Asymmetric tax competition in the presence of lobbying

Transcription

1 Int Tax Public Finance (2014) 21:66 86 DOI /s Asymmetric tax competition in the presence of lobbying Yu-Bong Lai Published online: 29 November 2012 Springer Science+Business Media New York 2012 Abstract This paper incorporates the influence of interest groups into the asymmetric tax competition model to explain the phenomenon that small countries do not necessarily set lower capital tax rates than large countries. In addition to the efficiency effect considered by the standard model, which leads the smaller country to set a lower capital tax rate, this present paper also takes account of the political effect arising from lobbying. We show that the smaller country may face less downward political pressure. If the political effect outweighs the efficiency effect, then the smaller country sets a higher tax rate than the larger country. This result has several welfare implications, which are in contrast to the conventional consequences. Keywords Capital mobility Globalization Interest groups Political economy Public good Tax competition JEL Classification F21 H41 H73 1 Introduction As globalization deepens, capital is likely to become more responsive to differences in capital tax rates (De Mooij and Ederveen 2003), and the issue of interjurisdictional tax competition has become the focus of much attention and debate. Most models of tax competition assume that competing jurisdictions are identical. However, countries involved in foreign direct investment often differ in terms of population and factor endowments. Thus, capital tax competition among heterogeneous jurisdictions Y.-B. Lai ( ) Department of Public Finance, National Chengchi University, 64, Sect. 2, ZhiNan Road, Taipei 11605, Taiwan, ROC yblai@nccu.edu.tw

2 Asymmetric tax competition in the presence of lobbying 67 Fig. 1 The relationship between the country size and the effective tax rate. Sources: World Bank; Deloitte International Tax Source is another important issue (see, e.g., Wilson (1999) and Wilson and Wildasin (2004) for a survey of the related literature). The existing papers dealing with asymmetric tax competition predict that small countries will set lower capital tax rates than large countries. The empirical evidence, however, does not entirely support this prediction. For example, the empirical evidence provided by Devereux et al. (2002), Devereux and Sørensen (2005), Overesch (2005), and Schratzenstaller (2007) show mixed results, in which the capital tax rates in small countries are not necessarily lower than those in large ones. 1 Similar results can also be found in Fig. 1, which illustrates the relationship between the population and the effective corporate tax rates in the European Union. 2 All the evidence mentioned contrasts with the predictions of the standard model, and thus certain modifications to the standard model seem necessary. The first theme of this paper is to provide an explanation of the mixed empirical evidence. We argue that the mixed empirical evidence can be attributed to the influ- 1 For example, Devereux et al. (2002) analyze the effective corporate tax rates set by several OECD countries, and their Fig. 7 illustrates that the effective tax rates in Belgium and the Netherlands are higher than those in the United Kingdom. 2 Population has been generally used to measure the size of a country. See Alesina and Spolaore (2003).

3 68 Y.-B. Lai ence of special interest groups. Our model, which is based on Bucovetsky (1991) and Wilson (1991), considers an economy consisting of a larger country and a smaller one. Each country contains two types of resident, namely, capitalists and workers. Capital is perfectly mobile across borders, whereas labor is immobile. Each country taxes the capital according to the source principle, and uses the tax revenues to finance a public good. We put the emphasis on the case where the capitalists organize themselves into a group to lobby for the capital tax rate. The conventional view, which assumes that policymakers are benevolent, indicates that the smaller country faces a larger marginal cost of public funds of taxing capital, inducing it to choose a lower capital tax rate than its larger counterpart. One may question why voting plays no role in this present paper. What we are really concerned with is the effective capital tax rate, rather than the statutory tax rate. In addition to the statutory tax rate, the effective capital tax rate also depends on, e.g., the way in which depreciation is deducted, the investment tax credit, and so on. The statutory tax rate may be determined by majority voting, whereas there are generally loopholes through which interest groups can influence the effective tax rate. Moreover, since capital income is more concentrated than labor income, capital owners have a stronger incentive to organize a group to lobby. Thus, we believe that the setting in which only capitalists lobby and no elections are driving the tax rate seems acceptable. In addition to the efficiency facet mentioned above, this present paper also takes account of the political effect arising from lobbying, which leads the smaller country to set a higher tax rate than the larger country. Since the capitalists own a perfectly mobile factor of production, and given that there is no residence-based taxation of capital income, the income of the capitalists depends on the tax policy of their home country only to the extent that the home country has an effect on the net rate of return on capital. 3 In the extreme case of a small open economy where the effect of domestic tax rate changes converges to zero, the impact of the domestic tax policy on the income of capitalists is zero. In this setting, the capitalists would prefer a revenue maximizing capital tax rate because they benefit from domestic public goods provision, and the burden of taxation is fully shifted to the immobile workers. Clearly, this is reminiscent of the idea of Hirschman (1970). If groups are mobile, then they have fewer incentives to use voice, i.e., to take part in the political process. In the present model, the capitalists are mobile with regard to their private income but immobile with regard to their public goods consumption. That is why they have strong incentives to lobby for more public goods provision and weak incentives to lobby for tax rate reductions. If the political effect outweighs the efficiency effect, then the smaller country will set a higher capital tax rate than the larger country. In addition to the above positive issue, this present paper also derives several welfare implications, which constitute our second theme. A well-known consequence of the standard model is that if the differences in country size are large enough, then the smaller country receives a higher per capita utility level than the larger country 3 The author is grateful to a reviewer for clarifying the explanation, and also for linking the result in the present paper to the idea of Hirschman (1970).

