Journal of Tax Reform
Modelling of a relative income tax bracket-based progression with the effect of a slower tax burden growth
D.E. Lapov 1, I.A. Mayburov 2
1 Novosibirsk State University of Economics and Management (NSUEM), Novosibirsk, Russian Federation
2 Ural Federal University, Ekaterinburg, Russian Federation
Abstract
This study aims to model the distribution of the tax burden in schedular progressive taxation and to describe the key characteristics of such models, in particular their differences from the models based on continuously increasing smooth functions of the relationship between the tax burden and the taxpayer's income. Our hypothesis is that the use of the Gompertz function to model the main indicators of tax burden distribution of the schedular progressive income tax will help us approximate and formalize the distribution of the tax burden in a relative income tax bracket-based progression. Our research relies on the hypothetico-deductive model, more specifically, on mathematical hypothesis testing. The methodological framework comprises models of progressive taxation and mathematical methods, including data approximation based on the use of the Gompertz function, analysis of the antiderivative and convexity of functions and their properties. The resulting model can be used to describe the dynamic characteristics of the relationship between the tax burden and certain parameters of schedular taxation. This model can help identify the level of income beyond which the progression of the tax burden becomes formal and does not generate commensurately high revenue growth. The existence of such income level results in what can be considered the key drawback of the relative progression in question – the impossibility to provide a significant difference (step) of the tax burden progression in the whole interval of the taxpayer's income. What makes this research practically significant is that the proposed methodology allows us to take into account the actual tax burden in modelling the parameters of the relative progression.
Keywords
income tax; progressive scale; schedule; tax rates; Gompertz function
JEL classification
H24, J31, O15References
1. Popescu M.E., Militaru E., Stanila L., Vasilescu M.D., Cristescu A. Flat-Rate versus Progressive Taxation? An Impact Evaluation Study for the Case of Romania. Sustainability. 2019;11(22):6405. https://doi.org/10.3390/su11226405
2. Chambers C.Р., Moreno-Ternero J.D. Taxation and poverty. Social Choice and Welfare. 2017;48(1):153–175. https://doi.org/10.1007/s00355-015-0905-4
3. Krajewski P., Piłat K. Does a Progressive PIT Stabilize the Economy? A Comparison of Progressive and Flat Taxes. Comparative Economic Research. 2017;20(1):21–34. https://doi.org/10.1515/cer-2017-0002
4. Mirrlees J.A. An Exploration in the Theory of Optimum Income Taxation. Review of Economic Studies. 1971;38(2):175–208. https://doi.org/10.2307/2296779
5. Luksic J. The extensive macro labor supply elasticity: Integrating taxes and expenditures. European Economic Review. 2020;121:103325. https://doi.org/10.1016/j.euroecorev.2019.103325
6. Kireenko A.P., Nevzorova E.N., Kireyeva A.F., Filippovich A.S., Khoroshavina E.S. Lab experiment to investigate tax compliance: the case of future taxpayers’ behavior in Russia and Belarus. Journal of Tax Reform. 2018;4(3):266–290. https://doi.org/10.15826/jtr.2018.4.3.056
7. Oishi S., Kushlev K., Schimmack U. Progressive Taxation, Income Inequality, and Happiness. American psychologist. 2018;73(2):157–168. https://doi.org/10.1037/amp000016
8. Garcia-Muniesa J. Economic crisis and support for progressive taxation in Europe. European Societies. 2018;21(2):256–279. doi.org10.1080/14616696.2018.1547836
