Equilibrium Audit Strategies Against Tax Treaty Shopping Sunghoon Hong April 2019 Abstract This paper examines game-theoretic models of tax treaty shopping. An investor can choose a direct or indirect investment route across countries to minimize tax. A tax agency can audit the investor. The audit is costly but it can give additional revenue to the tax agency. In simultaneous-move games, regardless of whether incomplete information exists and whether a home country allows foreign tax credits, there are mixed-strategy equilibria where the investor may choose taxminimizing indirect routes and the tax agency may audit the investor. This equilibrium random audit strategy helps the tax agency raise revenue and reduce treaty shopping. Comparative statics yields an implication consistent with empirical evidence. However, if the home country has a foreign tax credit system with a high tax rate, or if the tax agency observes the investor s action in a sequential-move game, the investor always chooses the direct route, and no treaty shopping occurs in equilibrium. JEL classification: H25, H87, K34 Keywords: tax treaty shopping, tax-minimizing route, random audit, foreign tax credit, incomplete information I would like to thank Professor Myrna Wooders for her advice and encouragement. Korea Institute of Public Finance, 336 Sicheong-daero, Sejong 30147, South Korea, sunghoonhong@kipf.re.kr. 1
1 Introduction Tax treaty shopping, or simply treaty shopping, generally refers to the use of indirect investment structures through countries with beneficial tax treaties. 1 Multinational investors can remit profits to their home countries through taxminimizing indirect routes. Treaty shopping is considered to be an improper use of tax treaties, especially under the circumstances where obtaining treaty benefits is one of the principal purposes of using indirect investment structures. OECD (2015) emphasizes that treaty shopping is one of the most serious concerns regarding the Base Erosion and Profit Shifting (BEPS) project. In this paper, I develop game-theoretic models of treaty shopping and study equilibrium strategies of a tax agency and a multinational investor. The investor lives in a home country and plans to invest in a source country. From this investment the investor will earn dividend income in the source country and remit her income to the home country. The investor intends to minimize tax, i.e., to maximize her net-of-tax income, by choosing an investment route from home to source. The investor can choose a direct route or an indirect route, which may pass through intermediate entities established in countries with beneficial tax treaties. Meanwhile, the tax agency of the source country can choose to audit the investor to find out the investment route. The audit is costly. If the audit reveals that the investor chose an indirect route, the tax agency imposes a penalty tax. This situation can be viewed as a simultaneous-move game. In simultaneous-move games, regardless of whether incomplete information exists and whether the home country allows foreign tax credits, there are mixed-strategy equilibria where the tax agency audits the investor with positive probability and the investor chooses tax-minimizing indirect routes 1 For instance, a US multinational company, Corning, invested in a Korean manufacturer, Samsung Corning, through a Hungarian subsidiary, Corning Hungary Data Services Kft., where Kft. is a form of a Limited Liability Company (LLC) in Hungary. According to the Korea-US tax treaty, withholding tax rates on dividends are set at 10 or 15 percent depending on percentages of shares. However, the Korea-Hungary tax treaty sets the minimum withholding tax rate at 5 percent, and in Hungary, there is no withholding tax on dividends paid to non-residents. 2
with positive probability. Comparative statics shows an interesting implication about the relationship between foreign direct investment (FDI) and tax-minimizing direct routes, which is consistent with empirical evidence in Hong (2018). If the penalty tax rate is high enough, the equilibrium random audit strategy helps the tax agency increase revenue and decrease the probability of treaty shopping. When designing audit rules to counter treaty shopping, tax agencies may consider using the equilibrium random audit strategy with a high penalty tax rate. However, if the home country operates a foreign tax credit system with a relatively high tax rate, or if the tax agency observes the investor s action in a sequential-move game, the investor always chooses the direct route, and no treaty shopping occurs in equilibrium. The contribution of this paper is threefold. Broadly, this paper contributes to the economics of international taxation. In the literature, a central theme has been tax competition between countries, which can choose tax rates, as well as tax relief rules, such as foreign tax credit, deduction, and exemption systems. 2 Another important issue is to examine empirical relations between FDI and tax treaties. Blonigen and Davies (2004) examine the effects of tax treaties on FDI stocks in the United States, and discover substantial heterogeneity in treaty effects across countries. Hong (2018) and van t Riet and Lejour (2018) examine the structure of tax-minimizing investment routes in tax treaty networks. In addition, Hong (2018) finds a positive and significant relationship between FDI and tax-minimizing direct routes. Recently, increasing attention has been paid to international tax policies regarding the BEPS project. Dharmapala (2014) provides a survey of empirical studies to assess the magnitude of BEPS. 3 Bloch and Demange (2018) analyze efficient taxation and privacy protection on a monopolistic digital platform. 4 In contrast, this paper analyzes 2 For related studies, see Stöwhase (2013) and Eggert and Itaya (2014). Gauthier (2018) studies consumption tax competition in a trade model with home bias. 3 Regarding specific BEPS actions, Johannesen (2016) studies tax avoidance with debt financing. Behrens et al. (2014) examine transfer pricing regulation. 4 Kind and Koethenbuerger (2018) examine consumption taxes in a platform model. 3
