Lecture on Tax Competition (3) PDF

Countries tend to set tax rates non-cooperatively leading to tax competition Is this good or bad?  Tax competition is bad if it leads to international tax divergence, for instance a low tax rate in a small country. This leads to misallocation of capital if both countries use source-based taxati...

Countries tend to set tax rates non-cooperatively leading to tax competition Is this good or bad?  Tax competition is bad if it leads to international tax divergence, for instance a low tax rate in a small country. This leads to misallocation of capital if both countries use source-based taxation  It is bad if it leads to a relatively high combined tax rate on cross- border activity. This also leads to misallocation of the factors of production. Therefore, in practice there tends to be alleviation of international double taxation  It is bad if it leads to tax revenues that are too low to finance public goods adequately. Tax competition can be a threat to redistribution and the welfare state  It is good if it prevents tax revenues from getting too high if tax revenues tend to be wasted by politicians 1 Papers by Feldstein and Hartman (1979) and by Bond and Samuelson (1989) are about the second point. Specifically, they are about the relative merits of deductions and foreign tax credits as ways of alleviating international double taxation of cross- border income flows. We consider these papers in turn. 2 Paper by Feldstein and Hartman (1979) Main options to alleviate international double taxation are a foreign tax credit and a deduction:  Foreign tax credit: foreign taxes are deducted from the domestic tax liability  Deduction: foreign taxes are deducted from domestic taxable income For given tax rates, a foreign tax credit is more generous towards tax payers. Regarding the choice between these two options, we take the perspective of the domestic tax authority of a multinational firm. 3 The model  There is a single domestic multinational firm that owns a capital amount 𝐾 ̅  The multinational firm has a domestic plant and a foreign plant, and ̅ , between domestic capital, 𝐾, and foreign divides overall capital, 𝐾 capital 𝐾 ∗  Output at the domestic plant is given by the following production function: 𝑓(𝐾), with 𝑓𝐾 (𝐾) > 0, and 𝑓𝐾𝐾 (𝐾) < 0 Thus, there is a decreasing marginal product of capital  Similarly, output abroad is given by a potentially different production function𝑓 ∗ (𝐾 ∗ ) also with a decreasing marginal product of capital 4 Tax variables  𝜃 ∗ ∶ foreign tax rate  𝜃 𝑠 : domestic tax rate applicable to foreign income after foreign taxes  𝛾: credit parameter: share of foreign taxes returned to the firm by the domestic tax authority in the form of a foreign tax credit  𝜃: domestic tax rate applicable to domestic income 5 The domestic tax authority has to determine the international tax parameters 𝜃 𝑠 and 𝛾. In doing so, it takes the regular domestic tax rate 𝜃 and the foreign tax rate 𝜃 ∗ as given. 6 We first consider the multinational’s problem of allocating capital between the two countries  The after-tax marginal product of domestic capital is: (1 − 𝜃)𝑓𝐾 (𝐾)  The after-tax marginal product of foreign capital is: [(1 − 𝜃 𝑠 )(1 − 𝜃 ∗ ) + 𝛾𝜃 ∗ ]𝑓𝐾∗ (𝐾 ∗ ) where 𝑓𝐾∗ (𝐾) is the marginal product of capital at the foreign plant  To maximize after-tax worldwide profits, the firm sets the two after- tax marginal products equal to each other as follows: (1 − 𝜃)𝑓𝐾 (𝐾 ) = [(1 − 𝜃 𝑠 )(1 − 𝜃 ∗ ) + 𝛾𝜃 ∗ ]𝑓𝐾∗ (𝐾 ∗ ) 7 Next, we consider how the domestic tax authority sets the foreign tax parameters 𝜃 𝑠 and 𝛾  One option is a deduction. In particular, note that a deduction can be implemented by setting 𝜃 = 𝜃 𝑠 and 𝛾 = 0 as then: (1 − 𝜃 𝑠 )(1 − 𝜃 ∗ ) + 𝛾𝜃 ∗ = (1 − 𝜃)(1 − 𝜃 ∗ )  Alternatively, the domestic tax authority can implement a foreign tax credit by setting 𝜃 𝑠 and 𝛾 so that (1 − 𝜃 𝑠 )(1 − 𝜃 ∗ ) + 𝛾𝜃 ∗ = 1 − 𝜃 8 In the case of a foreign tax credit, after-tax profit maximization by the firm implies 𝑓𝐾 (𝐾 ) = 𝑓𝐾∗ (𝐾 ∗ )  This is a necessary condition for an efficient allocation of capital in the world as this condition is consistent with maximizing world output given by 𝑓(𝐾 ) + 𝑓 ∗ (𝐾 ∗ )  Is the foreign tax credit also optimal from the perspective of the domestic country? 