Restricting preferential tax regimes to avoid harmful tax competition

Restricting preferential tax regimes to avoid harmful tax competition

Regional Science and Urban Economics 35 (2005) 493 – 507 Restricting preferential tax regimes to avoid harmful tax c...

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Regional Science and Urban Economics 35 (2005) 493 – 507

Restricting preferential tax regimes to avoid harmful tax competition Alexander Haupt*, Wolfgang Peters European University Viadrina, Department of Economics, P.O. Box 1786, D-15207 Frankfurt (Oder), Germany Received 2 June 2003; received in revised form 12 July 2004; accepted 22 July 2004 Available online 20 December 2004

Abstract Governments fear that tax competition erodes national revenues. Preferential tax regimes, which levy different taxes on distinguishable tax bases, are particularly criticized for accelerating a race to the bottom. According to both the EU and the OECD, countries should refrain from this kind of tax discrimination. This viewpoint was recently queried by [Keen, M., 2001. Preferential regimes can make tax competition less harmful. National Tax Journal 54, 757–762]. He argues that preferential regimes soften interjurisdictional competition. The present paper, by contrast, defends the original objections to preferential treatments. If investors have a home bias (which is in line with empirical evidence), moderate restrictions on preferential regimes always increase equilibrium revenues. Moreover, we present sufficient conditions under which a total ban on preferential treatments is optimal from the governments’ perspectives. D 2004 Elsevier B.V. All rights reserved. JEL classification: F 21; F 42; H 87 Keywords: Preferential tax regime; Tax competition; Tax discrimination; Capital taxation; Code of conduct

1. Motivation In the era of globalization, regional markets have become increasingly integrated into a single world market. Dismantling barriers to the international movement of production factors has enhanced particularly the mobility of capital. This development intensifies not * Corresponding author. Tel.: +49 335 5534 2430; fax: +49 335 5534 2238. E-mail addresses: [email protected] (A. Haupt)8 [email protected] (W. Peters). 0166-0462/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.regsciurbeco.2004.07.002


A. Haupt, W. Peters / Regional Science and Urban Economics 35 (2005) 493–507

only the rivalry between firms. It also fosters competition between countries, since capital, as a major component of regional tax bases, responds more and more sensitively to international tax differentials. As a consequence, a substantial proportion of international investment flows to low-tax countries. The keen, emerging interjurisdictional competition pushes down the public burden on mobile bases. Whether this is good or bad is open to dispute. On the one hand, tax competition seems to be a good firewall against governments’ biases towards increasing their budgets beyond efficient levels. On the other hand, it might restrict the governments’ ability to finance dbeneficialT public expenditures.1 Recent political strategies can be interpreted as a compromise between the two extreme positions. The EU and OECD aim at restricting so-called dharmfulT tax practices without attempting to eliminate tax competition totally. This policy intends to prevent a ruinous race to the bottom which drastically erodes national revenues. In this context, the OECD (2000) identified 47 dharmfulT regimes and 35 jurisdictions operating as tax havens, and the EU’s Code of Conduct Group (2000) listed scores of regulations with dharmful featuresT that had been implemented in EU member countries. According to both the OECD (1998) and the Council of the European Union (1998), applying different tax rates to residents and non-residents and ring-fencing national tax bases by other means are key indicators of undesirable measures.2 In line with the previous literature, we refer to these practices as preferential tax regimes. It is important to notice that preferred treatment of foreign residents is often granted indirectly rather than directly. Take the famous case of Ireland which only levied a 10% tax rate on corporate income in the manufacturing and financial services sectors instead of the standard rate (32%).3 On the surface, this measure was discrimination between sectors. In fact, it was largely for the benefit of foreign investors, who were major players in the low-tax sectors. We think it is fair to say that this discrimination induced in favor of investments of non-residents was intentional. As a consequence of this preferential treatment, huge amounts of foreign investments were attracted to Ireland and became a main factor in the rapid growth of GDP in the nineties. Since Ireland dring-fencedT its domestic tax base to a high degree, it raised its total base without risking drops in its tax revenues stemming from economic activities of domestic investors.

1 Both stances are widespread among economists. Most papers on tax competition support the notion that interjurisdictional competition leads to inefficiently low tax rates (see, for instance, the early contribution of Wildasin, 1989). A comprehensive survey of this literature is provided by Wilson (1999). The idea that tax competition corrects the oversized public sector is largely based on the seminal contribution of Brennan and Buchanan (1980). According to their line of reasoning, government expenditures tend to reach too high a level as a result of political failure. These very different evaluations of competition among governments is in striking contrast to the broad consensus that competition between private agents is, in principle, welfare enhancing. See the discussion in Oates (2001). 2 A comprehensive guideline on the features of ‘harmful’ tax regimes is given in OECD (1998) and Council of the European Union (1998). 3 Ireland implemented a variety of measures to give these preferential treatments. For instance, companies engaged in financial services activities and located in the Shannon Airport Zone or the International Financial Services Centre in Dublin could qualify for these tax benefits. See Code of Conduct Group (2000) for details.