the effects of tax treaties, tax relief systems, and incomplete information on strategic interactions between investors and tax agencies. More specifically, this paper contributes to the literature on treaty shopping and the ownership structures of multinational firms. This literature uses firm-level data to examine tax variables affecting ownership structures. Mintz and Weichenrieder (2010) show that there is a growing number of German firms organizing indirect ownership structures for foreign subsidiaries and suggest that treaty shopping is a main reason for indirect structures. Dyreng et al. (2015) examine indirect ownership structures of American multinational firms. Weyzig (2013) finds that reductions in withholding tax rates on dividends are significant determinants of FDI indirectly routed through the Netherlands. To the best of my knowledge, this paper is the first attempt to analyze strategic interactions in the context of treaty shopping. This paper also contributes to the theory of auditing. This literature has developed principal-agent models to examine optimal audit design. For instance, Mookherjee and Png (1989) analyze a model where a risk-averse agent has private information about her income and reports it to a riskneutral principal who then chooses to audit the agent at a cost. In their model, random audits turn out to be optimal because random audits can reduce expected costs without significantly distorting the agent s incentive to report truthfully. Border and Sobel (1987) also show the efficiency of random auditing in a model with a risk-neutral agent. These studies only deal with auditing against underreported income in a single jurisdiction. In contrast, this paper examines random audit strategies against tax planning techniques in a multi-jurisdictional setting. The rest of this paper is organized as follows. Section 2 develops a gametheoretic model of treaty shopping. Section 3 analyzes equilibrium behavior and random audit strategies. Section 4 extends the equilibrium analysis in various models. Section 5 concludes. 4
2 Model An investor, individual or corporate, plans to invest in country s but lives in country h. From this investment, the investor will earn income m R ++ as dividends in country s and remit her income to country h. Country s is called the source country. Country h is called the residence (or home) country. The investor intends to minimize tax when she remits her income to country h, i.e., the investor intends to maximize her net-of-tax income in the residence country. An investment route, or simply a route, is defined as a series of countries, h, i,..., j, s, from country h to country s. A route h, i,..., j, s is often written as h i j s when it is necessary to highlight the direction of the route. The investor chooses a route b. If b = h, s, she chooses the direct route h s. If b = h, i,..., j, s, she chooses an indirect route h i j s by using entities in countries i through j and making her investment indirectly through these entities. Countries i through j are called pass-through countries. When the investor remits her income from country s to country h, the remittance route follows the reverse order of the countries in the investment route. In the source country, a tax agency chooses an action a to audit the investor. If a = 1, the tax agency audits the investor. If a = 0, the tax agency does not. When auditing the investor, the tax agency incurs the audit cost c R ++. The tax agency and the investor know a corporate income tax (CIT) rate t i in country i and a withholding tax (WHT) rate t ij on dividends paid from an entity in country i to another entity in country j. Tax treaties determine WHT rates on dividends paid across countries. Let w(b) denote the withholding tax rate of a route b at source such that w(b) = t sh if b = h, s and w(b) = t sj if b = h, i,..., j, s. Let f(b) denote the foreign tax rate of a route b such that f(b) = t sh if b = h, s and f(b) = 1 (1 t sj )(1 t j ) (1 t i )(1 t ih ) if b = h, i,..., j, s. 5
When the investor chooses a route b, the net-of-tax income in country h is m(1 f(b))(1 t h ), and the tax revenue of country s is mw(b). Here I assume that country h has either a deduction or an exemption system. Later I will consider a foreign tax credit system in the residence country. 5 Let p R ++ and let p(a, b) denote the penalty tax rate of an action a and a route b such that p(a, b) = p if a = 1 and b = h, i,..., j, s and p(a, b) = 0 otherwise. If the investor chooses an indirect route and the tax agency audits the investor, the tax agency imposes the penalty tax mp. Otherwise, there is no penalty tax. The tax agency incurs the audit cost ca. To summarize, the payoff function of the tax agency (or player A) can be written as follows: u A (a, b) = mw(b) + mp(a, b) ca The payoff function of the investor (or player B) can be written as follows: u B (a, b) = m(1 f(b))(1 t h ) mp(a, b) The tax agency and the investor play a simultaneous-move game with complete information. Later I will consider a sequential-move game as well as a game with incomplete information. Let R(h, s) denote the set of all routes from country h to country s. A route b R(h, s) is tax-minimizing if for each b R(h, s), f(b ) f(b). The treaty shopping rate among routes from country h to country s is defined as t sh f(b ), the difference between the foreign tax rates of the direct route and a tax-minimizing route b. 3 Analysis In this section I analyze the (Nash) equilibrium of the model under the following assumptions: First, the direct route h s is not tax-minimizing, 5 These tax relief systems may affect the net-of-tax income of investors in home countries. Under deduction systems, foreign taxes are deducted as costs from taxable income before taxes are imposed by home countries. Under exemption systems, certain items of foreign-source income, such as dividends, are exempt from home country taxation. Under tax credit systems, foreign taxes are credited against tax liabilities in home countries. 6