9. Carriero R., Filandri M. Support for conditional unemployment benefit in European countries: The role of income inequality. SAGE Journals. Collection. 2018;29(4):498–514. https://doi.org/10.25384/SAGE.c.4347047.v1
10. Oh J. Are progressive tax rates progressive policy? New York University Law Review. 2017;92(6):1909–1976. Available at: https://www.nyulawreview.org/wp-content/uploads/2018/08/NYULawReview-92-6-Oh.pdf
11. Mehrotra A. Making the Modern American Fiscal State: Law, Politics, and the Rise of Progressive Taxation. New York: Cambridge University Press; 2013, pp. 1877–1929. Available at: https://assets.cambridge.org/97811070/43923/frontmatter/9781107043923_frontmatter.pdf
12. Barrios S., Ivaškaitė-Tamošiūnė V., Maftei A., Narazani E. & Varga J. Progressive Tax Reforms in Flat Tax Countries. Eastern European Economics. 2019;58(2):83–107. https://doi.org/10.1080/00128775.2019.1671201
13. Balatsky E., Ekimova N. Evaluating scenarios of a personal income tax reform in Russia. Journal of Tax Reform. 2019;5(1):6–22. https://doi.org/10.15826/jtr.2019.5.1.057
14. Di Nola A., Kocharkov G., Vasilev A. Envelope wages, hidden production and labor productivity. The B.E. Journal of Macroeconomics. 2019;19(2):20180252. https://doi.org/10.1515/bejm-2018-0252
15. Vlad C., Brezeanu, P. European taxation– between flat and progressive tax. In: Brătianu C., Zbuchea A., Pînzaru F., Vătămănescu E.-M., Leon R.-D. (eds) Strategica: Local Versus Global. International Academic Conference, Bucharest, Romania, October 29–31, 2015. 3th ed. Bucharest; 2015, pp. 528–534.
16. Mayburov I.A. Marking the centenary of income tax in Russia: theoretical analysis of key stages of the reform. Journal of Tax Reform. 2015;1(2-3):161–176. (In Russ.) https://doi.org/10.15826/jtr.2015.1.2.010
17. Jin Kwon Hyun, Seung-Hoon Jeon, Byung In Lim. The Discrepancy between Statutory Tax and Real Tax Burden: The Case of Korea. Journal of the Korean Economy. 2009;10(1):81–92. Available at: https://www.researchgate.net/publication/253489980_The_Discrepancy_between_Statutory_Tax_and_Real_Tax_Burden_The_Case_of_Korea
18. Holter H.A., Krueger D., Stepanchuk S. How do tax progressivity and household heterogeneity affect Laffer curves? Quantitative Economics. 2019;10(4):1317–1356. https://doi.org/10.3982/QE653
19. Belozyorov S.A., Sokolovska O.V. Personal income taxation and income inequality in Asia-Pacific: a cross-country analysis. Journal of Tax Reform. 2018;4(3):236–249. https://doi.org/10.15826/jtr.2018.4.3.054
20. Landier A., Plantin G. Taxing the Rich. Review of Economic Studies. 2017;84(3):1186–1209. https://doi.org/10.1093/restud/rdw033
21. Stephenson A. The Impact of Personal Income Tax Structure on Income Inequality for Belgium, Bulgaria, Germany, Lithuania, and Poland: A Comparison of Flat and Graduated Income Tax Structures. Atlantic Economic Journal. 2019;46(4):405–417. https://doi.org/10.1007/s11293-018-9601-y
22. Musgrave R. A., Tun T. Income Tax Progression. 1929–1948. Journal of Political Economy. 1948;56(6):498–514. https://doi.org/10.1086/256742
23. Chistyakov S.V., Kvitko A.N., Kichinsky D.B., Vasesov M.E., Uspasskaya I.S. A system of models for constructing a progressive scale of income tax. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes. 2020;16(1):4–18. (In Russ.) https://doi.org/10.21638/11702/spbu10.2020.101
24. Kim H.-J. Some models for progressive taxation. Communications of the Korean Mathematical Society. 2018;33(3):823–831. https://doi.org/10.4134/CKMS.c170272
25. Smirnov R.O. Modeling of Choosing the Parameters of the Income Tax Schedule. St Petersburg University Journal of Economic Studies. 2011;(4):141–148. (In Russ.) Available at: https://economicsjournal.spbu.ru/article/view/2935
