1 Introduction
Much of the tax competition literature argues that non-cooperative regional tax policy causes inefficiency because it involves interregional externalities. Although each region’s tax policy affects the welfare of other regions, the resulting external effects are ignored under decentralized decision making. Wilson (1999), Wilson and Wildasin (2004), Fuest et al. (2005), and Keen and Konrad (2013) provide comprehensive reviews of related studies.
In the literature, there has been continued interest in the role of interregional fiscal transfers in achieving efficiency.1 Wildasin (1989) derives efficient revenue matching grants under which the external effects of non-cooperative tax policy are internalized. Köthenbürger (2002) argues that tax base equalization, called the representative tax system (RTS), has the advantage of removing the inefficiency of capital tax competition. Under RTS, a region receives a transfer equal to the difference between its tax base and the average tax base of all regions multiplied by the average tax rate of all regions.2 This system is helpful in internalizing interregional externalities because regions are compensated for the loss of tax bases when they raise their tax rates.3
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Recently, Liesegang and Runkel (2018) examine the efficiency effect of RTS. Whereas this effect has been discussed for per unit tax on capital, they show that when corporate income is subject to tax, inefficient tax competition persists even if RTS is implemented.4 Under corporate income tax competition, the external effects of regional tax policy arise not only from tax base mobility, but also from changes in factor returns in other regions. Liesegang and Runkel (2018) show that a transfer system composed of tax revenue and private income equalization can internalize these externalities.5 In contrast, RTS leads to under-taxation of corporate income.
In this paper, we show that the efficiency effect of tax base equalization is preserved even under corporate income tax competition if the equalization formula is modified such that each region’s tax base is evaluated by the average factor return of all regions, not by each region’s factor return (as in RTS). We call this equalization system the “average-return” tax base equalization system (ATS). The inefficiency of corporate income tax competition is due to the external effect on other regions’ tax revenues through policy-induced changes in their capital stock. Other externalities due to changes in factor returns are mutually offset and, thus, they do not distort non-cooperative tax policy after all. Our ATS precisely corrects the externalities that are the sources of inefficiency.
This paper is organized as follows. Section 2 provides a simple model of corporate income tax competition and interregional fiscal transfers. Section 3 considers the nature of interregional externalities caused by non-cooperative tax policy and explains how our ATS achieves efficiency and how RTS fails. A discussion and concluding remarks are presented in Sect. 4.
2 The model
The structure of our model follows that of Liesegang and Runkel (2018). We consider a federation composed of \(N\) identical regions. The assumption of identical regions may not seem appropriate when analyzing fiscal equalization. However, as in related studies, we make this assumption to highlight the efficiency implications of fiscal transfer policy. Non-cooperative regional governments play a Nash game under which each region takes other regions’ public policies as given in its decision making. As in Liesegang and Runkel (2018), we analyze a symmetric equilibrium in which all regions choose the same public policy.
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In a representative region, competitive private firms produce a numeraire output from mobile capital and immobile labor. The well-behaved regional production function is given by \(F(K, L)\), where \(K\) is the regional capital stock and \(L\) is labor. Whereas the regional supply of labor is exogenous, the regional capital stock is endogenous due to mobility. Private firms are subject to corporate income tax. The objective function of firms’ profit maximization is given by:where \(\Pi\) is net corporate income (net profits), \(t\) is the tax rate, \(w\) is the wage rate, and \(r\) is the net return to capital.6 The first-order conditions for profit maximization are:where \(q\) represents the gross return to capital. Throughout this paper, the subscripts attached to the production function represent partial derivatives. Equations (2) and (3) imply that marginal products are equal to the gross factor returns. As the regional labor supply is constant, Eq. (2) provides the regional capital stock as a function of \(r\) and \(t\): \(K(r, t)\).
$$\Pi = \left( {1 - t} \right)\left[ {F\left( {K, L} \right) - wL} \right] - rK,$$
(1)
$$F_{K} \left( {K, L} \right) = \frac{r}{1 - t} = q\left( {r,t} \right),$$
(2)
$$F_{L} \left( {K,L} \right) = w,$$
(3)
In capital market equilibrium, the aggregate capital demand of all regions is equal to capital endowment in the federation. To formalize this equilibrium condition, we denote capital demands in other \(N-1\) regions as \({K}^{*}(r,{t}^{*})\): throughout this paper, asterisk represents the other region’s variables.7 The equilibrium condition can then be described as follows:where \(\overline{K }\) is each region’s capital endowment. This equation gives the net return to capital as a function of the tax rates: \(r(t, {t}^{*})\). The capital stock in a representative region is \(K(r(t, {t}^{*}), t)\), whereas each of the other regions’ stock is equal to \({K}^{*}(r(t, {t}^{*}), {t}^{*})\). Substituting \(K(r(t, {t}^{*}), t)\) into (3) yields \(w(t, {t}^{*})\). We can easily confirm that \(\frac{dK}{dt}<0\) and \(\frac{d{K}^{*}}{dt}>0\).8 When capital and labor are complements in production (\({F}_{LK}>0\)), Eq. (3) implies that \(\frac{dw}{dt}<0\) and \(\frac{d{w}^{*}}{dt}>0\).
