Modeling of pension income and expenditures based on the Verhulst equation and polynomial regression with demographic projections
- Authors: Suo S.1, Kostyrin E.V.1
-
Affiliations:
- Bauman Moscow State Technical University (National Research University)
- Issue: Vol 60, No 2 (2024)
- Pages: 50-66
- Section: Problems of national economy
- URL: https://journals.rcsi.science/0424-7388/article/view/263054
- DOI: https://doi.org/10.31857/S0424738824020054
- ID: 263054
Open Access
Access granted
Abstract
To calculate the demographic load factor in this work, the forecasting of the working-age population of Russia was carried using the polynomial regression equation of the fourth degree with an accuracy of 0.227% and forecasting the number of people older than working age using the Verhulst equation (prediction accuracy of 1.084%) for the period from 2023 to 2031 (9 years). An economic and mathematical model was developed for calculating pension income and expenses for the implementation of individual (personalized) pension accounts of citizens and a stress analysis of the model was carried out based on an assessment of the impact of the pension contribution rate, average monthly salary, average investment income rate for transactions with pension funds of citizens (rate of return) and growth rates salaries, ensuring a balance between pension income and pension expenses of citizens. The practical implementation of the developed economic and mathematical model shows that the minimum value of the rate of return, ensuring balance between pension income and pension expenses of citizens, is 1.408%. The minimum average monthly salary is 22,949.39 rubles; the contribution rate to the Pension fund is estimated at 18.813%.
Full Text
About the authors
S. Suo
Bauman Moscow State Technical University (National Research University)
Author for correspondence.
Email: sisuo1997@gmail.com
Russian Federation, Moscow
E. V. Kostyrin
Bauman Moscow State Technical University (National Research University)
Email: kostyrinev@bmstu.ru
Russian Federation, Moscow
References
- Алексашенко С. В. (2019). Русское экономическое чудо: что пошло не так? М.: АСТ. 320 с. [Aleksashenko S. В. (2019). Russian economic miracle: What went wrong? Moscow: AST. 320 p. (in Russian).]
- Биткина И. К. (2020). К вопросу об эффективности накопительных элементов пенсионной системы: международный опыт // Финансы: теория и практика. № 5. С. 24–40. doi: 10.26794/2587-5671-2020-24-5-24-40 [Bitkina I. K. (2020). Efficiency of the funded elements of the pension system: International practices. Finance: Theory and Practice, 5, 24–40 (in Russian).]
- Головкина А. Г., Козынченко В. А., Клименко И. С. (2022). Метод последовательных приближений для построения модели динамической полиномиальной регрессии // Вестник Санкт-Петербургского университета. Т. 18. Вып. 4. С. 487–500. [Golovkina A. G., Kozychenko V. A., Klimenko I. S. (2022). Method of successive approximations for the dynamic polynomial regression model building. Saint-Petersburg University Bulletin, 4, 18, 487–500 (in Russian).]
- Гурвич Е. Т. (2019). Развилки пенсионной реформы: российский и международный опыт // Вопросы экономики. № 9. С. 5–39. [Gurvich E. Т. (2019). Pension reform developments: Russian and international experience. Voprosy Ekonomiki, 9, 5–39 (in Russian).]
- Костырин Е. В., Дрынкин С. Г. (2023). Экономический эффект от внедрения персонифицированных пенсионных счетов в систему пенсионного обеспечения граждан России // Экономика и управление: проблемы, решения. Т. 3. № 9. С. 129–144. [Kostyrin E. V., Drynkin S. G. (2023). Economic effect of the introduction of personalized pension accounts into the pension system of Russian citizens. Economics and Management: Problems, Solutions, 3, 9, 129–144 (in Russian).]
- Питиляк Д. А., Драненко Л. П., Базиль Т. В., Черняева М. А. (2019). Оценка и применение незадействованных резервов стабилизации пенсионной системы // Экономика. Налоги. Право. № 12 (3). С. 103–115. [Pitilyak D. A., Dranenko L. P., Bazil T. V., Chernyaeva M. A. (2019). Assessment and utilization of uncommitted reserves of the pension system stabilization. Economics, Taxes & Law, 12 (3), 103–115 (in Russian).]
- Соколов Е. В., Костырин Е. В. (2021). Экономический эффект от использования персонифицированных пенсионных счетов вместо существующей системы пенсионного обеспечения граждан России // Экономика и управление: проблемы, решения. Т. 1. № 3. С. 78–85. [Sokolov E. V., Kostyrin E. V. (2021). Economic effect from the use of personalized pension accounts instead of the existing system of pension provision for Russian citizens. Economics and Management: Problems, Solutions, 1, 3, 78–85 (in Russian).]