4 Asymmetric tax competition in the presence of lobbying 69 in the non-cooperative equilibrium. However, we show that the presence of lobbying can reverse this result. If the smaller country chooses a higher tax rate, causing capital flight, then it receives a lower per capita or average utility level. Although the average utility level is lower, the higher tax rate leads the capitalists in the smaller country to be better off than those in the larger country. Whether public goods are provided efficiently is another major issue in the literature on tax competition. Bucovetsky (1991) points out that if the differences in country size are great enough, then the smaller country provides a suboptimally low level of the public good, and the larger country supplies the public good efficiently. In Sect. 4, we show that, in the presence of lobbying, the larger country unambiguously under-provides the public good, and the smaller country may provide the public good efficiently. Moreover, the standard model also indicates that if differences between the two countries are great enough, then the smaller country will be better off in the non-cooperative equilibrium than in the cooperative equilibrium. Section 5 shows that the opposite can occur, namely, the smaller country can benefit from cooperation. The literature on asymmetric tax competition goes back to Bucovetsky (1991) and Wilson (1991), which we refer to as the standard model. A number of papers have extended the standard model, including, e.g., Haufler and Wooton (1999), Stöwhase (2005), Peralta and van Ypersele (2005, 2006), and Sato and Thisse (2007). 4 However, none of them adopts a political economy framework. Persson and Tabellini (1992), Lockwood and Makris (2006), and Haufler et al. (2008) investigate the effect of capital market integration on capital taxes through voting mechanisms. Lorz (1998) and Lai (2010) incorporate lobbying into the framework of tax competition, but these two papers deal with symmetric tax competition. Haufler (1997) considers the political asymmetry between two regions, in which the exogenous political weight of workers is higher in one region than in the other. While he emphasizes the effects of a reduction in the capital mobility cost on the workers political influence, we follow the standard model and assume that capital is perfectly mobile across countries. In addition, Haufler (1997) incorporates a fixed government budget constraint, and thus the issue of the provision of public goods is absent from his model. This issue, however, is one of our major concerns. The remainder of the paper is organized as follows. Section 2 introduces the model underlying the analysis. Section 3 discusses the political effect arising from lobbying and explains why the smaller country may set a higher capital tax rate. We turn to the effect of lobbying on the provision of public goods in Sect. 4. Section 5 compares the non-cooperative equilibrium with the cooperative equilibrium. Concluding remarks are provided in Sect The model We consider two countries, indexed by i = 1, 2. The total population in country i is N i. Without loss of generality, we assume that N 1 <N 2. Each country consists of 4 Sato and Thisse (2007) obtain some results that are similar to those in this present paper, but their setting, which incorporates an imperfect labor market, is quite different from that of the standard model.

5 70 Y.-B. Lai two types of resident, capitalists and workers. In country i, the number of capitalists in country i is M i, which equals α i N i, and that of workers is L i, which equals (1 α i )N i. The two countries are identical in other respects. In the standard model, where each country contains homogeneous residents, the country size is clearly defined. With heterogeneous residents, it is not straightforward to define a smaller country. For example, it is possible that a country has a larger amount of capital endowment and a smaller number of workers. In order make a direct comparison with the conventional results, we assume that α 1 = α 2 = α throughout this paper. This assumption imposes the restriction that country 1 has both a smaller amount of capital endowment and fewer workers, so that it can be defined as a smaller country. Without loss of generality, we focus on the situation where workers constitute the majority of the population, such that α<1/2. In each country, all residents are internationally immobile, and residents of the same type are homogeneous. Each capitalist is endowed with k units of capital, regardless of his or her location. Each worker is endowed with one unit of labor. Workers inelastically supply their labor to local firms. Capital can freely move across countries. Perfect capital mobility ensures that the net rate of return on capital, denoted by r, is the same in both countries. 5 Both countries produce a homogeneous commodity, which can be shipped at zero cost between the two countries. The price of the commodity is normalized to unity. The production function is identical across countries, and exhibits constant returns to scale, so that it can be expressed as f(k i ), where k i = K i /L i is the capital-labor ratio. This function is twice continuously differentiable, with the properties f (k i )>0 and f (k i )<0. The commodity and factor markets are perfectly competitive. We assume that all firms in each country are identical, so that the number of the firms can be normalized as unity. The objective function of the representative firm in country i is given by L i f(k i ) (r + t i )L i k i L i w i, (1) where t i is the source-based tax per unit of capital. For the firm, the gross cost of using capital, which is denoted by ρ, is the sum of the net rate of return on capital and the tax rate. The profit-maximization of the firm requires that f (k i ) = r + t i ρ i. (2) Equation (2) shows that capital is employed until its marginal product, f, equals the gross cost of capital. This first-order condition defines the capital demand function, k i = k i (ρ i ). Totally differentiating (2) gives the effect of ρ i on k i as follows: k i = 1 ρ i f < 0, (3) (k i ) indicating that an increase in ρ reduces the firm s demand for capital. 5 In this paper, we consider only the case where r is positive. See Bucovetsky (1991) for the case in which r is negative.

