2.1 Workhorse Models

Formal thinking on this, and on many other issues reviewed here, has largely revolved around two, complementary modeling approaches. We start by setting these out.

2.2 Sequential Decision Making

There is some evidence that countries’ tax reforms do not occur simultaneously. The results of Altshuler and Goodspeed (2002), for instance, suggest that sequential choices between the US and European countries have existed since the 1986 US tax reform, with the USA acting as a Stackelberg leader and European countries acting as followers vis-á-vis the USA and moving simultaneously vis-á-vis each other.³¹ This raises the question of how the possible sequentiality of choices among governments can change the outcome.

This has been addressed in theoretical contributions by Wang (1999) for indirect taxes (in the setting of the KK model discussed in Section 2.1.2 above) and Kempf and Rota Graziosi (2010), who analyze endogenous timing, using the workhorse ZMW model.

Figure 4 illustrates the Stackelberg leadership case, under the assumption that tax rates are strategic complements. It shows the same best reply functions for the linear variant of the workhorse model as in Figure 2, and the Nash equilibrium that emerges from simultaneous tax-rate choices. Suppose now that, for some reason, country 1 has to choose its tax rate first while country 2 is the follower who observes this choice and chooses on the basis of that observation. In this case, country 1 anticipates that, whatever it selects, country 2 will choose a in line with its reply curve. Hence, by choosing and anticipating subgame perfect play, the country can essentially choose from all combinations () that are graphically described by the reply function . If country 1 optimizes, it chooses the point along that maximizes its objective function. Graphically, such a point is found where an iso-payoff curve for country 1 is tangent to , as it is drawn in Figure 4. It follows that, in a Stackelberg equilibrium, and given strategic complementarity, both countries choose higher taxes than in the Nash equilibrium. Starting from the latter, there would be no advantage to country 1 from raising its tax rate if country 2 continued to choose the Nash equilibrium tax rate—as would happen in the simultaneous game, because country 2 would have no reason to anticipate this deviation from . However, if country 1 chooses first and country 2 can observe this choice, country 2 re-optimizes and finds that, given , its optimal tax rate is also higher. By setting , country 1 induces a higher , and it is this strategic effect that benefits country 1.

It is clear from the figure that country 2 is also better off than at the Nash equilibrium, being on a higher iso-payoff curve. Indeed in the symmetric country case it may well benefit more than the leader, since the latter charges the higher rate: for both then benefit from the increase in both tax rates to the level that the follower sets in the Stackelberg equilibrium, but the follower then benefits in addition (and the leader suffers) from the further increase in the leader’s rate.

While sequential choice is in the interest of all countries here, it requires commitment. In the symmetric case in Figure 4 the Stackelberg follower is seemingly at an advantage, and the commitment problem is one of staying flexible and out-waiting the other country. Procedural rules, the timing of government formation, and so on may yield some differences in the timing in different countries. But the cyclic nature of most of these institutional procedures does not clearly answer the question of who would be expected to move first.

A solution to this problem comes from the theory of endogenous sequential choices, first developed in the context of duopoly by Hamilton and Slutsky (1990) and applied in the context of tax competition duopolies by Kempf and Rota Graziosi (2010). A Stackelberg leader-follower outcome can typically be obtained as the outcome of a game which is augmented by an earlier stage in which each country first chooses its timing of choice (what Hamilton and Slutsky call “the extended game with observable delay”). Let there be two points of time for tax rate choices: , with the point occurring after the point in the time line. First, let each country simultaneously choose whether it would like to choose and fix its tax rate at time or . One can then show that there is a subgame perfect equilibrium in which one country, say, country 1, chooses and the other country 2, chooses ; the Stackelberg game just discussed is the continuation game. To confirm this, we need to show that, assuming subgame perfect play in all possible continuation games, and are mutually optimal replies. Suppose that, for whatever reason, country 1 assumes that country 2 chooses . Then, country 1 has essentially two options. It can also choose . In this case, both countries choose their tax rate at time and simultaneously. They end up in the Nash equilibrium . Alternatively, country 1 can choose . In this case they end up in the sequential subgame with country 1 the Stackelberg leader and country 2 the follower, with an equilibrium at in Figure 5. As just discussed, this outcome is superior to the Nash equilibrium outcome for country 1; hence, . Turning now to country 2, it remains to confirm that, given , country 2 prefers . Supposing that country 2 anticipates , it has essentially two options. It can choose . This yields simultaneous tax rate choices in the continuation game, and the equilibrium is the Nash equilibrium with tax rates . Or country 2 can choose instead. In this case, the subgame is the Stackelberg game discussed above, which country 2 prefers to the Nash equilibrium.

Two difficulties remain with this concept. One is the coordination problem. As was argued in the context of Figure 4 above, both countries prefer the Stackelberg game to the Nash game. But, they typically prefer being in the position of Stackelberg follower (i.e., to be the country that chooses ) if the other country chooses . If the countries cannot coordinate on who becomes follower and who becomes leader, they may randomize independently about their commitment choices. This leads to an equilibrium with mixed strategies at the stage in which they choose timing. In some of the subgames, the mixed strategies result in or , in which case a Nash game follows as the continuation game; in other subgames they manage to end up with , leading to the Stackelberg equilibrium or , leading to the Stackelberg equilibrium in the continuation game. Kempf and Rota Graziosi (2010) use an equilibrium selection argument (the risk-dominance criterion) to argue that—focusing on country differences in capital productivity—the less productive country is more likely to be the leader. If the countries become sufficiently asymmetric, this order of moves can even become Pareto dominant.³²

The second problem that remains is to explain what makes the commitment feasible and credible at the stage when countries commit on their timing. In an institutional context in which tax reforms are feasible only in some time windows, within an electoral cycle, for instance, the choice of the timing of elections may induce some sequential ordering of decision making.

2.3 Pure Profits and International Portfolio Diversification

If aggregate production is a function of internationally mobile capital and other, internationally immobile, factor inputs, and if some of these inputs can be used costlessly, then the ownership of the production facilities in a country may include entitlements in pure profits. The assumption in the ZMW workhorse model above was that any such rents all accrue to domestic residents and are untaxed. Such rents are of course an attractive target for taxation, being non-distorting insofar as these rents are genuinely location-specific. Allowing for such rent taxes adds little when rents all accrue domestically, simply implying that source-based taxes need to be used only insofar as such taxes cannot raise all the revenue required.³³ Foreign ownership, however, raises more substantial issues.

