zbMATH — the first resource for mathematics

The supermodularity of the tax competition game. (English) Zbl 1417.91377
Summary: Tax competition is often associated with the “race to the bottom”: a decrease in the tax rate of one jurisdiction (country, region or municipality) triggers similar reactions in neighboring jurisdictions. This race can be related to two properties of the tax competition game: positive tax spillovers and the strategic complementarity of tax rates. Using tools from generalized concavity, more precisely \(\mathbf{r}\)-concavity, and supermodular games, this paper offers a simple yet unifying perspective on the fundamental forces that shape tax competition. The main results characterize sufficient conditions on the marginal productivity of tax competing jurisdictions to predict a “race to the bottom”. These conditions bind the curvature of the demand for capital of each tax-competing jurisdiction. Quadratic production function respects these, while Cobb-Douglas form requires an additional condition. We deduce several results: at least one pure-strategy Nash equilibrium exists and is unique. Going beyond our specific framework, we apply some results of supermodular games with positive spillovers: in case of multiple equilibriums, tax coordination is Pareto improving; but the coalition of a subgroup of countries does not achieve neither tax coordination, nor tax cooperation. Establishing similar sufficient conditions for the supermodularity of the tax competition game with welfare maximizers raises multiple issues. Besides the question of the nature of public spending, we discuss the role of capital by considering an elastic worldwide stock of capital, capital ownership, and offshore centers.
91B64 Macroeconomic theory (monetary models, models of taxation)
91A10 Noncooperative games
Full Text: DOI
[1] Aguirre, I.; Cowan, S.; Vickers, J., Monopoly price discrimination and demand curvature, Amer. Econ. Rev., 100, 4, 1601-1615, (2010)
[2] Amir, R., Cournot oligopoly and the theory of supermodular games, Games Econom. Behav., 15, 2, 132-148, (1996) · Zbl 0859.90034
[3] Amir, R., Supermodularity and complementarity in economic: An elementary survey, South. Econ. J., 71, 3, 636-660, (2005)
[4] Anderson, S. P.; Renault, R., Efficiency and surplus bounds in Cournot competition, J. Econom. Theory, 113, 253-264, (2003) · Zbl 1059.91024
[5] Aumann, R., Values of markets with a continuum of traders, Econometrica, 43, 4, 611-646, (1975) · Zbl 0325.90082
[6] Avriel, M., r-convex functions, Math. Program., 2, 309-323, (1972) · Zbl 0249.90063
[7] Avriel, M. A.; Diewert, W. E.; Schaible, S.; Zang, I., Generalized Concavity, (1988), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia, PA · Zbl 0679.90029
[8] Bagnoli, M.; Bergstrom, T., Log-concave probability and its applications, Econom. Theory, 26, 2, 445-469, (2005) · Zbl 1077.60012
[9] Balogh, T.; Ewerhart, C., On the Origin of r-concavity and Related ConceptsTechnical Report 187, (2015), University of Zurich, Department of Economics
[10] Bayindir-Upmann, T.; Ziad, A., Existence of equilibria in a basic tax-competition model, Reg. Sci. Urban Econ., 35, 1, 1-22, (2005)
[11] Brennan, G.; Buchanan, J., The Power to Tax: Analytical Foundations of a Fiscal Constitution, (1980), Cambridge University Press: Cambridge University Press New York
[12] Bucovetsky, S., Asymmetric tax competition, J. Urban Econ., 30, 2, 167-181, (1991) · Zbl 0729.90720
[13] Bucovetsky, S., Honor among tax havens, J. Public Econ., 110, 3, 74-81, (2014)
[14] Bulow, J. I.; Geanakoplos, J. D.; Klemperer, P. D., Multimarket oligopoly: Strategic substitutes and complements, J. Political Econ., 93, 3, 488-511, (1985)
[15] Caplin, A.; Nalebuff, B., Aggregation and imperfect competition: On the existence of equilibrium, Econometrica, 59, 1, 25-59, (1991) · Zbl 0738.90012
[16] Chirinko, B., Wilson, D.J., 2007. Tax competition among U.S. States: Racing to the bottom or riding on a seesaw? Working Paper Series 2008-03. Federal Reserve Bank of San Francisco.