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Regarding the Irish preferential regime as a dharmful strategyT, the EU intervened, and Ireland abandoned its dual-rate structure. However, the underlying assertion that this kind of discrimination necessarily reinforces a race to the bottom and totally erodes national tax revenues is challenged by Keen (2001). He analyzes two countries that compete for two tax bases. These bases differ in their international mobility. As he argues, an international ban on discrimination in favor of the more mobile tax base extends the domain of fierce tax competition to the less mobile base. In the end, a total renunciation of preferential regimes yields lower revenues for each country than competition without constraints on discriminatory regulations does. Janeba and Smart (2003), in turn, show that this very surprising outcome is less likely to occur if the aggregate tax base depends on the tax rates in the two competing regions and is not exogenously fixed as in Keen (2001).4 We qualify the result in Keen (2001) too, but take a different avenue from Janeba and Smart (2003). Our paper diverges from Keen’s approach in two major aspects. First, we assume that tax bases have dregional preferencesT. An average US agent prefers to invest in the United States unless economic activities abroad yield substantially higher returns. Similarly, Europeans prefer to keep their savings in their own country. This home bias is empirically well-established and persists despite the decline of international barriers to the movement of capital. It reflects the fact that investment abroad involves higher information, monitoring, and transaction costs and implies greater uncertainty than investments at home.5 Neither Keen (2001) nor Janeba and Smart (2003) take this home bias into account. They consider tax bases which differ in their degree of international mobility without favoring one region over the other. We, however, show that, once we introduce regional preferences in the framework used by Keen (2001), his results might reverse even if aggregate tax bases are exogenously fixed. For a wide range of functional specifications, a total ban on preferential regimes indeed maximizes the countries’ payoffs, and we provide a sufficient condition for this outcome. Second, the present paper also analyzes marginal restrictions on preferential regimes while Keen (2001) considers a complete switch from unregulated tax discrimination to uniform taxes on the residents’ and non-residents’ incomes. We show that, even in cases in which a total renunciation of preferential regimes is not desirable, competition without any constraints on the regulations allowed always yields lower revenues than competition with dmoderatelyT restricted tax differentials. This conclusion supports the political notion that at least small limitations on preferential tax regimes help to prevent the erosion of revenues. 4

An even more radical conclusion is drawn in Janeba and Peters (1999). They show that a total renunciation of preferential regimes makes at least one government strictly better off without worsening the position of its opponent. Their argument, however, rests on the rather extreme assumption that there exists a completely immobile domestic, i.e. faultlessly ring-fenced, tax base in addition to a perfectly mobile (or infinitely elastic) one. 5 Pinkowitz et al. (2001) regard the home bias as bperhaps the least controversial stylized fact in international financeQ (p. 1). According to them, US stocks amount to more than 90% of the portfolio of US investors in 1997, although they constitute less than 50% of world market portfolio. French and Poterba (1991), for instance, provide further empirical evidence of the investor’s home bias in the industrialized countries, and Lewis (1999) surveys the literature on this issue.


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Before we turn to the results in detail, in the next section we present our framework. After this, the case of unconstrained tax competition is analyzed. We examine the case of restricted tax competition in Section 4. There we show how tax revenues change if preferential regimes are kept within limits. This part of the paper contains our main results. In Section 5, we compare our results with Keen’s contrasting conclusions in detail, sketch possible extensions and provide some final comments.

2. Tax bases and their properties We consider a simple world with two symmetric countries 1 and 2. The regions’ governments compete for two tax bases consisting of the aggregate investments of 1’s and 2’s residents, respectively. These bases are internationally mobile. Europeans transferring their savings to the United States and American agents investing in projects on the other side of the Atlantic are classic examples of this mobility. These international capital flows take place in many different forms. Nonetheless, we refer, for brevity, to them as foreign direct investments (FDIs), but we have in mind mobile capital in general. To make our point as simple as possible, aggregate investments of each country’s residents are fixed and normalized to unity.6 Their international allocation is assumed to depend only on tax differentials Ti t j (i, j=1, 2), where Ti and t j denote government i’s rate levied on domestic investments of its own residents and country j’s tax burden on the investments of non-residents in its jurisdiction, respectively. These differentials drive the agents’ decisions about where they invest their savings. To be precise, the erosion function F(Ti t j ) captures the magnitude of the tax base generated by i’s residents but located abroad and thus not taxable by i’s government.7 The resulting contributions of the two population groups to the taxable activities in the two countries are shown in Table 1. Bdi and Bfj denote country i’s tax bases, which are generated by the domestic investments of i’s residents and FDIs of j’s investors in region i. They are subject to i’s tax legislation. Since the aggregate investments of each region’s agents is fixed to one, the figures in the rows in Table 1 of course add up to unity. All that remains is to make some sensible assumptions about the erosion function and the range of the tax rates.

