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Erschienen in: International Tax and Public Finance 5/2020

24.03.2020

Kant–Nash tax competition

verfasst von: Thomas Eichner, Rüdiger Pethig

Erschienen in: International Tax and Public Finance | Ausgabe 5/2020

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Abstract

In a two-country economy, we analyze how tax competition differs from the standard all-Nashian tax competition, if one or both countries are Kantians in Roemer’s sense. Kantians are shown to choose a higher tax rate than Nashians for any given tax rate of the other country, which indicates that they seek to mitigate the (Nashian) race to the bottom. In case of symmetric countries, the all-Kantian tax competition turns out to be efficient and the inefficient race to the bottom is weakened in economies with a Nashian and a Kantian. That confirms the intuitive idea that countries following the Kantian categorical imperative avoid or at least soften the socially undesirable impact of (Nashian) self-interest. We also investigate the incentives of opportunistic countries to choose Nashian or Kantian behavior out of self-interest and find that either both governments choose to behave as Kantians or that—under different conditions—the robust Nashian self-interest supersedes Kantian moral principles such that the inefficient all-Nashian tax competition results.

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Fußnoten
1
That inefficiency conclusion relies on the assumption that governments are benevolent in the sense that they care for their self-interested citizens. An alternative approach suggested by Brennan and Buchanan (1980) is to conceive of governments as Leviathans seeking to maximize tax revenues. The tax rate reducing effect of tax competition would then be beneficial.
 
2
Roemer (2015) proposed two different Kantian rules of behavior, the multiplicative rule and the additive rule. The actual sentence describes the multiplicative rule, which we are going to apply in Sects. 3 and 4. After that, we compare the results with those under the additive rule in Sect. 5.1.
 
3
The Kantian approach does not rely on the practice of behavioral economics to include “ad hoc” arguments into preferences (e.g., altruism or fairness) to model behavior that cannot be explained by self-interest.
 
4
In these games, the equilibrium is a state of mutually best replies.
 
5
In an extension of the analysis, we show in Sect. 5.2 that we can avoid both multiple equilibria and zero rates of return to capital (with some loss of informative results) by replacing the assumption of linear utility function with nonlinear utility.
 
6
Here, we refer to the unique equilibria of the Kant–Kant game, the Kant–Nash game, the Nash–Kant game and the Nash–Nash game under the assumptions of symmetry and the symmetric equilibrium of the Kant–Kant game.
 
7
For an excellent survey of this literature see Keen and Konrad (2013).
 
8
To ease the notation, we apply the following convention. If there is a formula, in which only the index "i" appears, as, e.g., in (1), the model contains the same formula with all indexes i replaced by j. To avoid clutter, we do not write down that second formula with indexes "j," however. Correspondingly, in addition to each formula, in which the two indexes "i" and "j" appear, there exists the same formula with all indexes i and j interchanged.
 
9
We choose the restrictive functional forms (1) and (2) for reasons of tractability. Production functions of type (1) and/or utility functions of type (2) are employed among others by Keen and Lahiri (1998), Bucovetsky (2009), Kempf and Rota-Graziosi (2010), Ogawa (2013) and Breuillé and Zanaij (2013).
 
10
Due to our representative-consumer assumption, there is no analytical difference between a local public good and a publicly provided private good.
 
11
The condition \(a_i > 2 b {\bar{k}}\) ensures that the marginal productivity \(X^i_{k_i}(k_i)\) is always positive even if all capital is employed in one country. The inequality \(a_i \ge a_j\) serves to fix ideas without restricting generality. \(a_i \ge a_j\) is the only exception to the rule introduced in footnote 8. Throughout the paper, we assume that country i is equally productive as or more productive than country j.
 
12
\(\sum _h z_h\) is short for \(z_i+z_j\).
 
13
Nonnegativity constraints are also taken into account by, e.g., Bucovetsky (2009) and Kempf and Rota-Graziosi (2010).
 
14
The derivation of (10) and (11) can be found in the Appendix.
 
15
For a further discussion of the Rosen equilibrium we refer to Long (2010).
 
16
Rather than attempting to clarify the relation between Roemer’s concept of Kantian optimization and informal notions of the categorical imperative (see, e.g., Elster 2017), we provide a non-technical explanation of that concept. Roemer (2017) considers his approach as a proposal of “how cooperation of economic agents can be formalized as a mathematical first cousin of Nash optimization.” For further details and possible interpretations of his concept of Kantian equilibrium, see Roemer (2019).
 
