Should tax policy favor high- or low-productivity

Transcription

1 Should tax policy favor high- or low-productivity firms? Christian J. Bauer Andreas Haufler Dominika Langenmayr July 2012 Preliminary and incomplete Abstract Heterogeneous firm productivity seems to provide an argument for governments to pursue pick-the-winner strategies by subsidizing highly productive firms more, or taxing them less, than their less productive counterparts. We study the optimal choice of differentiated investment taxes in a small open economy with heterogeneous firms in an oligopolistic industry. We show that the optimal structure of tax differentiation depends critically on the feasible level of corporate profit taxation, which in turn depends on the degree of international tax competition. When international tax competition is moderate, allowing relatively high rates of profits taxation, then favoring high-productivity firms is indeed the optimal policy. With aggressive tax competition and low corporate profit tax rates, however, the discriminatory investment policy is reversed and low-productivity firms are tax-favored. Keywords: business taxation, firm heterogeneity, tax competition JEL Classification: H25, H87, F15 We thank Pol Antràs, Mihir Desai, Monika Schnitzer and seminar participants at the Universities of Munich and Würzburg, and the 2011 Munich-Tübingen international economics workshop for valuable comments and discussion. Affiliations: Bauer: University of Munich and CESifo, christian.bauer@lrz.uni-muenchen.de. Haufler: University of Munich and CESifo, andreas.haufler@lrz.uni-muenchen.de. Langenmayr: University of Munich and Bavarian Graduate Program in Economics, dominika.langenmayr@lrz.uni-muenchen.de. Financial support from the German Research Foundation (Bauer and Haufler) and the Bavarian Graduate Program in Economics (Langenmayr) is gratefully acknowledged.

2 1 Introduction It is a well known fact that corporate tax rates have fallen substantially over the last decades. While statutory corporate tax rates among the OECD members have averaged around 50% in the early 1980s, with several countries imposing profit taxes of 60% and above, the average has fallen to 30-35% by 2010 and no OECD member country currently maintains a corporate tax rate above 40% (see OECD, 2011). There is also a widespread consensus, as well as econometric evidence, that international tax competition for mobile capital and firms has been one of the key factors in bringing down corporate tax rates, particularly in Europe. 1 Similar trends of falling corporate tax rates can also be observed in other, less-developed parts of the world (Klemm and van Parys, 2012). In this paper we relate the fall in corporate profit tax rates to another development in corporate tax policy that has received much recent attention: the differential taxation of multinational enterprises (MNEs) vis-a-vis domestic firms. Empirical evidence suggests that multinational firms pay substantially less taxes, per dollar of gross profits earned, than their nationally operating counterparts (Bartelsmann and Beetsma, 2003; Egger et al., 2010a). During the last ten to fifteen years these discriminatory tax advantages for MNEs have come under heavy attack, however. At a coordinated level, both the OECD (1998, 2000) and the European Union (European Communities, 1998, 1999) have identified practices of harmful, discriminatory tax competition and have proposed and enacted measures to eliminate them. 2 At the same time, individual countries also undertook uncoordinated measures to limit the tax advantages of multinational firms. A first example is the increasing number of countries applying thin capitalization rules, in order to restrict the ability of MNEs to engage in international debt shifting. 3 The share of OECD countries adopting such a 1 See Devereux et al. (2008) for empirical evidence on tax competition in Europe. Devereux et al. (2002) provide a detailed analysis of the trends in corporate tax policy from 1980 to For a more recent summary, see Auerbach et al. (2010). 2 Typical cases of discriminatory tax policies in favor of foreign-based MNEs were the special tax rules applied to foreign-based co-ordination centers in Belgium, and the split corporate tax rate in Ireland. Both of these practices were targeted specifically by the European Union s Code of Conduct for business taxation (see European Communities, 1998, 1999) and have meanwhile been discontinued. 3 Tax savings from debt shifting follow from the fact that interest payments for intra-company loans are deductible from the corporate profit tax base. A MNE can thus reduce its worldwide tax 1

