Leadership in Tax Competition with Fiscal Equalization Transfers

Junichi Haraguchi; Hikaru Ogawa

doi:10.1515/bejeap-2017-0217

Article

Leadership in Tax Competition with Fiscal Equalization Transfers

Junichi Haraguchi and Hikaru Ogawa

Published/Copyright: June 8, 2018

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal The B.E. Journal of Economic Analysis & Policy Volume 18 Issue 3

Abstract

We propose a timing game of asymmetric tax competition with fiscal equalization scheme. The study finds that governments tend to play a sequential-move game as the scale of equalization transfer increases, which explains the emergence of tax leaders in tax competition. The presence of a tax leader is likely to exacerbate capital misallocation among countries, suggesting that equalization transfers aimed at narrowing the interregional fiscal gap might cause an inefficient capital allocation.

Keywords: endogenous timing; equalizationtransfers; leadership; tax competition

JEL Classification: H30; H87

Funding statement: We are grateful to participants of the seminars at Nanzan University for their helpful comments and suggestions. We also thank Keisuke Kawachi for his helpful comments, The authors acknowledge the financial support of JSPS Grant nos.16K12374, 17J07949, and 17H02533.

Appendix

A Appendix

We derive the sequential equilibrium in game GL, in which country L leads and country S follows. The maximization problem of the larger country is given by

maxtLuL=(AL−kL)kL+r(θkˉ−kL)+α(tSkS−tLkL),s.t.(3),(4),(5),and(7).

The first-order conditions give the equilibrium tax rates as

(14)tLL(α,θ)=21−2α2−5α+4α2Λ−8kˉ4θ+14α−18α2+8α3−9θα+4θα2−425−4α1−2α2,

(15)tSL(α,θ)=Λ1−α1−2α4α−1−4kˉ3θ+12α−18α2+8α3−7θα+4θα2−35−4α1−2α2.

Using eqs. (14) and (15) with eqs. (3)–(5), we obtain the equilibrium values:

kLL(α,θ)=kˉ+1−2αΛ−21−θkˉ21−2α5−4α,kSL(α,θ)=kˉ−1−2αΛ−21−θkˉ21−2α5−4α,rL(α,θ)=Ω2−1−2αΛ−4kˉ7θ+50α−72α2+32α3−16θα+8θα2−1225−4α1−2α2.

Notice that kiL\gt0 for i=S,L if Assumption 2 holds. Substituting these values into the objective functions, we obtain the following utility:

(16)uLL(α,θ)=N(α,θ)+Λkˉ(36α2−16α3−47−θα+8−3θ)21−2α5−4α,

(17)uSL(α,θ)=Z(α,θ)+kˉΛ(224α3−64α4−4α273−4θ+4α43−8θ+11θ−36)21−2α5−4α2,

where

N(α,θ)≡Ωkˉθ2+Λ24(5−4α)+kˉ216−32θ+11θ2(5−4α)1−2α2−4k2α(4α23−4θ−α27−40θ+4θ2−31θ+7θ2+18)1−2α25−4α,Z(α,θ)≡Ωkˉθ2+Λ2(3−4α)45−4α2−kˉ2(216θ−83θ2−108)1−2α25−4α2−4αkˉ2(16α34θ−3+8α221−30θ+2θ2−α215−340θ+56θ2+122−219θ+62θ2)1−2α25−4α2.

B Appendix

We derive the sequential equilibrium in game GS, in which country S leads and country L follows. The maximization problem of country S is given by

maxtSuS=(AS−kS)kS+r(θkˉ−kS)+α(tLkL−tSkS),s.t.(3),(4),(5),and(6).

The first-order condition yields the equilibrium tax rate as

(18)tLS(α,θ)=Λ1−α1−2α4α−1+4kˉ3θ+12α−18α2+8α3−7θα+4θα2−34α−51−2α2,

(19)tSS(α,θ)=21−2α2−5α+4α2Λ+8kˉ4θ+14α−18α2+8α3−9θα+4θα2−424α−51−2α2.

Using eqs. (18) and (19) with eqs. (3)–(5), we obtain the following equilibrium values:

kLS(α,θ)=kˉ+1−2αΛ+2kˉ1−θ21−2α5−4α,kSS(α,θ)=kˉ−1−2αΛ+2kˉ1−θ21−2α5−4α,rS(α,θ)=Ω2+1−2αΛ+4kˉ7θ+50α−72α2+32α3−16θα+8θα2−1225−4α1−2α2.