17
\(2 b \varepsilon {\bar{k}} > (a_i-a_j) (1+ \varepsilon )\) is satisfied for identical countries and also for asymmetric countries as long as the productivity advantage of country i over j is not too large.
 
18
Keep in mind that (23) also holds for Kantian j after interchanging all subscripts i and j.
 
19
The functions \( {\overline{H}}(b, {\bar{k}}, \varepsilon , a_i-a_j)\) and \( {\underline{H}}(b, {\bar{k}}, \varepsilon , a_i-a_j)\) are defined in the proof of Proposition 4 of the Appendix. It holds \({\overline{H}} \ge {\underline{H}}>0\).
 
20
\( \left( t_i^{KK}, t_j^{KK} \right) \gg \left( t_i^{NN}, t_j^{NN} \right) \) means that \( t_i^{KK} > t_i^{NN}\) and \(t_j^{KK}>t_j^{NN}\).
 
21
In Table 1,K and N stand for the strategies “Kantian behavior” and “Nash behavior,” respectively.
 
22
Figure 4b shows, however, that \(w_i^{NN}\) is only slightly greater than \(w_i^{KN}\).
 
23
The welfare levels are \(w_i^{NK} =a {\bar{k}} - \frac{(1+ 2 \varepsilon -12 \varepsilon ^2 -16 \varepsilon ^3) b {\bar{k}}^2}{2(1+\varepsilon )^2}\), \(w_i^{NN} = a {\bar{k}} - \frac{(1+\varepsilon -4 \varepsilon ^2) b {\bar{k}}^2 }{2(1+\varepsilon )} \) and \(w_i^{KN} = a {\bar{k}} - \frac{(1+ 2 \varepsilon ) b {\bar{k}}^2 }{2(1+\varepsilon )^2}\).
 
24
Observe that the solution of \( t_i = T^{Ni} (t_i) \) does not depend on whether the plus-sign or minus-sign in front of the root holds.
 
25
We ran several more simulations but did not find any other welfare rankings than those of Example 1 and 2.
 
26
\(W^i_\lambda (\lambda t_i, \lambda t_j)=0\) has three solutions. Two of them consist of complex roots and are ignored.
 
27
As mentioned by Long (2010), a major problem with the concept of Rosen equilibrium is that it is not clear how the weights are determined.
 