i.e., there is a tax-minimizing indirect route b with f(b ) < t sh. Second, the audit cost is smaller than the penalty tax, i.e., c < mp. Third, the treaty shopping rate net of home country taxation is smaller than the penalty tax rate, i.e., (t sh f(b ))(1 t h ) < p. Remark 1. Under these assumptions, there is no pure-strategy equilibrium. If the tax agency audits, the investor s best response is to choose the direct route, because (t sh f(b ))(1 t h ) < p. If the investor chooses the direct route, the tax agency s best response is no audit, because c > 0. However, if the tax agency does not audit, the investor s best response is to choose a tax-minimizing indirect route, because the direct route is not tax-minimizing, and because any indirect route that is not tax-minimizing is dominated by a tax-minimizing indirect route. If the investor chooses a tax-minimizing indirect route, the tax agency s best response is to audit, because c < mp. Remark 2. If one of these assumptions is violated, the following purestrategy equilibrium exists: (i) If the direct route is tax-minimizing, there is an equilibrium where the tax agency chooses not to audit and the investor chooses the direct route. If the investor chooses the direct route, the tax agency s best response is no audit, because c > 0. Given no audit, the investor s best response is to choose the direct route, because the direct route is tax-minimizing. (ii) If the penalty tax is smaller than the audit cost, i.e., if mp < c, there is an equilibrium where the tax agency chooses not to audit and the investor chooses a tax-minimizing indirect route. Even if the investor chooses a taxminimizing indirect route, the tax agency s best response is no audit, because mp < c. Given no audit, the investor s best response is to choose a taxminimizing indirect route, because the direct route is not tax-minimizing, and because any indirect route that is not tax-minimizing is dominated by a tax-minimizing indirect route. (iii) If the penalty tax rate is smaller than the treaty shopping rate net of home country taxation, i.e., if p < (t sh f(b ))(1 t h ), there is an equilibrium 7
where the investor chooses a tax-minimizing indirect route, regardless of whether the tax agency audits the investor. If the tax agency does not audit, the investor s best response is to choose a tax-minimizing indirect route, because the direct route is not tax-minimizing, and because any indirect route that is not tax-minimizing is dominated by a tax-minimizing indirect route. Even if the tax agency audits, the investor s best response is to choose a tax-minimizing indirect route, because p < (t sh f(b ))(1 t h ). Now I characterize the equilibrium. Proposition 1. (i) If there is a unique tax-minimizing indirect route b, there is a unique equilibrium where the tax agency audits the investor with probability α = (t sh f(b ))(1 t h )/p and the investor chooses the indirect route b with probability β = c/mp. (ii) If there is more than one tax-minimizing indirect route, in equilibrium, β is the total probability of the investor choosing tax-minimizing indirect routes. The tax agency s equilibrium audit strategy remains the same. Proof. Because any indirect route that is not tax-minimizing is dominated by a tax-minimizing indirect route, in equilibrium, the investor will choose either the direct route or a tax-minimizing indirect route. Because there is no pure-strategy equilibrium, as in Remark 1, it is sufficient to show that each player is indifferent between the pure strategies played with positive probability in equilibrium. (i) Suppose there is a unique tax-minimizing indirect route b = h, i,..., j, s. Given α, the investor is indifferent between the direct route b and the taxminimizing indirect route b, since u B (α, b) = m(1 t sh )(1 t h ) = u B (α, b ). Given β, the tax agency is indifferent between no audit a = 0 and audit a = 1, since u A (0, β) = mt sh (c/p )(t sh t sj ) = u A (1, β). Thus, (α, β) characterizes a unique equilibrium. (ii) Suppose there are l 2 tax-minimizing indirect routes. Each of the taxminimizing indirect routes is denoted by b k = h, i k,..., j k, s, where k = 1,..., l, and is played with probability β k, where l k=1 β k = β. Given 8
(β 1,..., β l ), the tax agency is indifferent between no audit a = 0 and audit a = 1, because u A (0, (β 1,..., β l )) = mt sh l k=1 β km(t sh t sjk ) = u A (1, (β 1,..., β l )). Given α, the investor is indifferent between the direct route b and a tax-minimizing indirect route b k = h, i k,..., j k, s, because u B (α, b) = m(1 t sh )(1 t h ) = u B (α, b k ). Thus, (α, (β 1,..., β l )) characterizes a unique equilibrium. In equilibrium, the probability α of the tax agency auditing the investor is calculated with treaty shopping rate, home CIT rate, and penalty tax rate, and the probability β of the investor choosing tax-minimizing indirect routes is calculated with audit cost and penalty tax. The comparative statics of the unique equilibrium shows interesting implications. Remark 3. In equilibrium: (i) The audit probability α is increasing in the treaty shopping rate t sh f(b ), decreasing in the home CIT rate t h, decreasing in the penalty tax rate p, while independent of the income m. (ii) The indirect-route probability β is increasing in the audit cost c, decreasing in the income m, decreasing in the penalty tax rate p, while independent of the source WHT rate t sj. These equilibrium results are not in contradiction with the situation when the signing of a tax treaty induces more investment activity. Investors may choose the direct route more frequently to obtain the benefits of the new tax treaty, such as low or zero WHT rates. Remark 4. Proposition 1, as well as the comparative statics in Remark 3, holds when f(b ) < t sh, i.e., when the direct route is not tax-minimizing. In contrast, as Remark 2 (i) shows, when the direct route is tax-minimizing, the investor may choose the direct route with probability 1 in equilibrium. Thus, if home and source countries sign a new tax treaty to make the direct route tax-minimizing, the direct-route probability increases from 1 β to 1 as the new treaty enters into force. However, if the new treaty still makes an indirect route tax-minimizing, Remark 3 (ii) implies that the direct-route probability remains the same, because it is independent of the WHT rates. 9