[17] Cooper, R. W., Coordination Games. Complementarites and Macroeconomics, (1999), Cambridge University Press: Cambridge University Press Cambridge, UK
[18] Costa-Font, J.; De-Albuquerque, F.; Doucouliagos, H., Do jurisdictions compete on taxes? A meta-regression analysis, Public Choice, 161, 3, 451-470, (2014)
[19] Cowan, S., The welfare effects of third-degree price discrimination with nonlinear demand functions, Rand J. Econ., 38, 2, 419-428, (2007)
[20] Cremer, H.; Gahvari, F., Tax evasion, fiscal competition and economic integration, Eur. Econ. Rev., 44, 9, 1633-1657, (2000)
[21] De Jong, F. J., Dimensional Analysis for Economists, (1967), North Holland · Zbl 0183.24301
[22] de Mooij, R. A.; Vrijburg, H., Tax rates as strategic substitutes, Int. Tax Public Financ., 23, 1, 2-24, (2016)
[23] Desai, M.A., Foley, C.F., Hines, J.R., 2004. Economic effects of regional tax havens. NBER Working Papers 10806. National Bureau of Economic Research, Inc.
[24] Devereux, M.; Loretz, S., What do we know about corporate tax competition?, Natl. Tax J., 66, 3, 745-773, (2013)
[25] Dharmapala, D., What problems and opportunities are created by tax havens?, Oxf. Rev. Econ. Policy, 24, 4, 661-679, (2008)
[26] Dharmapala, D., What do we know about base erosion and profit shifting? A review of the empirical literature, Fisc. Stud., 35, 421-448, (2014)
[27] Eaton, B. C., The elementary economics of social dilemmas, Can. J. Econ., 37, 4, 805-829, (2004)
[28] Eichner, T.; Runkel, M., Interjurisdictional spillovers, decentralized policymaking, and the elasticity of capital supply, Amer. Econ. Rev., 102, 5, 2349-2357, (2012)
[29] Ewerhart, C., Cournot games with biconcave demand, Games Econom. Behav., 85, C, 37-47, (2014) · Zbl 1290.91115
[30] Hamilton, J. H.; Slutsky, S. M., Endogenous timing in duopoly games: Stackelberg or Cournot equilibria, Games Econom. Behav., 2, 1, 29-46, (1990) · Zbl 0753.90074
[31] Hines, J. R.; Rice, E. M., Fiscal paradise: Foreign tax havens and American business, Q. J. Econ., 109, 1, 149-182, (1994)
[32] Houthakker, H. S., The Pareto distribution and the Cobb-Douglas production function in activity analysis, Rev. Econom. Stud., 23, (1955)
[33] IMF, Spillovers in International TaxationBoard Paper, (2014), International Monetary Fund: International Monetary Fund Washington
[34] Johannesen, N., Imperfect tax competition for profits, asymmetric equilibrium and beneficial tax havens, J. Int. Econ., 81, 2, 253-264, (2010)
[35] Jones, C. I., The shape of production function and the direction of technical change, Games Econom. Behav., 120, 2, 517-549, (2005)
[36] Kanbur, R.; Keen, M., Jeux sans frontières: Tax competition and tax coordination when countries differ in size, Amer. Econ. Rev., 83, 4, 877-892, (1993)
[37] Keen, M.; Konrad, K. A., The theory of international tax competition and coordination, (Alan J. Auerbach, M. F.; Raj Chetty; Saez, E., Handbook of Public Economics. Handbook of Public Economics, Handbook of Public Economics, vol. 5, (2013), Elsevier), 257-328, (Chapter 5)
[38] Keen, M.; Wildasin, D., Pareto-efficient international taxation, Amer. Econ. Rev., 94, 1, 259-275, (2004)
[39] Kempf, H.; Rota-Graziosi, G., Endogenizing leadership in tax competition, J. Public Econ., 94, 9-10, 768-776, (2010)
[40] Kimbal, M. S., Precautionary savings in the small and in the large, Econometrica, 58, 53-73, (1990)
[41] Konrad, K. A.; Schjelderup, G., Fortress building in global tax competition, J. Urban Econ., 46, 1, 156-167, (1999)