9 The domestic tax authority chooses its tax parameters 𝜃 𝑠 and 𝛾 so as to maximize domestic national income given by 𝑁 = 𝑓 (𝐾 ) + (1 − 𝜃 ∗ )𝑓 ∗ (𝐾 ∗ ) ̅ − 𝐾 ∗ , this becomes After substituting for 𝐾 = 𝐾 ̅ − 𝐾 ∗ ) + (1 − 𝜃 ∗ )𝑓 ∗ (𝐾 ∗ ) 𝑁 = 𝑓 (𝐾 The domestic tax authority chooses 𝜃 𝑠 and 𝛾 to maximize N knowing that 𝐾 ∗ is a function of these two tax variables that can be represented as 𝐾 ∗ = 𝐾 ∗ (𝜃 𝑠 , 𝛾). 10 Hence, ̅ − 𝐾 ∗ (𝜃 𝑠 , 𝛾)) + (1 − 𝜃 ∗ )𝑓 ∗ (𝐾 ∗ (𝜃 𝑠 , 𝛾)) 𝑁 = 𝑓(𝐾 We differentiate w.r.t. 𝜃 𝑠 to get the following first order condition: 𝑑𝑁 𝑑𝐾 ∗ ∗ ) ∗ ( ∗ ) 𝑑𝐾 ∗ = −𝑓𝐾 (𝐾 ) + (1 − 𝜃 𝑓𝐾 𝐾 =0 𝑑𝜃𝑠 𝑑𝜃𝑠 𝑑𝜃𝑠 ∗ ∗ ) ∗ ( ∗ ) 𝑑𝐾 ⟹ [−𝑓𝐾 (𝐾 ) + (1 − 𝜃 𝑓𝐾 𝐾 ] 𝑠 =0 𝑑𝜃 ⟹ 𝑓𝐾 (𝐾 ) = (1 − 𝜃 ∗ )𝑓𝐾∗ (𝐾 ∗ ) 11 The first order conditions of the country and the firm together imply: ∗) (1− 𝜃𝑠 )(1− 𝜃 ∗ )+ 𝛾𝜃∗ (1 − 𝜃 = 1− 𝜃 This condition is met if 𝜃 𝑠 = 𝜃 and 𝛾 = 0. This amounts to allowing a deduction of foreign taxes from domestic taxable income. Thus, optimally the domestic country allows the firm to deduct foreign taxes from domestic taxable income as is common with other costs of doing business. 12 Paper by Bond and Samuelson (1989) As the paper by Feldstein and Hartman (1979), the paper by Bond and Samuelson (1989) is about how a domestic capital exporting country chooses between a foreign tax credit and a deduction as possible ways to alleviate international double taxation. A main difference is that in the paper by Bond and Samuelson both the domestic (capital exporting) country and the foreign (capital importing) country actively set tax rates w.r.t. to the return on the international capital flow. 13 The domestic and foreign tax authorities are engaged in a 2-stage game. The order of events, corresponding to the two stages, is as follows: 1)The domestic country decides on a deduction or a foreign tax credit as a way to alleviate international double taxation. 2)The two countries set their tax rates given the choice made at stage 1). 14 We analyze the model backwards. In particular, we first analyze the two possible tax setting games under 2) given that the domestic country has chosen either a deduction of a foreign tax credit at stage 1). Subsequently, we analyze whether the home country prefers a deduction or a foreign tax credit at stage 1). While making the choice between a deduction and a foreign tax credit at stage 1), the domestic country knows the tax setting games that ensue at stage 2) after either a deduction or a foreign tax credit has been chosen at stage 1). 15 Details of the model  Let 𝐾 and 𝐾 ∗ be the original capital stocks in the home and foreign countries (and owned by residents of these countries)  Let Z be the flow of capital from home to foreign  After the capital flow the amounts of capital employed in the home and foreign countries are given by 𝐾 − 𝑍 and 𝐾 ∗ + 𝑍, respectively.  The return that the domestic owners of the capital flow Z obtain is the after-tax marginal product of capital in the foreign country (taking into account taxation by possibly both the domestic and foreign countries). 16  We assume that originally the marginal product of capital in the home country is lower than in the foreign country, i.e. 𝐹𝐾 (𝐾 ) < 𝐹𝐾∗ (𝐾 ∗ )  Without any taxation, capital will flow from home to foreign, i.e. Z > 0. Capital will flow until the marginal returns to capital are equal, i.e. 