Abstract
What explains the power-law distribution of top incomes? This paper tests the hypothesis that it is firm hierarchy that creates the power-law income distribution tail. Using the available case-study evidence on firm hierarchy, I create the first large-scale simulation of the hierarchical structure of the US private sector. Although not tuned to do so, this model reproduces the power-law scaling of top US incomes. I show that this is purely an effect of firm hierarchy. This raises the possibility that the ubiquity of power-law income distribution tails is due to the ubiquity of hierarchical organization in human societies.
Notes
The constant c is equal to \( (\alpha - 1) / (x_{ \text {min} })^{1 - \alpha } \), where \(x_{ \text {min}}\) is the lower bound of the power law (i.e., the beginning of the income distribution tail).
References
Pareto, V. (1897). Cours d’economie politique (Vol. 1). Geneva: Librairie Droz.
Atkinson, A. B. (2017). Pareto and the upper tail of the income distribution in the UK: 1799 to the present. Economica, 84(334), 129.
Aoyama, H., Souma, W., Nagahara, Y., Okazaki, M. P., Takayasu, H., & Takayasu, M. (2000). Pareto’s law for income of individuals and debt of bankrupt companies. Fractals, 8(03), 293.
Coelho, R., Richmond, P., Barry, J., & Hutzler, S. (2008). Double power laws in income and wealth distributions. Physica A: Statistical Mechanics and its Applications, 387(15), 3847.
Clementi, F., & Gallegati, M. (2005). Pareto’s law of income distribution: Evidence for Germany, the United Kingdom, and the United States. In A. Chatterjee, S. Yarlagadda, & B. K. Chakrabarti (Eds.), Econophysics of wealth distributions (pp. 3–14). Berlin: Springer.
Clementi, F., & Gallegati, M. (2005). Power law tails in the Italian personal income distribution. Physica A: Statistical Mechanics and Its Applications, 350(2–4), 427.
Di Guilmi, C., Gaffeo, E., & Gallegati, M. (2003). Power law scaling in world income distribution. Economics Bulletin, 15, 1–7.
Drgulescu, A., & Yakovenko, V. M. (2001). Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A: Statistical Mechanics and its Applications, 299(1–2), 213.
Nirei, M. (2009). Pareto distributions in economic growth models. IIR working paper WP#09-05
Toda, A. A. (2012). The double power law in income distribution: Explanations and evidence. Journal of Economic Behavior & Organization, 84(1), 364.
Silva, A. C., & Yakovenko, V. M. (2004). Temporal evolution of the thermal and superthermal income classes in the USA during 19832001. EPL (Europhysics Letters), 69(2), 304.
Souma, W. (2001). Universal structure of the personal income distribution. Fractals, 9(04), 463.
Lydall, H. F. (1959). The distribution of employment incomes. Econometrica: Journal of the Econometric Society, 27(1), 110.
Audas, R., Barmby, T., & Treble, J. (2004). Luck, effort, and reward in an organizational hierarchy. Journal of Labor Economics, 22(2), 379.
Baker, G., Gibbs, M., & Holmstrom, B. (1993). Hierarchies and compensation: A case study. European Economic Review, 37(2–3), 366.
Dohmen, T. J., Kriechel, B., & Pfann, G. A. (2004). Monkey bars and ladders: The importance of lateral and vertical job mobility in internal labor market careers. Journal of Population Economics, 17(2), 193.
Grund, C. (2005). The wage policy of firms: Comparative evidence for the US and Germany from personnel data. The International Journal of Human Resource Management, 16(1), 104.
Lima, F. (2000). Internal labor markets: A case study. FEUNL working paper, vol. 378.
Morais, F., & Kakabadse, N. K. (2014). The corporate gini index (CGI) determinants and advantages: Lessons from a multinational retail company case study. International Journal of Disclosure and Governance, 11(4), 380.
Treble, J., Van Gameren, E., Bridges, S., & Barmby, T. (2001). The internal economics of the firm: Further evidence from personnel data. Labour Economics, 8(5), 531.
Ariga, K., Brunello, G., Ohkusa, Y., & Nishiyama, Y. (1992). Corporate hierarchy, promotion, and firm growth: Japanese internal labor market in transition. Journal of the Japanese and International Economies, 6(4), 440.
Bell, B., & Van Reenen, J. (2012). Firm performance and wages: Evidence from across the corporate hierarchy. CEP discussion paper, vol. 1088.
Eriksson, T. (1999). Executive compensation and tournament theory: Empirical tests on Danish data. Journal of Labor Economics, 17(2), 262.
Heyman, F. (2005). Pay inequality and firm performance: Evidence from matched employer–employee data. Applied Economics, 37(11), 1313.
Leonard, J. S. (1990). Executive pay and firm performance. Industrial and Labor Relations Review, 43(3), 13.
Main, B. G., O’Reilly, C. A, I. I. I., & Wade, J. (1993). Top executive pay: Tournament or teamwork? Journal of Labor Economics, 11(4), 606.
Mueller, H. M., Ouimet, P. P., & Simintzi, E. (2016). Within-firm pay inequality. SSRN working paper.
Rajan, R. G., & Wulf, J. (2006). The flattening firm: Evidence from panel data on the changing nature of corporate hierarchies. The Review of Economics and Statistics, 88(4), 759.
Tao, H. L., & Chen, I. T. (2009). The level of technology employed and the internal hierarchical wage structure. Applied Economics Letters, 16(7), 739.
Kumamoto, S. I., & Kamihigashi, T. (2018). Power laws in stochastic processes for social phenomena: An introductory review. Frontiers in Physics, 6, 20.