To address these, we consider a simplified version of the ideas outlined in Huizinga and Nielsen (1997, 2002, 2008) and Fuest (2005). Pure profits, it is assumed, cannot be taxed directly but a source tax on capital can be levied—perhaps because paper profits are easier to conceal, or shift across jurisdictions, than productive capital. Production in each country uses capital as the single variable factor in combination with some unpriced fixed factor, which can be thought of as a natural public good. Then is the total pure profits that accrue to the owners of the production facilities in country . Denote by the share of the production facilities in country that is owned by the citizens of country . Then the national welfare function becomes

(28)

(with Eq. (4) above being the special case in which and for ). An assumed interior equilibrium characterized by the first-order conditions can be determined by

(29)

Comparing this with Eq. (5) above, the relocation of capital away from the country induced by an increase in its tax rate has different welfare effects in the presence of international portfolio investment. First, country bears only the share of any loss in rents () on domestically employed capital, since its citizens own only a share of these rents. This makes an increase in more attractive than when . Second, the citizens in benefit from the increase in production rents that accrue in other countries, in proportion to the shares which they own in these rents. As an increase in increases these production rents, this effect also makes an increase in more attractive than for . Starting from the values that characterize a Nash equilibrium for and and fully symmetric countries (including in population size), the first-order welfare effect of an increase in ’s own tax rate is

(30)

This is unambiguously positive for and . Again assuming strategic complementarity of tax rates, this implies that international portfolio diversification weakens tax competition and leads to higher equilibrium tax rates than in the benchmark case.³⁴

This result—that a high degree of international ownership reduces the incentives for a race to the bottom—in turn suggests a potential strategic relationship between the degree of international firm ownership and the intensity of tax competition. If portfolio investors in a country could coordinate on a joint portfolio policy, and if (as seems plausible) they were less interested in the public good than the policy maker (or the median voter), then those investors would have an incentive to reduce their international investment activities in order to induce lower domestic tax rates. Indigenization—encouraging national ownership in national firms and their profits—is a well-known means to reduce the government’s incentive to generate tax revenue from them.³⁵

This indigenization effect is well-known from other contexts. For instance, it has been argued that indigenization, or joint ventures with host country citizens reduce the incentives of the national government in the host country to expropriate or nationalize foreign direct investment. Konrad and Lommerud (2001) show that the problem of ex-post opportunistic behavior can also be moderated if the host country government has incomplete information about the true profitability of the FDI project and if a large share of the foreign company is owned by citizens of the host country. Key to their argument is that this incomplete information shields an information rent of the firm from being extracted, even if the host government applies the most sophisticated extortionary means to extract as much revenue as possible. Similarly, it has been argued that a country with sovereign debt should be less inclined to default if its debt is held mainly by its own nationals (Broner, Martin, & Ventura, 2010).

2.4 Tax Competition with Multiple Instruments

A common feature of both ZMW and KK is that each country deploys only one tax instrument. Many contributions to the literature relax, in one way or another, this unrealistic assumption.

Even allowing for taxes on immobile factors can make an important difference. In ZMW, a country that could also tax rents to the domestic factors generating the concavity of the production function but was unable to affect the common return would optimally choose not to impose a source-based tax on capital: this is the well-known result that small countries should not tax capital.³⁶ Bucovetsky and Wilson (1991) show that the same applies when labor supply is variable, and wage income can be taxed directly. The intuition is the same in both cases: with the required return on world markets fixed, the real burden of any tax on capital is passed onto labor—and it is then better to tax labor directly than to distort capital intensity. The fundamental inefficiency remains, however, if the global capital stock is fixed, since a common tax on that base is then lump sum.

The case in which distinct instruments bear directly on the allocation of production and tax bases across countries is of obvious direct interest. One such instance—in which different types of mobile capital can be taxed, in ZMW fashion, at differing rates—is discussed at some length in Section 4.2. Here we consider another. For with ZMW attuned to modeling movements of real capital and KK to the shifting of paper profits—and both important in practice—it is natural to combine the two. This is the essence, for example, of the model set out in Devereux et al. (2008), a stripped down version of which suffices here.

Suppose then that there are two countries, each, in the spirit of ZMW, with a fixed endowment of capital that is freely mobile between them. In each there is a single multinational enterprise, which undertakes real production only there but which, in the spirit of KK, can also, at some increasing and strictly convex cost , shift an amount of taxable profits to the other country (the assumption being that it has unmodeled taxable income arising there to which it can add or subtract). Country levies both a source-based tax on the real capital located there and a profit tax on output net of profits shifted abroad, financing costs , and the source-based tax. With all investment-related costs deductible, is effectively a tax on rents, so that this structure³⁷ captures two core components of the corporate tax discussed in Section 2.1.1. The after-tax profits of the multinational located in 1 are thus

(31)

with the net return taken as given by the multinationals but determined in equilibrium, as in ZMW, so as to clear the global capital market; and the tax revenue collected in country 1 is

(32)

the final term reflecting revenue raised from profits shifted in by the multinational headquartered in country 2.

Maximizing in (31), the multinational headquartered in country 1 shifts an amount of profit such that

(33)

and invests to the point at which

(34)

In terms of behavioral impact, there is thus a simple dichotomy of effects: the extent of profit-shifting depends only on the difference in rates of rent taxation (reminiscent of (23) in the KK case), while the allocation of capital depends only on the difference in effective rates of source-based taxation.

For policy-making, however, there is no such simplifying decoupling of the two tax instruments. In considering acting on profit-shifting by changing the rate of its rent tax, for instance, a country needs to be mindful that although this does not affect the real capital employed there, it does affect the revenue it collects on the earnings generated by that capital. The interactions between the tax instruments, both within and across countries, become complex, and are not discussed here.³⁸ One lesson worth noting, however, is that it is no longer the case that a small country with access to a rent tax would not wish to impose a source-based tax: it generally will, to provide some safeguard against the erosion of its ability to tax those rents as a consequence of profit-shifting.