$$K\left( {r, t} \right) + \left( {N - 1} \right)K^{*} \left( {r,t^{*} } \right) = N\overline{K},$$
(4)
Corporate income tax revenue is spent on a public good \(g\). One unit of the numeraire output can be transformed into one unit of \(g\) or a private good. Moreover, interregional fiscal transfers are in place. The regional public budget constraint is:where \(T(t)\) is the entitlement of fiscal transfer. We assume that the transfer is conditional on regional taxes. In each region, the tax rate is chosen to maximize the welfare of regional residents \(U(c, g)\), where \(c\) is private good consumption. In addition to labor and capital endowments, residents have the ownership of regional firms. Denoting the exogenous labor supply as \(\overline{L }\), consumption is equal to \(c=w\overline{L }+r\overline{K }+\Pi\). Taking \({t}^{*}\) as given, each regional government maximizes:subject to \(r=r(t, {t}^{*})\), \(K=K(r(t, {t}^{*}), t)\), and \(w=w(t, {t}^{*})\).
$$g = t\left[ {F\left( {K, L} \right) - wL} \right] + T\left( t \right),$$
(5)
$$U\left( {w\overline{L} + r\overline{K} + \Pi , t\left[ {F\left( {K, \overline{L}} \right) - w\overline{L}} \right] + T\left( t \right)} \right),$$
(6)
3 Analysis
3.1 Non-cooperative tax policy
Our analysis begins with non-cooperative tax policy. From (6), the first-order condition for the tax rate is \({U}_{c}\frac{dc}{dt}+{U}_{g}\frac{dg}{dt}=0\). For private consumption, we have:where (2) was applied. As the symmetry assumption implies that \(\overline{K }=K\) in equilibrium, Eq. (7) yields thatUsing (2), the change in \(g\) is given by:From (8) and (9), the first-order condition for \(t\) can be expressed as follows:
$$\frac{{d\pi }}{{dt}} = - \left[ {F - w\bar{L} + \left( {1 - t} \right)\bar{L}\frac{{dw}}{{dt}} + K\frac{{dr}}{{dt}}} \right],$$
(7)
$$\frac{dc}{{dt}} = t\overline{L}\frac{dw}{{dt}} - \left( {F - w\overline{L}} \right).$$
(8)
$$\frac{dg}{{dt}} = F - w\overline{L} - t\overline{L}\frac{dw}{{dt}} + tq\frac{dK}{{dt}} + \frac{dT}{{dt}}.$$
(9)
$$(U_{g} - U_{c} )\frac{dc}{{dt}} = U_{g} \left( {tq\frac{dK}{{dt}} + \frac{dT}{{dt}}} \right).$$
(10)
In the present model, efficiency requires that \({{U}_{g}=U}_{c}\). (Note that \(\frac{dc}{dt}<0\).) The first term on the right-hand side of (10) is the distortional effect of corporate income tax, which should be corrected by fiscal transfer policy. This term captures the fiscal externalities caused by capital mobility, which have been discussed in the literature on capital tax competition (see Wildasin 1989 for the basic argument). A region’s tax increase reduces its capital supply by \(\frac{dK}{dt}\), thereby raising the capital stock of other regions by the same amount. Because Eq. (4) implies that \((N-1)\) \(\frac{d{K}^{*}}{dt}+\frac{dK}{dt}=0\), the resulting increase in other regions’ tax revenues is equal to \({t}^{*}{q}^{*}(N-1)\frac{d{K}^{*}}{dt}=-tq\frac{dK}{dt}\) in symmetric allocations where \(t={t}^{*}\) and \(q={q}^{*}\).