6 Asymmetric tax competition in the presence of lobbying 71 The zero-profit condition determines the wage rate, which is given by w i = f(k i ) k i f (k i ). (4) Differentiating w i with respect to k i gives w i / k i = k i f (k i )>0, showing that the wage rate increases with the capital-labor ratio. The worldwide capital market clearing condition is given by 6 ( ) M1 + M 2 s 1 k 1 (ρ 1 ) + s 2 k 2 (ρ 2 ) = k, (5) L 1 + L 2 where s i = N i /(N 1 + N 2 ) denotes country i s share of the total population. This condition implies that the net rate of return on capital, r, depends on both t 1 and t 2. Equation (5) allows us to derive the effect of t i on r: r s i f (k j ) = t i s 1 f (k 2 ) + s 2 f 0. (6) (k 1 ) As expected, the net rate of return on capital decreases with t i, as long as s i > 0. The larger that s i is, the stronger that the negative impact of an increase in t i on r will be. With the help of (6), totally differentiating (2) and some rearrangements give the effect of t i on the demand for capital as follows: k i s j = t i s 1 f (k 2 ) + s 2 f (k 1 ). (7) The above equation shows that a unilateral tax increase in the smaller (resp. larger) country results in a larger (resp. smaller) decline in its capital-labor ratio. These asymmetric responses to an increase in tax are crucial in the analysis of the standard model. The preferences of a representative capitalist in country i are given by u κ i = xκ i + H (z i ), (8) where x is the level of the private consumption, and z is the amount of the public consumption good. A capitalist s private budget constraint is xi κ = r k. The function H has the properties that H > 0 and H < 0 for all non-negative z, and also lim z 0 H (z) =. The public consumption good is financed by the capital tax revenues. Since country i s government budget constraint is given by N i z i = t i K i, z i can be written as follows: z i = (L i /N i )t i k i = (1 α)t i k i. (9) Similarly, the preferences of a representative worker in country i are given by u l i = xl i + H (z i ). (10) The private budget constraint of a worker is x l i = f(k i) k i f (k i ). 6 The worldwide capital market clearing condition requires that the aggregate demand for capital be equal to the aggregate capital endowment, i.e., L 1 k 1 + L 2 k 2 = (M 1 + M 2 ) k. Then dividing both sides by (L 1 + L 2 ) gives (5).

7 72 Y.-B. Lai 3 Political equilibrium In this section, we introduce the influence of interest groups to the model. This causes the present paper to deviate away from the standard model, in which policymakers are benevolent. Since the net rate of return on capital depends t 1 and t 2, the capitalists in each country have incentives to organize themselves as a lobbying group. Workers are assumed to constitute a large part of the total population, and are too numerous to overcome the free-rider problem, so that they are unorganized. 7 The capitalists provide their policymaker with a campaign contribution schedule, i.e., a schedule relating their promised payment to the policy chosen by the policymaker. These schedules will not be formal contracts, nor will they usually be explicitly announced (Grossman and Helpman 1995). Given the contribution schedule, the policymaker in each country chooses the capital tax rate to maximize a weighted sum of total political contributions and aggregate social welfare. The contribution schedules are chosen to maximize the aggregate welfare of the interest group s members. Specifically, the capitalists in country i submit the contribution schedule C i ( ) that maximizes V κ i = W κ i (t i,t j ) C(t i ; t j ), (11) where Wi κ represents the gross-of-contributions joint welfare of the capitalists in country i, which is defined as Wi κ (t [ i,t j ) = M i r k + H(z i ) ]. (12) Equation (12) shows that Wi κ depends on t i and r. Since r depends on both t i and t j, as indicated by (5), we express Wi κ as a function of t i and t j. The contribution schedule C i ( ) maps every t i into a level of political contribution. Equation (11) indicates that C i conditions on t j. We will discuss this issue in more detail later. Before moving further, we define the joint welfare of the workers in country i as follows: Wi l = L i[ f(ki ) k i f (k i ) + H(z i ) ]. (13) Then country i s social welfare function is defined as W i = Wi κ + Wi l. Following Grossman and Helpman (1994, 1995), the policymaker in country i is assumed to maximize a weighted sum of the political contributions received and the social welfare, which is given by θc i (t i ; t j ) + W i (t i,t j ), (14) where θ 0 is the weight the policymaker attaches to the political contributions relative to social welfare. The parameter θ is exogenously determined, which may depend on the interest groups lobbying skills or political connections. In order to focus on the asymmetry in factor endowments rather than in political weight, θ is assumed to be the same in the two countries. 7 The situation where workers also engage in lobbying is briefly discussed in Sect. 6.

8 Asymmetric tax competition in the presence of lobbying 73 The events unfold as follows. First, each country s capitalists offer their policymaker a contribution schedule, which is contingent upon the policy chosen by the policymaker. The lobbies act simultaneously and non-cooperatively, each taking as given the schedule of its counterpart in the other country. Then the two policymakers simultaneously determine their capital tax rates and collect the political contributions. Finally, given the capital tax rates, the firms determine their demand for capital and output. Following the setting of Grossman and Helpman (1995), we assume that the implicit contract between the policymaker and the capitalists in one country is not observable to the policymaker in the other. The importance of this assumption will become clear later. According to Definition 1 in Grossman and Helpman (1995), we define an equilibrium response by each country to an arbitrary policy choice of the other as follows. We adopt country 1 to illustrate, and a similar definition applies to country 2. Definition 1 Let t 2 be an arbitrary capital tax rate of country 2. Then a contribution function, C 1, and a tax rate, t 1, are an equilibrium response to t 2,if(a) t 1 = arg max θc 1 (t 1; t 2 ) + W 1 (t 1,t 2 ), and (b) there does not exist a contribution function C 1 (t 1 ; t 2 ) and a capital tax rate t 1 such that (i) t 1 = arg max θ C 1 (t 1 ; t 2 ) + W 1 (t 1,t 2 ), and (ii) W1 κ ( t 1,t 2 ) C 1 ( t 1 ; t 2 )>W1 κ ( ) ( ) t 1,t 2 C 1 t 1 ; t 2. A contribution schedule and a capital tax rate constitute an equilibrium response. Condition (a) of the definition states that country 1 s policymaker chooses t 1 to maximize his or her objective function, given the tax rate of country 2. Condition (b) indicates that the capitalists are unable to enhance their welfare by choosing a contribution schedule C 1 ( ) different from C1 ( ), thereby inducing the policymaker to set t 1. We note that Definition 1 presumes that the capitalists condition their political contributions on the expected tax rate of the other country. Although the lobbies act earlier than the policymakers, the lobbies take the other country s policy as given. This result is based on the assumption that contribution schedules cannot be observed abroad. 8 According to Grossman and Helpman (1995), two reasons can justify this assumption. Firstly, it may be illegal or problematic for lobbies to explicitly reveal their willingness to pay politicians for favorable treatment; secondly, a lobby s promise of its contribution schedule generally carries little commitment value, so that policymakers abroad would not know whether there were further details in addition to those that had been announced explicitly. 8 If contribution schedules can be observed abroad, then the lobby in one country may influence the policy of the other country. See Grossman and Helpman (1995) for more discussions on this issue.

