween counries in an environmen of perfec capial mobiliy. Since ax raes a he Nash equilibrium differ very lile from he ax raes a he pre-ax compeiion seady sae, he prices and allocaions a he Nash equilibrium also remain nearly unchanged and he effecs of ransiional dynamics on welfare calculaions are negligible. 18

21 When counries cooperae, he resuling ax raes on capial income are higher han under he Nash equilibrium. 8 The capial income ax rises almos 10 percenage poins and he labor income ax declines abou 3 percenage poins. This is because he labor income ax is highly disoring and i is in boh counries ineres o subsiue higher capial income axes for somewha lower labor income axes. In his case, here are changes in prices and allocaions a he new seady sae under cooperaive axaion and here are significan ransiional dynamics beween he pre-ax-compeiion equilibrium and his new seady sae. Despie hese changes, however, he welfare gains from cooperaion over Nash are small, a roughly one quarer of one percen of rend consumpion. Thus, hese resuls may explain why lile progress has been made in coordinaing capial income axes and why he burden of axaion has shifed ono labor, he immobile facor of producion. We nex urn o he ax compeiion game when he consumpion ax is used o mainain fiscal solvency (see Table 2.A.2 and Figure 5). Given he small disorion associaed wih increasing he consumpion ax, Nash compeiion riggers he familiar race o he boom in capial income axes. Nash compeiion leads o a large reducion in he capial income ax in each counry from 26.5 percen in he pre-compeiion equilibrium o a subsidy of 11.1 percen. 9 To mainain he presen value of ax revenue equal o he presen value of he unchanged governmen oulays, each counry raises he consumpion ax from 16.6 o 24.1 percen. Sill, Nash compeiion is beneficial in he sense ha households in boh counries obain a gain in lifeime uiliy relaive o he pre-ax compeiion saionary sae ha is equivalen o an increase of 0.68 percen in consumpion in every period. This welfare gain is much larger han exising esimaes of he welfare gains of eliminaing business cycles bu i is also smaller han exising measures of he welfare gains of replacing capial income axes wih consumpion axes in he Unied Saes, which range beween 2 and 4 percen (see Lucas (2003) and Mendoza and Tesar (1998)). Thus, our findings sugges ha hese esimaes of he benefis of ax reforms may be significanly oversaed because hey do no ake ino accoun he high degree of inernaional capial mobiliy and he incenives i provides for sraegic behavior in ax policy seing. The driving force of he race o he boom in capial income axes is he incenive ha each counry has o aemp o undercu he capial income ax in he oher counry, and use he 8 There exiss a range of cooperaive equlibria ha are Pareo improvemens over he Nash equilibrium. For symmeric games, we focus on he cooperaive equilibrium for which he planner assigns equal weighs o each counry. For asymmeric games we repor he full range of cooperaive equilibria. 9 Noe ha ax compeiion does no drive axes on capial o zero in his model because counries are large enough o affec he world ineres rae. A he poin of zero capial income axes, each counry has an incenive o subsidize capial, pushing up he world ineres rae and forcing some of he coss of capial accumulaion ono he res of he world. 19