𝐹𝐾 (𝐾 − 𝑍) = 𝐹𝐾∗ (𝐾 ∗ + 𝑍) This increases welfare in both countries. 17  The determination of Z in case there are no taxes: Note: 𝑟 = 𝐹𝐾 (𝐾) 𝑟 ∗ = 𝐹𝐾∗ (𝐾 ∗ ) 𝑟 𝑤 = 𝐹𝐾 (𝐾 − 𝑍) = 𝐹𝐾∗ (𝐾 ∗ + 𝑍) A: welfare gain for foreign B: welfare gain for home 18  Let t and 𝑡 ∗ be the domestic and foreign tax rates applicable to the income from the capital flow, Z. These are the only taxes in the model  Determination of the capital flow, Z, in case of a deduction system: 𝐹𝐾 (𝐾 − 𝑍) = 𝐹𝐾∗ (𝐾 ∗ + 𝑍)(1 − 𝑡)(1 − 𝑡 ∗ )  An increase in one of the tax rates t or 𝑡 ∗ will trigger a reduction in Z.  Thus, Z is a function of t and 𝑡 ∗ , i.e. Z(t, 𝑡 ∗ ) 19  Alternatively, we can consider the determination of the capital flow, Z, in case of a credit system: 𝐹𝐾 (𝐾 − 𝑍) = 𝐹𝐾∗ (𝐾 ∗ + 𝑍)[1 − max(𝑡, 𝑡 ∗ )] 20  With the foreign tax credit in place, two cases can be distinguished depending on the relative magnitude of t and 𝑡 ∗.  Case 1: t > 𝑡 ∗ (the domestic tax is higher than the foreign tax) The tax payer pays tax at a rate 𝑡 ∗ in the foreign county. The domestic tax authority now provides the tax payer with a tax credit equal to the foreign tax 𝑡 ∗. Effectively, the tax payer thus pays domestic tax at a rate of 𝑡 − 𝑡 ∗. The tax burden experienced by the tax payer, i.e. max(𝑡, 𝑡 ∗ ), now is t, which is the sum of 𝑡 ∗ and 𝑡 − 𝑡 ∗. 21  Case 2: t ≤ 𝑡 ∗ (the domestic tax is equal to or less than the foreign tax) The tax payer pays tax at a rate 𝑡 ∗ in the foreign county. The domestic tax authority now provides the tax payer with a tax credit equal to the domestic tax t, as the foreign tax credit cannot exceed the domestic tax. Effectively, the tax payer thus pays domestic tax at a rate of t – t = 0. The tax burden experienced by the tax payer, i.e. max(𝑡, 𝑡 ∗ ), now is 𝑡 ∗ , which is the sum of 𝑡 ∗ and 0.  The foreign tax credit case also gives rise to a function Z(t, 𝑡 ∗ ) that is different from the one in the case a deduction is provided 22 The credit system is more generous for the tax payer, as 1 − max(𝑡, 𝑡 ∗ ) > (1 − 𝑡)(1 − 𝑡 ∗ ) for positive tax rates that are less than 1.  To illustrate whether the deduction or the foreign tax credit is more conducive to a positive capital flow Z, we can consider what combinations of values of the two tax rates t and 𝑡 ∗ give rise to Z > 0 given that either a deduction or a foreign tax credit is in place.  To start, we consider combinations of t and 𝑡 ∗ where we see Z > 0 given that there is a deduction. 23  Define 𝑡𝑚 to be the maximum single tax rate such that the capital flow, Z, is just equal to 0. This definition of 𝑡𝑚 implies 𝐹𝐾 (𝐾 ) = 𝐹𝐾∗ (𝐾 ∗ )( 1 − 𝑡𝑚 ) [ We can solve this expression for 𝑡𝑚 to yield 𝐹𝐾∗ (𝐾 ∗ ) − 𝐹𝐾 (𝐾) 𝑡𝑚 = ∗ ∗ >0] 𝐹𝐾 (𝐾 ) 24  With the deduction system, the capital flow, Z, will just be zero if (1 − 𝑡)(1 − 𝑡 ∗ ) = ( 1 − 𝑡𝑚 )  We can solve this expression for t as a function of 𝑡 ∗ to give: 𝑡𝑚 − 𝑡 ∗ 𝑡= 1− 𝑡 ∗ This expression gives the value of 𝑡 given 𝑡 ∗ so that we just have Z = 0. 25 This graph indicates when we just have Z = 0 in case of a deduction: 26 ‘Inside’ the Z = 0 schedule, we have Z > 0, while ‘outside ‘ of it we also have Z = 0 27  Next, we consider for what combinations of t and 𝑡 ∗ there will be a positive capital flow, i.e. Z > 0, given that there is a foreign tax credit. In this case, the capital flow, Z, is just zero if 1 − max(𝑡, 𝑡 ∗ ) = 1 − 𝑡𝑚 or equivalently max(𝑡, 𝑡 ∗ ) = 𝑡𝑚 28 This graph indicates when we just have Z = 0 in case of a foreign tax credit: 29 ‘Inside’ the Z = 0 schedule, we have Z > 0, while ‘outside ‘ of it we also have Z = 0 30 Now we start to analyze the 2-stage game, starting with the tax competition at stage 2 given the existence of either a deduction or a foreign credit system.  