2.5 Vertical Externalities and the Strategic Role of Internal Governance Structure

The analysis so far has abstracted from the complex multiplayer decision-making process generating national tax policy choices, treating these decisions as if they were made by single players acting in the interest of their citizens. In fact, many countries have multilayered governance systems, with each layer of government imposing taxes with (explicitly or implicitly)³⁹ partially overlapping tax bases and, often, systems of intergovernmental grants. This internal architecture can have significant effects on the tax competition games played both within and between countries.

To illustrate this, Figure 6 shows three prototype countries with very different federal structures. Country is fully centralized, all choices about tax rates and the tax system being made at the most central level; it resembles most closely the type of player usually considered in the context of tax competition, as elsewhere in this survey. Country has one central government and a considerable number of regional governments , with capital horizontally mobile between them. Country has several vertically related governments, all drawing on the same national tax base, but no horizontal competition between regions inside the country. The “vertical” tax competition induced by these layers of government would generally be expected to lead to inefficiently high tax rates, as more decision makers independently extract tax revenue from the same tax base: in considering an increase in its own tax rate, each level is likely to take account of the consequent contraction of the tax base, but attach relatively little weight to the losses that this also implies for other levels. (The point is especially clear when policy makers at each level are simple revenue-maximizers, in which case, as first noted by Flowers (1988), combined tax rates in the Nash equilibrium may be beyond the peak of the Laffer curve.)

Consider country more carefully. Suppose the central and local governments each independently choose a unit tax on capital at source. The capital that is applied in region will then be taxed by both the central and the local government. In each region, these unit taxes add to the total tax burden on capital in the respective region. The tax rate choice of the central government will presumably be guided by the preferences of the citizens in all regions. The regions, however, are likely to focus more narrowly on the well-being of their own citizens. One aspect of the problem they face is the potential for their tax choices to induce capital to move into, or from, other regions: this “horizontal” tax competition is of essentially the same form as discussed above. But there is another set of constraints arising from the vertical relation between regional and central governments. In making their rate decisions, while the regional governments presumably anticipate some tax base deterioration or other distortions that will diminish the revenue accruing to the central level, since they do not receive all the benefit of that revenue they will attribute too low a shadow price to it. Also, the double taxation of the same tax base by the different layers of government may cause an aggregate tax burden in country that is too high. These effects of vertical tax competition and their interaction with horizontal tax competition between regions and between nations—especially the question of whether tax rates will ultimately be too low or too high—have been quite extensively analyzed (see Keen & Kotsogiannis, 2002, 2004; Wrede, 1999).

Within federations, particularly if regions have some tax autonomy, there are often systems of interregional or vertical intergovernmental transfer systems in place. An analysis of these transfer arrangements can lead to policy conclusions about the disincentive of tax enforcement they can create in the different regions, and to other negative incentive effects of such systems. It is therefore interesting to note that horizontal and vertical transfer systems inside a federal country can and partially do counterbalance the internal forces of vertical and horizontal tax competition inside this federation and can partially correct for the problems caused by interregional or vertical tax competition (see, for instance, Fenge & Wrede, 2007; Kelders & Koethenbuerger, 2010; Kotsogiannis, 2010).

These aspects of domestic fiscal architecture can have strategic implications for international tax competition too. For instance, due to the presence of vertical externalities and absence of horizontal tax externalities, a country of type with revenue maximizing layers of government has a tendency to choose a higher tax rate on capital than would a country of type , when competing with each other. This remains the case in a framework with international tax competition between countries of types and . The internal governance structure of a country has strategic effects, affecting the tax rate choices in the country. As the internal governance structure of a country affects its tax choices, it can change equilibrium choices in other countries and create further strategic considerations. Wilson and Janeba (2005) and Kessing, Konrad, and Kotsogiannis (2009) highlight this point. Due to this strategic effect, a structure that induces vertical tax competition can be advantageous or disadvantageous. As the choice of governance structure is a long-term decision and cannot be adjusted in the short run as easily as the tax rate, the governance structure could be used as a commitment device by which countries can position themselves in a framework of international tax competition. More independent vertical tiers of governance may lead to higher effective tax rates, the anticipation of which will induce other countries—provided that tax rates are strategic complements—to also choose higher tax rates. This strategic effect is similar to the commitment of a Stackelberg leader and can be a similar source of benefit. However, this advantage becomes small when faced with many competitors, smaller than the negative side effect of deviating from what would have been the tax rate chosen from the perspective of unitary state. Hence, if the number of competitors of the country is sufficiently large, the overall effect will typically work to the disadvantage of this country in the context of capital taxation at source.

3.1 Asymmetries and the Limits of Harmonization

Harmonization, particularly to some average of non-cooperative tax rates, seems to have a natural appeal to policy makers as a response to tax-induced movements of tax base.⁴⁰ It is inherently flawed, of course, as a response to problems of tax competition in its neglect of overall levels of taxation: with symmetric countries, tax rates are expected to be spontaneously harmonized, but there are still gains from coordination.

Asymmetries create further difficulties for a strategy of harmonization. Returning to the linear case of the ZMW model in Section 2.1.1 above, for instance, Figure 7 shows the outcome in which country 1 has a higher capital endowment, per unit of labor than country 2, and so sets a lower tax rate in equilibrium. In such a case it may be, as drawn, that there is simply no harmonized tax rate at which both countries are better off than at the Nash equilibrium. The point emerges still more clearly in the KK model. In this case, the smaller country (1, say) is sure to be made worse off by harmonization to any tax rate between those of the Nash equilibrium, because its revenue is then

(35)

where the first inequality reflects the fixity of the national base and the second the definition of a best response.

3.2 Minimum Tax Rates

As one possible limitation on the amount of cooperation, countries may be unable to harmonize on common tax rates but able to agree on a range within which rates must lie. One leading example of such type of limited cooperation is agreement on minimum tax rates; as with, for example, the agreement in the West African Economic and Monetary Union of a minimum corporate tax rate of 25% and on minimum rates of excise duty both there and in the EU. Lower (and/or upper) limits for possible tax rate choices leave countries some flexibility to react to structural or macroeconomic developments, or to changes in their shadow price of public funds, which may be more appealing for the countries’ decision makers than a fully rigid system of coordinated taxes that can be changed and adjusted to their needs only by renegotiation (especially when, as in the EU, this requires the unanimous approval of all participating countries).

It might seem that the adoption of such minimum taxes must make those countries that are consequently forced to raise their tax rates worse off. This, however, is not the case: lower (or upper) bounds on tax rates can have surprising consequences for welfare in the resulting tax competition equilibrium.

