IDEAS home Printed from
   My bibliography  Save this paper

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


  • Maria Letizia Bertotti
  • Giovanni Modanese


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.

Suggested Citation

  • Maria Letizia Bertotti & Giovanni Modanese, 2014. "Micro to macro models for income distribution in the absence and in the presence of tax evasion," Papers 1403.0015,
  • Handle: RePEc:arx:papers:1403.0015

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Maria Letizia Bertotti & Giovanni Modanese, 2015. "Economic inequality and mobility in kinetic models for social sciences," Papers 1504.03232,
    2. Bertotti, M.L. & Chattopadhyay, A.K. & Modanese, G., 2017. "Stochastic effects in a discretized kinetic model of economic exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 724-732.
    3. Maria Letizia Bertotti & Amit K Chattopadhyay & Giovanni Modanese, 2017. "Economic inequality and mobility for stochastic models with multiplicative noise," Papers 1702.08391,
    4. M. L. Bertotti & G. Modanese, 2016. "Mathematical models describing the effects of different tax evasion behaviors," Papers 1701.02662,

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1403.0015. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.