3 measure to limit profit shifting by MNEs has gone up from less than one half in 1996 to roughly two thirds in 2005 (Buettner et al., 2012, Fig. 1). The authors show empirically that thin capitalization rules are not only effective in limiting intra-company financial transactions, but also in increasing the effective rate of capital taxation in MNEs. A prominent example of a tax reform that was explicitly aimed at limiting the tax advantages of MNEs is the German tax reform of Among other measures, this reform reduced the German corporate tax rate and it introduced a rigorous ceiling on the tax-deductibility of interest payments which was tailored so as to apply exclusively to highly profitable multinational firms. 4 A second example for reduced tax incentives for MNEs comes from less developed countries, where tax holidays represent one of the main policy measures to attract foreign direct investment. 5 Klemm and van Parays (2012, Fig. 1) document for a sample of 47 countries in Africa, Latin America and the Caribbean that the average length of tax holidays has fallen from more than 4 years in the late 1980s to around 2.5 years in As in the OECD countries, this reduction in the present value of investment incentives to MNEs was accompanied by falling corporate tax rates. In the present paper we provide an explanation for these tendencies to cut the tax advantages of multinational firms by relating them to the reduced potential of countries to tax corporate profits as a result of international tax competition. We pose the question in a more general way by setting up a small open economy model with two firms of different productivity, where we associate the high-productivity type with a multinational firm. This follows a robust empirical finding in the recent empirical literature that more productive firms self-select either into the export market (Clerides et al., 1998; Bernard and Jensen, 1999) or into foreign direct investment (Helpman et al., 2004). 6 We then set up a very simple model of how economic integration leads to intensified tax competition that reduces the equilibrium level of the corporate profit tax in the small country. payments by allocating equity capital primarily to the affiliate in a low-tax country, which then makes an interest-paying loan to the affiliate in the high-tax country. See Mintz (2004) for details. 4 Buslei and Simmler (2012) provide empirical evidence showing that the German MNEs affected by the 2008 corporate tax reform have reacted strongly, mostly by decreasing their debt ratio. 5 Tax holidays specify a time period during which reduced or no taxes have to be paid by a (typically large and foreign-owned) firm to the host country. For a detailed description of the working of corporate tax holidays, see Mintz (1990). 6 Markusen (2002, Ch. 1) summarizes some salient characteristics of multinational firms that support their high productivity, such as a high R&D intensity and a qualified workforce. 2

4 We analyze the implication of this change on the optimally differentiated investment tax rates applied to the high-productivity and the low-productivity firm, respectively. The optimal policy results from the trade-off that the country faces between raising the aggregate productivity by shifting production to the low-cost firm, and the incentive to increase competition in the market by reducing the cost disadvantage of the low-productivity firm. Our main result is that the optimal solution to this trade-off depends critically on the feasible rate of profit taxation. Granting tax advantages to the more productive, multinational firm turns out to be the optimal policy when tax competition is moderate and the possibility to tax the resulting profits is accordingly high. As economic integration proceeds and tax competition becomes more severe, however, the incentive to favor the highly productive firm is weakened. Eventually, for very low feasible rates of profit taxation, the pattern of discrimination is even completely reversed and the optimal policy is to favor the low-productivity firm, as a means to reduce the market power of its highly productive competitor. Hence our analysis predicts a fall in the tax advantages to MNEs as a result of tighter corporate tax competition, in line with the above-mentioned developments. Our analysis is related to three different strands in the literature. A first strand is the recent literature on tax competition in settings with heterogeneous firms (e.g. Davies and Eckel, 2010; Krautheim and Schmidt-Eisenlohr, 2011; Haufler and Stähler, 2012). This literature, however, does not allow for investment taxes or subsidies that are differentiated by the productivity level of the firm. Secondly, our paper is related to the literature on discriminatory tax competition. Janeba and Peters (1999) and Keen (2001) analyze whether discriminatory or non-discriminatory tax competition is preferable from a perspective of global optimality. Peralta et al. (2006) ask under which conditions countries may have an incentive to tax-discriminate in favor of MNEs by not monitoring international profit shifting. Hong and Smart (2010) analyze whether a high-tax country may even benefit from the competition with a tax haven, when the haven permits it to tax-discriminate in favor of the internationally mobile firm. None of these papers, however, incorporates productivity differences between firms. Thirdly, there is a renewed interest in the interaction of industrial policy and competition. Aghion et al. (2011), for example show that subsidies to sectors with intense competition foster productivity and innovation. But in their model the differentiation of policies depends on the market structure in different sectors, not on the productivity 3