Starting from an asymmetric Nash equilibrium with in the fully uncoordinated situation with , a common lower bound of has no impact given simultaneous rate setting (a less trivial observation than it may appear, as will become clear later). A bound in the interval between the two Nash equilibrium rates, generally binds country 1 and typically induces it to choose this lower bound. This is illustrated in Figure 8, where the kink in the new best reply function of the low tax country reflects the prohibition on setting a rate below . For the same reason, the best response for country 2 also acquires a kink, but in a range that is irrelevant for the equilibrium. The change of from to , taken in isolation, would benefit the high tax country 2, but would reduce welfare in the low tax country 1. Country 2, however, will not continue to choose in the new equilibrium. Using the Nash equilibrium conjecture , it will choose its optimal reply . Assuming strategic complementarity, this means a tax rate higher than . This change can be beneficial for both countries. With the new equilibrium at , the overall welfare effect for country 1, compared to the unconstrained Nash equilibrium, is in general unclear.

Consider, though, a marginal increase in from its level in the unconstrained Nash equilibrium, , to the very slightly higher level . This has a zero first-order effect for the welfare of country 1, as has a slope of zero at . But it induces an equilibrium reaction by country 2, which increases its tax rate by times the slope of . This increase in does have a first-order marginal effect for country 1’s welfare, and it is beneficial. Thus agreement on a minimum tax rate that is above but sufficiently close to the lower of the unconstrained Nash equilibrium rates is Pareto improving. In Figure 8, both countries gain if , on the upper right of , is to the left of the tax rate at which and intersect: any minimum rate induces an increase in both countries’ welfare, whereas lower bounds in the higher range make the low tax country 1 worse off.⁴¹

Matters are quite different when countries choose sequentially. Wang (1999) addresses this case in the KK model, but the same insights can be seen using the linear model illustrated in Figure 9. Focusing on the asymmetric case and taking the larger country 1 to be the Stackelberg leader, the initial equilibrium in the absence of any minimum taxes is at , the point of tangency between country 1’s iso-welfare curve and country 2’s reply function, which has . Now imposing a minimum tax rate between the two initial equilibrium rates may cause the tax rate of the Stackelberg leader to fall and, for a broad range of parameters and under quite general conditions, lead to higher welfare for the leader and lower welfare for the follower. Figure 9 illustrates. Here a minimum tax that is slightly higher than leads to kinked reply functions and , just as above. When country 1 chooses its most preferred point along the reply function of country 2, subject to the constraint , it selects . The Stackelberg leader thus chooses a tax rate that is considerably lower than its choice in the initial equilibrium , with the effect, as Figure 9 suggests, that the leader is better-off, but the follower may be worse off, than in the unconstrained Stackelberg equilibrium. Setting such a low rate was not attractive to the leader in the absence of the minimum tax rate, because the follower would react to such a choice by an even lower tax. The minimum tax prevents such a reaction, making attractive for the Stackelberg leader. Had the Ruding Committee proposal of a 30% minimum tax rate been adopted, for instance, EU members setting a higher rate could have reduced their rate secure in the knowledge that no other country would undercut them by going below 30%.Konrad (2009) goes one step further and considers a minimum rate a minimum, that is, below the lower of the two tax rates chosen in the unconstrained equilibrium. One might expect this to have no effect. But, in the Stackelberg case, even such seemingly unconstraining floors change the nature of the equilibrium and may induce all countries to reduce their tax rates. The reason for this can be seen in Figure 10, which is similar to Figure 9. With a lower bound of , the reply functions and

are drawn as closed lines, kinked as above at this very low minimum. Now is the new equilibrium, yielding an increased payoff for country 1 and a reduced payoff for country 2. Both countries thus switch to setting their rate at the minimum permissible level even though, in the initial equilibrium, both rates were higher than that. The intuition is essentially as above: without a floor, the leader refrains from setting because this would induce the follower to choose a very low tax rate chosen by country 2 in the unconstrained situation, but the imposition of the minimum cuts off this possibility. What is striking is that the same intuition continues to apply even for non-binding minima.

These are surprising results. But they also call for some caution in drawing policy conclusions, showing that such a straightforward and central policy idea as imposing a minimum rate can (but need not) lead to a Pareto improvement depending on the precise nature of the strategic interaction in tax-setting.

3.3 Coordination Among a Subset of Countries

A simultaneous coordination of all countries is hard to envisage if there is no supra-national agency that could enforce such an agreement. However, supra-national structures such as the European Union may enable their members to commit to joint action. But is it in the interest of subsets of countries to coordinate only among themselves? Non-participating countries’ equilibrium tax rates may then well be different from those they set in the fully non-cooperative Nash equilibrium. So even though participating countries can benefit from joint action in the absence of such strategic effects on non-participants (they can at least not do worse), it is not clear whether or not, once those effects come into play, the overall outcome of this coordinated action will be beneficial for them. The issue, it should be stressed, is a very real one for the several regional blocs facing the question of whether some degree of coordination toward higher taxation would be to their advantage or would simply make them more vulnerable to tax competition from non-participating countries.⁴²

This problem has been addressed formally by Burbidge, DePater, Myers, and Sengupta (1997) and Konrad and Schjelderup (1999). The latter addressed the general question in a modified version of the reaction curve figure above, now with three countries. Suppose that the symmetric Nash equilibrium in pure strategies exists and denote the uniform equilibrium tax rate . Could countries 1 and 2 gain if, rather than maximizing their own welfare individually and finding themselves in this Nash equilibrium, they join forces and credibly and publicly agree on choosing a common tax rate that maximizes their joint welfare , where is as in (4) above?

A first question is whether they can increase their welfare by both choosing a slightly higher tax rate, assuming first that country 3 still chooses . That they can follows on differentiating their aggregate welfare at = to find

(36)

where use is made of the first-order conditions . Intuitively, if both countries 1 and 2 slightly increase their tax rate starting at the non-cooperative Nash equilibrium, the direct first-order effect of the increase in their own tax rate on their own welfare is zero because the deviation occurs at the local optimum. However, each country enjoys a first-order gain from the increase in the other’s tax rate, due to the tax-base effect. The non-participating country 3 gains even more, since it benefits from the base effect from the increased tax rates in two countries, not just one.