Consistent with the implications in Remark 4, empirical studies show that the existence of a tax-minimizing direct route is positively and significantly related to FDI. For instance, Hong (2018) finds that the inward FDI stock via a tax-minimizing direct route is about 2.14 times larger than the inward FDI stock via a direct route that is not tax-minimizing. By subtracting the tax agency s equilibrium payoff from the maximum possible revenue, I compute the equilibrium loss of tax revenue in my model. 6 Remark 5. If there are l 1 tax-minimizing indirect routes, and if each tax-minimizing indirect route is played with equal probability (c/mp )(1/l) in equilibrium, the tax agency s payoff is mt sh (c/p )(1/l) l k=1 (t sh t sjk ), where j k is the last pass-through country in each tax-minimizing indirect route b k = h, i k,..., j k, s for k = 1,..., l. The tax agency s revenue would be mt sh if only the direct route was available to the investor. equilibrium loss of tax revenue is (c/p )(1/l) l k=1 (t sh t sjk ). Thus, the Note that t sjk < t sh for k = 1,..., l. Because b k is a tax-minimizing indirect route, f(b k ) < t sh. Because t sjk f(b k ), for k = 1,..., l, it holds that t sjk < t sh. Hence, the tax revenue loss in Remark 5 is positive. For countries h and s with l 1 tax-minimizing indirect routes, the tax rate spread is defined as (1/l) l k=1 (t sh t sjk ), the average difference of the WHT rates imposed by country s in the direct route and in the indirect routes. In country s, the tax agency can raise more revenue by adopting the equilibrium random audit strategy than by sticking to non-random strategies. Remark 6. When each tax-minimizing indirect route is played with equal probability, if the tax rate spread is smaller than the penalty tax rate, i.e., if (1/l) l k=1 (t sh t sjk ) < p, the tax agency raises more revenue by adopting the equilibrium random audit strategy than by sticking to nonrandom (pure) strategies. In equilibrium, the tax agency s payoff is mt sh 6 However, if a tax agency is expected to audit investors too frequently, investors may adjust their investment as well as their income, which is assumed to be given and fixed in my model. This adjustment may affect tax revenue loss as well. 10
(c/p )(1/l) l k=1 (t sh t sjk ), because each tax-minimizing indirect route is played with equal probability. To compare payoffs, consider two cases where the tax agency chooses pure strategies. First, suppose that the tax agency does not audit the investor at all, and knowing this, the investor always uses tax-minimizing indirect routes. In this case, the tax agency s payoff is (1/l) l k=1 mt sj k. This payoff is smaller than the equilibrium payoff because c < mp and t sjk < t sh for k = 1,..., l. Second, suppose that the tax agency always audits the investor, and knowing this, the investor always chooses the direct route. In this case, the tax agency s payoff is mt sh c, which is smaller than the equilibrium payoff, because (1/l) l k=1 (t sh t sjk ) < p. In both cases, the tax agency raises greater revenue by adopting the equilibrium audit strategy. In classical studies on random audits, e.g., Border and Sobel (1987) and Mookherjee and Png (1989), a taxpayer s avoidance technique is based on income underreporting. In this paper, the tax avoidance technique is based on indirect routing, i.e., treaty shopping. Even if the investor reports her income truthfully, she can still use a tax-minimizing indirect route. To deal with this situation, the tax agency can adopt a random audit rule with a sufficiently high penalty tax rate and raise more revenue. To counter treaty shopping, a number of countries have introduced limitation on benefits (LOB) and principal purpose test (PPT) provisions in tax treaties. 7 These treaty provisions give tax agencies the discretion to audit foreign investors who receive treaty benefits. When designing discretionary audit rules, tax agencies may consider using the equilibrium random audit strategy with a high penalty tax rate. 7 OECD (2015) discusses the development of LOB and PPT provisions. Under the LOB provision, tax agencies have the discretion to deny treaty benefits unless foreign investors meet certain residency requirements. Under the PPT provision, tax agencies have the discretion to deny treaty benefits if they reasonably conclude that obtaining the treaty benefits is one of the principal purposes of using indirect transaction structures. 11
4 Extension In this section I examine the equilibria of the models that incorporate foreign tax credit, sequential movement, and incomplete information. 4.1 Foreign tax credit Under a foreign tax credit system in country h, the investor s net-of-tax income is determined by the greater of the foreign tax rate f(b) and the home CIT rate t h. The payoff function of the investor (or player B) is given as follows: u B (a, b) = m(1 max{f(b), t h }) mp(a, b) If f(b) t h, foreign taxes are no greater than domestic tax liabilities, and thus, the investor pays m(t h f(b)) in country h and mf(b) in countries along the investment route b. The investor s net-of-tax income is m(1 t h ). However, if t h < f(b), foreign taxes are greater than domestic tax liabilities, and thus, the investor pays no tax in country h. The investor s net-of-tax income is m(1 f(b)). The following proposition shows equilibrium behavior under a foreign tax credit system. Proposition 2. Suppose that country h operates a foreign tax credit system. (i) If t sh t h, there is an equilibrium where the tax agency of country s chooses no audit and the investor chooses the direct route. (ii) If t h < t sh, there is an equilibrium where the tax agency audits the investor with probability (t sh max{f(b ), t h })/p and the investor chooses tax-minimizing indirect routes with probability c/mp. Proof. (i) Because t sh t h, if the investor chooses the direct route, the investor s payoff is m(1 t h ). However, if the investor chooses an indirect route b, the investor s payoff is at most m(1 max{f(b), t h }), which is obtained when the tax agency does not audit the investor. Because t h max{f(b), t h }, regardless of whether the tax agency audits the investor, it is a best response for the investor to choose the direct route. Given the investor s direct route, 12
