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Micro to macro models for income distribution in the absence and in the presence of tax evasion

Listed author(s):
  • Maria Letizia Bertotti
  • Giovanni Modanese
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    We investigate the effect of tax evasion on the income distribution and the inequality index of a society through a kinetic model described by a set of nonlinear ordinary differential equations. The model allows to compute the global outcome of binary and multiple microscopic interactions between individuals. When evasion occurs, both individuals involved in a binary interaction take advantage of it, while the rest of the society is deprived of a part of the planned redistribution. In general, the effect of evasion on the income distribution is to decrease the population of the middle classes and increase that of the poor and rich classes. We study the dependence of the Gini index on several parameters (mainly taxation rates and evasion rates), also in the case when the evasion rate increases proportionally to a taxation rate which is perceived by citizens as unfair. Finally, we evaluate the relative probability of class advancement of individuals due to direct interactions and welfare provisions, and some typical temporal rates of convergence of the income distribution to its equilibrium state.

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    Paper provided by in its series Papers with number 1403.0015.

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    Date of creation: Jan 2014
    Publication status: Published in Applied Mathematics and Computation (2014), pp. 836-846
    Handle: RePEc:arx:papers:1403.0015
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    1. Sascha Hokamp & Michael Pickhardt, 2010. "Income Tax Evasion in a Society of Heterogeneous Agents - Evidence from an Agent-based Model," International Economic Journal, Taylor & Francis Journals, vol. 24(4), pages 541-553.
    2. Georg Zaklan & Frank Westerhoff & Dietrich Stauffer, 2009. "Analysing tax evasion dynamics via the Ising model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(1), pages 1-14, June.
    3. Maria Letizia Bertotti & Giovanni Modanese, 2012. "Exploiting the flexibility of a family of models for taxation and redistribution," Papers 1207.6081,, revised Mar 2014.
    4. Mittone, Luigi, 2006. "Dynamic behaviour in tax evasion: An experimental approach," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 35(5), pages 813-835, October.
    5. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    6. M. Bertotti & G. Modanese, 2012. "Exploiting the flexibility of a family of models for taxation and redistribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(8), pages 1-10, August.
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