6 For notational convenience, the tax bases and the respective aggregate investments are regarded as identical. Assuming more generally that the bases are positively related to the economic activities does not change our results. 7 As Wilson (1999), among others, argues, taxing foreign-source income implies severe administrative and tax compliance problems. Thus, the success of residence-based taxation can only be a limited one. But even if it could be enforced in practice, this would not eliminate tax competition. In this case, the investors themselves are still able to move abroad to avoid domestic taxation. In recent years, for instance, American firms have reincorporated in island havens and thus keep their profits arising outside the United States out of reach of the American tax authorities. See, for instance, the political discussion in the Economist (2002).

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Table 1 Tax base

Located in country 1

Located in country 2


Generated by 1’s investors Generated by 2’s investors

B d1 =1F(T 1t 2) B f2 =F(T 2t 1)

B f1=F(T 1t 2) B d2 =1F(T 2t 1)

1 1

Assumptions. For the tax rates, (Ti ,t j )a[0,1]2 holds. Furthermore, the erosion function F( ) is twice continuously differentiable, and the relation 0VF( )V1 is fulfilled for all possible tax differentials. More interestingly, it has the additional properties:



(i) The erosion function F increases in the difference between the domestic and foreign tax burden Ti t j , i.e. FVN0. (ii) The erosion function is convex but not too convex, i.e. FUz0 and ( FU/FV)b2. (iii) The slope of the erosion function is sufficiently large for positive tax differentials Ti tj , i.e. FV(0)N1F(0). (iv) The agents have a home bias. This means that, if the tax burden is identical in the two regions, most of them locate their economic activities in their home country, i.e. F(0)b0.5. Assumption (i) simply tells us that the investors locate the more economic activities abroad, the higher the tax differentials. Part (ii) gives a simple dtechnicalT assumption that guarantees well-behaved revenue functions. This restriction on the convexity is a convenient sufficient condition for some of the following results but is far from being necessary. Assumption (iii) excludes corner solutions. Intuitively speaking, it guarantees sufficiently elastic tax bases such that tax rates fall short of unity (but are still strictly positive). Thereby, we avoid all the clumsy notations and proofs that would be otherwise necessary. Assumption (iv) is very important for our results. It reflects the observation that most agents prefer to invest in their home country even if this domestic investment is subject to a slightly higher taxation than an FDI. This apparently irrational behavior can be drationalizedT on various grounds. Economic activities abroad increase information and transaction costs. Furthermore, monitoring investments in foreign countries is more difficult than at home, and a lack of knowledge increases uncertainty. The resulting home bias proves to be decisive for our conclusions. Note that Assumption (iv) contains the only major deviation of our approach from that in Keen (2001). In his recent contribution, the two tax bases considered have no dregional preferenceT. They are both equally distributed over two countries if the tax rates are identical in the two regions. The current paper shows that, only by changing this assumption, the conclusion in Keen (2001) can be reversed.8 We return to this point and discuss it in detail in Section 5.


In addition, our dtechnicalT assumption (ii) constitutes a minor difference between us and Keen (2001). It proves to be slightly more restrictive than its counterpart in Keen (2001) who requires FFU/( FV)2b2. For the decisive values of T and t, all functions that are in line with our condition fulfill Keen’s requirement too. However, this issue is not that relevant, since assumption (ii) does not drive our conclusions.


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3. Tax competition and preferential regimes There are widespread objections to the policy of taxing investments of non-residents at a lower rate than those of residents. The criticism is based on the assertion that allowing this kind of tax differential intensifies interjurisdictional competition and robs the governments of the financial means needed to fulfill their tasks. As in the previous literature, we call this discrimination practice a preferential tax regime. To analyze the impact of this strategy on public budgets, it is sufficient to focus on decision-makers who are only interested in revenue maximization. Adding other targets to this Leviathan objective does not alter our basic insights. Moreover, the present approach makes a comparison of our conclusions with the results in Janeba and Smart (2003) and Keen (2001) more straightforward, since the governments in our model pursue the same goal as the politicians do in their frameworks. This section considers the benchmark case in which preferential regimes are allowed. Each non-cooperative government takes the decision of its opponent as given. Then the two countries simultaneously choose their rates (T 1, t 1) and (T 2, t 2) such that revenues (1)

are maximized. For both variables Ti and t i , the decision-makers face the usual trade-off. While higher rates increase the revenues from the remaining tax payers, they drive investments out of the country and thus reduce the tax bases. Balancing these two opposing effects yields the well-known inverse elasticity rule, which characterizes the optimal tax rates. The solution is given by the four conditions9 T1 ¼