5 of firms. Finally, Gersovitz (2006) is in some way closest to our paper by deriving the optimal pattern of income and consumption taxes when both have differential effects on firms with varying productivity. This paper does not tie its results to the effects of tax competition, however, and many of its findings have to rely on simulation results. The plan of the paper is as follows. Section 2 lays out our benchmark model with two firms of different productivity which are taxed by a general corporate profit tax and by differentiated investment taxes. Section 3 derives the market equilibrium for different market structures. Section 4 derives the optimally differentiated investment taxes, as a function of the level of corporate profit taxation that results from international tax competition. Section 5 analyzes the robustness of our results when the assumptions about firm ownership or market structure are changed. Section 6 concludes. 2 The benchmark model We study a small open economy that produces and consumes two homogenous goods, Y (the numeraire) and X. Firms in the X sector differ with respect to their unit production costs and interact strategically within the industry. Firms in the Y sector are homogenous and operate under perfect competition. Consumers in the small economy hold a total endowment of K units of capital, which is the only factor in the production of both goods. Capital and the numeraire good Y can be freely traded internationally and 1/r units of capital are needed to produce one unit of good Y. This fixes the world interest rate at r. 7 We concentrate on the market for good X, which is assumed not to be traded internationally. The most direct interpretation is that X is a non-tradeable service industry, for example banking and insurance, or a network utility. The focus of our analysis lies on the corporate tax structure that the small country s government applies in this market. 2.1 Consumers Consumers are homogeneous, with preferences given by a quasilinear utility function which is defined over the two private goods X and Y : U = ax 1 2 bx2 + Y D. (1) 7 Free trade in Y and K implies that the model does not pin down the location of production of the numeraire good. This, however, is immaterial for all our results. 4

6 In eq. (1), Y D is the quantity demanded of the numeraire, and a > r and b > 0 are parameters. Utility maximization is subject to the budget constraint Y D + px I, where p is the price of good X. To determine national income I, we need to specify the international allocation of profits. In our benchmark model we assume that consumers in the small country invest in perfectly diversified global portfolios. Hence the international integration of capital markets decouples dividend payments in the X industry from the capital income received by the small country s residents. Under this assumption it does not matter whether the firms operating in the X industry have their residence in the small country or abroad. 8 The income of domestic consumers is then given by I = rk + T, (2) where rk is the exogenous capital income of the small country s representative consumer and T is tax revenue, which is redistributed to the consumer as a lump-sum payment. Utility maximization yields linear demand functions, X = a p, Y D = I px, (3) b which imply that all income changes affect only the demand for the numeraire good Y. 2.2 Producers In the oligopolistic X sector, there is an exogenously given number of n potential entrants ( firms ). In our benchmark model we set n = 2, implying that only monopolistic and duopolistic market structures can occur. 9 Each potential entrant is exogenously assigned a capital requirement c i, i {L, H}, per unit of good X, where the indices L and H denote the low-cost and the high-cost firm, respectively. The output of firm i is denoted by x i so that industry output is given by X = x L + x H. For concreteness, let us suppose that the low-cost firm is a multinational enterprise (MNE), whereas the high-cost firm is a national corporation that operates only in the 8 Empirically, globally diversified portfolios are a plausible scenario when most of the small country s capital is invested through financial intermediaries, such as pension funds or insurance companies. From an analytical perspective the assumption of globally diversified portfolios eliminates the need to distinguish between different settings of firm ownership. In Section 5.1 we will, however, relax this assumption and introduce a home bias in the domestic portfolios. 9 In Section 5.3 we generalize the analysis to the case of more than two firms (still to be done). 5

7 small country. This is meant to capture the stylized facts from the empirical literature on heterogeneous firms that firms engaging in FDI are more productive, on average, than nationally operating firms (Helpman et al., 2004). Heterogenous firms may coexist in this industry, as the number of potentially active firms is fixed exogenously and even the high-cost firm can make positive profits in equilibrium. To simplify notation, we normalize c L 1 and define the capital requirement of the high-cost firm as c H 1 + (with > 0). Our analysis focuses on the case where the productivity gap is sufficiently small, relative to the firm s profit opportunities, so that it is not optimal for the low-cost firm to strategically choose output levels that prevent entry by the high-cost firm. 10 Hence, in the absence of government intervention, both firms will be active and we assume that they engage in Cournot competition. 11 As a result of government policy, one of the potential entrants may, however, anticipate negative profits and thus choose not to enter the market. In this case the remaining firm will act as a monopolist. To determine after-tax profits, we need to introduce the corporate tax system. Taxable profits in the small country are subject to the statutory corporate tax rate t, which applies uniformly to both firms. In addition, the government determines the taxable profit base by setting rules for the deduction of investment costs. These rules will generally affect the two firms differently. The low-cost, multinational firm will, for example, be able to engage in financial arbitrage transactions with other entities within the same group that allow it to deduct a larger share of its capital cost from the value of sales than is true for the national firm. As a result the effective tax rate, which results from the interaction of tax base and tax rate parameters, will in this case be lower for the multinational firm. 12 The reverse type of discriminatory treatment is also possible, however. For example, state guarantees for nationally operating banks reduce the interest cost of these banks and thus represent an implicit subsidization of their costs of capital. To model these differences in the tax bases of the two firms, and hence to capture the differences in the effective tax burden borne by them, we include firm- 10 It is shown in the appendix that this implies < (2/65) ( ) (a r) 0.07(a r). 11 The case of Bertrand competition is briefly analyzed in Section See Egger et al. (2010b) for empirical evidence on tax-minimizing financing structures within MNEs. Even in the absence of explicit profit-shifting strategies by multinational firms, the effective tax rate on MNE s profits will be lower when more productive firms self-select into an integrated production structure, whereas the transfer price for tax purposes is determined by less productive firms that outsource the production of intermediate inputs (Bauer and Langenmayr, 2011). 6