But country 3 is unlikely to continue to set given the higher rate set elsewhere. The new equilibrium is obtained as a set of taxes that fulfills two conditions. First, given country 3’s Nash conjecture that countries 1 and 2 both choose , country 3 chooses the that maximizes . Second, the joint tax rate is the argument that maximizes the sum of given the Nash conjecture about . Whether or not the coordinated choice of countries 1 and 2 improves their joint welfare in the new equilibrium will crucially depend on the new equilibrium value of . However, if tax rates are strategic complements, the optimal reply of country 3 to the conjectured is a choice of . This higher tax rate typically benefits countries 1 and 2, so that the overall welfare effect for countries 1 and 2 of their coordinated tax increase is positive in this case. Indeed it is greater with the strategic response of country 3 than it would be without. This analysis can easily be extended to more than three symmetric countries, with a subset of these partially coordinating.

These implications of regional cooperation have a parallel in work on the merger of firms in an oligopoly with firms and price competition (see Deneckere & Davidson, 1985). Merger of firms in this context means that they maximize their joint profits by a coordinated choice of their prices. If the prices of all firms are strategic complements, the merging firms typically choose higher prices. The strategic effect of this increase on bystanding firms is that they also increase their prices. Overall, the merger increases the profits of all firms.

Aspects of regional tax coordination are explored in several other studies. Conconi, Perroni, and Riezman (2008) essentially analyze coordination by subsets of countries in a context combining downward pressure on tax rates from tax competition and upward pressure due to time consistent confiscatory taxation. Coordination by a suitably chosen subgroup may be used to find the right balance for this trade-off. Haufler and Wooton (2006) apply a related logic in a competition for direct investment. Sørensen (2004a)explores a similar logic (as do Burbidge et al., 1997), focusing on the amount of redistributive taxation, rather than on the provision of public goods and providing numerical simulations of the welfare effects (compared to fully uncoordinated tax competition) of regional (subgroup) rather than global coordination. These suggest that the beneficial effect of coordination among a subset of all countries is small relative to the benefit for the country that is not part of the coordinating subgroup. Simulation results with a similar flavor which allow for asymmetries between the countries are presented in Parry (2003), Brochner, Jensen, Svensson, and Sørensen (2007), and Vrijburg and de Mooij (2010) highlight the importance of asymmetries between countries. Strategic complementarity of tax rates cannot be taken for granted in this case, and it is then no longer certain that the alliance partners 1 and 2 benefit from their cooperation.

Burbidge et al. (1997) also address the question of which subgroup of countries may enter into a tax alliance if this choice is endogenous. If there are symmetric countries, for instance, the formation of a subgroup of 2 typically is a Pareto improvement relative to no group formation at all. But the gains to those in the subgroup are typically smaller than those of outsiders—so which countries, if any, would voluntarily join such a subgroup? Moreover, an enlargement of the participating group from to , or what could be called the “grand tax alliance,” is typically not a Pareto improvement. Understanding how and which subgroups might form becomes a challenging theoretical question. In the case of Europe and potentially other supra-national entities, the set of candidate countries that may enter into a regional coordination agreement is given exogenously or has been determined by other factors outside the context of the tax competition problem.

3.4 Coordination Across a Subset of Instruments

As stressed earlier, countries generally have more than one tax instrument to deploy. Partial coordination in such contexts can mean that all countries agree on restrictions as regards some but not all of their instruments. Keen and Marchand (1997), for instance, consider coordination of tax rates in a framework in which countries can continue to compete along another dimension, which is their decision about infrastructure investment, and which works like an input subsidy; and Fuest and Huber (1999) consider a framework with multiple tax or subsidy instruments.

The key lessons in such contexts are straightforward. When countries have several policy instruments, some may be redundant, in that coordinated action that fixes the value of one instrument at some level can be undone by changes in the other instruments. And if the instruments available are only imperfect substitutes, coordinated action that constrains the value of one may lead to a substitute instrument being used more aggressively as a tool of competition. In Keen and Marchand (1997), for instance, coordination on higher capital tax rates may lead countries to distort their public spending patterns towards infrastructure and other items that raise the productivity of, and so tend to attract, mobile capital, and away from items that contribute directly to private welfare. The final effect of such distortions may be a Pareto-worsening relative to the non-cooperative outcome. Cremer and Gavhari (2000), for instance, consider a KK-type setting in which welfare-maximizing governments choose both a statutory rate of tax and the intensity with which it is enforced by auditing firms to detect evasion: a lower audit probability then has effects very similar to a reduction in the statutory rate (a possibility not without echoes in actual practice). Setting a common tax rate may—but need not (this depends on values of parameters and the harmonized tax rate)—lead to such a reduction in enforcement activities that, ultimately, both countries are worse off.

3.5 Dynamic Aspects

Tax competition takes place, in practice, in a dynamic framework. This has several implications. Where there is an unknown, possibly unending series of choices, the theory of infinitely repeated games becomes relevant. A second aspect of these dynamics is that decisions are made sequentially. Some early decisions may generate stock effects that determine the environment in which later decisions take place. Today’s capital stock is the result of earlier decisions on savings and consumption, and this may generate time consistency problems for the optimal tax policy that interact with the effects of tax competition. A third aspect is the relationship between stocks and flows and the trade-off between taxing stocks and attracting an inflow of new capital. We consider these three aspects in turn.

4.1 Bidding for Firms

Where countries compete for foreign direct investment, this is often not a competition for additional capital that is then used at the intensive margin, but for individual firms or projects: that is, it is competition at the extensive margin and makes the taxed subjects strategic players.

A number of contributions consider the bidding for firms by governments that stand to benefit from attracting them to their country. Ferrett and Wooton (2010a) provide a simple and fairly general framework of two countries bidding for one firm. They consider two countries and who can make bids and to attract a firm from the rest of the world. Let and be the gross profits of the firm when locating in and , respectively, and the difference between them. Further, let and be some additional benefits that accrue to countries and , respectively, should the firm locate there. This captures the idea, commonplace among policy makers, that inward foreign direct investment conveys external benefits to the wider economy. Possible channels by which this may happen include a reduction in the per-capita cost of provision of public goods or inputs⁴⁵, increases in wage income⁴⁶, technological spillovers, and other external effects. Denoting by and the shares in the firm owned by citizens of country and , welfare in country is then

(46)

Assuming a suitable tie-breaking rule for the case in which a firm is just indifferent, one can characterize the equilibrium as follows: The country that loses makes a bid such that it is indifferent to losing or winning, which, from (46), is the case if

(47)

The winning country makes a bid that is just large enough to win against this bid, and thus bids . Note that this latter condition implies and hence, from (47), , whereas . This equilibrium has attractive features. First, it can be shown, by way of contradiction, that if country wins the bid in this equilibrium, so that the firm allocates where it generates the higher social surplus. Second, both the bids and the equilibrium allocation are independent of the ownership shares in the firm. The reason for this is that by making a bid that is just large enough to attract the firm, that is for which , the winning country ensures that the firm’s owners are just indifferent to locating the firm in or .

