Income Distribution Management using Logistics and Fermi-Dirac Distribution in iran

Subject Areas : Financial Econometrics and Quantitative Methods

mohammad  forozan ¹ (Ph.D.Student in Accounting, Department of Accounting Group, Qaenat branch, Islamic Azad University, Qaenat, Iran.)
Seyyed Mohmood  Mousavi shiri ² (Accounting department, Payam Noor University, Mashhad, Iran)
mehdi  salehi ³ (Accounting department, Faculty of Economic and administrative Sciences, Ferdowsi University of Mashhad, Mashhad, Iran)

Received: 2021-05-25 Accepted : 2021-11-22 Published : 2021-11-22

Keywords: Income distribution, cumulative logistic function, Fermi-Dirac distribution, Pareto distribution,

Abstract :

Distributions such as Bose-Einstein, Maxwell Boltzmann, Lag Normal, and exponential have been used to describe income of the low- and middle sections of society. The Pareto distribution also have been used to describe the income of the wealthy section of society. Due to the complexity of these models, it is difficult to estimate macroeconomic indicators. Also, one of other disadvantage of these models is non-uniformity for all income levels. In this study, the cumulative logistic and Fermi-Dirac distribution were used for two categories of rural and urban data sets in the Iranian economy between 2009 to 2019. The results show that the proposed model was perfectefor all income levels in rural and urban areas at different times very well and covers all parts of the income distribution. Interpretation of Dirac Fermi distribution parameters and the correlation and significant relationship of these parameters with macroeconomic indicators show the superiority of Dirac Fermi distribution compared to logistics distribution.

References:

ابونوری، اسماعیل (1382). مدلسازی توزیع درآمد و ضریب جینی با کاربرد توزیع لگ لجستیک. مجله علوم اجتماعی و انسانی دانشگاه شیراز، 19(2)، 24-13.

ابونوری، اسمعیل؛ فراهتی، محبوبه (1394). ساختار تولید و توزیع درآمد در ایران. فصلنامه مدل‌سازی اقتصادی، 4(32)، 23-1.

بختیاری، صادق؛ محمود اوغلی، سجاد (1393). مدل‌سازی توزیع درآمد برای ایران: مقایسه ی الگوی داگوم با چند مدل منتخب. فصلنامه مدل‌سازی اقتصادی، 8(26)، 20-1. 

جمال شرق، سعید؛ خسروی نژاد، علی‌اکبر؛ گرائی نژاد، غلامرضا؛ میرزائی نژاد، محمدرضا (1400). بررسی اثر عوامل مؤثر بر توزیع درآمد در مناطق شهری استان‌های ایران: رویکرد پانل کوانتایل. فصلنامه نظریه‌های کاربردی اقتصادی، 8(2)، 238-207.

صادقی، سید کمال؛ بهشتی، محمدباقر؛ رنجپور، رضا؛ ابراهیمی، سعید (1396). سیاست‌های مالی و توزیع درآمد در ایران: رهیافت FAVAR. فصلنامه مدل‌سازی اقتصادی، 11(39)، 98–75.

طاهری، محمدعلی؛ خدابخشی، اکبر (1400). اثر تعاملی شاخص‌های آموزش و توزیع درآمد در کشورهای منتخب عضو سازمان کنفرانس اسلامی. فصلنامه پژوهش‌های برنامه و توسعه، 2(5)، 80-55.

گلی، یونس محمودیان، یعقوب، تیاترج، علی، گلی، یحیی (1397)، مقایسه و اندازه‌گیری نابرابری رفاهی از نظر اسلام و اقتصاد متعارف، دوفصلنامه علمی - پژوهشی مطالعات اقتصاد اسلامی، 10(2)، 29-7.

محمدزاده، یوسف؛ تقی‌زاده، نرگس؛ نظریان، علمناز (1396). نابرابری درآمد، فقر و سلامت عمومی. مجله دانشکده پیراپزشکی دانشگاه علوم پزشکی تهران (پیاورد سلامت)، 11(2)، 234-220.

نژاد عبدالله، معصومه، محتشمی برزادران، غلامرضا، یعقوبی اول ریابی، مهدی (1392). شاخص‌های توزیع درآمد در ایران. مجله اقتصادی (دوماهنامه بررسی مسائل و سیاست‌های اقتصادی)، 13(۹ و ۱۰)،۶۴-۴۹.

Abounoori, E. (2003). Modelling the income Distribution and Gini coefficient using the Log-logistic distribution. Journal of Social Sciences & Humanities of Shiraze University, 19(2), 13–23. [In Persian].

Abounoori, E., Farahati, M. (2016). The Structure of Production and Income Distribution in Iran. Economical Modeling, 9(32), 1-23. [In Persian].

