Modeling of the impact of information on tax audits on the risk statuses and evasions of individuals

E. A. Gubar ; E. M. Zhitkova ; S. Sh. Kumacheva ; G. A. Tomilina

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 2, pp. 245-258

Résumé

Tax system accomplishes several significant functions, concerned with different fields of its activities, such as fiscal, social, regulatory, distributive, incentive and control. The correctness of work of fiscal system depends on tax control; in turn, the most important part of tax control is tax audit. However, the previous studies have shown that the implementation of tax audits with an optimal probability is an expensive procedure. Due to the restricted budget of the tax authorities, such audits are not always feasible. Therefore, to increase tax collection, it is necessary to apply additional ways to stimulate taxpayers to fair tax payments. In this paper, we investigate a model of tax control taking into account the dissemination information about possible audits over the population of taxpayers as a tool to stimulate tax collection. We use an evolutionary approach to describe the behavior of taxpayers in total population, where each taxpayer has one of three different risk statuses: risk-loving, risk-neutral, and risk-avoiding. The idea of disseminating information in a population has been studied based on the Markov process in networks with different structures. We estimate the influence of the propagated information on the final distribution of risk statuses and the evasions of taxpayers. We design a series of numerical simulations with the different topology of the network and artificial centers of influence which can be included or not included in the network of contacts to corroborate our theoretical arguments. As well as we present a comparative analysis of the received numerical simulations.

Détail

Keywords: tax auditing, risk propensity, Markov processes on the network, dynamic of opinions.
Mots-clés : information dissemination

Bibliographie

[1] Chander P., Wilde L. L., “A general characterization of optimal income tax enforcement”, Rev. of Econ. Studies, 65 (1998), 165–183 | DOI | MR | Zbl

[2] Vasin A. A., Morozov V. V., Game theory and models of mathematical economics, Moscow University Publ., M., 2005, 272 pp. (In Russian)

[3] Bure V. M., Kumacheva S. Sh., “A model of audit with using of statistical information about taxpayers' income”, Vestnik of Saint Peterburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2005, no. 1–2, 140–145 (In Russian)

[4] Bure V. M., Kumacheva S. Sh., “A game theoretical model of tax auditing with using a statistical information about taxpayers”, Vestnik of Saint Peterburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2010, no. 4, 16–24

[5] Samuelson P. A., Nordhaus W. D., Economics, 18th ed., McGraw Hill Publ., New York, 2005, 776 pp.

[6] Kumacheva S. Sh., Gubar E. A., “Evolutionary model of tax auditing”, Contributions to Game Theory and Management, 8 (2015), 164–175 | MR

[7] Antoci A., Russu P., Zarri L., “Tax evasion in a behaviorally heterogeneous society: An evolutionary analysis”, Economic Modelling, 10:42 (2014), 106–115 | DOI

[8] Antunes L., Balsa J., Urbano P., Moniz L., Roseta-Palma C., “Tax compliance in a simulated heterogeneous multi-agent society”, Lecture Notes in Computer Science, 3891, 2006, 147–161 | DOI

[9] Gubar E., Kumacheva S., Zhitkova E., Kurnosykh Z., “Evolutionary behavior of taxpayers in the model of information dissemination”, Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the memory of V. F. Demyanov, IEEE Conference Publ., 2017, 1–4

[10] Gubar E., Kumacheva S., Zhitkova E., Kurnosykh Z., Skovorodina T., “Modelling of information spreading in the population of taxpayers: Evolutionary approach”, Contributions to Game Theory and Management, 10 (2017), 100–128 | MR

[11] Gubar E. A., Kumacheva S. Sh., Zhitkova E. M., Porokhnyavaya O. Yu., “Propagation of information over the network of taxpayers in the model of tax auditing”, 2015 Intern. Conference on Stability and Control Processes in memory of V. I. Zubov, SCP 2015, IEEE Conference Publ., 2015, 15637330, 244–247

[12] DeGroot M. H., “Reaching a consensus”, Journal of the American Statistical Association, 69:345 (1974), 118–121 | DOI | Zbl

[13] Borovkov A. A., Theory of probability, Edutorial URSS Publ., M., 2003, 472 pp.

[14] Bure V. M., Parilina E. M., Sedakov A. A., “Consensus in a social network with two principals”, Autom. Remote Control, 78:8 (2017), 1489–1499 (In Russian) | MR | Zbl

[15] Gubanov D. A., Novikov D. A., Chkhartishvili A. G., Social networks: Models of informational influence, control and opposition, Fizmatlit Publ., M., 2010, 228 pp. (In Russian)

[16] Kumacheva S. Sh., “Tax auditing using statistical information about taxpayers”, Contributions to Game Theory and Management, 5 (2012), 156–167 | MR | Zbl

[17] Tomilina G. A., “Modeling of scenarios for the dissemination of information on audits in the taxpayers network”, Control Processes and Stability, 5:1 (2018), 497–501 (In Russian)

[18] Niazashvili A. G., Hashchenko V. A., “Psychological readiness for economic risk”, Psychology and Economics, All-Russian scientific and practical conference of the Russian Psychological Society, eds. O. G. Posypanov, V. V. Spasennikov, Kaluzhskij filial MGEI, KGPU Publ., M., 2000, 160–162 (In Russian)

[19] Web site. Federal state statistics center (accessed: 02.03.2018)

[20] Kendall M. G., Stuart A., The advanced theory of statistics, Charles Griffin and Company Limited Publ., London, 1963, 585 pp. | MR | MR

[21] Kumacheva S., Gubar E., Zhitkova E., Tomilina G., “Evolution of risk-statuses in one model of tax control”, Static and Dynamic Game Theory: Foundations and Applications, 2018, 121–138 | DOI | MR | Zbl