26. Saez E. Using Elasticities to Derive Optimal Income Tax Rates. Review of Economics Studies. 2001;68(1):205–229. https://doi.org/10.1111/1467-937X.00166
27. Assabil S. Forecasting Maternal Mortality with Modified Gompertz Model. Journal of Advances in Mathematics and Computer Science. 2019;32(5):1–7. https://doi.org/10.9734/jamcs/2019/v32i530155
28. Jenner A., Kim P., Frascoli F. Oncolytic virotherapy for tumours following a Gompertz growth law. Journal of Theoretical Biology. 2019;480:129–140 https://doi.org/10.1016/j.jtbi.2019.08.002
29. Vaghi C., Rodallec A., Fanciullino R., Ciccolini J., Mochel J.P., Mastri M., et al. Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Comput Biol. 2020;16(2):e1007178. https://doi.org/10.1371/journal.pcbi.1007178
30. Vilanova A., Kim B.-Y., Kim C.K., Kim H.-G. Linear-Gompertz Model-Based Regression of Photovoltaic Power Generation by Satellite Imagery-Based Solar Irradiance. Energies. 2020;13(4):781. https://doi.org/10.3390/en13040781
31. Sake R., Akhtar M. Fitting of Gompertz Model Between Rainfall and Ground Water Levels – A Case Study. International Journal of Mathematics Trends and Technology. 2019;65(7):85–93. https://doi.org/10.14445/22315373/IJMTT-V65I7P514
32. Salinari G., De Santis G. One or more rates of ageing? The extended gamma-Gompertz model (EGG). Statistical Methods & Applications. 2020;29(2):211–236. https://doi.org/10.1007/s10260-019-00471-z
33. Niu Y., Yun J., Bi Y., Wang T., Zhang Y., Liu H. & Zhao F. Predicting the shelf life of postharvest Flammulina velutipes at various temperatures based on mushroom quality and specific spoilage organisms. Postharvest Biology and Technology. 2020;167:111235. https://doi.org/10.1016/j.postharvbio.2020.111235
34. Brites N.M., Braumann C.A. Harvesting in a Random Varying Environment: Optimal, Stepwise and Sustainable Policies for the Gompertz Model. Statistics, Optimization & Information Computing. 2019;7(3):533–544. https://doi.org/10.19139/soic.v7i3.830
35. Brites N.M., Braumann C.A. Fisheries management in randomly varying environments: Comparison of constant, variable and penalized efforts policies for the Gompertz model. Fisheries Research. 2019;216:196–203. https://doi.org/10.1016/j.fishres.2019.03.016
36. Figueira F.C., Moura N.J., Ribeiro M.B. The Gompertz-Pareto Income Distribution. Physica A: Statistical Mechanics and its Applications. 2010;390(4):689–698. https://doi.org/10.1016/j.physa.2010.10.014
37. Gompertz B. On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society. 1825;115:513–585. https://doi.org/10.1098/rstl.1825.0026
38. Mayburov I.A., Sokolovskaya A.M. Theory of Taxation. Advanced course: textbook for undergraduates. Moscow: UNITY-DANA; 2011. 591 p. (In Russ.)
Acknowledgements
The research was supported by the Russian Foundation for Basic Research within the framework of research project No. 19-010-00365A
About Authors
Dmitry E. Lapov – Lecturer of Department of Economic Theory, Novosibirsk State University of Economics and Management “NINH” (52 Kamenskaya St., Novosibirsk, 630099, Russia); ORCID: 0000-0002-2098-6853; e-mail: lapvd@rambler.ru
Igor A. Mayburov – Doctor of Economic Sciences, Professor, Head of the Department of Financial and Tax Management, Ural Federal University named the first President of Russia B. N. Yeltsin (19 Mira St., Yekaterinburg, 620002, Russia); ORCID: 0000-0001-8791-665X; e-mail: mayburov.home@gmail.com
For citation
Lapov D.E., Mayburov I.A. Modelling of a relative income tax bracket-based progression with the effect of a slower tax burden growth. Journal of Tax Reform. 2021;7(2):160–172. doi.org/10.15826/jtr.2021.7.2.096
Article info
Received May 30, 2021; Revised July 23, 2021; Accepted August 6, 2021
DOI: https://doi.org/10.15826/jtr.2021.7.2.096
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