Angle, John (2010): The Inequality Process vs. The Saved Wealth Model. Two Particle Systems of Income Distribution; Which Does Better Empirically?

PDF
MPRA_paper_20835.pdf Download (431kB)  Preview 
Abstract
The Inequality Process (IP) is a stochastic particle system in which particles are randomly paired for wealth exchange. A coin toss determines which particle loses wealth to the other in a randomly paired encounter. The loser gives up a fixed share of its wealth, a positive quantity. That share is its parameter, ω_ψ, in the ψth equivalence class of particles. The IP was derived from verbal social science theory that designates the empirical referent of (1ω_ψ) as worker productivity, operationalized as worker education. Consequently, the stationary distribution of wealth of the IP in which particles can have different values of ω (like workers with different educations) is obliged to fit the distribution of labor income conditioned on education. The hypothesis is that when a) the stationary distribution of wealth in the ψth equivalence class of particles is fitted to the distribution of labor income of workers at the ψth level of education, and b) the fraction of particles in the ψth equivalence class equals the fraction of workers at the ψth level of education, then c) the model's stationary distributions fit the corresponding empirical distributions, and d) estimated (1ω_ψ) increases with level of education. The Saved Wealth Model (SW) was proposed as a modification of the particle system model of the Kinetic Theory of Gases (KTG). The SW is isomorphic to the IP up to the stochastic driver of wealth exchange between particles. The present paper shows that 1) the stationary distributions of both particle systems pass test c): they fit the distribution of U.S. annual wage and salary income conditioned on education over four decades, 2) the parameter estimates of the fits differ by particle system, 3) both particle systems pass test d), but 4) the IP's overall fits are better than the SW's because 5) the IP's stationary distribution conditioned on larger (1ω_ψ) has a heavier tail than the SW's fitting the distribution of wage income of the more educated better, and 6) since the level of education in the U.S. labor force rose, the IP's fit advantage increased over time.
Item Type:  MPRA Paper 

Original Title:  The Inequality Process vs. The Saved Wealth Model. Two Particle Systems of Income Distribution; Which Does Better Empirically? 
Language:  English 
Keywords:  labor income distribution; goodness of fit; Inequality Process; particle system model; Saved Wealth Model 
Subjects:  D  Microeconomics > D3  Distribution > D31  Personal Income, Wealth, and Their Distributions C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling B  History of Economic Thought, Methodology, and Heterodox Approaches > B5  Current Heterodox Approaches > B59  Other 
Item ID:  20835 
Depositing User:  John Angle 
Date Deposited:  20 Feb 2010 16:52 
Last Modified:  26 Aug 2016 06:55 
References:  1. Angle, John. 2009. "Two similar particle systems of labor income distribution conditioned on education". In JSM Proceedings, Business and Economics Statistics Sections. Pp. 10031017. CDROM. Alexandria, VA: American Statistical Association. 2. Angle, John. 1983. "The surplus theory of social stratification and the size distribution of personal wealth." 1983 Proceedings of the American Statistical Association, Social Statistics Section. Pp. 395 400. Alexandria, VA: American Statistical Association. 3. Angle, John. 1986. "The surplus theory of social stratification and the size distribution of Personal Wealth." Social Forces 65:293 326. 4. Angle, John. 1990. "A stochastic interacting particle system model of the size distribution of wealth and income." 1990 Proceedings of the American Statistical Association, Social Statistics Section. Pp. 279 284. Alexandria, VA: American Statistical Association. 5. Angle, John. 1992. "The Inequality Process and the distribution of income to blacks and whites". Journal of Mathematical Sociology 17:77 98. 6. Angle, John. 1996. "How the gamma law of income distribution appears invariant under aggregation". Journal of Mathematical Sociology. 