the tax agency s best response is to choose no audit. Thus, there is an equilibrium where the tax agency chooses no audit and the investor chooses the direct route. (ii) To show the mixed-strategy equilibrium, it is sufficient to show that each player is indifferent between the pure strategies played with positive probability. Suppose there are l 1 tax-minimizing indirect routes. Each of the tax-minimizing indirect routes is denoted by b k = h, i k,..., j k, s, where k = 1,..., l, and is played with probability β k, where l k=1 β k = c/mp. Given (β 1,..., β l ), the tax agency is indifferent between no audit a = 0 and audit a = 1, because u A (0, (β 1,..., β l )) = mt sh l k=1 β km(t sh t sjk ) = u A (1, (β 1,..., β l )). Given the audit probability α = (t sh max{f(b ), t h })/p, if the investor chooses the direct route b, the payoff is u B (α, b) = m(1 max{f(b), t h }) = m(1 t sh ), because f(b) = t sh and t h < t sh. If the investor chooses a tax-minimizing indirect route b k, the payoff is u B (α, b k ) = m(1 t sh ). Thus, the investor is indifferent between the direct route b and a taxminimizing indirect route b k. Hence, (α, (β 1,..., β l )) is an equilibrium. If t sh t h, in the equilibrium of Proposition 2 (i), no treaty shopping occurs, and the source country earns the maximum possible tax revenue without incurring the audit cost. However, the residence country earns tax revenues reduced by foreign tax credits given to the investor. If t h < t sh, in the equilibrium of Proposition 2 (ii), the investor chooses tax-minimizing indirect routes with positive probability, and the source country earns less tax revenue due to treaty shopping. Moreover, the residence country earns zero tax revenue when foreign tax credits exceed domestic tax liabilities. Treaty shopping can be prevented by foreign tax credit systems in residence countries with relatively high CIT rates. When no treaty shopping occurs, source countries earn maximum possible tax revenue. However, this comes at the cost of tax credits given by residence countries. Source countries benefit from foreign tax credit systems in the residence countries that pay for the cost of the systems. Without overcoming such free-rider problems be- 13
tween countries, it may be difficult to sustain foreign tax credit systems in residence countries. Recently, major capital-exporting countries, i.e., investors residence countries, such as the United States, Japan, Germany, France, and the United Kingdom, have abolished tax credits for certain foreign-source dividends to introduce deduction or exemption systems. 4.2 Sequential movement Tax agencies often obtain certain information about investment structures. For instance, if a company s financial statements show that dividends are paid directly to entities in the residence country, tax agencies may presume that investors use direct investment structures and can choose not to audit. If dividends are paid to entities in countries other than the residence country, tax agencies may presume that investors use indirect investment structures and can choose to audit. This situation can be thought of as a two-stage (sequential-move) game between a tax agency and an investor. In the first stage, the investor chooses a direct or indirect investment route. In the second stage, the tax agency knows whether or not the investor chose the direct route and chooses whether to audit. 8 Nash) equilibrium of this two-stage game. I present the (subgame perfect Proposition 3. In the two-stage game where the investor moves first, there is a unique equilibrium where the investor chooses the direct route and the tax agency selectively audits the investor who chose an indirect route. Proof. The unique equilibrium is constructed by backward induction. Because the tax agency knows whether or not the investor chose the direct route, there are two subgames in the second stage. In the subgame after the investor chose the direct route, the tax agency earns a greater payoff by choosing not to audit, because c > 0. In the subgame after the investor chose an indirect route, the tax agency earns a greater payoff by auditing 8 Even if the tax agency knows that the investor chose an indirect route, the tax agency may still have to conduct an audit to gather sufficient evidence to impose a penalty tax. 14
the investor, because c < mp. Thus, in the second stage, the tax agency selectively audits the investor who chose an indirect route. By backward induction, in the first stage, if the investor chooses the direct route, the payoff is m(1 t sh )(1 t h ). If the investor chooses an indirect route, the payoff is at most m(1 f(b ))(1 t h ) mp, which is obtained when the investor chooses a tax-minimizing indirect route b. In the first stage, because (t sh f(b ))(1 t h ) < p, the investor earns a greater payoff by choosing the direct route. Therefore, in the unique equilibrium of the two-stage game, the investor chooses the direct route and the tax agency selectively audits the investor who chose an indirect route. In the two-stage game, the tax agency enjoys the second mover s advantage by observing whether or not the investor chose the direct route. In the unique equilibrium, the tax agency can prevent treaty shopping by selectively auditing the investor who did not choose the direct route. 4.3 Incomplete information So far I assumed complete information. But what if the tax agency and the investor face incomplete information about each other s type? In reality, the tax agency may not know the investor s residence country, and the investor may not know the tax agency s audit cost. In these circumstances, are random audit rules supported as equilibrium strategies? Let us consider a game with incomplete information. The investor s type is determined by her residence country h {1, 2}. The direct route is not tax-minimizing from residence country 1 to source country s. The direct route is tax-minimizing from residence country 2 to source country s. A strategy of the investor, denoted by b( ), is a function mapping each type h to a route b(h). The tax agency s type is determined by the audit cost c {c L, c H }, where c L < c H. A strategy of the tax agency, denoted by a( ), is a function mapping each type c to an action a(c) {0, 1}. The investor knows her own type h {1, 2} but the tax agency may 15