[42] Kydland, F. E.; Prescott, E. C., Rules rather than discretion: The inconsistency of optimal plans, J. Political Econom., 85, 3, 473-491, (1977)
[43] Lagos, R., A model of TFP, Rev. Econom. Stud., 73, 4, 983-1007, (2006) · Zbl 1201.91103
[44] Laussel, D.; Le Breton, M., Existence of Nash equilibria in fiscal competition models, Reg. Sci. Urban Econ., 28, 3, 283-296, (1998)
[45] Leibrecht, M.; Hochgatterer, C., Tax competition as a cause of falling corporate income tax rates: A survey of empirical literature, J. Econ. Surv., 26, 4, 616-648, (2012)
[46] Levhari, D., A note on Houthakker’s aggregate production function in a multifirm industry, Econometrica, 36, 1, 151-154, (1968)
[47] Martos, B., Nem-Linearis Programzoasi Modszerek HatokoreTechnical Report, (1966), A Magyar Tudomanyos Akademia Kozgazdasagtudomanyi Intezetenek Kozlemenyei Budapest
[48] Milgrom, P.; Roberts, J., Rationalizability, learning, and equilibrium in games with strategic complementarities, Econometrica, 58, 6, 1255-1277, (1990) · Zbl 0728.90098
[49] Milgrom, P.; Roberts, J., Coalition-proofness and correlation with arbitrary communication possibilities, Games Econom. Behav., 17, 1, 113-128, (1996) · Zbl 0886.90189
[50] Milgrom, P.; Shannon, C., Monotone comparative statics, Econometrica, 62, 1, 157-180, (1994) · Zbl 0789.90010
[51] OECD, Harmful tax competition. An emerging global issuer, (1998), OECD Publishing: OECD Publishing Paris
[52] OECD, Addressing Base Erosion and Profit Shifting, (2013), OECD Publishing: OECD Publishing Paris
[53] Parchet, R., Are Local Tax Rates Strategic Complements or Strategic Substitutes?IdEP Economic Papers 1407, (2014), USI Università della Svizzera italiana
[54] Rota-Graziosi, G., 2015. Tax coordination and harmonization: A solution à la Schelling, Working paper. CERDI-CNRS. University of Auvergne.
[55] Slemrod, J.; Gillitzer, C., Tax Systems, (2014), The MIT Press
[56] Slemrod, J.; Wilson, J. D., Tax competition with parasitic tax havens, J. Public Econ., 93, 11-12, 1261-1270, (2009)
[57] Taugourdeau, E.; Ziad, A., On the existence of Nash equilibria in an asymmetric tax competition game, Reg. Sci. Urban Econ., 41, 5, 439-445, (2011)
[58] Topkis, D., Supermodularity and Complementarity, (1998), Princeton University Press: Princeton University Press Princeton, New Jersey
[59] Vives, X., Nash equilibrium with strategic complementarities, J. Math. Econom., 19, 3, 305-321, (1990) · Zbl 0708.90094
[60] Vives, X., Olipoly Pricing. Old Ideas and New Tools, (1999), The MIT Press: The MIT Press Cambridge, Massachusetts
[61] Vives, X., Complementarities and games: New developments, J. Econ. Lit., 43, 2, 437-479, (2005)
[62] Wildasin, D. E., Nash equilibria in models of fiscal competition, J. Public Econ., 35, 2, 229-240, (1988)
[63] Wildasin, D. E., Some rudimentary ’Duopolity’ theory, Reg. Sci. Urban Econ., 21, 3, 393-421, (1991)
[64] Wilson, J. D., A theory of interregional tax competition, J. Urban Econ., 19, 3, 296-315, (1986)
[65] Wilson, J. D., Tax competition with interregional differences in factor endowments, Reg. Sci. Urban Econ., 21, 3, 423-451, (1991)
[66] Zhao, Y. X.; Wang, S. Y.; Coladas Uria, L., Characterizations of r-convex functions, J. Optim. Theory Appl., 145, 186-195, (2010) · Zbl 1231.90314
[67] Zodrow, G. R.; Mieszkowski, P., Pigou, Tiebout, property taxation, and the underprovision of local public goods, J Urban Econ., 19, 3, 356-370, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.