Literatur
Zurück zum Zitat Barrett, S. (2003). Environment and statecraft: The strategy of environmental treaty-making. Oxford: Oxford University Press.CrossRef Barrett, S. (2003). Environment and statecraft: The strategy of environmental treaty-making. Oxford: Oxford University Press.CrossRef
Zurück zum Zitat Baskaran, T., & Lopes da Fonesca, M. (2013). The economics and empirics of tax competition: A survey and lessons for the EU. Erasmus Law Review, 7, 3–12. Baskaran, T., & Lopes da Fonesca, M. (2013). The economics and empirics of tax competition: A survey and lessons for the EU. Erasmus Law Review, 7, 3–12.
Zurück zum Zitat Brennan, G., & Buchanan, J. (1980). The power to tax: Analytical foundations of a fiscal constitution. Cambridge: Cambridge University Press. Brennan, G., & Buchanan, J. (1980). The power to tax: Analytical foundations of a fiscal constitution. Cambridge: Cambridge University Press.
Zurück zum Zitat Breuillé, M.-L., & Zanaij, S. (2013). Mergers in fiscal federalism. Journal of International Economics, 105, 11–22. Breuillé, M.-L., & Zanaij, S. (2013). Mergers in fiscal federalism. Journal of International Economics, 105, 11–22.
Zurück zum Zitat Bucovetsky, S. (2009). An index of capital tax competition. International Tax and Public Finance, 16, 727–752.CrossRef Bucovetsky, S. (2009). An index of capital tax competition. International Tax and Public Finance, 16, 727–752.CrossRef
Zurück zum Zitat Edwards, J., & Keen, M. (1996). Tax competition and Leviathan. European Economic Review, 40, 113–134.CrossRef Edwards, J., & Keen, M. (1996). Tax competition and Leviathan. European Economic Review, 40, 113–134.CrossRef
Zurück zum Zitat Elster, J. (2017). On seeing and being seen. Social Choice and Welfare, 49, 721–734.CrossRef Elster, J. (2017). On seeing and being seen. Social Choice and Welfare, 49, 721–734.CrossRef
Zurück zum Zitat Ghosh, A., & Long, N. V. (2015). Kant’s rule of behavior and Kant-Nash equilibria in games of contribution to a public good. Paper presented at the CESifo conference on public sector economics, Munich, April 2015. Ghosh, A., & Long, N. V. (2015). Kant’s rule of behavior and Kant-Nash equilibria in games of contribution to a public good. Paper presented at the CESifo conference on public sector economics, Munich, April 2015.
Zurück zum Zitat Grafton, R. Q., Kompas, T., & Long, N. V. (2017). A brave new world? Kantian–Nashian interaction and the dynamics of global climate change mitigation. European Economic Review, 99, 31–42.CrossRef Grafton, R. Q., Kompas, T., & Long, N. V. (2017). A brave new world? Kantian–Nashian interaction and the dynamics of global climate change mitigation. European Economic Review, 99, 31–42.CrossRef
Zurück zum Zitat Hamilton, J., & Pestieau, P. (2005). Optimal income tax competition and the ability distribution: Implications for migration equilibria. International Tax and Public Finance, 12, 29–45.CrossRef Hamilton, J., & Pestieau, P. (2005). Optimal income tax competition and the ability distribution: Implications for migration equilibria. International Tax and Public Finance, 12, 29–45.CrossRef
Zurück zum Zitat Hamilton, J. H., & Slutsky, M. (1990). Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior, 2, 29–46.CrossRef Hamilton, J. H., & Slutsky, M. (1990). Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior, 2, 29–46.CrossRef
Zurück zum Zitat Heinrich, T. (2013). When is foreign aid selfish, when is it selfless. Journal of Politics, 75, 422–435.CrossRef Heinrich, T. (2013). When is foreign aid selfish, when is it selfless. Journal of Politics, 75, 422–435.CrossRef
Zurück zum Zitat Keen, M., & Konrad, K. A. (2013). The theory of international tax competition and coordination. In A. J. Auerbach, R. Chetty, M. Feldstein, & E. Saez (Eds.), Handbook of public economics (Vol. 5, pp. 257–338). Keen, M., & Konrad, K. A. (2013). The theory of international tax competition and coordination. In A. J. Auerbach, R. Chetty, M. Feldstein, & E. Saez (Eds.), Handbook of public economics (Vol. 5, pp. 257–338).
Zurück zum Zitat Keen, M., & Lahiri, S. (1998). The comparison between destination and origin principles under imperfect competition. Journal of International Economics, 45, 323–350.CrossRef Keen, M., & Lahiri, S. (1998). The comparison between destination and origin principles under imperfect competition. Journal of International Economics, 45, 323–350.CrossRef
Zurück zum Zitat Kempf, H., & Rota-Graziosi, G. (2010). Endogenizing leadership in tax competition. Journal of Public Economics, 94, 768–776.CrossRef Kempf, H., & Rota-Graziosi, G. (2010). Endogenizing leadership in tax competition. Journal of Public Economics, 94, 768–776.CrossRef
Zurück zum Zitat Laussel, D., & Le Breton, M. (1998). Existence of Nash equilibria in fiscal competition models. Regional Science and Urban Economics, 45, 323–350. Laussel, D., & Le Breton, M. (1998). Existence of Nash equilibria in fiscal competition models. Regional Science and Urban Economics, 45, 323–350.
Zurück zum Zitat Long, N. V. (2010). A survey of dynamic games in economics. Singapore: World Scientific Publishers.CrossRef Long, N. V. (2010). A survey of dynamic games in economics. Singapore: World Scientific Publishers.CrossRef