not know the investor s type. The tax agency has subjective beliefs about the investor s type, described by a probability distribution π. The investor s residence country is h with probability π h. The tax agency knows its own type c {c L, c H } but the investor may not know the tax agency s type. The investor has subjective beliefs about the tax agency s type, described by a probability distribution φ. The tax agency s audit cost is c L with probability φ L and c H with probability φ H. Given a probability distribution π and a type c, the payoff function of the tax agency (or player A) is defined as follows: u A (a( ), b( ); c) = E π [mw(b( )) + mp(a(c), b( )) ca(c)] Given a probability distribution φ and a type h, the payoff function of the investor (or player B) is defined as follows: u B (a( ), b( ); h) = E φ [m(1 f(b(h)))(1 t h ) mp(a( ), b(h))] I analyze (Bayesian Nash) equilibrium strategies under two assumptions. First, the low audit cost is smaller than the expected penalty tax when indirect routes are chosen only by the investor of country 1, i.e., c L < π 1 mp. Second, the treaty shopping rate net of home country taxation is smaller than the penalty tax rate discounted by the probability of the low audit cost, i.e., (t s1 f(b ))(1 t 1 ) < φ L p, where b is a tax-minimizing route from 1 to s. The following results are comparable with the equilibria of the model in Section 3. All proofs are presented in the Appendix. Remark 7. Under the assumptions, there is no pure-strategy equilibrium. Remark 8. If one of the assumptions is violated, the following equilibrium exists: (i) If π 1 mp < c L, there is an equilibrium where the tax agency of each type chooses not to audit, the investor of country 1 chooses a tax-minimizing indirect route, and the investor of country 2 chooses the direct route. (ii) If c L < π 1 mp < c H and φ L p < (t s1 f(b ))(1 t 1 ), there is an equilibrium where the tax agency of type c L chooses to audit, the tax agency of type 16
c H chooses not to audit, the investor of country 1 chooses a tax-minimizing indirect route, and the investor of country 2 chooses the direct route. (iii) If c H < π 1 mp and φ L p < (t s1 f(b ))(1 t 1 ) < p, there is an equilibrium where the tax agency of type c L audits for sure, the tax agency of type c H audits with probability ((t s1 f(b ))(1 t 1 ) φ L p )/φ H p, the investor of country 1 chooses tax-minimizing indirect routes with probability c H /π 1 mp, and the investor of country 2 chooses the direct route for sure. (iv) If c H < π 1 mp and p < (t s1 f(b ))(1 t 1 ), there is an equilibrium where the tax agency of each type chooses to audit, the investor of country 1 chooses a tax-minimizing indirect route, and the investor of country 2 chooses the direct route. Proposition 4. There is an equilibrium where (i) the tax agency of the low cost type c L audits the investor with probability (t s1 f(b ))(1 t 1 )/φ L p, (ii) the tax agency of the high cost type c H chooses no audit for sure, (iii) the investor of country 1 chooses tax-minimizing indirect routes with probability c L /π 1 mp, and (iv) the investor of country 2 chooses the direct route for sure. In the equilibrium of Proposition 4, for the tax agency of the low cost type, the audit probability is calculated with treaty shopping rate, home CIT rate, penalty tax rate, and the probability of the low cost type. For the investor of the country with tax-minimizing indirect routes, the indirectroute probability is calculated with audit cost, income, penalty tax rate, and the probability of the country with tax-minimizing indirect routes. As Remark 8 and Proposition 4 show, the indirect-route probability is minimized in the equilibrium of Proposition 4, which exists under the assumptions that c L < π 1 mp and (t s1 f(b ))(1 t 1 ) < φ L p. Under (i), (ii), and (iv) of Remark 8, the investor of the country with tax-minimizing indirect routes uses such routes for sure in equilibrium. Under (iii), the investor uses such routes with probability c H /π 1 mp, which is greater than the equilibrium probability c L /π 1 mp of Proposition 4. Therefore, to minimize the probability of using tax-minimizing indirect routes, the tax agency can 17
set up a penalty tax rate p satisfying the assumptions of Proposition 4. This penalty tax rate can be thought of as an optimal rate for the tax agency of the source country because it minimizes the probability of treaty shopping. 5 Conclusion In this paper I develop game-theoretic models of treaty shopping and analyze equilibrium strategies. In simultaneous-move games, regardless of whether incomplete information exists and whether a home country allows foreign tax credits, there are mixed-strategy equilibria where an investor chooses tax-minimizing indirect routes with positive probability and a tax agency audits the investor with positive probability. This equilibrium random audit strategy helps the tax agency increase revenue and decrease the probability of treaty shopping. However, if the home country operates a foreign tax credit system with a relatively high tax rate, or if the tax agency observes the investor s action in a sequential-move game, the investor always chooses the direct route, and no treaty shopping occurs in equilibrium. For future studies, it will be important to examine foreign tax credit systems from the perspectives of capital exporting or investors residence countries. Foreign tax credit systems can help prevent treaty shopping but may also be vulnerable to other tax planning techniques, such as foreign tax credit generators, unfairly reducing tax revenue in residence countries. In an extended model, residence countries may choose tax relief systems to maximize their own revenue, and then investors and source countries may play the game of treaty shopping and tax auditing. It will also be interesting to study a model where an investor can choose a destination of investment. In this paper, given a pair of residence and source (destination) countries, an investor chooses a direct or indirect route. However, if the tax agency of the source country is expected to be aggressive, or to audit frequently, the investor may want to adjust her destination. Moreover, expecting this adjustment, the tax agency may have to be more accommodating toward the investor who uses a tax-minimizing indirect route. 18