Notice that kiS\gt0 for i=S,L if Assumption 2 holds. Substituting these values into the objective functions, we obtain the following utility:

(20)uLS(α,θ)=Z(α,θ)−Λkˉ(224α3−64α4−4α273−4θ+4α43−8θ+11θ−36)21−2α5−4α2,

(21)uSS(α,θ)=N(α,θ)−Λkˉ(36α2−16α3−47−θα+8−3θ)21−2α5−4α.

C Appendix

Based on Theorems II, III, and IV shown in Hamilton and Slutsky (1990), we prove the equilibrium timing of moves by comparing the utilities with the three orders of moves, i.e., uiN,uiL, and uiS. The comparison of their utility gives the following inequalities.

uLN(α,θ)−uLS(α,θ)=HL{1−2αΛ−8kˉ1−α1−θ}≷0,uLL(α,θ)−uLN(α,θ)={1−2αΛ+8kˉ1−α1−θ}2645−4α1−2α21−α2>0,uSN(α,θ)−uSL(α,θ)=HS{Λ1−2α9−8α−8kˉ1−α11−8α1−θ}≷0,uSS(α,θ)−uSN(α,θ)={1−2αΛ−8kˉ1−α1−θ}2645−4α1−2α21−α2>0,

where

HL≡3−4α{8kˉ1−α11−8α1−θ+Λ1−2α9−8α}645−4α21−α21−2α2>0,HS≡3−4α{1−2αΛ+8kˉ1−α1−θ}645−4α21−α21−2α2>0.

Here, uLN≷uLS if Λkˉ≷8(1−θ)(1−α)1−2α and uSN≷uSL if Λkˉ≷8(1−θ)(1−α)(11−8α)(1−2α)(9−8α). Hence, when Λkˉ<8(1−θ)(1−α)1−2α, both countries prefer their Stackelberg follower utilities to the simultaneous-move utility: uLS\gtuLN and uSL>uSN. Then, with uLL>uLN and uSS>uSN, both sequential outcomes are Nash equilibria. When 8(1−θ)(1−α)(11−8α)(1−2α)(9−8α)<ΛkˉuLN\gtuLS and uSN<uSL. Then, with uLL>uLN and uSS>uSN, a sequential-move outcome in which country L is a Stackelberg leader is the unique subgame perfect Nash equilibrium. When Λkˉ>8(1−θ)(1−α)(11−8α)(1−2α)(9−8α), each country prefers its simultaneous-move equilibrium utility to its payoff as a Stackelberg follower, i.e., uLN\gtuLS and uSN\gtuSL. Then, with uLL>uLN and uSS>uSN, the equilibrium is that both countries move early, yielding the simultaneous-move outcome.

D Appendix

The government i maximizes ui=(Ai−ki)ki+r(θkˉ−ki)+αtˉ(kj−ki). The reaction functions of countries L and S are given by

(22)tL=13tS+4kˉ(1−θ)3+4tˉα3+Λ3,

(23)tS=13tL+4kˉ(1−θ)3+4tˉα3−Λ3.

Notice that we here assume that the government i sees the standard tax rate, tˉ, to be given and chooses its tax rate, ti.

While each government does not account for its effects on tˉ,

the central government sets the standard tax rate to the average tax rates of both countries, tˉ=(tL+tS)/2. In this case, the actual reaction function can be given as follows:

tL=2α+13−2αtS+4kˉ(1−θ)+Λ3−2αandtS=2α+13−2αtL+4kˉ(1−θ)−Λ3−2α.

The equilibrium values in the simultaneous-move outcome are tLN=[8kˉ(1−θ)+Λ(1−2α)]/4(1−2α), tSN=[8kˉ(1−θ)−Λ(1−2α)]/4(1−2α), kLN=kˉ+(Λ/8), kSN=kˉ−(Λ/8), tˉN=2kˉ(1−θ)/(1−2α), and rN=0.5Ω+[2kˉ(θ−2(1−α))]/(1−2α). If we assume Λ/kˉ<8, kiN>0 is ensured.^[10] Using these values, we obtain the equilibrium utility levels:

(24)uLN=kˉAL−(1−θ)(2Ω−Λ)kˉ4+3Λ264+(2α(1−2θ)+6θ−2θ2−3)kˉ22α−1,

(25)uSN=kˉAS−(1−θ)(2Ω+Λ)kˉ4+3Λ264+(2α(1−2θ)+6θ−2θ2−3)kˉ22α−1.