1  F ð T1  t 2 Þ 1  F ð T2  t 1 Þ ; T2 ¼ ; FVðT1  t2 Þ FVðT2  t1 Þ

t1 ¼

F ðT2  t1 Þ F ðT1  t2 Þ ; t2 ¼ : FVðT2  t1 Þ FVðT1  t2 Þ


These rearranged first-order conditions determine the outcome of the tax competition. As can easily be checked, they yield a unique Nash equilibrium.10 In addition, these 9

Under assumption (ii), both revenue functions are strictly concave over the relevant domain (Ti ,t i )a[0,1]2. The first-order conditions imply well-behaved best-response functions. The optimal rate Ti always increases in the opponent’s choice t j . By contrast, the optimal t j might go up or down if Ti rises. In any case, the slopes of the reaction curves are smaller than unity and dTi /dt j is strictly positive. Furthermore, since assumption (i), (ii) and (iii) imply BR i /BTi |Ti =1=1F(1t j )F V(1t j ) b 1F(0)FV(0)b0 and BR i /BTi jTi =0=1F(t j )N0 for all t j a[0,1], 0bTi b1 results. Similarly, BR j /Bt j jtj=0=F(Ti ) N 0 for all Ti a[0,1] and thus t j N0. We show below that the reaction curves implied by (2) intersect in the area where Ti N t j holds. This conclusion, the slopes of the reaction curves and the results Ti b1 and t j N0 together guarantee uniqueness (cf. Friedman, 1991) and exclude a corner solution for either tax rate. Thus, we can focus on the interesting case of an interior Nash equilibrium, i.e. (Ti ,t i )a(0,1)2. 10

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conditions directly reveal that the unique solution is symmetric, i.e. T 1*=T 2*=T* and t 1*=t 2*=t* result. Therefore, the outcome is given by T* ¼

1  F ðD*Þ F ðD*Þ and t* ¼ ; FVðD*Þ FVðD*Þ


where D*=T*t* denotes the tax differential in Nash equilibrium. The decisive feature is that, in equilibrium, both governments implement a preferential regime. These policies are caused by the home bias. Since agents prefer to locate their economic activities in their own country, the domestic component of region i’s tax base Bdi responds less elastically to an increase in the tax rate than its foreign counterpart Bfj. Consequently, the inverse elasticity rule leads to higher rates on investments of residents than on those of non-residents.11 Foreigners have to receive a preferential treatment to loosen their regional ties. This conclusion is captured in Proposition 1. Proposition 1. Preferential tax regimes. (i) In Nash equilibrium, both regions apply a preferential tax regime. In each country, higher taxes are levied on investments of residents than on investments of nonresidents, i.e. Ti Nt i holds. (ii) Although domestic investments are subject to tax discrimination, most of the investments of i’s residents are made in their home country, i.e. F(D*)b0.5 results. Proof. (i) Using Eq. (2), the tax differential in equilibrium is given by D* ¼

1  2F ðD*Þ : FVðD*Þ


As F(D)b0.5 for all DV0 (since FVN0 and F(0)b0.5), we can exclude DV0 as a solution to Eq. (4). Consequently, D*N0 has to hold. (ii) The relation 12F(D*)N0 and thus F(D*)b0.5 directly follow from Eq. (4) and D*N0. 5 The second part of Proposition 1 shows that our model is consistent with empirical evidence. According to it, most agents locate their economic activities in their home country in spite of lower taxes on their investments abroad.


Note that this tax discrimination between domestic and foreign investors is in accordance with the OECD Model Convention with Respect to Taxes on Income and on Capital, first published in 1977. Article 24 of this document says that taxation should not be more (or other) burdensome for non-residents than for residents (see OECD, 2003). However, this does explicitly not exclude taxes on foreign investments being lower than on domestic investments. It is this kind of preferential treatment that the OECD, contrary to its proposal in the Model Convention, and the EU criticized in their recent reports.


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4. Restricted preferential regimes Having analyzed unconstrained interjurisdictional competition, we now turn to the question of whether limiting tax discrimination enables both countries to increase their revenues. We examine how an upper bound d for the difference between Ti and t i affects the governments’ payoffs. This limit is certainly only a second-best instrument. But, since more demanding forms of coordination do not seem to be politically attainable at the international stage for various reasons, from the governments’ perspectives an agreement on restricted competition might at least be a step in the right direction. If the constraint d is binding, each country can de facto choose only one tax rate independently, for instance Ti (d–’denotes the tax rates in the case of a restricted preferential regime). The second rate is then determined as a residual by the restriction such that t¯i =Ti d results. Consequently, a different equilibrium is obtained for each da[0,D*]. At the ends of the interval, we have either uniform taxation (d=0) or an unrestricted preferential regime (d=D*).12 The new rules of the game change the payoff functions as follows: P


P   P  P  P  P P R1 ¼ T 1 1  F T 1  T 2 þ d þ T 1  d F T 2  T 1 þ d P   P  P  P  P P R2 ¼ T 2 1  F T 2  T 1 þ d þ T 2  d F T 1  T 2 þ d :