Allocative efficiency of the bidding equilibrium can be destroyed, however, by additional considerations. Kessing et al. (2009), for instance, apply a very similar auction framework with two countries making bids for a foreign direct investment. One is a unitary country with a government that has essentially the same objective function as above. The other is a federal union in which several layers of government share the tax revenue that can be collected if the investment occurs in this country. As discussed in Section 2.2, this may create a vertical fiscal externality that may lead to an excessively high tax burden and taxation on the downward sloping part of the Laffer curve. In addition, while the governments at the different layers share a common interest in the bidding process, they face a collective good problem when making their contributions to the country’s overall bid. Vertical fiscal externalities and free-riding problems within the federal union generate a disadvantage for the federal union in a bidding competition with a unitary country.

Another set of effects derive from the dynamic nature of investments, particularly in a multiperiod framework. The analysis of King, McAfee, and Welling (1993) addresses some of these. First, the location choice of a firm may involve sunk costs and may reduce the firm’s mobility, thus exposing it to a host government that may then be tempted to extract from this firm. (This is true not only if the firm becomes fully immobile, but even if some capital investment is made that is immobile or that may lose some of its value if it is relocated.) As a result, and unless there are other means to overcome this hold-up problem, governments may compensate firms for the later extraction of tax revenue by making upfront subsidies. Also, a government may invest in infrastructure in order to increase the profitability of a firm should it locate in this country. If countries cannot coordinate on such investment choices, the result may be a non-cooperative equilibrium with asymmetric investment choices in which one country invests a lot and the other country little.⁴⁷

Bidding for firms occurs in a setup in which foreign direct investment may have a number of externalities. In similar spirit, Haufler and Wooton (1999) analyze the competition between two countries for a foreign owned monopolist and show that a large home market is advantageous if there are trade costs. The role of trade cost and market size is also important in the context of other types of imperfect competition, making this paper the starting point of a large literature exploring these effects.⁴⁸

4.2 Preferential Regimes

In its report on Harmful Tax Competition, the OECD (1998) pays particular attention to practices by which countries may apply different tax rules to different types of business activity, typically setting a lower tax rate for more mobile activities. The presumption in the OECD work was that such “preferential regimes” aggravate the inefficiencies associated with international tax competition. But this may not be right.

To see why, broaden the benchmark two-country ZMW model to allow for two capital tax bases rather than just one. Denote the tax bases that locate in country as and , respectively, and let and be the unit source-based taxes applied to each. Generally, these quantities are functions and where, as before, denotes the corresponding tax rate in the other country. Tax revenue in country is thus

(48)

A first and straightforward observation is that if the (semi-) elasticities of the two bases differ then, given any fixed tax policy of the other country, it is always possible to strictly increase tax revenue by appropriate rate differentiation. To see this, focusing on situations in which first-order conditions describe optimized choices and there is an interior equilibrium, note that if country must tax both tax bases at the same uniform rate then, maximizing in (48), it will choose that rate so that

(49)

where the optimal uniform rate is thus the inverse of a weighted average of the semi-elasticities of the two bases. When the two bases can be taxed differentially, however, the first-order conditions become

(50)

and thus the rate on each base will be set to the inverse of its own semi-elasticity. Since the ability to differentiate can never reduce revenue, optimal differentiation strictly increases revenue whenever the semi-elasticities differ. All this, of course, is well known from the theory of third-degree price discrimination in monopolies.

In the context of competition between countries, however, the strategic response of the other country cannot be ignored. How does a world in which all countries may apply a preferential regime differ from one in which they are constrained to apply a uniform regime? Are preferential regimes, in that sense, necessarily a harmful form of tax competition?

When preferential treatment is permitted, (50) implies that equilibrium tax revenues are

(51)

If on the other hand both countries apply uniform taxation, maximization of tax revenue in country , as in (49), yields

(52)

Keen (2001) compares the implied equilibrium tax revenues in these two cases when countries are symmetric, assuming also that , and ; the base in each country is thus assumed to depend solely on the difference in tax rates between them, essentially removing from the picture any effect of the general tax level on the aggregate tax base. The difference in each country’s tax revenues between the Nash equilibrium in which all countries are constrained to applying uniform taxation and that in which they may deploy preferential regimes is

(53)

with and . Equality only holds if , that is, only if there is no difference in elasticities in the two tax bases. In the general case, in which elasticities differ, however, revenue is now unambiguously higher when preferential regimes may be deployed. In that sense, preferential regimes actually make tax competition less harmful. The intuitive attraction of imposing uniformity as a coordination measure is in making it more costly for countries to tax mobile capital by ensuring that this implies a revenue loss from less mobile capital. But differentiation, while increasing the scope for competition for mobile capital, protects the revenue from the less mobile base. In the setting of Keen (2001), this latter effect always dominates.

