Tax competition under the threat of capital flight

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economics Economics Letters 53 (1996) 323-329

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Tax competition under the threat of capital flight Yong Yang* Department of Economics, University of Michigan, Ann Arbor, MI 48109, USA Received 20 June 1996; accepted 23 September 1996 Abstract

A tax competition model has been constructed in this paper. We have found that tax distortions can result from the mere threat of capital flight and the ensuing tax competition, even though inefficient allocation of the world capital resources may no longer be a problem.

Keywords: Capital flight; Private consumption; Public consumption; Tax competition JEL classification: H21; H26

1. Introduction

Tax competition has long been studied by economists. A classic paper on tax competition is that of Hamada (1966), who found that inefficient allocation of the world capital resources will stem flora tax competition. In a later paper, Bond and Samuleson (1989) compared tax competition under different tax regimes and found that a greater distortion will occur under the foreign-tax-credit regime than under the foreign-tax-deduction regime. Earlier economists, who studied tax competition, used to implicitly assume that the government of the investor country has perfect information regarding how much its residents have earned abroad. Therefore, the government can effectively tax foreign-source capital income. However, th~.e is strong evidence that the government has encountered a greater deal of difficulties in enforcing taxation on foreign-source capital income owing to lack of information. Capital flight is a common problem faced by both developed and developing countries) Only recently have economists started to take into account of capital flight in their studies of capital taxation. Frenkel et al. (1991) discussed how small economies, when facing capital flight, should tax capital income. Surprisingly, their conclusion is that small economies should * Tel.: (313)764-11~1; fax: (313)764-2769; e-mail: [email protected]. t See, for example, Cumby and Levich (1987) and Dooley (1987, 1988) for evidence on capital flight. 0165-1765/96/$12.00 © 1996 Elsevier Science S.A. All ,'ignts reserved PII S0165-1765(96)00932-9

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not tax capital income at all. Gordon (1992) discussed how a large capital exporting country, which can act as a Stackelberg leader, will set its tax rate in tax competition. His finding is that this Stackeiberg leader will use its unique position to set a tax rate worldwide. Different from the earlier studies, this paper focuses on a different type of distortions resultit g from tax competition, i.e. inefficient allocation of national income between private and public consumption. Even though misallocation of the world capital resources may no longer be a problem, distortions between private and public consumption are inevitable owing to tax competition. Our model is more general than that of Frenkel, Razin and Sadka (1991) in the sense that our model can generate the same result as theirs. We also differentiate our paper from Gordon (1992) by studying a Cournot tax competition game.

2. The set.up For expositional purposes, we assume that there are two identical countries, domestic and foreign. Each country has one representative individual who derives utility from consuming both a private good C and a public good G. The utility function is given as u(C, G ) , which is assumed to be strictly increasing in C and G and strictly quasi-concave. Each individual is endowed with an equal amount of capital R. The two individuals can choose to invest their capital in their own country or abroad. The technology of production that each country possesses is also the same. The production function in the two countries is given as f ( K ) , which is strictly increasing and strictly concave in K, i.e. f ' ( K ) > 0 and f " ( K ) < 0. Here we suppressed all other immobile production factors, such as labor, land and so on. Assume that the objective of each government is to maximize the utility u(C, G ) of it~ own individual through taxation of income and provision of the public good. Each government first chooses to tax pure profits fully. However, we assume that the public good is so important that it is warranted to impose a further tax on capital income. The tax rate on capital income is t. Assume that, owing to capital flight, the government of the investor country cannot observe how much its individual has earned abroad. Consequently, the tax revenue collected on the foreign-source capital income of its individual is zero. However, the domestic-source capital income of the foreign individual is fully subject to taxation by the domestic government. It is worth noting that, equivalently, it seems as if each government were restricted to use the source-based princip!e only. Let Z be the amount of capital that the domestic individual chooses to invest in the foreign country. If it is negative, it is the amount of capital that the foreign individual invests in the domestic country. The budget constraint of the domestic individual is C -- ( 1 - t, )f°(R - Z ) ( R - Z ) + (1 - t2)f'(R + Z ) Z .

(l)

Here subscript i - 1 represents the domestic country and i = 2 represents the foreign country. If the domestic individual chooses to invest in the foreign country, he or she will keep investing until he or she earns an equal return in the two countries. Therefore, (1-t,)f'(R-Z)=

( 1 - t~.)f'(R + Z ) .