8 specific taxes on the capital input costs of firms, τ i. In the following, we will also refer to these input taxes as investment taxes. Recalling that the world price of capital is denoted by r and denoting by π i the profits of firm i after the incorporation of taxes or subsidies on capital inputs, but before the deduction of the corporate profit tax, we get after-tax profits of the two firms by (1 t) π L = (1 t) x L [p (1 + τ L ) r], (4) (1 t) π H = (1 t) x H [p (1 + τ H ) (1 + ) r]. (5) 2.3 Government The government of the small country has three tax parameters at its disposal: the firm-specific capital input taxes or subsidies τ H and τ L and a general corporate profit tax rate t, which is levied on the tax bases π i defined in eqs. (4) and (5). 13 Our main interest is in the relationship between τ L and τ H. The formulation in eqs. (4) and (5) allows a simple representation of the government s ability to affect production decisions both on the intensive margin (how much each firm produces) and on the extensive margin (whether or not a firm enters the market). In principle, it is possible for each firm that capital inputs are taxed (τ i > 0), or that they are subsidized (τ i < 0). Irrespective of the sign of optimal investment taxes, the tax system favors the low-cost firm if τ L < τ H, whereas it favors the high-cost firm if τ L > τ H. In choosing its corporate tax rate t, the government is constrained by international tax competition. We model tax competition by assuming that firms are able to shift profits into a low-tax country in the rest of the world. Shifting profits is costly to the firms, with the costs being proportional to the share of profits being shifted abroad. Given the government s tax choices, aggregate tax revenues are given by T = t(π L + π H ) + τ L x L r + τ H x H (1 + )r. (6) We impose no constraint on the sign of T. As is seen from equation (2), positive tax collections are redistributed to the representative consumer lump sum. Conversely, if total tax revenue from the corporation tax system turns negative, then lump-sum taxes are available to finance effective subsidy payments to the two firms. 13 This specification implies that positive taxes on capital inputs are deductible from the base of the corporate profit tax, whereas capital subsidies are treated as taxable profit income. 7

9 3 Market equilibria Our following analysis is based on a three-stage game. In the first stage, the government sets its tax policy, taking into account the impact of taxation on intensive and extensive margins of production, consumer prices, as well as on profit-shifting. Since differentiated taxation may prevent one firm from producing, we derive separate solutions under a monopolistic and a duopolistic market structure. We then compare the implied levels of indirect utility to determine which industry structure is optimal for the government. In the second stage, the potential entrants anticipate expected profits and choose whether to enter the market, taking the tax system as given. In the third stage, firms produce output and consumption occurs. We solve the model by backward induction and begin by deriving the market outcomes in both the duopoly and the monopoly case (stage 3). Cournot duopoly: When two firms compete in Cournot oligopoly, profit maximization gives standard best response functions equal to x L = (1/2b) [a bx H (1 + τ L )r] and x H = (1/2b) [a bx L (1 + τ H )(1 + )r]. This yields optimal quantities x L = 1 3b [a + (1 + τ H)(1 + )r 2(1 + τ L )r], x H = 1 3b [a 2(1 + τ H)(1 + )r + (1 + τ L )r]. (7) Combining the market demand for good X in eq. (3) with (7) gives the equilibrium price as an increasing function of unit costs and investment taxes: p = 1 3 [a + (1 + τ H)(1 + )r + (1 + τ L )r]. (8) Maximized profits, before deduction of the corporate profit tax t, are then given by π L = bx 2 L, π H = bx 2 H. (9) Evaluating the utility function (1) with the optimal demands for X and Y using (2), (6), (8), and (9), indirect utility in the duopoly case (superscript d) equals V d = 1 2 b (x L + x H ) 2 + rk + tb(x 2 L + x 2 H) + τ L x L r + τ H x H (1 + ) r, (10) with equilibrium quantities given by (7). 8