This argument on distortional externalities is essentially equivalent to that discussed by Liesegang and Runkel (2018, Eq. 16). Surprisingly, even under corporate income tax, the sole source of distortional externalities is due to the direct impact on other regions’ tax revenues arising from policy-induced changes in capital movements. As Liesegang and Runkel (2018, Sect. 4) argue, one would expect that non-cooperative corporate income tax causes various external effects on other regions’ private consumption and tax revenues by affecting their profits, capital, and labor income. In particular, one would expect that the effect of \(t\) on \({q}^{*}\) and \({w}^{*}\) would influence the corporate income tax bases of other regions. However, interregional externalities other than the change in the regional capital stock do not distort non-cooperative tax policy because they are mutually offset. These offset externalities can be ignored when considering corrective fiscal transfer policy.9 Consequently, as in the analysis of Köthenbürger (2002) on per unit tax on capital, the efficiency role of fiscal transfer policy is to neutralize the effect of non-cooperative tax policy on tax base mobility. From (4) and (10), the efficient transfer in the present model must satisfy:
$$\frac{dT}{{dt}}\left( t \right) = { }t^{*} q^{*} \left( {N - 1} \right)\frac{{dK^{*} }}{dt}.$$
(11)
3.2 Tax base equalization
The standard system of tax base equalization (the representative tax system, RTS) assumes that each region’s entitlement is equal to the difference between its tax base and the average tax base of all regions multiplied by the average tax rate of all regions.where \(\overline{t }\) is the average tax rate of all regions and \(\Delta\) is the average corporate tax base:As argued later, the transfer formula in (12) cannot satisfy the efficiency condition stated in (11). This inefficiency of RTS is argued by Liesegang and Runkel (2018, Proposition 1).
$$T^{RTS} \left( t \right) = \overline{t}\left\{ {\Delta - \left[ {F\left( {K, \overline{L}} \right) - w\overline{L}} \right]} \right\},$$
(12)
$$\overline{t} = \frac{{\left( {N - 1} \right)t^{*} + t}}{N}, \Delta = \frac{{\left( {N - 1} \right)\left[ {F\left( {K^{*} , \overline{L}} \right) - w^{*} \overline{L}} \right] + F\left( {K, \overline{L}} \right) - w\overline{L}}}{N}.$$
(13)
Our “average-return” tax base equalization system (ATS) assumes that each region’s tax base is evaluated by the average factor returns of all regions. As the output price is normalized to one, a region’s fiscal capacity under ATS is equal to \(F(K, \overline{L })-\overline{w }\overline{L }\), where \(\overline{w }\) is the average wage rate of all regions: \(\overline{w }=\frac{\left(N-1\right){w}^{*}+w}{N}\). The equalization entitlement is then given by:where \(\delta\) is the average tax base under ATS:Our main result is described as follows.
$$T^{ATS} \left( t \right) = \overline{t}\left\{ {\delta - \left[ {F\left( {K, \overline{L}} \right) - \overline{w}\overline{L}} \right]} \right\},$$
(14)
$$\delta = \frac{{\left( {N - 1} \right)\left[ {F\left( {K^{*} , \overline{L}} \right) - \overline{w}\overline{L}} \right] + F\left( {K, \overline{L}} \right) - \overline{w}\overline{L}}}{N}.$$
Proposition 1
The average-return tax base equalization system meets the efficiency condition for fiscal transfer policy stated in (11). Under this system of tax base equalization, non-cooperative corporate income tax policy is efficient.
Differentiating (13), using (2), and evaluating the outcome in a symmetric equilibrium (\(\overline{t }=t={t}^{*}\) and \(q={q}^{*}\)) yields:where the last equality is based on (\(N-1\))\(\frac{d{K}^{*}}{dt}+\frac{dK}{dt}=0\). This proves Proposition 1.
$$\frac{{dT^{ATS} \left( t \right)}}{dt} = \frac{{\left( {N - 1} \right)}}{N}\overline{t}\left( {q^{*} \frac{{dK^{*} }}{dt} - q\frac{dK}{{dt}}} \right) = \left( {N - 1} \right)t^{*} q^{*} \frac{{dK^{*} }}{dt},$$
(15)
We explain how our ATS achieves efficiency and how RTS fails. Under RTS, Eq. (12) implies thatshowing that RTS cannot achieve efficiency. Under this system of tax base equalization, each region’s entitlement is influenced by changes in the relative fiscal capacity due to the effects of tax policy on regional wages. Recall that \(\frac{dw}{dt}<0\) and \(\frac{d{w}^{*}}{dt}>0\) under factor complementarity (see Sect. 2). These changes in the wage rates raise the tax base in the region with a higher tax rate while reducing other regions’ tax bases. Therefore, the marginal impact of the tax increase on the equalization entitlement is smaller under RTS than under ATS. This reduction in the marginal entitlement is harmful because it gives regional governments an incentive to lower their tax rates below the efficient level.10 A prominent feature of ATS is that policy-induced changes in regional factor returns are ignored in the calculation of entitlement. This feature is desirable from the viewpoint of efficiency because the effect of tax policy on other regions’ factor returns does not represent inefficiency under corporate income tax competition. As argued in Sect. 3.1, internalizing the external effect of tax policy on other regions’ capital stock is sufficient to achieve efficiency. Our ATS is customized to meet this requirement.