9 74 Y.-B. Lai In addition to condition (a) of Definition 1, Proposition 1 in Grossman and Helpman (1994) requires that the equilibrium policy response to t 2 satisfy the following condition, which is implied by condition (b): t 1 = arg max W κ 1 (t 1,t 2 ) C 1 (t 1; t 2 ) + [ θc 1 (t 1; t 2 ) + W 1 (t 1,t 2 ) ]. (15) This condition stipulates that the equilibrium capital tax rate should maximize the joint welfare of the lobby and the policymaker. If this condition is not satisfied, then the lobby can reformulate its contribution schedule to induce the policymaker to choose the jointly optimal policy, and could capture some of the surplus from the change in policy. In equilibrium, there cannot exist such a possibility for the capitalists to improve their welfare. We also note that a condition similar to (15) applies to country 2 s equilibrium tax rate. When the tax rates are chosen, the policymaker in each country makes an equilibrium response to what he or she expects the other s tax rate will be. We can define a Nash equilibrium as follows: Definition 2 A non-cooperative equilibrium consists of a pair of political contribution schedules {C 1,C 2 }, and a pair of capital tax rates {t 1,t 2 }, such that {C 1,t 1 } is an equilibrium response to t 2, and {C 2,t 2 } is an equilibrium response to t 1. By using the equilibrium conditions, we can characterize the equilibrium tax rates. We assume that the contribution schedules are differentiable, at least around the equilibrium point. With differentiability, (15) implies the first-order condition for the equilibrium t 1 as follows: W1 κ(t 1,t 2) C 1 (t 1 ; t [ 2) + θ C 1 (t 1 ; t 2) + W 1(t1,t ] 2) = 0. (16) t 1 t 1 t 1 t 1 According to condition (a) of Definition 1, the maximization of the objective function of the policymaker in country 1 ensures that θ C 1 (t 1 ; t 2) + W 1(t1,t 2) = 0. (17) t 1 t 1 Combining (16) with (17) implies W1 κ(t 1,t 2) = C 1 (t 1 ; t 2). (18) t 1 t 1 Equation (18) indicates that, around the equilibrium point, the capitalists set their contribution schedule so that the marginal change in the contribution for a small change in t 1 equals the impact on the capitalists gross welfare of the tax change. This property is known as that the contribution schedules are locally truthful around the equilibrium point. Then by substituting (18)into(17), we obtain θ Wκ 1 (t 1,t 2) t 1 + W 1(t 1,t 2) t 1 = 0. (19)

10 Asymmetric tax competition in the presence of lobbying 75 This equation characterizes the equilibrium t 1 response to an arbitrary t 2. Similarly, we have θ Wκ 2 (t 2,t 1) + W 2(t2,t 1) = 0, (20) t 2 t 2 which characterizes the equilibrium t 2 response to an arbitrary t 1. Equations (19) and (20) indicate that when the policymaker chooses the capital tax rate, he or she should balance two effects: the effect of t on the social welfare and that on the political contributions received. If the policymaker were immune from the influence of the lobby, which is characterized by θ = 0, then the policymaker would set t to maximize the social welfare function. However, if θ is positive, then the policymaker encounters a trade-off between efficiency and political contributions. The second term on the left-hand side of (19) and (20) measures the effect of t on social welfare, which we refer to as the efficiency effect. The first term on the left-hand side of the two equations reflects how the tax rate affects the amount of political contributions, which we refer to as the political effect. Let us examine these two effects in more detail below. The standard tax competition model considers only the efficiency effect, which is obtained by differentiating the social welfare function with respect to t i : W i t i = L i k i { 1 + r t i [( α 1 α )( ) ] } k 1 + H (1 ε i ), (21) where ε i = ( k i / t i )(t i /k i ) 0 denotes the elasticity of capital demand with respect to t i. The elasticity ε i is assumed to be less than unity to ensure that the economy is in the upward sloping area of the Laffer curve. 9 The terms on the right-hand side of (21) denote the various effects arising from an increase in t i. The first term in the braces, 1, reflects the decline in the aggregate private consumption, the second term measures the terms-of-trade effect, and the last term is the increase in the provision of the public good. 10 Other things being the same, a larger ε i brings about a larger marginal cost of public funds (MCPF) of the capital tax, because an increase in t i causes a greater capital outflow. This leads to a lower t i. In addition to the efficiency effect, the level of ti also depends on the political effect, which equals the product of θ and Wi κ/ t i. We define the term Wi κ/ t i as the capitalists political pressure, which is derived by differentiating (12) with respect to t i : W κ i t i = M i k i [( k k i k i ) ] r + H (1 α)(1 ε i ). (22) t i From (22), the capitalists political pressure, which can be either downward or upward, depends on two forces. The first one is the private-consumption effect, which 9 Differentiating (9) with respect to t i gives z i / t i = (1 α)(1 ε i )k i. The assumption ε i < 1 ensures that the provision of z i increases with t i. Much of the literature estimates the elasticity of foreign direct investment with respect the tax treatment as being about 0.6 (see, e.g., the survey of Hines (1999)), which justifies our assumption. 10 Since our focus is on the political effect, for further details regarding the efficiency effect the reader is referred to Haufler (2001), Chap. 5.