In either case, each country aims to maximize its national income  Domestic national income 𝑌(𝑡, 𝑡 ∗ ) = 𝐹 (𝐾 − 𝑍(𝑡, 𝑡 ∗ )) + (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ ))𝑍(𝑡, 𝑡 ∗ )  Foreign national income 𝑌 ∗ (𝑡, 𝑡 ∗ ) = 𝐹 ∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ )) − (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ ))𝑍(𝑡, 𝑡 ∗ ) 31  In these expressions (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ )) is the after-tax price that the foreign country pays for using the capital.  Further, (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ ))𝑍(𝑡, 𝑡 ∗ ) is the total sum (= after- tax price * quantity) that the foreign country pays the domestic country for the capital flow. 32 A Nash equilibrium occurs if each country has set its tax rate so as to maximize its national income given the other country’s tax rate. In particular,  The domestic country sets t to maximize 𝑌(𝑡, 𝑡 ∗ ) given 𝑡 ∗  The foreign country sets 𝑡 ∗ to maximize 𝑌 ∗ (𝑡, 𝑡 ∗ ) given 𝑡 33 Tax competition with a deduction  As seen before, Z is determined by 𝐹𝐾 (𝐾 − 𝑍) = 𝐹𝐾∗ (𝐾 ∗ + 𝑍)(1 − 𝑡)(1 − 𝑡 ∗ )  We first consider tax setting by the home country. 34 First consider that the foreign country has a tax rate of zero, i.e. 𝑡 ∗ = 0.  Should then the domestic country choose a value of t above 0?  Consider the effect of raising t above zero. This reduces the capital flow Z. Hence, the amount of capital employed abroad 𝐾 ∗ + 𝑍 will be lower, and the marginal product of capital abroad 𝐹𝐾∗ (𝐾 ∗ + 𝑍) will be higher. The marginal product of capital is the price the foreign country pays for using the domestic capital.  It is in the interest of the domestic country to raise this price, and hence the optimal value of t is positive given 𝑡 ∗ = 0. 35 This is essentially the optimal export tax argument. It is in the interest of the capital exporting country to tax the capital export (by taxing its return) in the same way that a banana exporting country can benefit from taxing the exports of bananas, thereby raising its price in the international market. By taxing the return to the capital export, the domestic country exploits its power in the international market for capital. 36 How far should the domestic country raise its tax t above zero?  The domestic country is not interested in raising the domestic tax to a level 𝑡𝑚 as this would reduce the capital flow to zero, and hence also all benefits of the capital flow (for both countries).  Let the optimal domestic capital tax given 𝑡 ∗ = 0 be denoted 𝑡0.  We thus have 0 < 𝑡0 < 𝑡𝑚. 37 Now consider that the foreign country levies a positive tax, i.e. 𝑡 ∗ > 0. What then is the optimal domestic tax t? As before, there are two considerations:  The domestic country wants to levy a positive tax so as to increase the international price of capital given by (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ ))  However, it will not raise the domestic tax to a level so as to reduce 𝑡𝑚 − 𝑡 ∗ the capital flow to zero, i.e. 𝑡 < 1− 𝑡 ∗ 38 Now we can trace the domestic reaction function 𝑡(𝑡 ∗ ) which gives the optimal domestic tax 𝑡 given a foreign tax 𝑡 ∗ ∶ 39 Analogously, we can trace out the foreign reaction curve 𝑡 ∗ (𝑡) that gives the optimal foreign tax given the domestic tax: In the picture 𝑡0∗ is the optimal foreign tax given that the domestic tax is zero, i.e. t = 0. 40 A Nash equilibrium occurs where the two reaction curves meet. This point is indicated by N in the picture below. The two countries’ tax rates in the Nash equilibrium are denoted 𝑡 𝑁 and 𝑡 𝑁∗. 41 Important to note about the Nash equilibrium:  In the Nash equilibrium, there is a positive capital flow 𝑍 𝑁.  This can be seen as the Nash tax rates, i.e. 