The respective optimum conditions are slightly more complicated than Eq. (2), since each region now applies a single independent tax instrument to two tax bases with different elasticities. Nevertheless, all results are relatively close to those of the case without restriction. There exists again a unique and symmetric Nash equilibrium. The countries’ first-order conditions, therefore, simplify such that we can solve for the tax on domestic investments   1 1 P P P T ¼ T1 ¼ T2 ¼ dþ : ð6Þ 2 FVðdÞ This outcome implies two interesting features. First, restricting preferential regimes ¯ definitely yields higher taxes on FDIs, i.e. t¯=t¯1=t¯2=TdNt* holds for dbD* (which is shown in the proof of Proposition 2 (i)). In that sense, this kind of low-key coordination fulfills its task. It serves, to some extent, as an imperfect substitute for a minimum tax for each of the two bases. The reason for this result is straightforward. The constraint on the tax gap makes it more costly to offer a discount to the price-elastic foreign component Bfj, since this measure also reduces the tax levied on the rather price-inelastic domestic base Bdi . Therefore, a declining difference d leads to a higher equilibrium rate ¯t . Second, the tax levied on the domestic base can increase or decline in response to a tighter restriction on preferential regimes. This ambiguity reflects conflicting forces P


Like in Janeba and Smart (2003), the whole range [0,D*] of possible upper bounds is considered and not only the extreme case of a total ban on any tax discrimination as in Keen (2001).

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affecting the optimal rate Ti . On the one hand, reducing the governments’ ability to differentiate between the two bases decreases the benefits from the former high rate on domestic investments, since it negatively affects the revenues stemming from Bfj. This antidiscrimination impact works in favor of a positive relationship between the policy variable Ti and the parameter d. On the other hand, limiting preferential treatments strengthens the incentive to impose a high tax on the base Bdi , because this kind of coordination results in a higher rate ¯t j . It restricts reciprocal dumping and, similarly to the implementation of a minimum tax rate, it consequently softens interjurisdictional competition. If this antidumping effect dominates over the whole range [0,D*], the taxes on the domestic bases are the higher, the lower the difference d is allowed to be. Since, under these circumstances, a stricter limit on tax differentials increases both rates T and ¯t =Td and thus each country’s revenues, a uniform taxation, i.e. d=0, is indeed optimal from the governments’ perspective. A total renunciation of discrimination maximizes the governments’ equilibrium payoffs, which amounts to R(d)=T (d)dF(d). Proposition 2 provides a condition for this outcome to occur. If, however, the antidiscrimination effect dominates and thus TbT* result, a strictly positive tax differential can be revenue maximizing. But even in this case, a marginal tightening of the tax restrictions, starting from d=D*, always raises the payoffs of both countries. Each government benefits from the fact that the limitation of preferential regimes impedes reciprocal dumping by means of tax discounts on FDIs. Thus, we can summarize our main results in Proposition 2. P





Proposition 2. Restricted preferential tax regimes. (i) The tighter the restriction on the preferential regimes, the higher the tax levied on the foreign tax base, i.e. Bt¯/Bdb0 holds. (ii) The degree of tax discrimination that maximizes each country’s revenues does not coincide with the equilibrium gap in the case of unrestricted preferential regimes, i.e. d*=arg max R(d)pD*. Moreover, an agreement on a marginally smaller tax difference d than that in the non-regulated Nash equilibrium increases revenues in both countries, i.e. BR/Bd b0 for d=D*. (iii) A total discrimination ban, i.e. d=0, maximizes each country’s equilibrium payoff if T/ByV0 results for all ya[0,D*]. This sufficient condition, in turn, is fulfilled if, and only if, F U(y)z(F V(y))2 holds for all ya[0,D*]. h i  FWðdÞ Bt¯ Proof. (i) From Eq. (6) it follows that Bd ¼ BðTBddÞ ¼  12 1þ ðFV 2 b0: ðdÞÞ P

(ii) Inserting the equilibrium tax rate (Eq. (6)) into the payoff functions (Eq. (5)) yields ðdÞ RðdÞ ¼ 1þdFV 2FVðdÞ  dF ðdÞ which can be differentiated with respect to d: " # BR 1 FWðdÞ ¼ 1  2F ðdÞ  2dFVðdÞ  : ð7Þ Bd 2 ð FVðdÞÞ2 To show our conjecture, we evaluate this   derivative at d=D*. Reconsidering Eq. FWðD*Þ BR 1 (4), Bd jd¼D * ¼  2 D*FVðD*Þ þ b0 directly follows, which proves the con2 ðFVðD*ÞÞ clusions in ii).


