Non-binding minimum taxes may foster tax competition

Transcription

1 Non-binding minimum taxes may foster tax competition KaiA.Konrad December 6, 2008 Abstract In a Stackelberg framework of capital income taxation it is shown that imposing a minimum tax rate that is lower than all countries equilibrium tax rates in the unconstrained non-cooperative equilibrium may reduce equilibrium tax rates in all countries. Keywords: tax competition, minimum tax, tax coordination, Stackelberg JEL classification numbers: H87 DepartmentofEconomics,FreeUniversityofBerlin,andSocialScienceResearchCenterBerlin(WZB). Correspondence address: Kai A. Konrad, WZB, Reichpietschufer 50, D Berlin, Germany, kkonrad@wzb.eu, phone , fax I thank Marie-Laure Breuillé, Clemens Fuest, Tim Goodspeed, Andreas Haufler, Peter Birch Sørensen, Tanguy van Ypersele and an anonymous reviewer for excellent comments. The usual caveat applies. Financial support by the DFG(SPP 1142) is gratefully acknowledged. 1

2 1 Introduction Europe is currently facing a period of income tax competition. In this context policy makers sometimes articulate concern that a downward adjustment of their own tax rates may initiate further tax rate cuts inside the European union, which suggests that they feel that they are operatinginasequential,leader-followergame. 1 Concernsregardingcross-bordershopping haveledtoanagreementonlimitingstandardsalestaxratesintheeuropeanuniontoa bandbetween15and25percent 2,LuxemburgandCypruscurrentlybeingthecountriesthat have a tax rate at the lower limit. 3 Agreements on minimum taxes for capital income at source and corporate income taxation have been proposed by experts(see, e.g., the report by therudingcommittee,1992,p. 202),buthavenotbeenimplemented,notevenatalevel thatislowerthanthetaxrateschosenbythecountriesinthenon-cooperativeequilibrium. 4 Thispapershows: aminimumtaxratethatislowerthanthelowesttaxrateinthe unconstrained equilibrium may have strong strategic effects. 5 It may induce all countries to make their tax rates lower than those they choose in the unconstrained equilibrium. Implications of the result are: sales tax rates need not be lower, but could potentially be higherthantheyarenowintheeuropeanunioniftherewerenotreatyonaminimumtax rate, and corporate taxes may be higher now than after implementing a minimum tax. Fuest, Huber and Mintz(2005) survey the literature and discuss minimum taxes on capital income at source. Minimum taxes have also been considered in the context of value added taxes and cross-border shopping (e.g., Kanbur and Keen, 1993, Wang, 1999, Hvidt and Nielsen, 2001). Wang (1999) is closest to the current paper. He considers minimum taxes that are binding in the unconstrained Stackelberg equilibrium in the sense that the minimum tax is strictly higher than the lowest tax rate that emerges in the unconstrained Stackelberg equilibrium. I consider a minimum tax that is strictly lower than all tax rates that emerge in the unconstrained Stackelberg equilibrium. Wang finds that the country with thehighertaxrate mayadjustits equilibriumtaxrate downwards asaresultof the 1 See,e.g.,AltshulerandGoodspeed(2002)forempiricalevidencesuggestingthatcountriesreacttotax rate changes in other countries. 2 SeeCouncilDirective2006/112/EC. 3 EuropeanCommission(2008). 4 Such an agreement on a level lower than actual rates may be seen as a safeguard against future tax competition in a situation with further increased tax base elasticity. 5 AminimumtaxratethatisabovethesmallesttaxratechoseninsidetheEUhasredistributionaleffects and thus makes minimum tax arrangements difficult to attain(see, e.g., Peralta and van Ypersele, 2006). 2