Next, we derive the sequential equilibrium in game GL, in which country L leads and country S follows. The government L maximizes uL=(AL−kL)kL+r(θkˉ−kL)+αtˉ(kS−kL) taking eq. (23) into account. The tax rate chosen by country L is tL=2tˉα+[16(1−θ)+3Λ]/5. Using tˉ=(tL+tS)/2 and eq. (23), we obtain the equilibrium tax rates in Game L as

tLL=9−11αΛ+12kˉ4−α1−θ15(1−2α)andtSL=11α−2Λ+12kˉα+31−θ15(1−2α).

Using these, we obtain the equilibrium values in Game L as kLL=kˉ+[Λ−3kˉ(1−θ)]/15, kSL=kˉ−[Λ−3kˉ(1−θ)]/15, rL=0.5Ω−(144kˉ+7Λ−84kˉθ−120kˉα)/30(1−2α), and tˉL=7[Λ+12kˉ(1−θ)]/30(1−2α), which yields the utility levels when country L leads are obtained as follows:

(26)uLL=3kˉ(4+θ)+Λ15AL−2α(4θ+3θ2−2)−32θ+11θ2+165(2α−1)kˉ2+(θ−1)15(6−5α)Λ+6(2α−1)Ω2α−1kˉ−Λ(3Ω−Λ)90,

(27)uSL=3kˉ(6−θ)−Λ15AS+2α(38−76θ+13θ2)+216θ−83θ2−10825(2α−1)kˉ2+(θ−1)75(17α+9)Λ+45(2α−1)Ω2α−1kˉ+Λ(5Ω−3Λ)150.

In a similar way, we obtain the utility levels in Game GS in which country S leads and country L follows:

(28)uSS=3kˉ(4+θ)−Λ15AS−2α(4θ+3θ2−2)−32θ+11θ2+165(2α−1)kˉ2+(θ−1)156(2α−1)Ω−(6−5α)Λ2α−1kˉ+Λ(3Ω+Λ)90,

(29)uLS=3kˉ(6−θ)+Λ15AL+2α(38−76θ+13θ2)+216θ−83θ2−10825(2α−1)kˉ2+(θ−1)7545(2α−1)Ω−(17α+9)Λ2α−1kˉ−Λ(5Ω+3Λ)150.

The comparison of utility levels reveals that

uLN><uLS↔Λ(1−θ)kˉ><247,uLL><uLN↔Λ(1−θ)kˉ<>24(6α+1)(1−2α),uSN><uSL↔Λ(1−θ)kˉ><8(33−26α)23(1−2α),uSS><uSN↔Λ(1−θ)kˉ<>247,

which gives Proposition 2 and the equilibrium classification in Figure 2.

E Appendix

The government i maximizes ui=ki2+rθkˉ+(1+β)[tiki+α(tjkj−tiki)]. The reaction functions of countries L and S are given by

tL=(1+2β)tS+4(2(1−α)β+1−θ−2α)k‾+Λ(2(1−α)β+(1−2α))4(1−α)β+3−4α,tS=(1+2β)tL+4(2(1−α)β+1−θ−2α)k‾+Λ(2(1−α)β−(1−2α))4(1−α)β+3−4α.

The equilibrium values in the simultaneous-move outcome are

tLN=2kˉ(1−2α)(1+β)+Λ(1−2α+2β(1−α))2(2(1−α)+β(3−2α)),tSN=2kˉ(1−2α)(1+β)−Λ(1−2α+2β(1−α))2(2(1−α)+β(3−2α)),kLN=kˉ+Λ(1+β)4(2(1−α)+β(3−2α)),kSN=kˉ−Λ(1+β)4(2(1−α)+β(3−2α)),

and

rN=Ω2−2kˉ(2(1−2α)+(3−4α)β−θ)(1−2α)(1+β).

Using these values, we obtain the equilibrium utility levels:

uLN=O(α,θ,β)+kˉΛ(1+β)(3−θ−6α+4α2+4β−8αβ+4α2β)2(β(3−2α)+2(1−α)),uSN=O(α,θ,β)−kˉΛ(1+β)(3−θ−6α+4α2+4β−8αβ+4α2β)2(β(3−2α)+2(1−α)),

where

O(α,θ,β)≡θΩkˉ2+Λ2(1+β)2(4β(1−α)+3−4α)16(β(3−2α)+2(1−α))2+kˉ2(41−αβ2+7−10αβ+31−2α−421−αβ+1−2αθ)(1−2α)(1+β).