10 Monopoly: Given that the ownership structure of both firms is globally diversified in our benchmark model, if it is optimal to have a monopoly at all, it is always optimal to have the low-cost firm be the monopolist. When the low-cost firm has a monopoly in the X sector, profit maximization given demand yields the equilibrium quantity and market price (denoted by a superscript m): x m L = 1 2b [a (1 + τ L m )r], p m = 1 2 [a + (1 + τ L m )r]. (11) These choices give monopoly profits before deduction of profit taxes equal to πl m = 1 4b [a (1 + τ L m )r] 2 = b(x m L ) 2. (12) By analogy to the oligopoly case, we then obtain indirect utility V m = 1 2 b(xm L ) 2 + rk + tb(x m L ) 2 + τl m x m L r, (13) with the equilibrium quantity given in (11). 4 Optimal policy We now derive the optimal policy chosen by the government, which correctly anticipates the optimal behavior of firms and consumers (stages 1 and 2). The central question is whether, in the presence of firm heterogeneity, the government has an incentive to tax-discriminate in favor of the high-productivity or in favor of the low-productivity firm. As we will see, this decision is critically affected by the statutory corporate profit tax rate that the government is able to levy in the national optimum. The statutory tax rate, in turn, is limited by international tax competition. The government s problem thus decomposes into two parts. The first is to choose the optimal profit tax rate t, taking into account that business income may be shifted abroad. The second is to impose possibly differentiated taxes or subsidies τ i on the capital inputs used by each firm. We begin with the determination of the profit tax rate and then derive optimal investment taxes separately for the duopoly and monopoly case. Finally, we compare indirect utility in the two regimes to determine the optimal policy. 9

11 4.1 Tax competition and the optimal profit tax rate The government s ability to collect taxes is limited by international tax competition. Specifically, we assume that the small country faces competition from a tax haven to which MNEs can shift profit income, if this increases their after-tax profits. Shifting profits imposes costs on firms, however. These costs may consist of transaction costs, fees for legal counseling, and the expected costs of being caught and fined. We assume that the cost of profit shifting are proportional to the share of profits that is shifted abroad. This implies that the firm will either shift all of its profits into the haven, or none at all. 14 The analytical advantage of this specification over the alternative of introducing a fixed cost of profit shifting is that it allows us to derive the tax rate in the small country solely as a function of exogenous shifting costs. With this specification, the home country will set its profit tax rate so as to ensure that shifting all of its profits is not worthwhile for the two firms. 15 Denoting by α the share of profits that firm i shifts to the tax haven, the corporate tax rate t must ensure α ( 1 t H) π i + (1 α)(1 t)π i αsπ i (1 t)π i i, (14) where t H (a mnemonic for haven ) is the profit tax rate in the tax haven, and s [0, 1] is a parameter that measures the costs of profit shifting. From eq. (14), tax revenues can be secured when the small country s profit tax is t t H + s. Given this profit tax rate in the small economy, however, the tax haven will no longer attract any profits, and thus it will lower its tax rate. Since the two countries tax rates are strategic complements, the tax haven s profit tax is competed down to zero 14 Excluding partial profit shifting at the level of each firm is a conventional assumption in the recent profit shifting literature, which incorporates firm heterogeneity. See e.g. Krautheim and Schmidt- Eisenlohr (2011), or Elsayyad and Konrad (2012). 15 If we stick to our above interpretation that only the low-cost firm is a MNE, then the option of profit shifting is not open to the national, high-cost firm. In this case the small country might find it attractive to switch to a high-tax regime where it forgoes all revenues from taxing the profits of the (multinational) low-cost firm, but instead taxes the profits of the high-cost firm at a high rate. See Janeba and Peters (1999) for a detailed analysis of a related setting. Since the focus in this paper is not on tax competition for profit shifting, however, we do not pursue this possibility here. One argument is that the national firm might also invest in a multinational structure, if the tax advantage of doing so becomes sufficiently large (see Bucovetsky and Haufler, 2008). 10