Appendix Proof of Proposition 4. This proof proceeds in five steps. Step 1. For the investor of type h = 2, it is weakly dominant to choose the direct route. Let b (2) = 2, s be the direct route. Because the direct route is tax-minimizing from 2 to s, for each b R(2, s), f(b (2)) f(b). For each b R(2, s) with b b (2), if a(c) = 0, then p(a(c), b (2)) = p(a(c), b) = 0 and u B (a(c), b; 2) u B (a(c), b (2); 2). If a(c) = 1, then p(a(c), b (2)) = 0 < p = p(a(c), b) and u B (a(c), b; 2) < u B (a(c), b (2); 2). Step 2. Suppose that the investor of type h = 2 chooses the direct route for sure. Also, suppose that the investor of type h = 1 chooses tax-minimizing indirect routes with probability c L /π 1 mp. Let b ( ) denote such a strategy. Given b ( ), the tax agency of type c H chooses not to audit. Let a (c H ) = 0 and a(c H ) = 1. Given b ( ), u A (a (c H ), b ( ); c H ) = E π [mw(b ( ))]. Also, u A (a(c H ), b ( ); c H ) = E π [mw(b ( ))] + E π [mp(a(c H ), b ( ))] c H. Because E π [mp(a(c H ), b ( ))] = c L and c L < c H, it holds that u A (a(c H ), b ( ); c H ) < u A (a (c H ), b ( ); c H ). Step 3. For the investor of type h = 1, it is dominated to choose an indirect route that is not tax-minimizing. Let b(h) = b denote such a route. Note that there is a tax-minimizing indirect route b = 1, i,..., j, s with f(b ) < t s1. Let b (h) = b. Because b and b are indirect routes, for each a(c) {0, 1}, p(a(c), b) = p(a(c), b ). Because b is tax-minimizing but b is not, f(b ) < f(b). Thus, for each a(c) {0, 1} and for type h = 1, it holds that u B (a(c), b; h) < u B (a(c), b ; h). Step 4. Suppose that there are l 1 tax-minimizing indirect routes from country 1 to country s. Each of such routes is denoted by b k = 1, i k,..., j k, s with k = 1,..., l, and is played with probability q k, where l k=1 q k = c L /π 1 mp. Let (a ( ), b ( )) denote the strategy profile specified as follows: 1 with probability (t s1 f(b ))(1 t 1 )/φ L p for c = c L a (c) = 0 with probability 1 (t s1 f(b ))(1 t 1 )/φ L p for c = c L 0 with probability 1 for c = c H 19
b k with probability q k for h = 1 b (h) = 1, s with probability 1 l k=1 q k for h = 1 2, s with probability 1 for h = 2 Given the investor s strategy b ( ), for type c L, E π [mp(1, b ( ))] = c L and u A (1, b ( ); c L ) = E π [mw(b ( ))]. Also, u A (0, b ( ); c L ) = E π [mw(b ( ))]. Thus, the tax agency of type c L is indifferent between a (c L ) = 1 and a (c L ) = 0. Given the tax agency s strategy a ( ), for type h = 1, it holds that u B (a ( ), b k ; h) = m(1 t s1 )(1 t 1 ) = u B (a ( ), h, s; h). Hence, the investor of type h = 1 is indifferent between b (h) = b k and b (h) = h, s. Step 5. From Step 1, it is weakly dominant for the investor of type h = 2 to choose the direct route. Thus, regardless of what the tax agency does, the investor of type h = 2 will choose the direct route, as specified in b ( ). Given b ( ), from Step 2, the tax agency of type c H will choose no audit, as specified in a ( ). Because it is dominated for the investor of type h = 1 to choose an indirect route that is not tax-minimizing, from Step 3, the investor of type h = 1 will only choose either the direct route or a tax-minimizing indirect route. By choosing the mixed strategy specified in Step 4, each player makes the other player indifferent between the actions played with positive probability. Therefore, (a ( ), b ( )) is an equilibrium. Proof of Remark 7. Because a(c) {0, 1} for c {c L, c H }, there are four pure strategies for the tax agency. Let a 1 ( ) denote the strategy such that a 1 (c L ) = 0 and a 1 (c H ) = 0. Let a 2 ( ) denote the strategy such that a 2 (c L ) = 0 and a 2 (c H ) = 1. Let a 3 ( ) denote the strategy such that a 3 (c L ) = 1 and a 3 (c H ) = 0. Let a 4 ( ) denote the strategy such that a 4 (c L ) = 1 and a 4 (c H ) = 1. This proof is divided into four cases. Case 1. Suppose that the tax agency chooses a 1 ( ). Given a 1 ( ), to maximize her expected payoff, the investor chooses a tax-minimizing indirect route when she is of type h = 1 and chooses the direct route when she is of type h = 2. Let b 0 ( ) denote such a strategy. Because b 0 ( ) is the best response to a 1 ( ), (a 1 ( ), b 0 ( )) is the only strategy profile that can be 20
an equilibrium. Given b 0 ( ), if the tax agency chooses a 1 ( ), for type c L, u A (a 1 ( ), b 0 ( ); c L ) = E π [mw(b 0 ( ))]. If the tax agency chooses a 3 ( ), for type c L, u A (a 3 ( ), b 0 ( ); c L ) = E π [mw(b 0 ( ))] + E π [mp(1, b 0 ( ))] c L. Because E π [mp(1, b 0 ( ))] = π 1 mp and c L < π 1 mp, it holds that u A (a 1 ( ), b 0 ( ); c L ) < u A (a 3 ( ), b 0 ( ); c L ). Thus, a 1 ( ) is not a best response to b 0 ( ), and (a 1 ( ), b 0 ( )) is not an equilibrium. Case 2. Suppose that the tax agency chooses a 2 ( ). By way of contradiction, suppose that for some b( ), (a 2 ( ), b( )) is an equilibrium. For type c H, u A (a 2 ( ), b( ); c H ) = E π [mw(b( ))]+E π [mp(1, b( ))] c H and u A (0, b( ); c H ) = E π [mw(b( ))]. Because (a 2 ( ), b( )) is an equilibrium, u A (a 2 ( ), b( ); c H ) u A (0, b( ); c H ), which implies E π [mp(1, b( ))] c H. Because c L < c H, c L < E π [mp(1, b( ))]. However, for type c L, u A (a 2 ( ), b( ); c L ) = E π [mw(b( ))] and u A (1, b( ); c L ) = E π [mw(b( ))] + E π [mp(1, b( ))] c L. Because (a 2 ( ), b( )) is an equilibrium, it must be that u A (a 2 ( ), b( ); c L ) u A (1, b( ); c L ), which implies that E π [mp(1, b( ))] c L. This is a contradiction. Thus, there is no b( ) for which (a 2 ( ), b( )) is an equilibrium. Case 3. Suppose that the tax agency chooses a 3 ( ). Given a 3 ( ), to maximize her expected payoff, the investor always chooses the direct route regardless of her type. This is because (t s1 f(b ))(1 t 1 ) < φ L p implies that, for the investor of type h = 1, u B (a 3 ( ), b ; 1) = m(1 f(b ))(1 t 1 ) φ L mp < m(1 t s1 )(1 t 1 ) = u B (a 3 ( ), 1, s; 1). For the investor of type h = 2, the direct route is tax-minimizing with no risk of the penalty tax. Let b 1 ( ) denote the strategy that the investor always chooses the direct route. Because b 1 ( ) is the best response to a 3 ( ), (a 3 ( ), b 1 ( )) is the only strategy profile that can be an equilibrium. Given b 1 ( ), if the tax agency chooses a 3 ( ), for type c L, the expected payoff is u A (a 3 ( ), b 1 ( ); c L ) = E π [mt sh ] c L. If the tax agency chooses a 1 ( ), for type c L, the expected payoff is u A (a 1 ( ), b 1 ( ); c L ) = E π [mt sh ]. Thus, a 3 ( ) is not a best response to b 1 ( ), and (a 3 ( ), b 1 ( )) is not an equilibrium. Case 4. Suppose that the tax agency chooses a 4 ( ). Because the tax agency of each type audits the investor, as in Case 3, b 1 ( ) is the best response to 21