11 76 Y.-B. Lai is reflected by the first term in the square brackets. The private-consumption effect is non-positive. If the private-consumption effect is negative, indicating that a lower tax rate increases the capitalists private consumption through raising r, then the capitalists will lobby for a lower t. According to (6), the magnitude of the privateconsumption effect is positively related to s i. The smaller that s i is, the larger is the share of the tax burden that the capitalists in country i can shift to the workers, and thus they have a weaker incentive to lobby for a lower tax rate. If s 1 approaches zero, then this effect vanishes in the smaller country. The second effect, characterized by the second term, is the public-consumption effect. This effect is positive, and indicates that an increase in t will enlarge the provision of the public good, thereby inducing the capitalists to lobby for a higher t. Since the public-consumption effect and the private-consumption effect work in opposite directions, whether the capitalists exert downward or upward political pressure on the tax rate depends on which force prevails. Inserting (21) and (22)into(19) and (20) gives { L i k i 1 + r [ ( )( ) ] } α k (1 + θ) 1 + (1 + αθ)h (1 ε i ) = 0. (23) t i 1 α k i With (23), we can determine the relationship between t1 and t 2. Following the approach adopted by Haufler (2001), we begin with the situation where both countries choose the same tax rate, t 1 = t 2, and thus have the same capital-labor ratio. With k 1 = k 2, from the capital market clearing condition we obtain And then we define k k 1 = k k 2 = L 1 + L 2 M 1 + M 2. (24) φ i = θ Wκ i (t i,t j ) + W i(t i,t j ). (25) t i t i Without loss of generality, we assume that t 2 = t 2, which ensures that φ 2(t 2,t 1 ) = 0. Using this condition and solving (23) forh (z 2 ) gives H (z 2 ) = 1 + s 2[(1 + θ) 1 α α L 1 +L 2 M 1 +M 2 1]. (26) (1 + αθ)(1 ε 2 ) In deriving (26) we use the relationship that r/ t 2 = s 2 f (k 1 )/[s 1 f (k 2 ) + s 2 f (k 1 )]= s 2. In addition, since z i = (1 α)t i k i, the relationships t 1 = t 2 and k 1 = k 2 imply that z 1 = z 2, which in turn gives H (z 1 ) = H (z 2 ). Then we insert (26) intoφ 1.Ifφ 1 (t 1,t 2 ) is equal to zero, then the two countries choose the same tax rate in equilibrium. If φ 1 (t 1,t 2 ) is positive, then the equilibrium t 1 is greater than the equilibrium t 2, otherwise the opposite occurs. By inserting (26) intoφ 1 (t 1,t 2 ) we obtain ( ) ( φ 1 t 1,t 2 ) L1 k 1 {ε2 = ε 1 + θ [ s 1 (1 ε 2 ) + s 2 (1 ε 1 ) ]}. (27) 1 ε 2

12 Asymmetric tax competition in the presence of lobbying 77 The sign of φ 1 (t 1,t 2 ) is ambiguous. To illustrate this idea clearly, we begin with the case where lobbying is absent, i.e., θ = 0. In this case, only the efficiency effect exists. With θ = 0, (27) reduces to ( ) ( φ 1 t 1,t 2 ) L1 k 1 = (ε 2 ε 1 )<0. (28) 1 ε 2 Because ε 2 is less than ε 1, 11 φ 1 (t 1,t 2 ) is unambiguously negative, indicating that t 1 is lower than t 2 in equilibrium. This replicates the conventional result. With a higher capital demand elasticity, the smaller country (country 1) faces a larger MCPF from raising t 1, inducing it to choose a lower tax rate than the larger country. Then we turn to the case with lobbying, namely, θ>0. In this case, the smaller country does not necessarily set a lower capital tax rate than the larger country, which contrasts with the conventional result. We have the following proposition: Proposition 1 Let ˆθ = ε 1 ε 2 s 2 (1 ε 1 ) s 1 (1 ε 2 ), (29) ŝ 1 = 1 ε 1 2 ε 1 ε 2. (30) 1. In the case where s 1 is less than ŝ 1,(i)if θ is greater than ˆθ, then country 1(the smaller country) sets a higher capital tax rate than country 2(the larger country); (ii) if θ is equal to ˆθ, then the two countries set the same tax rate; and (iii) if θ is less than ˆθ, then country 1 sets a lower capital tax rate than country If s 1 ŝ 1, then country 1 sets a lower capital tax rate than country 2, regardless of the value of θ. Proof See Appendix 1. The intuition behind Proposition 1 is as follows. As indicated by (28), through the efficiency effect, a larger ε confronted by the smaller country leads it to choose a lower tax rate. On the other hand, the relationship between the two countries political effects is described in the following lemma: Lemma 1 If s 1 is smaller than ŝ 1, then country 1(the smaller country) faces less downward political pressure on the capital tax rate than country 2(the larger country). Proof See Appendix The elasticity ε i is defined as ( k i / t i )(t i /k i ). Combining (7) with the relationships t 1 = t 2 and k 1 = k 2 ensures that ε 2 <ε 1.