- Фатхлисламова Г. Ф. (2019). Сравнительный анализ развития накопительной компоненты пенсионной системы и негосударственного пенсионного страхования России // Экономическое развитие России. № 26. С. 65–75. [Fatkhlislamova G. F. (2019). Comparative analysis of the development of the accumulative component of the pension system and non-governmental pension insurance of Russia. Economic Development of Russia, 26, 65–75 (in Russian).]
- Bloom D. E., Canning D., Moore M. (2014). Optimal retirement with increasing life expectancy. Scandinavian Journal of Economics, 116 (3), 838–858. doi: 10.2139/ssrn.1857565
- Borgschulte M., Heepyung C. (2018). Minimum wages and retirement. Discussion Paper Series, 11728, 18–20.
- Cai D. H., Zhu C. Y., Han W. J. (2017). Life cycle model with optimal working years and leisure time. Journal of Wuhan University, 63 (6), 533–537 (in Chinese). [蔡东汉, 朱长艳, 韩文晶 (2017). 具有最优工作年限与闲暇的生命周期模型. 武汉大学学报理学版, 63(6), 533–537.]
- Chen X., Xiao L. (2020). Improving logistic models and population forecasts in China. Journal of Chengdu University of Information Engineering, 35 (2), 239–243 (in Chinese). [陈霞, 肖岚 (2020). Logistic 模型的改进与中国人口预测. 成都信息工程大学学报, 35 (2), 239–243.]
- Holzmann R., Palmer E. (2006). Pension reform: Issues and prospects for non–financial defined contribution (NDC) schemes. The World Bank, 601–660.
- Honerlein E. M. (2019). Pension indexation for retirees revisited — normative patterns and legal standards. Global Social Policy, 19 (8), 246–265. doi: 10.1177/1468018119842028
- Hong S., Jin F., Yu Ya.W. (2021). The effect of reducing the social security contribution rate on corporate social security contributions and labor force hiring. Economic Studies, 01, 90–104 (in Chinese). [宋弘, 封进, 杨婉彧 (2021). 社保缴费率下降对企业社保缴费与劳动力雇佣的影响, 经济研究, 第1期, 90–104.]
- Ma S., Meng X., Gan L. (2014). Analysis of the impact of contributions of pension insurance companies on wages and employment of workers. Economics, 03, 969–1000 (in Chinese). [马双, 孟宪芮, 甘犁 (2014). 养老保险企业缴费对员工工资, 就业的影响分析. 经济学, 第3期, 969–1000.]
- Malthus T. R. (1978). Population: First essay. Ann-Arbor: University of Michigan Press.
- Sánchez-Romero M., Prskawetz A. (2016). Education, lifetime labor supply and improvement of life expectancy. Journal of Economic Dynamics and Management, 73, 118–141.
- Shi C., Yin X. (2021). Study of population size based on Leslie and logistic models. Journal of Liaoning Institute of Science and Technology, 23 (6), 89–91 (in Chinese). [史纯阳, 尹鑫鑫 (2021). 基于leslie和logistic模型的人口数量研究. 辽宁科技学院学报, 23 (6), 89–91.]
- Verhulst P. F. (1975). Mathematical investigations on the law of increasing population growth. Brussels: New Memoirs of the Royal Academy of Sciences and Fiction Brussels. Available at: https://link.springer.com/article/10.1007/BF02309004. First published in 1838 in Correspondence in Mathematical Physics, 10, 113–121. Transl. from French.
- Xinyan D., Jianwei G., Shuqing L. (2022). The impact of deferred retirement on workers’ utility maximization — an analysis based on the utility function “S”. Population and Economy, 1, 106–120 (in Chinese). [段欣言, 高建伟, 李淑清 (2022). 延迟退休对职工效用最大化的影响 — 基于“S”型效用函数的分析. 人口与经济, 第1期, 106–120 (in Chinese).]
- Zhao J., Lu Z. (2018). Does the share of pension insurance contributions affect the productivity of enterprises. Economic Studies, 10, 97–112 (in Chinese). [赵健宇, 陆正飞 (2018). 养老保险缴费比例会影响企业生产效率吗? 经济研究, 第10期, 97–112.]
- Zhou J., Qi X., Jiao J. (2008). MATLAB from entry to mastery. Beijing: People’s Post and Telecommunication Press. 467 p. (in Chinese). [周建兴, 岂兴明, 矫津毅 (2008). MATLAB从入门到精通. 北京人民邮电出版社, 467.]
- Zhao R., Fan Z. (2020). Pension coordination reform, tax incentives and corporate contribution rates. China Industrial Economics, 9, 29–43 (in Chinese). [赵仁杰, 范子英 (2020). 养老金统筹改革, 征管激励与企业缴费率. 中国工业经济, 第9期, 29–43.]