Mitzenmacher, M. (2004). A brief history of generative models for power law and lognormal distributions. Internet mathematics, 1(2), 226.
Newman, M. E. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323.
Gibrat, R. (1931). Les inegalites economiques. Paris: Recueil Sirey.
Champernowne, D. G. (1953). A model of income distribution. The Economic Journal, 63(250), 318.
Gabaix, X., Lasry, J. M., Lions, P. L., & Moll, B. (2016). The dynamics of inequality. Econometrica, 84(6), 2071.
Nirei, M., & Souma, W. (2007). A two factor model of income distribution dynamics. Review of Income and Wealth, 53(3), 440.
Rutherford, R. (1955). Income distributions: A new model. Econometrica: Journal of the Econometric Society, 23(3), 277.
Wold, H. O., & Whittle, P. (1957). A model explaining the Pareto distribution of wealth. Econometrica, Journal of the Econometric Society, 25(4), 591.
Yule, G. U, I. I. (1925). A mathematical theory of evolution, based on the conclusions of Dr. JC Willis, FR S. Philosophical Transactions of the Royal Society B, 213(402–410), 21.
Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42(3/4), 425.
Price, D. D. S. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the Association for Information Science and Technology, 27(5), 292.
Barabasi, A., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509.
Angle, J. (1986). The surplus theory of social stratification and the size distribution of personal wealth. Social Forces, 65(2), 293.
Angle, J. (2006). The inequality process as a wealth maximizing process. Physica A: Statistical Mechanics and Its Applications, 367(15), 388.
Chatterjee, A., Chakrabarti, B. K., & Chakraborti, A. (2007). Econophysics and sociophysics: Trends and perspectives. Milan: Wiley.
Chatterjee, A., & Chakrabarti, B. K. (2007). Kinetic exchange models for income and wealth distributions. The European Physical Journal B, 60(2), 135.
Hegyi, G., Neda, Z., & Santos, M. A. (2007). Wealth distribution and Pareto’s law in the Hungarian medieval society. Physica A: Statistical Mechanics and its Applications, 380(1), 271.
Kitov, I. O. (2009). Mechanical model of personal income distribution (pp. 1–220). arXiv preprint arXiv:0903.0203
Pianegonda, S., Iglesias, J. R., Abramson, G., & Vega, J. L. (2003). Wealth redistribution with conservative exchanges. Physica A: Statistical Mechanics and its Applications, 322, 667.
Scheffer, M., Bavel, B. V., Leemput, I. A. V. D., Nes, E. H. V. (2017) Inequality in nature and society. Proceedings of the National Academy of Sciences, 114, 201706412. https://doi.org/10.1073/pnas.1706412114
Yakovenko, V. M., & Rosser, J. B, Jr. (2009). Colloquium: Statistical mechanics of money, wealth, and income. Reviews of Modern Physics, 81(4), 1703.
Simon, H. A. (1957). The compensation of executives. Sociometry, 20(1), 32.
Roberts, D. R. (1956). A general theory of executive compensation based on statistically tested propositions. The Quarterly Journal of Economics, 70(2), 270.
Axtell, R. L. (2001). Zipf distribution of US firm sizes. Science, 293, 1818.
Fix, B. (2017). Energy and institution size. PLoS ONE, 12(2), e0171823. https://doi.org/10.1371/journal.pone.0171823.
Gaffeo, E., Gallegati, M., & Palestrini, A. (2003). On the size distribution of firms: Additional evidence from the G7 countries. Physica A: Statistical Mechanics and its Applications, 324(12), 117. https://doi.org/10.1016/S0378-4371(02)01890-3.
Clauset, A., Shalizi, C. R., & Newman, M. E. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661.
Piketty, T. (2014). Capital in the twenty-first century. Cambridge: Harvard University Press.
Brown, C. (1988). In Mangum, G. & P. Philips (Eds), Three worlds of labor economics (Vol. 51 pp. 515–530)
Brown, C. (2005). Is there an institutional theory of distribution? Journal of Economic Issues, 39(4), 915.
Dahrendorf, R. (1959). Class and class conflict in industrial society. Stanford: Stanford University Press.
Huber, E., Huo, J., & Stephens, J. D. (2017). Power, policy, and top income shares. Socio-Economic Review. https://doi.org/10.1093/ser/mwx027.
Kalecki, M. (1971). Selected essays on the dynamics of the capitalist economy 1933–1970. Cambridge: Cambridge University Press.
Lenski, G. E. (1966). Power and privilege: A theory of social stratification. Chapel Hill: UNC Press Books.
Marx, K. (1867). Capital (Vol. I). Penguin/New Left Review: Harmondsworth.
Mills, C. W. (1956). The power elite. Oxford: Oxford University Press.
Nitzan, J., & Bichler, S. (2009). Capital as power: A study of order and creorder. New York: Routledge.
Peach, J. T. (1987). Distribution and economic progress. Journal of Economic Issues, 21(4), 1495.
Sidanius, J., & Pratto, F. (2001). Social dominance: An intergroup theory of social hierarchy and oppression. Cambridge: Cambridge University Press.
Weber, M. (1978). Economy and society: An outline of interpretive sociology. Berkeley: University of California Press.
Wright, E. O. (1979). Class structure and income determination (Vol. 2). New York: Academic Press.
Acknowledgements
I would like to thank the Social Sciences and Humanities Resource Council of Canada (Grant no. 767-2015-1015) for its support. I thank also Jonathan Nitzan, who has offered feedback on aspects of this paper.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Fix, B. Hierarchy and the power-law income distribution tail. J Comput Soc Sc 1, 471–491 (2018). https://doi.org/10.1007/s42001-018-0019-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42001-018-0019-8