3 minimumtax. Ifindthatall countriesmayreducetheirtaxratesasanimplicationofthe introduction of a minimum tax. 2 The Analysis Consider a reduced form of capital income tax competition at source. Two countries L and F competebytheirchoicesoftaxratest L andt F,respectively,witht i [0,1]fori {L,F}, where the tax rates chosen have the standard implications for the equilibrium allocation of capital, tax revenues and the distribution of capital income. Countries payoffs are functions ofbothtaxratesanddefinedasπ L (t L,t F )andπ F (t L,t F ). Letthesefunctionsbecontinuously differentiableandstrictlyquasi-concaveint i andt j,implyingthattheiso-payoffcurvesare convextotheorigin. 6 Letargmax ti [0,1]{π i (t i,t j )} (0,1)besingle-valuedforallt j [0,1] and increasing in the other country s tax rate. This implies that the reaction correspondences determining i s optimal tax rate choices for a given tax rate of j are single-valued, upward sloping throughout 7 and can be written as functions t L (t F ) and t F (t L ) respectively, with t i (t j ) (0,1) for all t j [0,1]. The reaction functions and some representatives of the set of iso-payoff functions are depicted in Figure 1. A Nash equilibrium N is characterized byanintersectionofthereactionfunctionsasinfigure1. Afinalassumptionisthatthis equilibrium is unique. Together with the previous assumptions, this implies that t F (t L ) intersectst L (t F )fortaxratesintheinteriorof(0,1) (0,1)andfromtheupperleftatN. ConsidernowthesequentialgameinwhichcountryLactsasaStackelbergleaderand choosesitstaxratefirst,andf behavesasafollower. Thissequencingoftaxratechoices is exogenous here, but could be endogenized along the reasoning in Hamilton and Slutzky (1990). Byachoiceoft L theleaderlcanchooseanycombinationoftaxes(t L,t F (t L ))along thereactionfunctionoff. InFigure1eachtaxratecombinationismappedintoapairof countries payoffs, for the whole area of possible tax combinations. At point S the leader Lattains thehighestpayoffπ L fromallpoints(t L,t F (t L )) alongf s reactioncurve. This pointiseitheraninteriorpointsuchass,oracornersolutionats. Ast F (t L )neednotbe 6 Smoothreactionfunctionscanbegivenamicroeconomicunderpinninginthecontextofcapitaltaxation. Reaction functions may, however, become discontinuous if some stock of capital in one or both countries is immobile. In the context of sales tax competition analyzed by Wang (1999), reaction functions are discontinuous if countries are asymmetric. 7 Upward sloping reaction functions in the context of capital income taxation are also empirically confirmed, e.g., by Altshuler and Goodspeed(2002). 3

4 concave, the Stackelberg equilibrium also does not need to be unique. I concentrate on the caseofaninteriorstackelbergequilibriumsuchass,buttheargumentthatismadeabout the introduction of a minimum tax also applies for a corner equilibrium such as S. The Stackelberg equilibrium is generically unique in this framework, but the proof of the main result in this paper also works in the case of multiple Stackelberg equilibria. Figure 1 about here So far this characterizes the Nash and Stackelberg equilibrium in a reduced form of a standard tax competition framework. Suppose now that L and F, for some reason outside the scope of this analysis, are subject to a minimum tax constraint. Both countries choose theirtaxratesfreely,butcannotchooseataxratelowerthansomeminimumtaxratet 0 >0, i.e.,t i [t 0,1] forbothi {L,F}. Thetwocountrieschoosetheirtaxratesaccordingto the rules of the Stackelberg game that has been outlined above, with the only difference that theychoosetheirtaxesfromthismoreconstrainedinterval[t 0,1]. Icalltherespectivegame the constrained Stackelberg game. The following main result can be stated: Proposition1 Let (t S L,tS F ) be the Stackelberg equilibrium in the unconstrained game, and lett S L ts F. Aminimumtaxratet 0<t S F existssuchthatthestackelbergequilibriuminthe constrainedgamehaslowertaxratesforbothcountrieslandf thanintheunconstrained game. Proof. Let S in Figure 1 characterize the Stackelberg equilibrium in the unconstrained case; in the case of multiple equilibria, consider the equilibrium with the lowest tax rates. Consideraminimumtaxratet 0 =t S F ǫ, forǫ>0. Thisminimumtaxratechanges the optimal reply functions of both countries to ˆt i (t j )= { ti (t j ) for t i (t j )>t S F ǫ t S F ǫ for t i (t j ) t S F ǫ fori,j {L,F}andi j. (1) Thechoiceofˆt i (t j )=t 0 fort i (t j )<t 0 followsfromthepropertiesofthepayofffunctions: for agivent j,payoffofcountryiincreasesifitchangesitstaxratetowardstheunconstrained optimum t i (t j ). Figure 2 depicts the reply functions ˆt F (t L ) and ˆt L (t F ) as the solid lines. These coincide with the reply functions in the unconstrained case for all unconstrained optimalrepliesthatarehigherthantheminimumtaxt 0 andareequaltot 0 forallsmaller taxratest i (t j ). AStackelbergequilibriumischaracterizedby t 0 L arg max t L [t 0,t S L ] {π L (t L,ˆt F (t L ))}andt 0 F ˆt F (t 0 L). (2) 4

