區域政府對境內與境外資本的租稅競爭

Inter jur isdictional Tax Competition for Domestic and For eign Capital

區域政府對境內與境外資本的租稅競爭

計畫編號：NSC 88-2415-H-004-017

執行期限：87 年 8 月 1 日至 89 年 1 月 31 日

主持人：徐麗振

TEL: 02-29387313 FAX: 02-29390074

Email:

lchsu@nccu.edu.tw

執行機構：國立政治大學財政研究所

Abstr act: This paper examines the efficient provision of local public goods when jurisdictions compete for not only domestic capital but also the capital abroad. Capital is freely mobile between jurisdictions within the same country, but needs to pay a migration cost if it flows across countries. We find that the traditional result of underprovision of local public goods may not be held. In addition, if both domestic and foreign care complementary to the locally immobile factor, the jurisdiction will always tax foreign capital, and the jurisdiction may even tax foreign capital to subsidize domestic capital as the foreign capital becomes less mobile.

1.

INTRODUCTION

There are mainly two branches of studies on tax competition: interjurisdictional tax competition and international tax competition.1

These studies usually assume that jurisdictions or countries impose source-based taxes on capital, which is freely mobile but fixed in total supply, to provide public goods. The purpose to compete capital is to increase the level of public expenditure or raise the return of locally immobile factors. In this framework, jurisdictions or countries have incentives to cut their own tax rates in order to attract capital. As a consequence, the common conclusion of tax competition is that public expenditure will be kept at a lower than efficient level.

Problems of interjurisdictional and international tax competition are usually examined separately, despite that these two are very similar problems and the fact that in the absence of complete capital control, a jurisdiction’s capital taxation affects not only the migration of domestic capital but also the flow of foreign capital. In this paper, we examine jurisdictional competition for domestic and foreign capital. As pointed out by Gordon and Bovenberg (1996), capital is imperfectly mobile internationally due to information asymmetric. Therefore, in our model it is assumed that capital is freely mobile between jurisdictions within the same country, but incurs migration costs if it moves across countries. The migration costs characterize the information disadvantage of foreign capital. The main purpose of this paper is to examine the efficient provision of local public goods and jurisdictions’ choices of tax rates on domestic and foreign capital when jurisdictions compete for these two types of capital.

2.

THE MODLE

Consider an economy with two countries, H (home country) and F (foreign country),

each containing m jurisdictions. Each jurisdiction is inhabited by homogeneous and

immobile residents. The number of residents in each jurisdiction is normalized to one for simplicity. The resident consumes a local public good, g, and a private good, x. Her utility

function is u(g,x), which is strictly quasi-concave and twice continuously differentiable. Countries H and F are endowed with a fixed amount of capital k and b , respectively. To

simplify the model, it is assumed that k and b are owned by absentee capital owners.2

Capital is freely mobile between jurisdictions, but imperfectly mobile between countries. In contrast, residents are immobile. Let k be H’s capital endowment invested in jurisdiction_iH

i country H and b_iH F’s capital endowment invested in jurisdiction i country H. Likewise,

let kF_j be H’s capital endowment invested in jurisdiction j country F and bH_j F’s capital

endowment invested in jurisdiction j country F. The migration cost of the capital endowed

in country H but invested in jurisdiction j country F is M(kF_j ), which is twice-continuously differentiable and strictly convex in k . Similarly, the migration cost of the capitalF_j

1 _{For interjurisdictional tax competition, see for instance, Bucovetsky (1991), Hoyt (1991), Krelove (1992),} Myers (1990), Smith (1999), Wildasiin (1988), Wilson (1986), Zodrow and Mieszkowski (1986), and a recent review by Wilson (1999). For international tax competition, see for instance, Haufler and Wooton (1999), Kanbur and Keen (1993), Lockwood (1993), and Razin and Sadka (1991).

endowed in country F but invested in jurisdiction i country H is M(b_iH).