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2 (iii) The relation h FU(d)N ( iFV(d)) implies BR/Bdb0 for all dVD*. Furthermore, Eq. (6)  FWðdÞ 2 1 leads to BT 5 Bd ¼ 2 1  ðFVðdÞÞ2 V0ZFWðdÞzð FVðdÞÞ which finally proves our result.

To illustrate the different cases that can arise, we consider the following simple examples. First, assume a linear erosion function 8 if Dzð1  zÞ=c <1 F ¼ z þ cD if otherwise ð8Þ : 0 if Dz  z=c where zb0.5 stands for the home bias and cN1z guarantees absence of corner solutions (see assumptions (iii) and (iv), respectively). Under these circumstances, the tax rates T and ¯t monotonously converge towards each other if the constraint on the preferential regime is tightened (see Fig. 1a). The induced revenues of each country first rise and then drop in response to a declining tolerated tax differential d. Hence, a moderate restriction on tax competition, but not a uniform tax, is optimal from the governments’ view. This conclusion is illustrated in Fig. 1b. The revenue curve also shows that unconstrained preferential regimes still lead to higher revenues than a total ban on preferential treatments, i.e. R(D*)NR(0) holds (which is valid for all linear functions fulfilling our assumptions).13 If, like in Keen (2001), politicians only have a discrete choice between these two benchmarks, they feel comfortable with a fully unregulated tax system. In the case of a richer set of feasible instruments which permits partial discrimination, intermediate restrictions d*a(0,D*) dominate the two extreme cases. The situation is different when we consider a quadratic relationship between tax differentials and erosion. Take the example F(D)=min[0.4(D+1)2, 1], where the minoperator guarantees that the erosion function does not exceed unity. Contrary to the former case, the equilibrium taxes on domestic investments and on FDIs are the higher, the lower the gap d is set (see Fig. 1c).14 Consequently, each country’s revenues are maximized if uniform taxes Ti =t¯i are enforced (see Fig. 1d). In particular, a total ban on tax discrimination yields higher payoffs than an unrestricted preferential regime. This result reverses the finding in Keen (2001). Moreover, even a moderate discrimination cannot improve total tax revenues above the level achieved in the case of a uniform taxation. Let us discuss the explanation for the distinct conclusions that follow from the two examples in more detail, since doing this sheds some additional light on how limiting tax differentials influences interjurisdictional competition in general. As Eq. (6) shows, the restriction d affects the equilibrium tax on domestic investments directly through d and indirectly via the erosion function’s slope FV(d). While the former impact of a smaller d on



13 The values which lead to Fig. 1a and b can be easily calculated: D*=(12z)/3c and d*=(12z)/4c (note that  the revenues in equilibrium are strictly concave in d if the erosion function is linear). Moreover, BT /Bd=Bt¯ / Bd=0.5 shows the convergence of the tax rates. pffiffiffiffiffiffiffiffiffi  14 2 In Nash equilibrium, pffiffiffiffiffiffiffiffiffi the erosion function F has the propertyFU(d)N[ FV(d)]pfor ffiffiffiffiffiffiffiffiffiall da 0;  1 þ 1:25 2.  Since F  1 þ 1:25 ¼ 0:5 and F(D*)b0.5 (see Proposition 1 (ii)), D*b  1 þ 1:25 and thus FU(d)N[ FV(d)] 8da[0,D*] hold. Hence, for all da[0,D*] the taxes T and ¯t and the equilibrium payoff R are strictly decreasing in d (note that the revenue function R i is strictly concave in Ti , albeit assumption (ii) is not fulfilled). P


A. Haupt, W. Peters / Regional Science and Urban Economics 35 (2005) 493–507


Fig. 1. Restricted tax regimes, tax rates, and revenues.


tax T is negative, the latter effect is positive.15 But this positive influence disappears in our first example with a constant slope of the erosion function. Therefore, the tax on domestic investments falls if the tolerated preferential treatment d declines. By contrast, the curvature of the quadratic erosion function is sufficiently strong so that the indirect effect dominates the direct one. Consequently, the high tax T increases if the tax differential d is reduced. Since the optimal tax follows from the inverse elasticity rule, the economic interpretation of the relationships illustrated by these examples is straightforward. Consider the case of a sufficiently small (large) curvature of the erosion function. Then a tightening of the permitted tax differential implies that the shares of the tax bases located in country i, i.e. i’s domestic investments Bdi and j’s FDIs Bfj, respond more (less) elastic to changes of the high tax Ti . Therefore, the taxes T1 and T2 fall (rise), which reflects that the antidiscrimination (anti-dumping) effect dominates. As these two examples show, the curvature of the erosion function is decisive, since it determines how the tax elasticity varies with the restriction d. This is also stressed in the third part of Proposition 2. The condition FU(d)N( FV(d))2 guarantees a minimum curvature which ensures that both taxes, T and ¯t , rise in equilibrium. It holds in the case of a quadratic erosion function, but it is obviously not fulfilled by the linear functional specification. P





5. Understanding contrasting conclusions It is striking that our conclusions diverge from the result in Keen (2001), although we use an almost identical framework. Keen (2001) also considers two symmetric countries P


Differentiating Eq. (6) leads to dT /dd=0.5[1FU/( FV)2].