5 Theupperlimitt S L int L [t 0,t S L ]canbeadoptedin(2),becausets L isoptimalforlamong allt L [t S L,1]. *** Figure2aand2babouthere *** Considernowǫ 0. Theiso-payoffcurve π L thatpassesthroughs hasastrictly positiveslopeats. Forsufficientlysmallbutpositiveǫthisiso-payoffcurveintersectsˆt F (t L ) to the left of S, but for a value of t L > t 0. The latter follows from the assumption that t S L t S F >t 0 andǫ 0. Thechoicet 0 Lin(2)isthereforegivenby ˆt L (t 0 )=max{t 0,t L (t 0 )}. (3) TheFigure2adepictsthecasewithˆt L (t 0 )=t L (t 0 ),Figure2bdepictsthecasewithˆt L (t 0 )= t 0. Now,forǫ 0,itfollowsthatt 0 F =t 0=t S F ǫ<ts F andt0 L =max{t 0,t L (t 0 )}<t S L. The latterholds becauset 0 < t S L and becauset L (t 0 )<t S L =t L (t S F) byt 0 < t S F andbyt L (t F ) being strictly monotonically increasing. Proposition 1 shows that tax coordination that limits the choices of tax rates from below by a minimum tax that is smaller than anyof the tax rates that are chosen in the laissez-faire equilibrium can reduce the equilibrium tax rates of all countries to below their unconstrained laissez-faire equilibrium levels. The proof can be re-stated in intuitive terms. ConsidertheequilibriumS intheabsenceofaminimumtaxinfigure2a. Aminimumtax that is just equal to t 0 = t S F will allowthe leader to reduce his tax below t S L without any reaction by the follower s tax. The tax rates are strategic complements. The follower would liketoreducehistaxrate,too,butthisisnotpermitted, astheminimumtaxisbinding. Hence, asubstantialreductionint L fromt S L downtol soptimalpointŝ yieldsastrictly positive increase in L s payoff. This corresponds to the borderline case of Wang s (1999) analysisofminimumtaxest 0 >t S F,witht 0=t S F asthelimitingcaseinthecontextofsales taxcompetition. 8 NotethatProposition1considersaminimumtaxsmallerthant 0 =t S F. Supposethattheminimumtaxt 0 isslightlysmallerthant S F. Inthiscase,thereductionint L startingfromt S Lwillfirstinduceareductionint F alongt F (t L ),untilthepointk isreached infigure2. ThemovementfromS tok reducesl spayoffcomparedtothepayoffins. However, thetaxreactionbyf comestoaholdoncet F (t L )=t 0. Moreover,thedistance 8 Accordingly,theargumentregardingsmallerminimumtaxratesalsolocallyextendstoWang s(1999) salestaxframeworkbycontinuityatt 0 =t S F. 5

6 fromstok andthepayoffdecreaseforlalongthisdistancecanbemadearbitrarilysmall bychoosingt 0 arbitrarilycloseto(butsmallerthan)t S F. Oncet F(t L )=t 0 hasbeenreached, forfurtherdecreasesint L theargumentjustmadeapplies: afurtherdecreaseint L doesnot lead to a decrease in t F, as t F cannot fall belowt 0. The decrease in t L therefore leads to an increase in L s payoff. This strictly positive increase in payoff outweighs the decrease in payofffromthefirstfewmarginalunitsdecreaseint L froms tok ift 0 issufficientlyclose tot S F. Note that a sufficiently small minimum tax leaves the Stackelberg equilibrium S unchanged. However,iftheminimumtaxt 0 t S F <t S L changestheequilibrium(froms to ŜasinFigures2aand2b),thenthischangeharmsthefollowerandbenefitstheleader. The follower spayoffatŝislowerthanattheintersectionofaverticallinethroughŝwitht F(t S ), andhispayoffthereislowerthanats. Hence,thefolloweralwayshasalowerpayoffinŜ thanins. TheleaderbenefitsinŜ comparedtos. Thisfollowsfromarevealedpreference argument. TheleadercouldstillachieveSbychoosingt S L. IftheleaderdoesnotchoosetS L, this is because the alternative choice provides a higher payoff. 3 Conclusions The discussion here shows that constraints in the tax rate choice sets of countries that do not prohibit the choice of both countries equilibrium actions in the unconstrained problem maystillstronglyaffecttheequilibriumoutcome. Alowerboundontaxratesthatislower than the one any of the countries would have chosen in the unconstrained equilibrium can induce an equilibrium in which all countries choose a lower tax rate than in the unconstrained equilibrium. References [1] Altshuler, R., and T.J. Goodspeed, 2002, Follow the leader? Evidence on European and U.S. tax competition, mimeo., Hunter College. [2] European Commission, 2008, DOC.2441/2008- EN, VAT Rates Applied in the Member States of the European Union, Brussels. 6

7 [3] Fuest, C., B. Huber, and J. Mintz, 2005, Capital mobility and tax competition: a survey, Foundations and Trends in Microeconomics, 1(1), [4] Hamilton, J.H., and S.M. Slutzky, 1990, Endogenous timing in duopoly games, Stackelberg or Cournot equilibria, Games and Economic Behavior, 2, [5] Hvidt, M., and S.B. Nielsen, 2001, Non-cooperative vs. minimum-rate commodity taxation, German Economic Review, 2(4), [6] Kanbur, R., and M. Keen, 1993, Jeux sans frontières: tax competition and tax coordination when countries differ in size, American Economic Review, 83(4), [7] Peralta, S., and T. van Ypersele, 2006, Coordination of capital taxation among asymmetric countries, Regional Science and Urban Economics, 36, [8] Ruding Committee, 1992, Report of the Committee of Independent Experts on Company Taxation, European Commission, Brussels. [9] Wang, Y.-Q., 1999, Commodity taxes under fiscal competition: Stackelberg equilibrium and optimality, American Economic Review, 89(4),