(2)

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The budget constraint for the domestic government is

G =f(R-

Z)-

(1 - t l ) f ' ( R -

Z)(R-

Z).

(3)

This is a two-stage game. In the first stage, the two governments set their tax rates independently. Then, in the second stage, the individuals in the two countries decide how mr, ch to invest at home and how much abroad after learning the two tax rates. In relation to the other government, each government is a Cournot player and, in relation to the two individuals, the two governments are Stackelberg leaders. The Nash equilibrium is reached when the individuals' investment decisions maximize their total incomes, given the two tax rates, and each government has no incentive to alter its tax rate, given the tax rate of the other government.

3. The Nash equilibrium Since we assume that the two countries ar~ identical in every aspect, we abstract away any possible gains from reallocating the capital resources across the border. 2 Since there are no efficiency gains, the best outcome that each country could possibly achieve is the outcome that it could achieve if its economy were closed. It is easy to show that, if each economy were closed, the government in each country would choose to tax capital income in z,ich a way that the marginal utilities from private and public consumption were equalized. In the following, we show that distortions will arise from the threat of capital flight and the ensuing tax competition, and each country will end up in a worse-off oosition than they were in the closed-economy setting. Differentiating Eq. (2) with respect to t l gives 0Z 0Z - f ' ( R - Z ) - (1 - t.)f"(R - Z)-o-~= (1 - t,)f"(R + Z ) ~ - . Rearranging it, we obtain

OZ _ -f'(R- Z) Ot, - (1-- tt)f"(n - Z ) + (l - t2)f"(R + Z ) "

(4)

Note that OZ/Ot~ > 0 . The interpretation for this is straightforward. Given the tax rate of the foreign country, increasing the domestic tax rate will increase the volume of flight capital into the foreign country or reduce the volume of foreign flight capital into the domestic country. Private consumption of the domestic individual is given as C = (1 - t , ) f ' ( R - Z ) ( R - Z ) + (1 - tz)f'(R + Z ) Z

=(l-t,)f'(R-Z)R.

(5)

2Thus, the assumption of symmetry is really used to isolate capit~.l flight from capital mo,,emems for efficiency reasons.

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Here we used the arbitrage Eq. (2). The government objective is to maximize tbe domestic individual's utility, subject to the constraints of (3)-(5). The first-order condition is

ut ( - f ~R - ( 1 - t,)f~R-~t~ ) ( 0Z OZ 0Z) 4- u 2 - f ~"~1 4-f ~(R - Z) 4- (1 - t I )f'~(R - Z) ~ 4- (1 - tl )f~ - ~ = 0.

(6)

Here u, ffi u,(C, G), u, = u2(C, G), f; = f ' ( R - Z) and f'~ = f"(R - Z). We also let f~ = f ' ( R + Z) and f ~ = f ' ( R + Z). Substituting (4) into (6), we obtain

G) u2(C, G)

t,f; R- Z + ~ ( 1 - t:)Rf'~ R "

u,(C,

= - -

(7)

By symmetry, t~ = t 2 at equilibrium and it in turn implies that Z = 0. Thereby, Eq. (7) is reduced to (after dropping the subscript for country)

u,(C, G) u2(C, G) = (1-

tf' :)Rff +

1.

(7')

Noticing the concavity of the production function, i.e. f " < 0, then we have

u,(C,G) u~(C, c) < l . Thus, the public good is under-provided. The domestic government chooses to tax capital income at a lower rate than the optimal. The same is true for the foreign government. This is a new distortion which is caused by capital flight and the ensuing tax competition. Most interestingly, no capital flight really needs to occur at equilibrium. Here distortions arise simply because of the mere threat of capital flight and each government's incentive to lure the other's individual to invest across the b r rder. Since no capital flight takes place at equilibrium, the world capital resources are still efficiently allocated across countries; there is no loss caused by tax competition in terms of world total production. The distortions arise internally, however, from inefficient distribution of national income between private and public consumption. If we call inefficient allocation of world production resources between countries inter-country inefficiency, the distortion here can be appropriately dubbed intra-country inefficiency. Eq. (7 °) also gives the characterization of the equilibrium tax rate for both countries. Rewriting (7°), we obtain t

1 -t

l-s

~

,

(8)

where s - u~/u2, the marginal rate of substitution between private and public consumption; E - - f ' / R f ~, which is either the elasticity of the supply of capital of the domestic country or

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-t,)f'(l~,)

! i

! I

1

Z

! !