$$\frac{{dT^{RTS} \left( t \right)}}{dt} = \left( {N - 1} \right)t^{*} \left[ {q^{*} \frac{{dK^{*} }}{dt} + \overline{L}\left( {\frac{dw}{{dt}} - \frac{{dw^{*} }}{dt}} \right)} \right],$$
(16)
This can be clarified by considering the case of constant-returns to scale (CRS) production technology. When \(F(K, L)\) is CRS, corporate income tax is equivalent to capital income tax: regional tax revenue is equal to \(tqK\) because \(F={F}_{L}L+{F}_{K}K\). Then, Eqs. (12) and (13) are, respectively, modified to:where \(\overline{q }\) is the average gross return to capital of all regions, \(\Omega\) is the average capital income, and \(\kappa\) is the average capital stock:As (17) shows, under ATS, each region’s capital income tax base is evaluated by the average taxable return to capital. Under RTS, policy-induced changes in \(q\) and \({q}^{*}\), as well as those in \(K\) and \({K}^{*}\), affect the entitlement of fiscal transfer. However, the externalities that should be corrected by fiscal transfer arise from the change in \({K}^{*}\), not from that in \({q}^{*}\). The entitlement of fiscal transfer should not depend on policy-induced changes in the taxable return to capital.
$$T^{RTS} \left( t \right) = \overline{t}\left( {\Omega - qK} \right),$$
(17)
$$T^{ATS} \left( t \right) = \overline{t}\overline{q}\left( {\kappa - K} \right),$$
(18)
$$\overline{q} = \frac{{\left( {N - 1} \right)q^{*} + q}}{N}, \Omega = \frac{{\left( {N - 1} \right)q^{*} K^{*} + qK}}{N}, \kappa = \frac{{\left( {N - 1} \right)K^{*} + K}}{N}.$$
4 Discussion and concluding remarks
Starting with the work of Köthenbürger (2002), it has been argued that RTS can be used to correct inefficient tax competition. However, Liesegang and Runkel’s (2018) analysis of corporate income tax criticizes this conventional view. In general, their critical argument applies to the case in which ad valorem factor taxes are imposed (see also Sas 2017). This limitation of tax base equalization is particularly important because factor taxes are usually implemented as income or asset value taxes, not as per unit or specific taxes. Instead of tax base equalization, Liesegang and Runkel (2018) propose a combination of tax revenue and private income equalization. This policy combination is effectively oriented towards interregional welfare equalization. As Myers (1990) argues, welfare equalization through population mobility can eliminate the inefficiencies associated with interregional tax competition. The essence of Liesegang and Runkel’s (2018) remedy is that fiscal transfer policy can have the same effect as population mobility.11
This paper has shown that when RTS is modified to ATS, tax base equalization can be used to correct the distortion caused by corporate income tax competition. An important difference with Liesegang and Runkel’s (2018) equalization system is that ATS does not involve private income equalization: interregional transfers are conducted among regional public budgets. However, we do not intend to assert that our ATS is superior to the Liesegang-Runkel equalization system. Their system seems to be an interesting option for correcting inefficient tax competition, despite their concerns about practicality. A similar concern may apply to our ATS, too. Compared with RTS, it will be cumbersome to measure regional fiscal capacity evaluated by the average factor return of all regions. This paper intends to provide a new option for efficient fiscal transfers under tax competition. A comparison of different efficient fiscal transfers is beyond the scope of this paper because it depends on political and social environments and economic distortions other than tax competition. Also, one should keep in mind that regional tax coordination is an important policy option (see footnote 1).
This paper’s analysis is based on a simple model of corporate income tax competition. This simple model highlights the essence of our ATS in a transparent manner. Our results can be extended to a more general case in which factor supplies are endogenous and there are multiple tax instruments. Introducing ad valorem labor and capital taxes into Matsumoto’s (2022) model with endogenous savings and labor-leisure choices shows that ATS corrects interregional horizontal externalities whereas RTS does not.12 The intuition behind the difference between RTS and ATS is the same as that discussed in Sect. 3. Distortional externalities are due to changes in capital income tax revenues arising from policy-induced capital movements. Endogenous factor supplies and labor income tax cause additional externalities that do not appear in the present model. However, these externalities, as well as those arising from changes in factor returns, do not distort non-cooperative tax policy because they are mutually offset. Consequently, the feature of efficient tax base equalization is similar to that in the present simple model.
Acknowledgements
We would like to thank the co-editor (Marko Köthenbürger) and two reviewers for their helpful comments and suggestions. Matsumoto and Ogawa gratefully acknowledge financial support from JSPS KAKENHI (Grant Numbers JS18K01668 and JS22H00854, respectively).
Declarations
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this work.
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