12 in equilibrium. The costs of shifting profits then allow the small economy to set a tax rate of t = s, (15) without losing any tax revenue from profit shifting in equilibrium. This version of a standard model of tax competition is clearly a highly simplified one. However, our purpose in this section is only to link the corporate tax rate in the small country to exogenous changes in the economic environment, and eq. (15) does this in the simplest possible way. At the core of our analysis is the interaction between the development of the corporate tax rate t and the optimal pattern of differentiated capital input taxes τ i. This is the issue to which we turn now. 4.2 Optimally differentiated capital input taxes Apart from the profit tax rate t, the government also determines the corporate tax base by choosing the investment taxes (or subsidies) τ i. Together these tax parameters determine the effective tax burden, which may differ for firms with different productivity levels. This choice is subject to the entrants participation constraints. We begin with the case where the tax burden does not deter entry by the high-cost firm, that is with the optimal taxation of capital inputs in the Cournot duopoly regime. Cournot Duopoly. Choosing τ i to maximize indirect utility (10) and substituting out for t using (15) yields the optimal tax rates on capital inputs, which are derived in the appendix: τ H = τ L = (1/2 s) {(a r)(1 s) + /2}, (16) (1 s)(2 s) (1/2 s) {[a (1 + )r](1 s) /2}. (17) (1 s)(2 s)(1 + ) Comparing equations (16) and (17) allows us to answer the question of whether governments should favor the high-cost or the low-cost firm in the Cournot duopoly regime. We find that τ L < τ H iff s > 1/2. This implies that the low-cost firm is tax-favored for high levels of s (s > 1/2), whereas for low levels of s (s < 1/2), it is optimal to provide relative tax support to the high-cost firm. Moreover, we can infer from (16) and (17) that the government subsidizes investment of both firms when s > 1/2, whereas it imposes a positive marginal tax on investment when s < 1/2. Intuitively, when profit shifting is costly (s is high), it is possible for the small country to capture most of the profits in the X-sector by means of the general profit tax. This 11

13 reduces the costs of investment subsidies, which are aimed at increasing the aggregate output in the imperfectly competitive industry. In doing so, the government relies more heavily on the low-cost firm, as its production is more efficient. If, in contrast, firms find it easy to shift profits abroad (s is low), then subsidizing investment at the margin is no longer optimal, as the resulting increase in profit income can no longer be recuperated by means of a sufficiently high profit tax. Moreover, by our assumption of perfectly diversified investor portfolios, all untaxed profits, and hence dividend payments, accrue to shareholders in the large rest of the world. Consequently, the government will now find it optimal to tax capital inputs at the margin, as a means to reduce profit income accruing to foreign shareholders. In order to minimize the negative impact of investment taxes on industry output, the government will choose a tax structure that maintains the highest possible degree of competition among the oligopolistic firms. This is achieved by aligning the after-tax marginal costs of the two competitors, which implies to impose a higher tax on the capital inputs of the low-cost firm. In both of these scenarios, the differentiation of the marginal capital taxes will be more pronounced, if the productivity difference between the two firms is larger. This is seen by differentiating the optimal tax rates with respect to, yielding (τ L τ H ) < 0 iff s < 1 2 and (τ L τ H ) > 0 iff s > 1 2. We next consider the case where the government takes the policy of favoring the lowcost firm to the limit and taxes the high-cost firm out of the market. 16 Monopoly. From equation (13), the optimal investment tax on the monopoly firm is derived as τ m L = (1/2 s) (a r). (18) 3/2 s Noting that a > r and s 1, this implies a subsidy (τl m < 0) on the monopolist s investment when s > 1/2, and a positive investment tax when s < 1/2. This pattern is thus the same as in the duopoly regime discussed above, and the intuition is also analogous. Investment subsidies, which increase output towards its efficient level, will only be in the interest of the small country s government if it is able to tax a sufficiently high share of the resulting increase in the monopoly firm s profits. In the extreme case 16 Under the assumption that the ownership structure of the two firms is identical, the government will never find it optimal to have the high-cost firm as the only producer in the market. This result may change, however, when the high-cost firm is fully owned by domestic residents. This case is analyzed in Section