The private good is produced by capital and an immobile factor, for instance, labor (l),

with a constant returns to scale technology. The production function for jurisdiction i

country H is therefore f_iH(k_iH,b_iH), in which the notation for the fixed factor is suppressed. Likewise, the production function for jurisdiction j country F is f_jF(kF_j ,b_jF). f(⋅,⋅) is concave and twice continuously differentiable. Capital is paid by their marginal product, and the residual goes to the fixed factor.

Jurisdictions impose source-based taxes on capital invested within their boundaries to fund the local public goods. The tax rates on domestic and foreign capital can be different. The equilibrium of capital migration is characterized by the following four conditions:

, ..., , 1 , ) , (k b t i m f_{k i}H _iH _kH _H i H i − = ρ = (1) , ..., , 1 , ) ( ) , (k b t M k j m f H F j k k F j F j kFj − Fj − =ρ = (2) , ..., , 1 , ) , (k b t j m f_b F_j F_{j b}F _F j F j − =ρ = (3) . ..., , 1 , ) ( ) , (k b t M b i m f_{b i}H _iH _bH _{b i}H _F i H i − − =ρ = (4) Equation (1) says that if H’s capital endowment is invested in any jurisdiction, say i, of

country H, it will earn the net return equal to its marginal product, ( _iH, _iH)

k k b

f H

i , net of the

per-unit tax imposed on domestic capital by jurisdiction i, H i

k

t . If H’s capital endowment is

invested in any jurisdiction, say j, of country F, besides the per-unit tax imposed by this

jurisdiction, the capital owner needs to consider the marginal migration cost, M_k(kF_j ). This is described by (2). Because of the arbitrage possibility, in migration equilibrium the capital originally endowed in H must earn the same net return, ρ , no matter it is invested inH

H or F. Similarly, (3) and (4) are the migration equilibrium conditions for F’s capital

endowment. Each jurisdiction takes ρ and _H ρ as exogenous. This situation holds_F when each country involves many small jurisdictions or when both countries are small, facing a world return of capital.

In migration equilibrium the capital market must be cleared. The capital market clearance conditions are:

k k k_iH +∑ F_j = ∑ (5) b b b_iH +∑ F_j = ∑ (6) Equations (1) through (6) determine the allocation of capital across jurisdictions in both countries, (k₁H,...,k_mH,b₁H,...,b_mH,k₁F,...,k_mF,b₁F,...,b_mF), which is a function of capital tax rates in all jurisdictions.

Prices of both x and g are normalized to one. Thus, the balanced budget constraint for,

say jurisdiction i country H, is:

. H i b H i k H i t k t b g H i H i + = (7) The private good consumed by the resident is:

). , ( ) , ( ) , ( _iH _iH b H i H i H i k H i H i H i H i H i f k b k f k b b f k b x H i H i − − = (8)

We examine the symmetric Nash equilibrium of tax competition. We will focus on the problem for a representative jurisdiction, say jurisdiction i in country H. The problems for

jurisdictions in F can be analyzed analogously. Jurisdiction i’s problem is to maximize

) , ( _iH _iH H i g x u by choosing H i k t and H i b

t . When it chooses these tax rates, it considers the migration reaction of capital, but not the response in tax rate changes by other jurisdictions, in both home and foreign countries.

3. THE MIGRATION RESPONSE OF CAPITAL

TO CHANGES IN TAX RATES

From jurisdiction i’s perspective, there are two types of capital that it competes with

other jurisdictions: one is domestic capital, and the other is foreign capital. These two types of capital differ by the migration cost. The migration equilibrium conditions of these two types of capital are characterized by (1) and (4), respectively. Totally differentiating (1) and (4) yields: , 0 ) , ( ) , ( + − H = i k H i kb H i kk k b dk f k b db dt f (9) . 0 ) , ( ) , ( _iH + _{bb i}H − _b − _{bb i}H = bk k b dk f k b db dt M db f H i (10)

From (9) and (10), we obtain the migration response of capital to changes in tax rates:

, 0 < − = H M f dt dk _{bb bb} k H i H i (11) , H f dt db _bk k H i H i − = (12) , H f dt dk _kb b H i H i − = (13) , 0 < = H f dt db _kk b H i H i (14)

Equation (11) says that increasing the tax rate on domestic capital will drive out the capital originally endowed in home country. Likewise, (14) says that increasing the tax rate on foreign capital will discourage the import of capital. The migration direction of foreign capital due to the change in the tax rate on domestic capital and the migration direction of domestic capital due to the change in the tax rate on foreign capital are ambiguous, depending

on f , as shown by (12) and (13), respectively. Notice that if domestic capital and foreign_kb

are unrelated in production, thus f_kb =0, then the tax rate on domestic capital will not affect the migration of foreign capital and similarly, the tax rate on foreign capital will have no effect on domestic capital.

