Preferential tax regimes with asymmetric countries.

INTRODUCTION

One of the main current policy issues in corporate taxation is the proliferation of preferential tax regimes in national tax codes. These discriminatory tax measures come in one of two broad forms. A first category are preferential tax regimes that discriminate between domestically owned and foreign-owned firms, granting more favorable tax conditions to the latter. A second set of measures involves instead discrimination by industry, or by class of asset. In this case it is footloose industries, or mobile assets, that get the benefit of lower tax rates. In both cases preferential tax regimes, thus, work so as to grant tax concessions to those activities that are more mobile internationally.

In both the Organisation for Economic Co-operation and Development (OECD) and the European Union, coordinated policy initiatives are under way to reduce the number of preferential tax regimes. The OECD (1998, 2000) has issued a blacklist of predominantly small tax havens that have been induced to discontinue specific preferential tax regimes that were deemed as harmful. At the same time the European Union (EU) has identified a total of 66 "harmful tax measures," falling in both of the above--mentioned categories, which are to be phased out by 2008 (Primarolo Report, 1999, Annex C).

From a theoretical point of view, it is unclear, however, whether the elimination of preferential tax regimes is indeed desirable from a global economic efficiency perspective. In particular, it is feared that overall tax competition might be intensified when countries are forced to abolish tax preferences for the most mobile firms or activities. This is clearly expressed in the analysis of Keen (2001), who shows that when two symmetric countries compete for two different tax bases, both of which are internationally mobile (albeit to a different degree), the restriction to employ a single tax rate on both tax bases will unambiguously reduce tax revenues in each country. Later work has qualified Keen's result and has shown that a ban on tax preferences need not be revenue-reducing if either the size of the two tax bases is not given for the two countries taken together (Janeba and Smart, 2003) or investors in each country exhibit a home bias (Haupt and Peters, 2005). (1) Nevertheless, Keen's result is still a forceful one.

All the above-mentioned contributions assume, however, that the two competing countries are identical in all respects. (2) Given the perception that small countries are the main beneficiaries of preferential tax regimes, this is clearly an important restriction. A well-known result from the literature on asymmetric tax competition for a single tax base is that small countries will undercut their larger neighbors, and may even be better off under tax competition as compared to a situation where countries can fully coordinate their tax rates (Bucovetsky, 1991; Wilson, 1991; Kanbur and Keen, 1993). (3) It is, thus, a natural question to ask whether large countries--the principal supporters of the policy initiatives referred to above--may gain from the abolition of tax preferences, by restricting the ability of small countries to compete with them on unequal terms.

In this note, we combine Keen's (2001) analysis of discriminatory vs. non-discriminatory tax competition with the analysis of tax competition between countries of different size. We show that the smaller country unambiguously has lower tax rates, but higher per-capita tax revenue, under either restricted or unrestricted tax competition. Imposing a non-discrimination constraint hurts not only the small country, but also the large one. Hence, Keen's (2001) result turns out to be robust with respect to the introduction of size asymmetries between countries.

THE MODEL WITH DIFFERENTIATED TAXATION

We consider two countries, i [member of] {A, B}, which compete over two capital tax bases. The share of country i in their combined population is [s.sup.i] and, by convention, we let country A be the smaller of the two countries (so that [s.sup.A] [less than or equal to] 0.5 and [s.sup.B] [greater than or equal to] 0.5). There are two distinct capital tax bases, n [member of] {1, 2}, which differ in their degree of international mobility. The aggregate supply of each capital tax base is fixed. Each type of capital is combined with sector-specific labor that is immobile across countries. The smaller country, A, has the same share of workers in each sector; hence, [s.sup.i] bears no subscript. Shares sum to unity, [s.sup.A] + [s.sup.B] = 1. We employ the per-capita notation that is customary in the analysis of countries of different size and let [k.sup.i.sub.n] denote the per-capita employment of the capital base n in country i. Hence, denoting the fixed supply of tax base n by [[bar.k].sub.n], market clearing for both types of capital implies

[1] [s.sub.A][K.sup.A.sub.n] + [s.sub.B][K.sup.B.sub.n] = [[bar.k].sub.n] [for all] n [member of] {1,2}.