In the same way as before, we can derive the equilibrium utilities in two sequential-move outcomes as [uLL(α,θ),uSL(α,θ)] and [uLS(α,θ),uSS(α,θ)].^[11]

The comparison of utility levels reveal that

uLN−uLS=RL{Λ(1−2α)(1+β)2−4kˉ(1+β−θ)(3β−2αβ+2−2α)}≷0,uLL−uLN=(1+2β)2{4kˉ(1+β−θ)(3β−2αβ+2−2α)−Λ(1−2α)(1+β)2}216(1−2α)2(1+β)2(3β−2αβ+2−2α)2[42−αβ+5−4α]>0,uSN−uSL=RS{(1−2α)(1+β)2(14β−8αβ+9−8α)Λ−4kˉ(1+β−θ)(3β−2αβ+2−2α)(18β−8αβ+11−8α)}≷0,uSS−uSN=(1+2β)2{4kˉ(1+β−θ)(3β−2αβ+2−2α)−Λ(1−2α)(1+β)2}216(1−2α)2(1+β)2(3β−2αβ+2−2α)[42−αβ+5−4α]>0,

where RL and RS are the positive constant. Hence, we obtain the followings:

uLN≷uLS↔Λkˉ≷4(1+β−θ)(3β−2αβ+2−2α)(1−2α)(1+β)2,uSN≷uSL↔Λkˉ≷4(1+β−θ)(3β−2αβ+2−2α)(1−2α)(1+β)2(18β−8αβ+11−8α)(14β−8αβ+9−8α),

which shows the proposition.

References

Altshuler, R., and T. Goodspeed. 2002. “Follow the Leader? Evidence on European and US Tax Competition.” Working Papers 200226, Rutgers University.Search in Google Scholar

Altshuler, R., and T. Goodspeed. 2015. “Follow the Leader? Evidence on European and US Tax Competition.” Public Finance Review 43: 485–504.10.1177/1091142114527781Search in Google Scholar

Bucovetsky, S., and M. Smart. 2006. “The Efficiency Consequences of Local Revenue Equalization: Tax Competition and Tax Distortions.” Journal of Public Economic Theory 8: 119–144.10.1111/j.1467-9779.2006.00255.xSearch in Google Scholar

Bucovetsky, S. 2009. “An Index of Capital Tax Competition.” International Tax and Public Finance 16: 727–752.10.1007/s10797-008-9093-9Search in Google Scholar

Buettner, T. 2006. “The Incentive Effect of Fiscal Equalization Transfers on Tax Policy.” Journal of Public Economics 90: 477–497.10.1016/j.jpubeco.2005.09.004Search in Google Scholar

Cardarelli, R., E. Taugourdeau, and J. Vidal. 2002. “A Repeated Interactions Model of Tax Competition.” Journal of Public Economic Theory 4: 19–38.10.1111/1467-9779.00086Search in Google Scholar

Chatelais, N., and M. Peyrat. 2008. Are Small Countries Leaders of the European Tax Competition?, Documents de travail du Centre d’Economie de la Sorbonne 2008.58-ISSN: 1955-611X.2008.Search in Google Scholar

Egger, P., M. Köthenbürger, and M. Smart. 2010. “Do Fiscal Transfers Alleviate Business Tax Competition? Evidence from Germany.” Journal of Public Economics 94: 235–246.10.1016/j.jpubeco.2009.10.002Search in Google Scholar

Eichner, T. 2014. “Endogenizing Leadership and Tax Competition: Externalities and Public Goods Provision.” Regional Science and Urban Economics 46: 18–26.10.1016/j.regsciurbeco.2014.01.006Search in Google Scholar

Gaigne, C., and S. Riou. 2007. “Globalization, Asymmetric Tax Competition, and Fiscal Equalization.” Journal of Public Economic Theory 9: 901–925.10.1111/j.1467-9779.2007.00337.xSearch in Google Scholar

Hamilton, J., and S. Slutsky. 1990. “Endogenous Timing in Duopoly games: Stackelberg or Cournot Equilibria.” Games and Economic Behavior 2: 29–46.10.1016/0899-8256(90)90012-JSearch in Google Scholar

Hindriks, J., and Y. Nishimura. 2015. “A Note on Equilibrium Leadership in Tax Competition Models.” Journal of Public Economics 121: 66–68.10.1016/j.jpubeco.2014.11.002Search in Google Scholar

Hindriks, J., and Nishimura, Y. 2017. “Equilibrium Leadership in Tax Competition Models with Capital Ownership: A Rejoinder.” International Tax and Public Finance 24: 338–349.10.1007/s10797-016-9421-4Search in Google Scholar