13 78 Y.-B. Lai If s 1 is small enough, then the capitalists in country 1 can shift most of the tax burden to the workers. Thus the capitalists in the smaller country exert less downward political pressure than their counterparts in the larger country, giving rise to a higher tax rate in the smaller country. This explains Lemma 1. To sum up, the efficiency effect induces the smaller country to set a lower tax rate than the larger country. On the other hand, with a small s 1, the political effect leads t 1 to be greater than t 2.Ifθ is sufficiently large, then the political effect outweighs the efficiency effect, so that t1 is higher than t 2. However, if s 1 is greater than ŝ 1, then the capitalists in the smaller country will exert more downward pressure than those in the larger country. The greater downward political pressure combined with the larger MCPF brings about t1 <t 2. Proposition 1 also has normative implications. Bucovetsky (1991) and Wilson (1991) show that the smaller country has a higher per capita utility level than the larger country in the non-cooperative equilibrium. Since the smaller country sets a lower tax rate, which attracts capital inflow, residents living there receive a higher per capita utility level. In fact, Proposition 1 in Wilson (1991) shows that, under any Nash equilibrium, the region that levies a lower tax rate will have a higher per capita utility level. Since his proof is so general that no additional restrictions on the forms of the utility or production functions are required, we can directly apply his result. Proposition 1 in this present paper shows that if θ>ˆθ and s 1 < ŝ 1, then t1 >t 2, which ensures that the per capita utility level in country 1 is lower than that in country Thus, we have the following proposition: Proposition 2 If θ>ˆθ and s 1 < ŝ 1, then the smaller country has a lower per capita utility level than the larger country. Since residents are heterogeneous, it is also important to realize the per capita utility level of different types of resident. We can obtain the result that if θ>ˆθ and s 1 < ŝ 1, then the capitalists in the smaller country are better off than their counterparts in the larger country. Since the net rate of return on capital is identical across countries, and each capitalist is endowed with k units of capital, all capitalists have the same amount of private consumption. However, the conditions mentioned in Proposition 2 ensure that t1 >t 2, so that the provision in the smaller country is greater than that in the larger country, indicating that the capitalists in the smaller country have a higher per capita utility level than those in the larger country. Moreover, this result combined with Proposition 2 indicates that the workers in the smaller country are worse off than those in the larger country. 13 When the conditions that lead to t1 <t 2 are met, the opposite results occur, i.e., the capitalists are worse off, but the workers are better off in the smaller country. The following proposition summarizes the above results: 12 Since residents are heterogeneous in this paper, the per capita utility level in country i is defined as its social welfare divided by the number of residents, or W i /(L i + M i ). 13 If the workers in the smaller country are not worse off than those in the larger country, then the smaller country will have a higher per capita utility level than the larger country, which contradicts Proposition 2.

14 Asymmetric tax competition in the presence of lobbying 79 Proposition 3 If θ>ˆθ and s 1 < ŝ 1, then the capitalists in the smaller country are better off than those in the larger country, but the workers in the smaller country are worse off than those in the larger country. If (i) θ<ˆθ and s 1 < ŝ 1, or (ii) s 1 ŝ 1, then the capitalists in the smaller country are worse off than those in the larger country, but the workers in the smaller country are better off than those in the larger country. 4 Provision of public goods Another issue to do with capital tax competition concerns whether public goods are efficiently provided. The efficiency condition for the provision of public goods requires that the marginal rate of substitution (MRS) between z and x be equal to the marginal rate of transformation between x and z, which equals unity in this model. The condition for under-provision is that MRS is greater than unity. The standard model points out that if differences in country size are great enough, then the larger country supplies the public good efficiently, and the smaller country under-supplies it (Bucovetsky 1991; Wellisch 2000, Sect. 4.3). As demonstrated below, the presence of lobbying alters the conventional result, which is the main theme of this section. In order to make the argument as clear as possible, we assume that the country size differs by the maximum possible amount. That is, s 1 approaches zero. Let us first consider the case with θ = 0, i.e., there is no lobbying. Again, this will replicate the conventional results. From (23), the MRS of the two countries is given by H (z 1 ) = 1 > 1, (31) 1 ε 1 H (z 2 ) = 1. (32) In deriving (31) and (32), we apply the fact that when s 1 is small enough, the ratio K 2 /K 2 approaches arbitrarily close to unity. The terms on the right-hand side of (31) and (32) measure the MCPF confronted by the two countries, respectively. Since country 1 perceives the MCPF of its capital tax as being greater than unity, it sets a lower capital tax rate, and under-provides the public good. Country 2 is so large that it is almost like a closed economy. Because of this, the larger country perceives its MCPF as unity, and provides the public good efficiently even in the non-cooperative equilibrium. Now we turn to the case with lobbying. With θ>0, (23) gives the smaller country s MRS between z and x in equilibrium as follows: H (z 1 ) = 1 (1 + αθ)(1 ε 1 ). (33) The MRS can be either greater or smaller than unity. From (33), we can solve a threshold value of θ, denoted by θ, which equals ε 1 /[α(1 ε 1 )]. Ifθ = θ, then H (z 1 ) is equal to unity, and thus the public good in the smaller country is efficiently provided. If θ> θ, then the public good is over-supplied in the smaller country; if θ< θ, then the opposite occurs.