14 where the cost of shifting profits becomes prohibitive (s = 1) so that the government can tax profits completely, the investment subsidy will become so high that it induces the first-best level of output in the market. The last step is then to compare the two regimes with their respective optimal policies, in order to determine the government s choice of market structure. Monopoly vs Duopoly. We substitute the optimal tax policies under duopoly [eqs. (16) and (17)] and under monopoly [eq. (18)] into the respective indirect utility function [eqs. (10) and (13)] to determine optimized welfare in each regime. Comparing the two optimized welfare functions, we find that the government chooses the deter entry by the high-cost firm if s > s 1 2(a 1). (19) Equation (19) implies that the government will only give up competition within the industry and subsidize the (low-cost) monopolist when profit shifting is costly and the small country is therefore able to tax the monopolist s profits at a sufficiently high rate. From (19) we can infer that s > 1/2 when 2 < (a r). This condition is always fulfilled, however, by our assumption that the productivity gap between firms must be sufficiently low so as to preclude predatory pricing by the low-cost firm (see footnote 10). We are now in the position to state our main result. Proposition 1 The pattern of optimally differentiated taxation is a function of the degree of international tax competition. (i) With high costs of profit shifting (s > s > 1/2), the government subsidizes investment by the low-cost firm and deters the entry of the high-cost firm. (ii) With intermediate costs of profit shifting (1/2 < s < s ), investment in both firms is subsidized and the optimal policy favors the low-cost firm (τ L < τ H ). (iii) With low costs of profit shifting (s < 1/2), investment in both firms is taxed and the optimal policy favors the high-cost firm (τ L > τ H ). Proposition 1 is illustrated in Figure 1. We start on the right end of this graph, where full taxation of corporate profits is possible (t = s = 1). In this case, the investment of the low-cost firm (solid line) is heavily subsidized whereas the high-cost firm (dotted 13

15 Figure 1: Optimal input taxes and economic integration 1/2 s* 1 s line) is taxed to a sufficiently high degree to keep it from entering the market. As s and therefore t start to fall, the marginal investment subsidy for the low-cost firm declines (i.e. the tax rate rises), whereas the prohibitively high marginal tax rate on the highcost firm turns into a subsidy at s = s. At this point the tax rate on monopoly profits is sufficiently low so that the optimal policy switches to a duopolistic market structure, by allowing the high-cost firm to profitably enter the market. However, the government will still favor the low-cost firm by means of a higher subsidy as long as s > 1/2, in order to maintain a high average productivity. At s = 1/2 the two counteracting incentives of increasing aggregate productivity and increasing competition just offset each other so that investment tax rates on both firms are the same. At the same level of s = 1/2 the efficiency-enhancing effects of investment subsidies are just offset by the incentive to redistribute profits from foreign shareholders to domestic taxpayers by means of a positive investment tax. Hence the intersection of the two (s τ i )-graphs occurs at an investment tax rate of zero. As s and t fall below 1/2, the incentive to strengthen competition in the market dominates the motive to increase aggregate productivity. At the same time, the larger part of gross profits flows to foreign shareholders of the two firms, rather than to domestic 14

16 consumer-taxpayers. As a result, optimal investment taxes on both firms turn positive and the tax rate on the low-cost firm exceeds the tax on the high-cost firm. This strengthens duopoly competition by improving the competitive position of the highcost firm vis-a-vis its more productive competitor. This pattern of discrimination is maintained even at s = 0, where costless profit shifting prevents any taxation of pure profits. Investment can still be taxed, however, and investment taxes on both firms will therefore be at their highest at this point. 5 Extensions 5.1 Home bias in domestic portfolios In this section we relax the assumption that none of the profits earned by the two firms accrues to residents of the small economy. Instead we assume that the shares in the high-cost firm, which is associated with a national enterprise, are fully held by domestic consumers. The market equilibria and the analysis of tax competition carry over from our benchmark analysis in Sections 3 and 4.1 to this alternative setting. What changes, however, are the optimal firm-specific investment taxes. These are now given by τ L = (1 2s)r 2(1 s), τ H = 2[a (1 + )r](1 s) r(2s ). (20) 2(1 s)(1 + ) Hence, as in our benchmark model, the low-cost firm (which remains in the ownership of international investors) will be subsidized only when the feasible rate of profit taxation remains above s = t = 1/2. The high-cost firm, however, will now always be subsidized whenever it is active in equilibrium. Is it nevertheless possible that the government favors the low-cost firm, by setting τ H > τ L? Comparing the two terms in (20) shows that this holds when 1 > s > s 2a (a + 2 1) > 1 2. (21) Condition (21) implies that the threshold value of s, where capital input taxes are equal for the the two firms, now occurs at a higher level of s than in our benchmark case 15