4. THE NASH EQUILIBRIUM

We now investigate the Nash equilibrium. Jurisdiction i’s problem is:

) 4 ( ) 1 ( . . ) , ( , t s x g u t t Max H i H i H i b k H i H i

Substituting (7) and (8) into the objective function, the Nash equilibrium capital tax rates are obtained from the first order conditions:

, 1 ˆ         − = g x kl k u u lf t (15) . 1 ˆ bb g x bl b bM u u lf t _+       − = (16) Substituting (15) and (16) into (7), the jurisdiction’s budget constraint, we have

. 1 ₂ 2 l f g M b u u ll bb g x = − − (17) We then substitute (17) back into (15) and (16), the Nash equilibrium capital tax rates can be written as , ˆ 2 2     − = l f g M b lf t ll bb kl k (15’) . ˆ l f gf k f bM t ll bl lk bb b − − = (16’) Equation (17) shows that whether the local public good is provided efficiently depends on the relative magnitudes of M and _bb 2

/b

g . If 2

/b g

M_bb = , we have u_x/u_g =1, that is, the local public good is provided efficiently. If M is very high (when b is very high) so_bb

contrast, if M_bb =0, that is, constant marginal migration cost or no migration cost, or if

bb

M is very small such that M_bb <g/b2, then u_x/u_g <1; the local public good is

underprovided. The intuition behind these findings is that when M is very small or is_bb

equal to zero, capital is almost perfectly mobile across countries, thus we have the traditional result of tax competition that the local public good is underprovided. As M increases,_bb

capital becomes less mobile across countries, and the difference between domestic and foreign capital gets more obvious. Since the cost of local public good can be partially borne on foreign capital and the supply of foreign capital is relative inelastic to domestic, the jurisdiction tends to over-spend. Thus as M increases and reaches a cut-off _bb g/b2, the local public good attains the efficient level, and will be overprovided as M beyond this_bb

cut-off.

Notice first from (15) and (16) that if M_bb =g/b2, thereby the local public good is provided efficiently, then ˆ =0

k

t and ˆ = >0

bb b bM

t . The local public good is completely funded by taxes imposed on foreign capital. In all other cases, as observed from (15’) and (16’), whether the jurisdiction will tax or subsidize domestic and foreign capital is generally ambiguous, depending not only on the marginal migration cost but also the relation between capital and labor. Let us focus only on the case that f_lk >0 and f_bl >0. By (16’), tˆ is_b

always positive, and by (15’), ˆ >0

k

t when M is low or zero and _bb ˆ <0

k

t when M is_bb

high enough. This says that if both domestic and foreign capital are complementary to the fixed factor, the jurisdiction will always tax foreign capital, and the jurisdiction may even tax foreign capital to subsidize domestic capital as the foreign capital becomes less mobile. In other words, the jurisdiction will always tax the capital that is relatively inelastic in supply when both types of capital are complementary to the locally immobile factor.

5.

CONCLUSIONS

This paper examines the efficient provision of local public goods when jurisdictions compete for both domestic and foreign. It is found that the level of the local public good is ambiguous, depending on the shape of the migration cost function for foreign capital. If there is no migration cost or if the migration cost function is linear, we have the traditional result of tax competition that local public goods are underprovided, because the migration cost does not really play a role. However, if the migration cost function does not exhibit the above characteristics, the level of local public goods will be ambiguous. We also find that if both domestic and foreign care complementary to the locally immobile factor, the jurisdiction will always tax foreign capital, and the jurisdiction may even tax foreign capital to subsidize domestic capital as the foreign capital becomes less mobile.

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