15 80 Y.-B. Lai The intuition is as follows. According to (22), if s 1 is sufficiently small, then the public-consumption effect outweighs the private-consumption effect, and thus the political effect induces the capitalists in the smaller country to lobby for a higher tax rate. 14 If θ equals θ, then the political effect exactly offsets the efficiency effect, and the public good is efficiently provided. If θ is greater than θ, then the political effect outweighs the efficiency effect, thereby giving rise to the over-provision of the public good. Given that s 1 approaches zero, (23) shows that the larger country s MRS between x and z is given by H (z 2 ) = 1 + θ > 1. (34) 1 + αθ Equation (34) indicates that if the differences in country size are sufficiently large, then the larger country provides an inefficiently low level of the public good, for all θ>0. In country 2, the capitalists bear almost all of the tax burden, 15 and thus the private-consumption effect is so large that it outweighs the public-consumption effect. The capitalists downward political pressure on the capital tax rate explains the under-provision of the public good in the larger country. The following proposition summarizes what we have found above: Proposition 4 Supposing that the differences in country size are sufficiently large, the provision of the public good in the larger country is lower than the efficient level, for all θ>0, and the level of the public good in the smaller country is greater than, equal to, or lower than the efficient level, if θ is greater than, equal to, or lower than θ, which equals ε 1 /[α(1 ε 1 )]. 5 Non-cooperation vs. cooperation So far we have discussed the non-cooperative regime. In the standard model, it is well known that cooperation lowers the smaller country s welfare. This section will demonstrate that cooperation can enhance the smaller country s welfare in the presence of lobbying. In addition, we point out that there exists a symmetric noncooperative equilibrium, which is identical to the cooperative equilibrium in terms of both policy and welfare. Proposition 1 shows that there exists a symmetric non-cooperative equilibrium with asymmetric tax competition. Specifically, if θ = ˆθ, then t1 = t 2, which implies that K i /K i = 1,i = 1, 2. The condition K i /K i = 1 gives country i s MRS between z and x in the non-cooperative equilibrium as follows: H (z i ) = 1 + s i θ (1 + αθ)(1 ε i ). (35) 14 We acknowledge that the situation where the capitalists lobby for a higher capital tax rate seems unusual. However, since the public good is financed by the capital tax, the capitalists lobbying for a higher tax rate is equivalent to their lobbying for a larger amount of the public good. From this point of view, this result does not seem to be as unusual as it would at first appear. 15 This can be seen from (6), where r/ t 2 approaches 1 in this case.

16 Asymmetric tax competition in the presence of lobbying 81 Then inserting ˆθ into the above equation gives H (z 1 ) = H s 2 s 1 (z 2 ) = s 2 (1 ε 1 ) s 1 (1 ε 2 ) + α(ε 1 ε 2 ). (36) We then turn to the cooperative regime, in which the two countries merge into a unified country. The capital tax rate under cooperation is denoted by t c. All the capitalists in this unified country are organized to lobby the capital tax rate by providing a contribution schedule C(t c ). The goal of the capitalists is to maximize W κ (t c ) C(t c ), where W κ = W1 κ + W 2 κ denotes the aggregate welfare of the capitalists in the unified country. The objective function of the policymaker is given by θc(t c ) + W(t c ), (37) where W = W 1 + W 2 denotes the aggregate welfare of the unified country. Since there is only one country in this scenario, we can directly apply the proposition of Grossman and Helpman (1994), which can deal with the one country situation. According to their Proposition 1, if {C,tc } is an equilibrium of the cooperative regime, then (a) tc maximizes θc (t c ) + W(t c ); (b) tc maximizes [W κ (t c ) C (t c )]+θc (t c ) + W(t c ). Condition (a) states that given the contribution schedule provided by the capitalists, the policymaker chooses t c to maximize his or her objective function. The meaning of condition (b) is similar to that of (15), so that we do not repeat it here. We assume that the contribution schedule is differentiable. Given that {C,tc } is an equilibrium outcome, condition (b) implies a first-order condition as follows: dw κ (t c ) dt c dc (t c ) dt c + [ θ dc (t c ) dt c + dw(t c ) dt c Moreover, condition (a) requires the following first-order condition: ] = 0. (38) θ dc (tc ) + dw(t c ) = 0. (39) dt c dt c Combining (38) with (39) gives dc (t c ) dt c = dwκ (t c ) dt c. (40) Like (18), (40) implies that the contribution schedule is locally truthful around t c.we then insert (40)into(39) to obtain θ dwκ (t c ) dt c + dw(t c ) dt c = 0. (41) This equation characterizes the equilibrium capital tax rate under the cooperative regime.

17 82 Y.-B. Lai As in the non-cooperative case, (41) indicates that the equilibrium capital tax rate depends on the political effect and the efficiency effect. To derive the efficiency effect, we differentiate the social welfare function with respect to t c : dw dt c = (L 1 + L 2 )k [ 1 + H (z c ) ], (42) where k = (K 1 + K 2 )/(L 1 + L 2 ). In deriving this equation, we apply the fact that ε c = (dk/dt c )(t c /k) is equal to zero. 16 This is because the unified country is a closed economy, and thus a change in t c does not alter the capital allocation. The political effect is obtained by differentiating W κ with respect to t c, which gives dw κ [ ( ) ] k = (M 1 + M 2 )k + (1 α)h (z c ). (43) dt c k In deriving this equation, we apply the facts that ε c = 0 and dr/dt c = By inserting (42) and (43)into(41), we solve the equilibriummrs between z and x as follows: H c (z c) = 1 + θ 1 + αθ. (44) In deriving (44), we use the relationship that k/k = (L 1 + L 2 )/(M 1 + M 2 ) = (1 α)/α. One may notice that (44) is identical to (34), because when s 2 approaches unity, country 2 is essentially a closed economy. If we insert ˆθ into H c, then we obtain H c = s 2 s 1 s 2 (1 ε 1 ) s 1 (1 ε 2 ) + α(ε 1 ε 2 ). (45) The above equation is identical to (36), meaning that if θ = ˆθ, then the equilibria in the two regimes are the same in terms of the policy and welfare. The same tax rate set by the two countries in the non-cooperative equilibrium eliminates the incentive to reallocate capital across borders, and thus the two countries act as if they were a unified country. This explains the equivalence of the equilibria in the two regimes. We note that this result does not require the differences in country size to be large. Proposition 5 If θ = ˆθ, then (1) the non-cooperative equilibrium is symmetric, i.e., the two countries have the same tax rate and per capita utility level under the noncooperative equilibrium, and (2) the equilibrium policy and welfare of the two countries are identical under both the cooperative and the non-cooperative regimes. 16 This result can be seen from the equilibrium condition of the capital market, (L 1 +L 2 )k = (M 1 +M 2 ) k. Differentiating this equilibrium condition with respect to t c gives dk/dt c =[(M 1 + M 2 )/(L 1 + L 2 )] d k/dt c = Differentiating the first-order condition of the firm s profit maximization, f (k) = r + t c, with respect to t c gives dr/dt c = 1 + f kk (dk/dt c ).Sincedk/dt c = 0, dr/dt c is equal to 1.