!

.'t

RIi

2

Fig. I. Capital flight induced by the different tax rates of two identical c'~untries.

the elasticity of the demand for capital ot the foreign country at equilibrium, depending on the direction in which capital flight occurs. Note that t is inversely related to E. When E is large, a small change in the tax rate of one country will trigger a great amount of flight capital, and thus the threat of capital flight is more serious. Therefore, each government will be forced to tax capital income at a lower rate. This is illustrated by Fig. 1. When ~ is large, it implies that the curve of ( 1 - t)f'(K), for a given t, will be relatively flat. An increase in t, will shift downwards the curve of ( 1 - t, ff'(K~), thus resulting in capital flight. The volume of flight capital will be given by the horizontal distance between the two intersections. As we can see, the flatter the curves, the larger the volume of flight capital. On the other hand, t is negatively related to s. The more important the public good, the greater the marginal utility of public consumption. Then s is smaller for any given t. To maintain the equality of the two sides, t is required to be larger. This implies that, other things being equal, each government will want to tax capital income more heavily when public consumption is more important. Therefore, the importance of public consumption imposes a restraint on tax competition.

4. Extension of the model

It is easy to generalize the above result to a case in which there are n identical countries. If there are n countries, Eq. (7') becomes

u,(C, c) (n- l )tf' u2(C, G) = ( 1 - t)R'f;' +1

(7")

and Eq. (8) becomes t

l-s m

1-t

(n-1)E"

(8')

From Eqs. (7") and (8'), we can see that, the more countries involved, the lower the tax rate and the more severe the distortions. The intuition behind this is as follows. When there are only a few countries, the flight capital of the individual in each country cannot be spread

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widely. Hence, returns to capital in foreign countries will be quickly driven down to a level equal to that in the home country, and then capital flight will come to a stop without too much capital drain on the home country. However, when there are many countries, the individual of the home country can spread his or her flight capital very thinly over a large number of countries. Capital returns ii~ foreign countries will be reduced rather slowly. Before capital flight comes to a stop, a large amount of domestic capital must be drained out of the home country. Therefore, the threat of capital flight in response to a tax increase is much greater when more countries are involved. When n is extremely large, the home country becomes a small economy in the world and faces a very elastic demand for its capital or a very elastic supply of foreign capital. In particular, as n--~ ~, t--*0. This result is similar to one of the results given by Frenkel et al. (199!), vho found that, when a country is a small open economy and faces a capital flight problem, the government should not choose to tax capital income at all.

S. Conclusions A tax competition model has been constructed in this paper. We have found that tax distortions can result from the mere threat of capital flight and the ensuing tax competition, even though inefficient allocation of the world capital resources may no longer be a problem. The degree of tax competition depends on the elasticity of capital demand or supply and the marginal rate of substitution between private and public consumption As the number of countries involved increases, tax competition will be intensified. In the limit, each country becomes a small open economy and faces a perfectly elastic demand for or supply of capital. As a result, each government is forced to choose a zero tax rate on capital income.

Acknowledgements 1 would like to thank ~oger Gordon, Jeffrey MacKie-Mason, .,oel Slemrod and Bernard Yeung for helpful comments. All remaining errors in this paper are my own.

References Bond, E,W, and L. Samuleson, 1989, Strategic behavior and the rules for international taxation of capital. Economk Journal 99, 1099-I i I I. Cumby, R. and R, Levich, 1987, On the defirition and magnitude of recent capital flight, in: D.R. Lassard and l. Williamson, eds,, Capital flight and third world debt (Institute for International Economics, Washington, DC) 27-67, Dooley, M.P., 1987, Comment, in: D.R. Lassard and J. Williamson, eds., Capital flight and third world debt, (Institute for International Economics, Washington, DC) 79-84. Dooley, M.P., 1988, Capital flight, a response to differences it?financial risks, international monetary fund slaff papers 35, 422-436.

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Frenkel, J.A., A. Razin and E. Sadka, 1991, International taxation in an integrated world, (MIT Press, Cambridge, MA), Chapter 10. Gordon, R., 1992, Can capital income taxes survive in open economies?, Journal of Finance 47, 1159-1180. Hamada, K., 1966, Strategic aspects of taxation on foreign investment income, Quarterly Journal of Economics 80, 361-375.