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competing for two tax bases. These bases are distinct in their degree of international mobility. Not surprisingly, the two governments set a lower rate on the base whose location choice responds more elastically to tax differentials between the regions. For instance, income from highly mobile financial capital faces lower taxes in both countries than that of less mobile direct investments. Keen (2001) then shows that a total ban on this kind of preferential treatment reduces both regions’ revenues compared to the unconstrained outcome. As he puts it, bit may be desirable to limit the domain of tax competition by protecting the countries’ ability to tax less mobile bases more heavilyQ (p. 760). The decisive difference between his and our approach is that the two bases considered in the present paper are home-biased. Our concept of home bias is naturally related to that of international mobility, but the two notions do not exactly coincide. As we have been arguing, investors tend to keep most of their capital in their home country. This regional preference is captured by the assumption F(0)b0.5. Note that this assumption is equivalent to requiring that the tax elasticities fulfill the condition e Bdi,Ti =(BBid /BTi )(Ti /Bid )b(BBif / Bt j )(t j /Bif )=e Bif ,t j for Ti =t j . So home bias means that, for instance, the response of American investments abroad to tax changes in the foreign country is more elastic than the response of American investments at home to domestic alterations. But this relationship does not tell us whether American investments are more internationally mobile than, say, German ones. In the present paper, e Bd1,T 1=(BB 1d/ BT 1)(T 1/B 1d)=(BB 2d/BT 2)(T 2/B 2d)=eB d2,T 2 holds for T 1=T 2 and t 1=t 2. Thus, the relative impact of a rising domestic tax on the international relocation of the native tax base is identical in the two regions. In this sense, country 1’s capital is exactly as mobile internationally as region 2’s.16 In contrast to the present paper, Keen (2001) assumes that, expressed in our notation, eBdi,Ti =eBif,tj (for Ti =t j ) and eB d1,T 1 p eB d2,T 2 (for T 1=T 2 and t 1=t 2) hold. Thus, the two tax bases are not home-biased according to our definition, but they differ in their international mobility.17 Consequently, both governments regard the same base as the more elastic one and impose lower taxes on it than on its less mobile counterpart. In the case of a home bias, by contrast, from each country’s perspective the native base of its competitor is the more elastic one. Both governments, therefore, offer foreign investors a discount to attract them. In the non-cooperative equilibrium, they undercut the taxes that the investors face in their home country. This kind of reciprocal dumping is completely absent in Keen (2001), where the two governments concentrate on competing for the same particularly mobile base. As a consequence, in our model each base is subject to a distinct equilibrium tax in each country (i.e. T 1pt 2 and t 1pT 2), while in Keen’s scenario both countries levy the same tax on each base in the unrestricted equilibrium (i.e., again expressed in our notation, T 1=t 2 and t 1=T 2). This difference provides the key to understanding the contrasting conclusions. In our context, limiting preferential treatments restricts the countries’ capabilities for reciprocal 16 The same argument is valid if we refer to changes in the dforeignT tax rate, since eB d2,t 2=(BB d1/Bt 2)(t 2/ B d1)=(BB d2/Bt 1)(t 1/B d2)=e B d2,t 1 holds for T 1=T 2 and t 1=t 2. 17 Like Keen (2001), Janeba and Smart (2003) consider two tax bases that vary in their mobility without showing any home bias. Note that our definition of international mobility is in line with the interpretation in Janeba and Smart (2003).