21:325358. 7. Angle, John. 1997. "A theory of income distribution". 1997 Proceedings of the American Statistical Association, Social Statistics Section. Pp. 388393. Alexandria, VA: American Statistical Association. 8. Angle, John. 2002. "The statistical signature of pervasive competition on wages and salaries". Journal of Mathematical Sociology. 26:217270. 9. Angle, John. 2003a. "Imitating the salamander: a model of the right tail of the wage distribution truncated by topcoding@. November, 2003 Conference of the Federal Committee on Statistical Methodology, [ http://www.fcsm.gov/events/papers2003.html ]. 10. Angle, John. 2003. AInequality Process, The@. An entry in T. Liao, et al., (eds.), The Encyclopedia of Social Science Research Methods. Volume 2: 488490. Thousand Oaks, CA: Sage. 11. Angle, John. 2006. AThe Inequality Process as a wealth maximizing process@. Physica A 367: 388414. 12. Angle, John. 2007a. AThe Macro Model of the Inequality Process and The Surging Relative Frequency of Large Wage Incomes@. Pp. 171196 in A. Chatterjee and B.K. Chakrabarti, (eds.), The Econophysics of Markets and Networks (Proceedings of the Econophys Kolkata III Conference, March 2007). Milan: Springer. 13. Angle, John. 2007b. AThe Inequality Process is an evolutionary process@. The Constructal Theory of Social Dynamics. Adrian Bejan and Gilbert Merkx, eds. (Proceedings of the Conference on the Constructal Theory of Social Dynamics, Duke University, April 2006). New York: Springer. 14. Angle, John, François Nielsen, and Enrico Scalas. 2009. “The Kuznets Curve and the Inequality Process”. In Banasri Basu, Bikas K. Chakrabarti, Satya R. Chakravarty, Kausik Gangopadhyay, editors, Econophysics and Economics of Games, Social Choices and Quantitative Techniques. Milan: Springer. 15. Chakraborti, A., B.K. Chakrabarti. 2000. “Statistical mechanics of money: How saving propensity affects its distribution”. European Physics Journal B: 17: 167 170. 16. Chatterjee, A., B.K. Chakrabarti, and S. Manna. 2004. “Pareto law in a kinetic model of market with random saving propensity”. Physica A 335: 155163. 17. Patriarca, M., A. Chakraborti, and K. Kaski. 2004. “A statistical model with a standard gamma distribution”. Physical Review E 70: article # 016104. 18. Lux, Thomas. 2005. AEmergent statistical wealth distributions in simple monetary exchange models: a critical review@.Pp. 5160 in A. Chatterjee, S. Yarlagadda, and B.K. Chakrabarti, (eds.), Econophysics of Wealth Distributions, (the proceedings volume of the International Workshop on the Econophysics of Wealth Distributions, March, 2005, Kolkata, India). Milan, Italy: Springer. 19. Lux, Thomas. 2008. “Applications of Statistical Physics in Economics and Finance”. In J. Barkley Rosser Jr., (ed.). Handbook of Research on Complexity. London: Edward Elgar. 20. Patriarca, Marco, Els Heinsalu, and Anirban Chakraborti. 2006. "The ABCD's of statistical manyagent economy models". [ online at http://arxiv.org/abs/physics/0611245/ ]. 21. Scalas, Enrico, Mauro Gallegati, Eric Guerci, David Mas, and Allessandra Tedeschi. 2006. "Growth and Allocation of Resources in Economics: The Agentbased Approach". 22. Yakovenko, Victor. forthcoming. "Econophysics, Statistical Mechanical Approaches to". Encyclopedia of Complexity and System Science. [ online at http://arxiv.org/abs/0709.3662 ]. 23. Whitney, Charles. 1990. Random Processes in Physical Systems. New York: Wiley, page 220. 24. Dragulescu, A. and V.Yakovenko. 2000. “Statistical mechanics of money”. European Physics Journal B 17: 723729. 25. Dragulescu, A.. and V. Yakovenko. 2001. “Exponential and powerlaw probability distributions of wealth and income in the United Kingdom and the United States”. Physica A 299: 213221. 26. Lenski, G. 1966. Power and Privilege. New York: McGrawHill. 27. Current Population Surveys, March 19622004. [machine readable data files]/ conducted by the Bureau of the Census for the Bureau of Labor Statistics. Washington, DC: U.S. Bureau of the Census [producer and distributor], 19622004. Santa Monica, CA: Unicon Research Corporation [producer and distributor of CPS Utilities], 2005. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/20835 