a 4 ( ). However, a 4 ( ) is not a best response to b 1 ( ), and (a 4 ( ), b 1 ( )) is not an equilibrium. Proof of Remark 8. This proof is divided into four parts. (i) Assume π 1 mp < c L. Let a 1 ( ) be the strategy that the tax agency of each type chooses no audit. Let b 0 ( ) be the strategy that the investor of country 1 chooses a tax-minimizing indirect route and the investor of country 2 chooses the direct route. Show that (a 1 ( ), b 0 ( )) is an equilibrium. Let a 1 ( ) be given. Because the tax agency of each type chooses not to audit at all, the investor of country 1 can maximize her payoff by choosing a tax-minimizing indirect route and the investor of country 2 can maximize her payoff by choosing the direct route. Thus, for the investor, b 0 ( ) is a best response to a 1 ( ). Let b 0 ( ) be given. Because π 1 mp < c L and c L < c H, when the investor of country 1 chooses an indirect route and the investor of country 2 chooses the direct route, the tax agency of each type can maximize its payoff by not auditing. Thus, for the tax agency, a 1 ( ) is a best response to b 0 ( ). Therefore, (a 1 ( ), b 0 ( )) is an equilibrium. (ii) Assume c L < π 1 mp < c H and φ L p < (t s1 f(b ))(1 t 1 ). Let a 3 ( ) be the strategy that the tax agency of type c L chooses to audit and the tax agency of type c H chooses not to audit. Let b 0 ( ) be the strategy that the investor of country 1 chooses a tax-minimizing indirect route and the investor of country 2 chooses the direct route. Show that (a 3 ( ), b 0 ( )) is an equilibrium. Let a 3 ( ) be given. For the investor of country 1, it is dominated to choose an indirect route that is not tax-minimizing, as shown in the proof of Proposition 4. Also, because φ L p < (t s1 f(b ))(1 t 1 ), it holds that u B (a 3 ( ), 1, s; 1) = m(1 t s1 )(1 t 1 ) < m(1 f(b ))(1 t 1 ) φ L mp = u B (a 3 ( ), b ; 1). Thus, the investor of country 1 earns a greater payoff by choosing a tax-minimizing indirect route b than by choosing the direct route. Moreover, for the investor of country 2, it is weakly dominant to choose the direct route, as in the proof of Proposition 4. Thus, for the investor, b 0 ( ) is a best response to a 3 ( ). Let b 0 ( ) be given. Because c L < π 1 mp, u A (0, b 0 ( ); c L ) = E π [mw(b 0 ( ))] < E π [mw(b 0 ( ))] + π 1 mp c L = 22
u A (1, b 0 ( ); c L ). Thus, the tax agency of type c L earns a greater payoff by auditing. However, because π 1 mp < c H, the tax agency of type c H earns a greater payoff by not auditing. Thus, for the tax agency, a 3 ( ) is a best response to b 0 ( ). Therefore, (a 3 ( ), b 0 ( )) is an equilibrium. (iii) Assume c H < π 1 mp and φ L p < (t s1 f(b ))(1 t 1 ) < p. Let a ( ) be the strategy that the tax agency of type c L audits for sure and the tax agency of type c H audits with probability α = ((t s1 f(b ))(1 t 1 ) φ L p )/φ H p. Let b ( ) be the strategy that the investor of country 1 chooses tax-minimizing indirect routes with probability β = c H /π 1 mp and the investor of country 2 chooses the direct route for sure. Show that (a ( ), b ( )) is an equilibrium. Let a ( ) be given. As in the proof of Proposition 4, the investor of country 1 chooses either the direct route 1, s or a tax-minimizing indirect route b. Because E φ [mp(a ( ), b )] = φ L mp + φ H αmp = m(t s1 f(b ))(1 t 1 ), it holds that u B (a ( ), 1, s; 1) = m(1 t s1 )(1 t 1 ) = u B (a ( ), b ; 1). Thus, the investor of country 1 is indifferent between 1, s and b. Moreover, for the investor of country 2, it is weakly dominant to choose the direct route. Thus, for the investor, b ( ) is a best response to a ( ). Let b ( ) be given. For the tax agency of type c, because E π [mp(1, b ( ))] = π 1 βmp = c H, u A (1, b ( ); c) = E π [mw(b ( ))] + c H c. Because u A (0, b ( ); c) = E π [mw(b ( ))], the tax agency of type c L prefers audit, and the tax agency of type c H is indifferent between audit and no audit. Thus, for the tax agency, a ( ) is a best response to b ( ). Therefore, (a ( ), b ( )) is an equilibrium. (iv) Assume c H < π 1 mp and p < (t s1 f(b ))(1 t 1 ). Let a 4 ( ) be the strategy that the tax agency of each type chooses to audit. Let b 0 ( ) be the strategy that the investor of country 1 chooses a tax-minimizing indirect route and the investor of country 2 chooses the direct route. Show that (a 4 ( ), b 0 ( )) is an equilibrium. Let a 4 ( ) be given. For the investor of country 1, it is dominated to choose an indirect route that is not tax-minimizing, as shown in the proof of Proposition 4. Also, because p < (t s1 f(b ))(1 t 1 ), it holds that u B (a 4 ( ), 1, s; 1) = m(1 t s1 )(1 t 1 ) < m(1 f(b ))(1 t 1 ) mp = u B (a 4 ( ), b ; 1). Thus, the investor of country 1 earns a greater payoff by 23
choosing a tax-minimizing indirect route b than by choosing the direct route. Moreover, for the investor of country 2, it is weakly dominant to choose the direct route, as in the proof of Proposition 4. Thus, for the investor, b 0 ( ) is a best response to a 4 ( ). Let b 0 ( ) be given. Because c L < c H and c H < π 1 mp, u A (0, b 0 ( ); c L ) = E π [mw(b 0 ( ))] < E π [mw(b 0 ( ))] + π 1 mp c L = u A (1, b 0 ( ); c L ). Thus, the tax agency of type c L earns a greater payoff by auditing. Similarly, because c H < π 1 mp, the tax agency of type c H earns a greater payoff by auditing. Thus, for the tax agency, a 4 ( ) is a best response to b 0 ( ). Therefore, (a 4 ( ), b 0 ( )) is an equilibrium. References [1] Behrens, K., Peralt, S., & Picard, P. M. (2014). Transfer pricing rules, OECD guidelines, and market distortions. Journal of Public Economic Theory, 16, 650 680. [2] Border, K. C., & Sobel, J. (1987). Samurai accountant: A theory of auditing and plunder. Review of Economic Studies, 54, 525 540. [3] Bloch, F., & Demange, G. (2018). Taxation and privacy protection on internet platforms. Journal of Public Economic Theory, 20, 52 66. [4] Blonigen, B. A., & Davies, R. B. (2004). The effects of bilateral tax treaties on U.S. FDI activity. International Tax and Public Finance, 11, 601 622. [5] Dharmapala, D. (2014). What do we know about Base Erosion and Profit Shifting? A review of the empirical literature. Fiscal Studies, 35, 421 448. [6] Eggert, W., & Itaya, J.-I. (2014). Tax rate harmonization, renegotiation, and asymmetric tax competition for profits with repeated interaction. Journal of Public Economic Theory, 16, 796 823. [7] Gauthier, S. (2018). Efficient tax competition under the origin principle. Journal of Public Economic Theory, 20, 85 99. 24