This result, running exactly counter to the commonplace presumption against preferential regimes of various kinds has triggered much further consideration—see, for instance, Bucovetsky and Haufler (2007), Haupt and Peters (2005), Janeba and Peters (1999), and Janeba and Smart (2003)—exploring the robustness of this result. The variant of the benchmark model which yields the largest divergence maintains the assumption of symmetry between countries and two tax bases, but assumes that one of them is completely immobile and inelastic up to a maximum tax rate of in each of the countries. Above this rate, the owners of the tax base make use of a disposal option and the tax base vanishes. The other type of capital has a perfectly elastic tax base of that floats freely between the two countries and locates in whichever has the lower tax rate, and locates symmetrically between them if they tax it at the same rate. In this case, the equilibrium with preferential taxation is characterized by and : both countries make full use of their monopoly power as regards their immobile tax base, but face cutthroat competition as regards the fully mobile tax base. In case of uniform taxation, an equilibrium in pure strategies typically does not exist. However, an equilibrium in mixed strategies does. For symmetric countries, applying the logic of Narasimhan (1988), this mixed strategy equilibrium is characterized by uniform tax rates and that are random draws from a distribution that is defined by a cumulative distribution function and supports . The expected tax revenue in this equilibrium is equal to for each of the two countries. Accordingly, preferential treatment generates exactly the same tax revenue as uniform taxation in the equilibrium.⁴⁹

4.3 Information Exchange and Implementation of the Residence Principle

As noted in Section 2.1, it is the residence principle—not the source principle, which most of the formal literature reviewed here presumes—that is the international norm for personal-level taxation of capital income,⁵⁰ and which continues to be important at corporate level too. Its implementation, however, can be problematic, for two reasons. One is that residence country taxes are generally not imposed until income is repatriated there, so that the real liability can be reduced by retaining funds abroad. A number of countries seek to address this at corporate level through “controlled foreign corporation” (CFC) legislation, which enables them to tax income remaining abroad—albeit generally only income that is “passive” in the sense of not arising from immediate business activities. Deferral, nonetheless, remains a key instrument of international tax planning (though not the only one, of course). The second difficulty, which arises primarily at the individual level, is simply the risk that taxpayers will not reveal to their home authorities income arising abroad. The most obvious remedy for this is for the tax authorities to provide their counterparts abroad with information on the income arising in their country to residents of others. Fostering such information sharing has been the focus of considerable (indeed unprecedented) action in recent years,⁵¹ as is described in the next subsection, and has attracted some theoretical interest.

Much of the literature on information exchange has focused on the question of whether or not countries might choose to provide such information voluntarily.⁵² At first sight, it might seem that those which are net recipients of income undeclared to the investors’ home authorities would not, since by providing information they would enable the residence country to levy additional taxation and so make themselves less attractive a location for such funds. Strategic considerations, however, again come into play, a point first stressed by Bacchetta and Espinosa (1995). For if it can commit to providing such information—and double tax treaties and tax information exchange agreements may provide a vehicle for doing so—a low tax country enables the residence country to charge a higher tax rate than would otherwise be the case, which in itself tends to increase the inflow of capital that it receives—an effect that counteracts and may outweigh the directly harmful impact.⁵³

To see this, consider again a world of just two countries, with . In the high tax country 2, there is a fixed amount of savings that can be invested in either country, in amounts and ; the former incurring expected (non tax-deductible) costs of , with increasing and strictly convex. There are no savings in the low tax country (to avoid the complication of cross-hauling of savings). The authorities in low tax country 1 collect taxes at the rate on all savings located there, and will provide information to the authorities in country 2 only on some proportion of their residents’ savings there. These are then liable to additional taxation in country 2 at (credit being given for taxes paid abroad). Assuming the gross rate of return to be the same in both countries (and normalizing it to unity), country 2’s investors will allocate their savings in order to minimize the sum of taxes paid and transaction costs incurred, which is given by

(54)

with the first term being the tax paid on savings retained at home, the second that paid on income abroad that is successfully concealed, and the third being total tax paid on income abroad that is reported and so ultimately subject to the full home rate. Maximizing this to trade off the tax advantage of saving abroad against the transactions cost of doing so, savings allocated abroad, , are an increasing function of the tax saved by doing so, per unit of saving, given by . Thus

(55)

so that, as one would expect, the amount saved abroad increases with the tax rate at home. Similarly, it decreases with both the foreign tax rate and (at constant tax rates) the extent of information sharing. For simplicity, assume that revenue rather than welfare is the object of policy-making. In country 1, this is simply

(56)

while in country 2 it is

(57)

With the degree of information sharing assumed to be determined at the first stage of the game (being more in the nature of a long-term commitment, perhaps embodied in a treaty), each country chooses its tax rate taking as given both and the tax rate of the other country. The tax rate chosen in the high tax country, in particular, is thus . Suppose then that the low tax country commits to a small increase in the extent of information sharing . From (57), the revenue impact in the high tax country, given that the effect of any induced change in its own tax rate vanishes as an envelope property, is

(58)

and so is unambiguously positive: there is a gain from both the increased taxation of any income invested abroad and the reduction in the extent of such investments. For the low tax country 1, matters are more complex. With revenue being , the effect is given by

(59)

Here the first term is the direct, adverse effect on the low tax country: it becomes less attractive as a venue for tax evasion. The second is the strategic effect: to the extent that the fuller information induces the high tax country to increase its tax rate—as is plausible, but not assured without further restriction of functional forms—this leads to more evasion into the low tax country. The overall impact of the low tax country is thus, in principle, unclear.It is possible, however, that the strategic effect dominates. Indeed, in the simple structure above, this is, under plausible conditions, sure to be the case. To see why, suppose that the high tax country 2 reacts to increased information sharing by raising its own tax rate just enough to leave the tax saved by investing abroad, , unchanged in the face of the higher . This means that the amount of savings allocated abroad is also unchanged, and hence revenue in the low tax country remains as it initially was. Recalling (55), however, the higher means that savings invested abroad are now less responsive than they were to the tax set by the high tax country 2, which tips the balance of country 2’s considerations towards increasing its tax rate further—pushing savings further in country 1’s direction, and implying that it too is ultimately better off.⁵⁴

This, of course, is a strong and quite special result. Fuller treatments allow also for the adjustment of country 1’s tax rate and endogenize the choice of tax rates (relating them in particular to country size, with the standard conclusion that rates tend to be lower in smaller countries). They allow too for cross-hauling of savings, and explore the implications of differential tax treatment of residents and non-residents. Importantly, the strategic effect clearly becomes much less powerful when there is more than one low tax country: greater information sharing by one will then be met in part by a shifting of savings to other low tax countries, so that the impact on the tax-setting decisions of the high tax country will be greatly muted. The most robust result is probably the most obvious: there can be a sharp divergence of interests, with high tax countries being much more certain to gain from mutual information exchange than are low tax countries.⁵⁵

4.4 Tax Havens

Though widely used, the precise meaning of the term “tax haven” is elusive, and even in the practical world of policy there is no agreed definition. A low or zero tax rate on some activities or forms of income is clearly a necessary ingredient, but is not enough to capture common usage: Very resource-rich countries, for example, may simply not need tax rates at the same levels found elsewhere, and have little interest in how that affects capital or other cross-border flows. Beyond low taxation, the term carries the connotations that it is paper rather than real economic activity that is being attracted, and moreover that these are jurisdictions which encourage, or at least do not adequately discourage, tax avoidance or evasion that undermines tax revenues of other countries, perhaps by providing secrecy laws or other restrictions that preclude their sharing of information.⁵⁶ Quite what the standard of adequacy should be is, of course, by no means clear. Where the line lies that defines a tax haven remains hazy, but three features seem to capture the essence: low taxation that is not a reflection of high revenue, relative to needs, from other sources; the attraction of profit-shifting and other tax arbitrage activities more than real activity; and imperfect sharing of information.