Hindriks, J., S. Peralta, and S. Weber. 2008. “Competing in Taxes and Investment Under Fiscal Equalization.” Journal of Public Economics 92: 2392–2402.10.1016/j.jpubeco.2007.11.012Search in Google Scholar

Ida, T. 2014. “International Tax Competition with Endogenous Sequencing.” International Tax and Public Finance 21: 228–247.10.1007/s10797-012-9264-6Search in Google Scholar

Itaya, J., and C. Yamaguchi. 2015. Does Endogenous Timing Matter in Implementing Partial Tax Harmonization?, Discussion paper series no. 286, Hokkaido University.Search in Google Scholar

Kawachi, K., H. Ogawa, and T. Susa. 2015. “Endogenous Timing in Tax and Public Investment Competition.” Journal of Institutional and Theoretical Economics 171: 641–651.10.1628/093245615X14307274621224Search in Google Scholar

Keen, M., and K. A. Konrad 2013. The Theory of International Tax Competition and Coordination, Chapter 5. In Handbook of Public Economics, vol. 5, edited by A.J. Auerbach, R. Chetty, M. Feldstein, E. Saez, 257–328. Amsterdam: North-Holland.10.1016/B978-0-444-53759-1.00005-4Search in Google Scholar

Kempf, H., and G. Rota-Graziosi. 2010. “Endogenizing Leadership in Tax Competition.” Journal of Public Economics 94: 768–776.10.1016/j.jpubeco.2010.04.006Search in Google Scholar

Kempf, H., and G. Rota-Graziosi. 2015. “Further Analysis on Leadership in Tax Competition: The Role of Capital Ownership–A Comment.” International Tax and Public Finance 22: 1028–1039.10.1007/s10797-014-9339-7Search in Google Scholar

Köthenbürger, M. 2002. “Tax Competition and Fiscal Equalization.” International Tax and Public Finance 9: 391–408.10.1023/A:1016511918510Search in Google Scholar

Köthenbürger, M. 2005. “Leviathans, Federal Transfers, and the Cartelization Hypothesis.” Public Choice 122: 449–465.10.1007/s11127-005-7518-xSearch in Google Scholar

Köthenbürger, M. 2007. “Ex-Post Redistribution in a Federation: Implications for Corrective Policy.” Journal of Public Economics 91: 481–496.10.1016/j.jpubeco.2006.08.004Search in Google Scholar

Kotsogiannis, C. 2010. “Federal Tax Competition and the Efficiency Consequences for Local Taxation of Revenue Equalization.” International Tax and Public Finance 17: 1–14.10.1007/s10797-008-9094-8Search in Google Scholar

Ogawa, H. 2013. “Further Analysis on Leadership in Tax Competition: The Role of Capital Ownership.” International Tax and Public Finance 20: 474–484.10.1007/s10797-012-9238-8Search in Google Scholar

Ogawa, H., and T. Susa. 2017. “Majority Voting and Endogenous Timing in Tax Competition.” International Tax and Public Finance 24: 397–415.10.1007/s10797-016-9424-1Search in Google Scholar

Ogawa, H., and W. Wang. 2016. “Asymmetric Tax Competition and Fiscal Equalization in a Repeated Game Setting.” International Review of Economics and Finance 41: 1–10.10.1016/j.iref.2015.10.004Search in Google Scholar

Pi, J., and X. Chen. 2017. “Endogenous Leadership in Tax Competition: A Combination of the Effects of Market Power and Strategic Interaction.” The B.E. Journal of Economic Analysis & Policy 17: 1–8.10.1515/bejeap-2016-0191Search in Google Scholar

Redoano, M. 2007. “Fiscal Interactions Among European Countries: Does the EU Matter?,” CESifo Working Paper Series No.1952.10.2139/ssrn.980667Search in Google Scholar

Smart, M. 2007. “Raising Taxes Through Equalization.” Canadian Journal of Economics 40: 1188–1212.10.1111/j.1365-2966.2007.00448.xSearch in Google Scholar

Wang, W., K. Kawachi, and H. Ogawa. 2014. “Fiscal Transfer in a Repeated Interaction Model of Tax Competition.” FinanzArchiv 70: 556–566.10.1628/001522114X685483Search in Google Scholar

Published Online: 2018-06-08

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/bejeap-2017-0217

Keywords for this article

endogenous timing; equalizationtransfers; leadership; tax competition