18 Asymmetric tax competition in the presence of lobbying 83 In the case of symmetric tax competition, Wilson (1986) and Zodrow and Mieszkowski (1986) have shown that all countries are better off under the cooperative regime than under the non-cooperative regime. Proposition 5, however, indicates that their assertion is not true, if the symmetric non-cooperative equilibrium exists. Now we move on to the comparison between the cooperative equilibrium and the asymmetric non-cooperative equilibrium. Again we assume that the differences in country size are large in order to make a clear comparison. With this assumption, the following proposition shows that the smaller country can be better off with cooperation, which is quite different from the conventional result. Proposition 6 If the differences in country size are large enough, and θ>ˆθ, then the smaller country will have a higher per capita utility level with international cooperation than with tax competition. Proof See Appendix 3. The intuition behind Proposition 6 is as follows. In the cooperative equilibrium, the two countries set the same tax rate tc. In the non-cooperative equilibrium, with s 2 approaching unity, the larger country behaves the same as the unified country, so that t2 = t c. However, in the non-cooperative equilibrium, if θ>ˆθ, then according to Proposition 1, t1 is greater than t 2. Combining these relationships gives t 1 >t 2 = t c. This indicates that the smaller country will set a higher tax rate under non-cooperation than under cooperation. We can explain Proposition 6 in an alternative way. The smaller country chooses tc with cooperation. Under non-cooperation, the large level of MCPF of the capital tax leads the smaller country to set a tax rate that is lower than tc. On the other hand, as indicated previously, when s 1 is small enough, the policymaker in country 1 faces an upward political pressure in the non-cooperative equilibrium. We also note that the policymaker in the unified country encounters a downward political pressure, due to the absence of capital mobility. Other things being the same, the upward political pressure results in t1 >t c.ifθ is sufficiently large, then the latter force outweighs the former one, and t1 is greater than t c. Because of this, the smaller country attracts more capital inflow with cooperation, and thus it receives a higher per capita utility level relative to the non-cooperative regime. 18 Again, we are interested in comparing the per capita utility level of different types of resident under the two regimes. Let us consider the case in which θ>ˆθ. Since t1 >t c and t 2 = t c, the smaller country has a smaller amount of public good with cooperation. In addition, the private consumption of the capitalists in the smaller country remains the same under the two regimes, because of its small size. Combining the two results means that the capitalists in the smaller country are worse off with cooperation. Conversely, the relationship whereby t1 >t c ensures that the workers are 18 This result is not totally immediate. A unilateral tax reduction in country 1 reduces the public good on the one hand, but increases labor income through attracting capital inflow on the other. The capital income remains the same because s 1 approaches zero. Proposition 6 implies that the welfare gain from the increase in labor income outweighs the welfare loss from the reduction in the public good.

19 84 Y.-B. Lai better off with cooperation, because of the higher wage income arising from capital inflow. The result is reversed in the larger country. 6 Concluding remarks We incorporate lobbying into the model of asymmetric tax competition, and obtain results that are different from those in existing papers. First, we find that the smaller country does not necessarily set a lower capital tax rate than the larger country. Secondly, the smaller country may have a lower per capita utility than the larger country in the non-cooperative equilibrium. Thirdly, the larger country under-provides the public good, but the smaller country may provide the public good at the efficient level. Finally, international cooperation can enhance the smaller country s welfare. These results can be attributed to the political effect arising from lobbying. Since the capitalists in the smaller country can shift most or even all of the tax burden to the workers, they exert less downward political pressure on the capital tax rate than those in the larger country. If the political effect is dominant, then the smaller country sets a higher tax rate than the larger country. We have so far considered only the capitalists as being active in lobbying. Here we briefly discuss the case where only the workers lobby. The workers in the smaller country bear most of the capital tax burden, so they have a strong incentive to lobby for a lower tax rate. However, on the other hand, the workers in the larger country bear a smaller share of the tax burden than those in the smaller country; thus, they have a weaker incentive to lobby for a lower tax rate. Confronted by stronger downward political pressure and a larger MCPF of the capital tax, the smaller country sets a lower tax rate and receives a higher per capita utility level than the larger country. In the case where both the capitalists and workers engage in lobbying, since the two groups lobbying works in opposite directions, the result depends on the weights the policymaker attaches to the two groups lobbying. 19 If the two groups weights are equal, then the non-cooperative equilibrium policy is the same as the policy that maximizes each country s social welfare. 20 If the capitalists receive a larger weight, which seems more likely to occur according to daily observations, then the results in the text remain qualitatively unchanged. Acknowledgements I thank the editor Professor Eckhard Janeba and two anonymous referees for valuable comments and suggestions. I also thank the assistance from Peggy Chao. The remaining errors are the author s sole responsibility. Financial support from the National Science Council [Grant NSC H MY2] and National Chengchi University is gratefully acknowledged. Appendix 1: The proof of Proposition 1 As indicated in (27), the sign of φ 1 (t 1,t 2 ) is ambiguous. In what follows, we attempt to find the conditions that lead φ 1 (t 1,t 2 ) to be less than zero, which implies that t 1 is 19 Settings in which the policymaker attaches different weights to different interest groups can be found in, e.g., Hillman (1982), Bernheim and Whinston (1986), and Rama and Tabellini (1998). 20 A similar result can be found in Grossman and Helpman (1994).