17 (where the corresponding threshold value was s = 1/2). Hence the range in which the low-cost firm is tax-favored is unambiguously smaller under this differential pattern of ownership. For sufficiently high levels of s, however, it is still the case that the optimal tax policy discriminates in favor of the low-cost firm, in order to increase average productivity. Moreover, the parameter range for s in which this pattern occurs is larger if the productivity advantage of the low-cost firm is higher. Hence the fundamental trade-off studied in our benchmark model remains intact when the highcost firm is domestically owned, even though the borders at which the regime switches occur are shifted in favor of the domestically owned firm. 5.2 Bertrand competition The case of Bertrand competition between the two firms is easily dealt with. As is well-known from the asymmetric case of the Bertrand duopoly model, the equilibrium in this case has the low-cost firm produce all output, at a price of ε below the costs of its competitor. In this case the pattern for the optimal policy is clear-cut: it is optimal to subsidize the marginal cost of the high-cost firm down to a level that is marginally above the unit costs of the low-cost firm. Hence τ H = + ε < 0 and τ L = 0. In equilibrium only the low-cost firm will then produce, but the threat of entry by the high-cost firm forces it to set prices at marginal cost. Hence a first-best policy can be implemented without the need for subsidy payments in equilibrium, and for any level of corporate tax rates t. Bertrand competition thus eliminates the policy tradeoff between fostering competition and increasing aggregate productivity that is at the heart of our benchmark model. 5.3 Generalization to more than two firms or types to be added 6 Conclusion In this paper we have linked the pattern of differential capital input taxes levied on firms with different productivity to the feasible rate of profit taxation in a small country facing international tax competition. When tax competition is moderate, and the 16

18 equilibrium profit tax rate is therefore sufficiently high, then it is optimal for the small country to grant discriminatory tax breaks that reduce the costs of capital in the highly productive firm. When tax competition becomes more aggressive, however, so that it is no longer possible to tax profits at sufficiently high rates, then the optimal tax policy changes. Instead of fostering aggregate productivity, the primary policy goal becomes to intensify competition in the oligopolistic sector, and this is achieved by granting a preferential tax treatment to the low-productivity firm. The model presented in this paper thus offers an explanation for existing trends to reduce tax advantages for highly productive, multinational firms vis-a-vis their less productive national competitors. It argues that this is the optimal policy response to the need to cut corporate tax rates as a result of tightened international capital tax competition. In addition to the evidence presented in the introduction, there are other developments that point in the same direction. In Europe, for example, the number of large-scale state subsidy cases, where host governments have granted high subsidies as a share of the firms investment, seems to have peaked in the early 2000s (see Haufler and Mittermaier, 2011, Table 1), but has significantly fallen in the last few years. A still different example is the increasing focus on tough regulation and competition in network utility markets, which cut into the profits of privatized incumbent firms. It would be highly desirable to replace this suggestive evidence by a rigorous econometric test of our central hypothesis, linking quantifiable indicators of tax advantages for highly productive, multinational firms to the development of statutory corporate tax rates. Even if a falling trend of tax advantages to multinational firms can be rigourously shown in the data, there are other, complementary explanations to the one presented here. It is obvious, for example, that a tax system that permits highly profitable firms to pay substantially lower effective tax rates than their smaller and less profitable competitors may be perceived as highly unfair. This perception by itself may have detrimental effects on tax morale in small businesses and for individuals, or it may induce nationally operating firms to establish an additional presence in a low-tax country for the primary reason of saving taxes. How our explanation for existing trends in corporate tax policy fares against such alternative hypotheses is thus a further question for empirical research. 17

19 Appendix A.1. The critical productivity gap This appendix studies the conditions under which the low-cost firm does not find it preferable to price its high-cost competitor out of the market. To ensure this the duopoly profits of the low-cost firm must be higher than in an alternative scenario where the low-cost firm sets its price equal to the marginal cost of the high-cost firm and captures the entire market: π D L > π M,LP L, (A.1) where the superscript D stands for duopoly, M for monopoly, and LP stands for the limit price 1+. The low-cost firm s profit under limit pricing would be π M,LP L = x M L, with x M L = [a (1 + )]/b from (3). Hence π M,LP L = [a (1 + )] b. (A.2) Using this and (4) in (A.1), we get the condition 1 9b [a + (1 + τ H)(1 + ) 2(1 + τ L )] 2 > [a (1 + )] b. (A.3) Solving this and using optimal values for τ L and τ H yields < 2(a 1)(s 1)(4s((s 5)s + 8) 15) 4 2 φ 16(s 3)s[(s 3)s + 4] + 65 (A.4) where φ = (a 1) 2 (s 2) 2 (s 1) 3 {2s[(s 5)s + 7] 5}. As the RHS in (A.4) is rising in s for 0 s 1, the condition will always hold when it holds for s = 0. This yields the following condition for the critical productivity differential c : < c 2 65 ( 15 4 ) 10 (a r) 0.07(a r). (A.5) A.2. Derivation of (16) and (17) 18

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