Aydiner, E., Cherstvy, A. G., & Metzler, R. (2018). Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models. Physica A: Statistical Mechanics and Its Applications, 490, 278–288.

bakhtiari, S., mahmoodoghli, S. (2014). Income Distribution Modeling in Iran: Comparison of Dagum Model and Other Models Selected. Economical Modeling, 8(26), 1-20. [In Persian].

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, 471, 724–732.

Chakrabarti, B. K., Anirban Chakraborti, Chakravarty, S. R., & Chatterjee, A. (2013). Econophysics of Income and Wealth Distributions. Cambridge University Press.

Chakraborti, A., & Chakrabarti, B. K. (2000). Statistical mechanics of money: how saving propensity affects its distribution. The European Physical Journal B, 17(1), 167–170.

Chatterjee, A., & Chakrabarti, B. K. (2007). Kinetic exchange models for income and wealth distributions. The European Physical Journal B, 60(2), 135–149.

Clementi, F., Gallegati, M., & Kaniadakis, G. (2009). A κ-generalized statistical mechanics approach to income analysis. Journal of Statistical Mechanics: Theory and Experiment, (02), P02037.

Dil, E., & Dil, E. (2021). Sociophysics of income distributions modeled by deformed fermi-dirac distributions. The Journal of Mathematical Sociology, 1–26.

Dragulescu, A., & Yakovenko, V. M. (2000). Statistical mechanics of money. The European Physical Journal B, 17(4), 723–729.

Jamalshargh, S., Khosravinejad, A., Geraei Nezhad, G., Mirzaeinejad, M. (2021). Investigate the Effect of Effective Factors on Income Distribution in Urban Areas of Iran's Provinces. Quarterly Journal of Applied Theories of Economics, 8(2), 207-238. [In Persian].

Goli, Y., Mahmodian, Y., Tiatoraj, A., Goli, Y. (2018). Comparison and Measurement of Welfare Inequality According to the Islamic and Conventional Economics. Islamic Economics Studies Bi-quarterly Journal, 10(2), 7-29. [In Persian].

Ksenzhek, O., & Petrova, S. (2008). Inequality and economic efficiency of society through the prism of thermodynamics. Hungarian Electronic Journal Economics, Manuscript No. ECO-080111-A.

Kürten, K. E., & Kusmartsev, F. V. (2011). Bose-Einstein distribution of money in a free-market economy. II. EPL (Europhysics Letters), 93(2), 28003.

Luckstead, J., & Devadoss, S. (2017). Pareto tails and lognormal body of US cities size distribution. Physica A: Statistical Mechanics and Its Applications, 465, 573–578.

Mohammadzadeh Y, Taghizadeh N, Nazariyan A. (2017) Income inequality, poverty and public health, Journal of Paramedical School of Tehran University of Medical Sciences (Palavered Salamat), 11(2), 220-234. [In Persian].

Nejadabdoalih, M., Mohtashamibarzadrdn, GH., Yaghubiavalrobaee, M., (2014). Income distribution indices in Iran. Economic Journal (Bimonthly review of economic issues and policies), 13(9,10), 49-64. [In Persian].

Oltean, E. (2014). An Econophysical Approach of Polynomial Distribution Applied to Income and Expenditure. American Journal of Modern Physics, 3(2), 88.

Oltean, E., & Kusmartsev, F. V. (2014). Applications of Statistical Physics Distributions to Several Types of Income. American Journal of Physics and Applications, 2(2), 61-66.

Oskarsson, M. L., & Johansson, P. (2019). A game of wealth inequality A Monte Carlo simulation of wealth inequality using Monopoly, Master Thesis. Uppsala University.

Sadeghi, S., Beheshti, M., Ranjpour, R., Ebrahimi, S. (2017). Fiscal Policies and Income Distribution in Iran: FAVAR Approach. Economical Modeling, 11(39), 75-98. [In Persian].

Shaikh, A., & Jacobo, J. E. (2020). Economic Arbitrage and the Econophysics of Income Inequality. Review of Behavioral Economics, 7(4), 299–315.

Silva, A. C., & Yakovenko, V. M. (2005). Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001. Europhysics Letters (EPL), 69(2), 304–310.

Taheri, M., Khodabakhshi, A. (2021). Interactive Effect of Education Indicators and Income Distribution in Selected Countries of the Islamic Conference Organization. Program and Budget Research, 2(1),55-80 . [In Persian].

Vermeulen, P. (2018). How Fat is the Top Tail of the Wealth Distribution? Review of Income and Wealth, 64(2), 357–387.

Xin, C., & Huang, J.-P. (2017). Recent progress in econophysics: Chaos, leverage, and business cycles as revealed by agent-based modeling and human experiments. Frontiers of Physics, 12(6).