To arrive at reduced-form expressions in our analysis, we assume that the production functions in both sectors, n [member] {1, 2}, are quadratic. The production functions differ across sectors but, for each sector, are the same across countries. Per-capita production in country i and in sector n is [f.sup.i.sub.n] = [a.sub.n][k.sup.i.sub.n] - [0.5b.sub.n] ([k.sup.i.sub.n]).sup.2], leading to linear marginal productivity conditions for each type of capital:

[2] [partial derivative] [f.sup.i.sub.n]/[partial derivative] [k.sup.i.sub.n] = [a.sub.n] - [b.sub.n] [k.sup.i.sub.n]

[for all] i [member of] {A, B}, n [member of] {1,2}.

The slope parameter [b.sub.n] may differ between tax bases.

It is worth pausing a moment to link this model to the different types of preferential tax regimes mentioned in the introduction. The model considered here applies in particular to those preferential tax regimes that discriminate by industry, or by class of assets. Prominent examples are financial services, insurance and shipping, all of which are activities that are highly mobile internationally. Both the OECD (2000) and the Primarolo Report (1999) single out these sectors as industries where special tax regimes apply in many countries, large and small alike. In contrast, tax regimes that discriminate between foreign-owned and domestically owned firms are less well captured in this model. (4)

Following a standard procedure in the literature, we assume that taxes are levied as source-based unit taxes on capital. Without loss of generality, we normalize units so that the return per unit of capital, were there no taxes, is the same for each type of capital:

[3] [a.sub.1] - [b.sub.1] [[bar.k].sub.1] = [a.sub.2] [[bar.k].sub.2].

By equating the gross returns to each type of capital, this normalization ensures that equal unit taxes on each type of capital are equivalent to equal ad valorem tax rates. From [2], net-of-tax arbitrage by internationally mobile investors implies

[4] [t.sub.B.sub.n] - [t.sub.A.sub.n] = [b.sub.n] ([k.sub.A.sub.n]-[k.sub.B.sub.n]) [for all]n [member of] {1,2}.

Using [1] in [4] we can derive per-capita tax bases in each country as a function of the two tax rates:

[5] [k.sub.i.sub.n] = [[bar.k].sub.n] + (1 - [s.sup.i)/[b.sub.n] ([t.sub.j.sub.n] - [t.sub.i.sub.n]

[for all]i, j [member of] {A,B}, i [not equal to] j, n [member of] {1,2}.

Differentiating [k.sup.i.sub.n] [5] with respect to [t.sup.i] shows that the response of either capital tax base to a tax change is larger, in per-capita terms, for the smaller country, A. From [5], the net return to capital of type n, defined by [r.sub.n] = f' ([k.sub.A.sub.n]) - [t.sub.A.sub.n] = f'([k.sub.B.sub.n]) - [t.sub.b.sub.n], must be

[6] [r.sub.n] = [a.sub.n] - [b.sub.n] [[bar.k].sub.n]] - [s.sub.A][t.sup.A.sub.n] - [s.sub.B][t.sup.B.sub.n].

Equation [6] shows how the endogenous rate of return in each sector ([r.sub.n]) is affected by the tax policies of each country. Both countries' taxes depress the net rate of return, but the larger country's tax rate carries the higher weight. Moreover, in combination with the normalization [3] above, equation [6] shows that the net return to capital will be equal in the two sectors whenever both countries apply a non-discriminatory tax with equal (unit or ad valorem) rates for both sectors.

As in Keen (2001), governments are assumed to maximize tax revenues. The sensitivity of the results to this assumption is discussed below. In the benchmark case, each government is allowed to levy differentiated tax rates (subscript D) on the different capital tax bases. Hence, each government maximizes

[7] [T.sup.i.sub.D] = [t.sup.i.sub.1] [k.sup.i.sub.1] + [t.sup.i.sub.2] [k.sup.i.sub.2] [for all] i [member of] {A,B}.

Substituting capital tax bases from [5] and differentiating with respect to [t.sup.i.sub.n] yields Nash equilibrium tax rates in reduced form:

[8][t.sup.A*.sub.n] = [b.sub.n][[bar.k].sub.n](1 + [s.sub.B]/3[s.sup.A] [s.sub.B] [for all] n.

In each country, the tax rate on tax base n, expressed as a fraction of its gross return, will be proportional to the elasticity of that return with respect to the supply of capital. The "more mobile" tax base is the one for which [b.sub.n] [[bar.k].sub.n]] is lower, implying a greater sensitivity of capital supply to its net return. Moreover, the equilibrium tax rates show that the smaller country (country A) levies the lower tax rate on each tax base n.