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dumping. Since this results in smaller discounts on the taxes on FDIs, it serves to some extent as an imperfect substitute for a minimum tax. Like a lower bound for rates in traditional tax-competition models, it can soften overall interjurisdictional rivalry. Therefore, restricting preferential regimes not only raises the low taxes on the foreign base, it can even increase the domestic taxes on the native base. In the case of a total ban on preferential regimes, the resulting uniform tax can thus exceed the burden on domestic investment in the unconstrained equilibrium. At least this form of harmonization need not reduce the high tax on the originally ring-fenced domestic base substantially. Let us contrast these implications with the results in Keen (2001). He compares the two extreme solutions, either a total renunciation of preferential regimes or absolutely unrestricted interjurisdictional competition. In his approach, abandoning preferential regimes also raises taxes on the more mobile base. But this positive effect is definitely at the expense of a lower tax on the rather immobile base to which fierce interjurisdictional competition is redirected. The uniform rate falls substantially below the high tax on domestic investments in the case of unrestricted competition. It is exactly this negative impact that is reversed, or at least mitigated, by the existence of a home bias. Therefore, a total ban on preferential regimes is, in contrast to Keen (2001), beneficial for the governments for a variety of erosion functions. This conclusion qualifies Keen’s result, but it does not of course totally override his arguments. As one of our numerical examples above stresses, his basic assertion can be still valid even in the case of a home bias. But Keen’s very interesting possibility result does not hold if the antidumping effect is sufficiently strong (which in turn requires a sufficiently strong curvature of the erosion function). However, Proposition 2 in the previous section also points out that, even if a uniform taxation decreases the countries’ revenues, the governments always gain from a small restriction on the tolerated tax differential within a country. This result has no counterpart in Keen (2001), since the issue of limiting preferential regimes without eliminating them totally is not considered in his paper. A straightforward extension of our paper and Keen’s is to combine the two approaches and to consider two bases that differ in their international mobility and are home-biased. In this case, the effects stressed by Keen (2001) as well as those of the present paper occur. Which of the partly opposing impacts dominate depends on the degree of the bases’ mobility and the extent of the home bias. The conclusions, however, should contain a combination of the results obtained in Keen (2001) and in the current paper. A more interesting extension would be to allow different country sizes captured by different sizes of the two native tax bases. As a simple starting point, let us assume that region 1’s total native base amounts to aN1 instead of unity. The erosion function still captures the share of this base located abroad so that B 1d=a[1F(T 1t 2)] and B 1f=aF(T 1t 2) holds, while B 2d=1F(T 2t 1) and B 2f=F(T 2t 1) remain unaltered. This modification does not change the basic equilibrium properties in the case of unrestricted competition. The taxes are independent of the country sizes and are still given by Eqs. (2) and (3). The two regions, moreover, discriminate in favor of foreign investments as before. The only difference is that the smaller country now attracts more FDIs in absolute terms


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than the larger rival and thus receives more revenues in relation to its size than its counterpart.18 But once tax differentials are restricted to y, the interplay between the two regions becomes more complicated. Under this regulation, the smaller country chooses lower taxes on both domestic investments and FDIs than its neighbor, i.e. T 2bT 1 and t 2bt 1 result. But despite this new feature, the basic conclusions derived in the case of symmetric regions are likely to hold. In particular, both countries can benefit from limiting preferential treatments. In the example with a linear erosion function discussed above, the relationships illustrated in Fig. 1a and b still hold for each region. Only the levels of the taxes and revenues differ in the two countries. Even the optimal restriction d*, which maximizes revenues, remains unaltered and is identical for the two rivals.19 Although this particular result cannot be generalized, the special case of a linear erosion function provides a hint that our major results might be robust, at least with respect to asymmetries in the country size. Finally, note that our qualification of Keen’s claim differs fundamentally from the objections of Janeba and Smart (2003). They generalize the approach of Keen (2001) by endogenizing the total size of each of the two tax bases. The levels of the aggregate bases depend on the two countries’ absolute tax burdens rather than on the differences between these figures. In their extended approach, Janeba and Smart (2003) show that a limitation of the preferential regimes influences the total size of the bases. This base effect might counteract and dominate the impact analyzed in Keen (2001). Unlike Janeba and Smart (2003), we argue that, even in a framework with a fixed aggregate tax base, Keen’s conclusions can be reversed if a home bias is introduced. To summarize, Keen (2001) shows the very interesting possibility that restricting preferential treatment reduces the countries’ revenues. This possible outcome is less likely to occur if the total tax base is variable (as Janeba and Smart, 2003, show) or if tax bases are home-biased (as we point out). Moreover, countries can always benefit from marginal restrictions on preferential regimes.

Acknowledgements We are grateful to two anonymous referees and to the participants at the conference of the Verein fqr Socialpolitik in Zurich and at a seminar of the Free University of Berlin for 18

The results are consistent with conclusions more generally derived in a loosely related context in Haupt and Peters (2003). In this paper, two gerontocracies of different size compete for young people who are distinct in terms of their attachment-to-home (i.e. their home bias). The young generation has to contribute to a pay-as-yougo financed pension system. Each gerontocracy grants foreign-born workers discounts on their contribution payments to attract them. Like in the present paper, equilibrium contribution rates do not depend on the countries’ sizes if the gerontocracies can perfectly discriminate between native and foreign workers. However, Haupt and Peters (2003) do not analyze the impact of continuous restrictions on preferential regimes. 19 In the linear example F=z+cD, the values of all endogenous figures including the derivative of the equilibrium revenues with respect to the restriction d can be explicitly calculated without difficulties (cf. footnote 13).

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very valuable comments. We also benefited from discussions with Eckhard Janeba, particularly while Alexander Haupt was visiting the Economics Department of the University of Colorado at Boulder. Alexander Haupt is very grateful to the members of the department for their hospitality and inspiration and to the Fritz Thyssen Stiftung for funding his research visit. We also thank the Deutsche Forschungsgemeinschaft DFG and the European Science Centre at the Collegium Polonicum in Slubice for financial support.

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