Zurück zum Zitat Long, N. V. (2016). Kant–Nash equilibrium in a quantity-setting oligopoly. In P. von Mouche & F. Quartieri (Eds.), Equilibrium theory for cournot oligopolies and related games: Essays in honor of Koji Okuguchi (pp. 179–202). Berlin: Springer.CrossRef Long, N. V. (2016). Kant–Nash equilibrium in a quantity-setting oligopoly. In P. von Mouche & F. Quartieri (Eds.), Equilibrium theory for cournot oligopolies and related games: Essays in honor of Koji Okuguchi (pp. 179–202). Berlin: Springer.CrossRef
Zurück zum Zitat Long, N. V. (2017). Mixed-strategy Kant–Nash equilibrium in games of voluntary contributions to a public good. In W. Buchholz & D. Rübbelke (Eds.), The theory of externalities and public goods (pp. 107–126). Berlin: Springer.CrossRef Long, N. V. (2017). Mixed-strategy Kant–Nash equilibrium in games of voluntary contributions to a public good. In W. Buchholz & D. Rübbelke (Eds.), The theory of externalities and public goods (pp. 107–126). Berlin: Springer.CrossRef
Zurück zum Zitat Long, N. V. (2019). A dynamic game model with Kantian and Nashian players. In P. Pineau (Ed.), Games in management science: Essays in honor of Georges Zaccour, chapter 14. Berlin: Springer. Long, N. V. (2019). A dynamic game model with Kantian and Nashian players. In P. Pineau (Ed.), Games in management science: Essays in honor of Georges Zaccour, chapter 14. Berlin: Springer.
Zurück zum Zitat Ogawa, H. (2013). Further analysis on leadership in tax competition: The role of capital ownership. International Tax and Public Finance, 20, 474–484.CrossRef Ogawa, H. (2013). Further analysis on leadership in tax competition: The role of capital ownership. International Tax and Public Finance, 20, 474–484.CrossRef
Zurück zum Zitat Roemer, J. E. (2010). Kantian equilibrium. Scandinavian Journal of Economics, 112, 1–24.CrossRef Roemer, J. E. (2010). Kantian equilibrium. Scandinavian Journal of Economics, 112, 1–24.CrossRef
Zurück zum Zitat Roemer, J. E. (2015). Kantian optimization: A micro foundation for cooperation. Journal of Public Economics, 127, 45–57.CrossRef Roemer, J. E. (2015). Kantian optimization: A micro foundation for cooperation. Journal of Public Economics, 127, 45–57.CrossRef
Zurück zum Zitat Roemer, J. E. (2017). Embedding cooperation in general equilibrium models. Cowles foundation discussion paper no. 2098. Roemer, J. E. (2017). Embedding cooperation in general equilibrium models. Cowles foundation discussion paper no. 2098.
Zurück zum Zitat Roemer, J. E. (2019). How we cooperate: A theory of Kantian optimization. New Haven: Yale University Press.CrossRef Roemer, J. E. (2019). How we cooperate: A theory of Kantian optimization. New Haven: Yale University Press.CrossRef
Zurück zum Zitat Rosen, J. B. (1965). Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33, 520–534.CrossRef Rosen, J. B. (1965). Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33, 520–534.CrossRef
Zurück zum Zitat Van der Pol, T., Weikard, H.-P., & van Ierland, E. (2012). Can altruism stabilise international climate agreements? Ecological Economics, 81, 112–120.CrossRef Van der Pol, T., Weikard, H.-P., & van Ierland, E. (2012). Can altruism stabilise international climate agreements? Ecological Economics, 81, 112–120.CrossRef
Zurück zum Zitat Wagener, A. (2013). Tax competition, relative performance, and policy imitation. International Economic Review, 54, 1251–1264.CrossRef Wagener, A. (2013). Tax competition, relative performance, and policy imitation. International Economic Review, 54, 1251–1264.CrossRef
Zurück zum Zitat Weichenrieder, A. J., & Busch, O. (2007). Delayed integration as possible remedy for the race to the bottom. Journal of Urban Economics, 61, 565–575.CrossRef Weichenrieder, A. J., & Busch, O. (2007). Delayed integration as possible remedy for the race to the bottom. Journal of Urban Economics, 61, 565–575.CrossRef
Zurück zum Zitat Wildasin, D. (1988). Nash equilibria in models of fiscal competition. Journal of Public Economics, 35, 229–240.CrossRef Wildasin, D. (1988). Nash equilibria in models of fiscal competition. Journal of Public Economics, 35, 229–240.CrossRef
Zurück zum Zitat Wildasin, D. (1991). Income redistribution in a common labor market. American Economic Review, 81, 757–774. Wildasin, D. (1991). Income redistribution in a common labor market. American Economic Review, 81, 757–774.
Zurück zum Zitat Wilson, J. D. (1986). A theory of inter-regional tax competition. Journal of Urban Economics, 19, 296–315.CrossRef Wilson, J. D. (1986). A theory of inter-regional tax competition. Journal of Urban Economics, 19, 296–315.CrossRef
Zurück zum Zitat Zodrow, R. G., & Mieszkowski, P. (1986). Pigou, Tibout, property taxation, and the underprovision of local public goods. Journal of Urban Economics, 19, 356–370.CrossRef Zodrow, R. G., & Mieszkowski, P. (1986). Pigou, Tibout, property taxation, and the underprovision of local public goods. Journal of Urban Economics, 19, 356–370.CrossRef
Metadaten
Titel
Kant–Nash tax competition
verfasst von
Thomas Eichner
Rüdiger Pethig
Publikationsdatum
24.03.2020
Verlag
Springer US
Erschienen in
International Tax and Public Finance / Ausgabe 5/2020
Print ISSN: 0927-5940
Elektronische ISSN: 1573-6970
DOI
https://doi.org/10.1007/s10797-020-09597-3

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