4.5 Formula Apportionment

The incentive for companies to use transfer pricing and other devices to shift profits between jurisdictions—and for governments to design their tax systems to affect that incentive—would be removed if, instead of seeking to identify profits earned in particular jurisdictions, taxes were simply levied on the aggregate of a multinational’s profits over all jurisdictions.⁶⁰ “Formula apportionment” is an alternative to either residence or source principles that goes some way in this direction, by using indicators of the extent of a company’s activities in particular countries (“apportionment factors”) to attribute to each a share of those aggregate profits, which it may then tax at whatever rate it chooses. This is the norm for state-level corporate taxation in the US and Canada, for instance (generally using as apportionment factors some combination of the shares of sales, payroll, and assets located in each state), and has been proposed by the European Commission, as a “common consolidated corporate tax base” (CCCTB) for the EU.⁶¹

Consider the simple case in which there is a single apportionment factor, so that with some indicating the extent of a multinational’s activity in country and countries, the total tax payable on a multinational’s groupwide profit of is

(60)

The attraction of this approach is that, for given decisions there is no gain in simply reallocating paper profits across jurisdictions, even though they may charge different tax rates. There is, however, a potential distortion to those decisions. Assuming to be strictly concave in the , these would be chosen in the absence of taxation (or with tax levied directly on aggregate profit) so that , for all . Under formula apportionment, however, cross-country differences in tax rates distort these choices, it being straightforward to show that maximization of net profits implies if the tax rate in country is below the -weighted average and the converse where it is above: broadly speaking, whatever the factor in the apportionment, it will tend to be reallocated from high to low tax countries.⁶²

Of particular interest here is that revenue-seeking governments will generally have an incentive to set tax rates with the intention of manipulating the multinational’s choice of the .⁶³ Suppose, for instance, that capital is used as the sole apportionment factor , and consider a multinational with some fixed amount of capital to allocate between just two identical countries. Then the multinational will maximize after-tax profits

(61)

where we assume that “true” profits can meaningfully be ascribed to countries (that earned in each depending only on the capital located there), and where the average tax rate

(62)

is endogenous to the investment decision. The solution to the firm’s optimization problem leads to an allocation of capital with the property that, where ,

(63)

Supposing revenue to be the governments’ sole concern, that in country 1 (say) then chooses to maximize ; the necessary condition for which, using (63), implies that in symmetric equilibrium where ,

(64)

where “FA” stands for formula apportionment. This outcome is clearly inefficient, since any higher common tax rate would yield both countries greater revenue.

More striking, however, is the comparison with the non-cooperative outcome under source taxation. In this case, the total tax paid by the multinational is , and, by steps analogous to those leading to (64), the symmetric equilibrium tax rate has a tax rate in each country of

(65)

where “ST” refers to source taxation. Comparing this with (64) gives

(66)

the inequality being from the strict concavity of . Tax competition thus leads to an unambiguously lower equilibrium tax rate under formula apportionment than under source taxation, and so, in that sense, to unambiguously more intense tax competition. To see the intuition for this, suppose that initially both countries charge the same tax rate. Under source taxation, attracting an additional unit of capital raises revenue of , reflecting the marginal product of that capital; under formula apportionment, however, it raises additional revenue of , reflecting—because the country is taking a share in aggregate profits, wherever earned—the average profit rate . So long as the average rate of return exceeds the marginal rate, the incentive to attract capital is thus greater under formula apportionment.

This comparison of regimes is somewhat unnatural in that there is assumed to be no scope for manipulating liability under the source regime other than by relocating real activities: the profit-shifting to which formula apportionment is seen as a possible response is thus absent. What the result does suggest, nonetheless, is that formula apportionment can be preferred only if the distortions to firms’ and governments’ behavior that profit-shifting leads to are sufficiently large to outweigh what would otherwise be an adverse strategic effect. Introducing the possibility of transfer pricing, at some cost to the multinational, into a framework similar to that above, Nielsen, Raimondos-Mller, and Schjelderup (2010) provide a fuller treatment of the issue, elaborating on the circumstances, which turn on the level of profitability and the ease of transfer pricing, under which profit-shifting concerns dominate and formula apportionment consequently leads to a Pareto-superior non-cooperative outcome.

4.6 Political Economy and Agency Issues

There has long been debate as to whether international tax competition is good or bad from a welfare perspective. In the workhorse model, tax competition is (almost) certainly bad, in the sense that (leaving aside the time consistency issue discussed in Section 3.5.2) a central planner could implement any tax rates that can emerge in a decentralized equilibrium but could also choose the potentially many other tax rate combinations that cannot. Hence, coordinated tax rate choices—complemented as need be with international transfers of tax revenue—are at least as good, in a Pareto sense, as decentralized choices, and, since there are several externalities at work, will generally be Pareto-superior.⁶⁴

But comparing a decentralized tax competition equilibrium outcome with the centrally coordinated solution brought about by a fully benevolent government is not a very satisfying exercise. If there were no more to say, then for the same reason all private market economies should be transformed into centrally planned ones. The aim in this section is to review the implications for tax competition and coordination of richer views of policy-making.

Both centralized and decentralized political decision making suffer from problems other than the possible externalities between decentralized decision makers. One can doubt, in particular, if policy decisions are well described as those of a benevolent dictator who maximizes the utility of a representative citizen. Political decision making reflects distributional conflicts, with the electoral process, perhaps giving the median voter a key role, and special interest groups may lobby for their preferred tax policy.⁶⁵ And, perhaps most importantly, power is delegated to governments which generates a number of accountability problems between the government and its constituency. We focus on these problems.