𝑡 𝑁 and 𝑡 𝑁∗ , are such that (1 − 𝑡 𝑁 )(1 − 𝑡 𝑁∗ ) > (1 − 𝑡𝑚 ) Graphically, this is seen by the fact that the combination of tax rates 𝑡 𝑁 and𝑡 𝑁∗ lies inside the curve where Z is just zero and where (1 − 𝑡)(1 − 𝑡 ∗ ) = ( 1 − 𝑡𝑚 ) 42 Tax competition when the domestic country provides a foreign tax credit  We again need to picture the domestic and foreign reaction curves.  We start with the domestic reaction curve 𝑡(𝑡 ∗ ) indicating the optimal value of t given a value of 𝑡 ∗. First consider that 𝑡 ∗ = 0.  As before, the domestic country is interested in raising its tax rate above zero to increase the international price of capital given by 𝐹𝐾∗ (𝐾 ∗ + 𝑍).  In fact, if 𝑡 ∗ = 0, it does not matter whether the domestic country provides a deduction or a foreign tax credit, as there will be no foreign tax to be deducted or credited either way.  Thus, as before, the optimal domestic tax is 𝑡0 with 0 < 𝑡0 < 𝑡𝑚. 43 Now consider that the foreign country levies a positive tax, i.e. 𝑡 ∗ > 0. What then is the optimal domestic tax t?  As before, there are two considerations: The domestic country wants to levy a positive tax so as increase the international price of capital (1 − 𝑡 ∗ )𝐹𝐾∗ (𝐾 ∗ + 𝑍(𝑡, 𝑡 ∗ )). To do this, the domestic county has to raise its tax rate t above 𝑡 ∗ as otherwise the effective domestic tax after the foreign tax credit would be zero. However, the domestic country will not raise the domestic tax to a level so as to reduce the capital flow to zero. This now means that it will set 𝑡 < 𝑡𝑚. 44 Now we can trace out the domestic reaction function 𝑡(𝑡 ∗ ) which gives the optimal domestic tax 𝑡 given a foreign tax 𝑡 ∗ ∶ 45 Now we consider the foreign reaction curve 𝑡 ∗ (𝑡) when the domestic country provides a foreign tax credit.  If the domestic tax is zero, then it does not matter whether the domestic tax authority allows a deduction or a foreign tax credit. Hence, the optimal foreign tax is 𝑡0∗ as before.  Now consider that the domestic tax rate t is positive. What then is the optimal foreign tax 𝑡 ∗ ? We have to consider two cases: Case 1: 𝑡 ≤ 𝑡0∗ Economically, this is equivalent to the case of t = 0, as the domestic tax authority gives a tax credit at a rate t as long as 𝑡 ≤ 𝑡0∗. Therefore, the optimal foreign tax remains 𝑡0∗. 46 Case 2: 𝑡 > 𝑡0∗ Now the foreign country wants to raise its tax rate at least to the level of t, as raising the tax towards this level increases foreign tax revenues without affecting Z. The reason is that the domestic tax authority raises the foreign tax credit one-for-one with the foreign tax as long as 𝑡 ∗ < 𝑡. Will the foreign country raise 𝑡 ∗ above t? The answer is no, as previously 𝑡0∗ was argued to be the optimal foreign tax in case the domestic country receives no tax revenue (which is the case because of the foreign tax credit). Hence, optimally 𝑡 ∗ = 𝑡. 47 We can now picture the foreign reaction curve 𝑡 ∗ (𝑡) that gives the optimal foreign tax given the domestic tax: 48 The Nash equilibrium occurs where the two reaction curves meet. This point is indicated by N in the picture The two countries’ tax rates in the Nash equilibrium are denoted 𝑡 𝑁 and 𝑡 𝑁∗. 49  Important to note about the Nash equilibrium when there is a foreign tax credit: In the Nash equilibrium, there is no capital flow, i.e. now 𝑍 𝑁 = 0. This can be seen as the Nash tax rates, i.e. 𝑡 𝑁 = 𝑡𝑚 and 𝑡 𝑁∗ = 𝑡𝑚 , are such that 𝑍 𝑁 = 0 Thus, with a foreign tax credit there is no capital flow, and the countries do not experience any positive welfare effect on account of a positive capital flow. Therefore, at stage 1, the domestic country will prefer to install a deduction system as this yields this country (and the foreign country) higher welfare (with a positive capital flow) compared to the foreign tax credit system (with no capital flow). 50