# Two-component structure of household income distributions in Poland

## Main Article Content

## Abstract

Research background: Studies of the structures of the income distributions have been performed for about 15 years. They indicate that there is no model which describes the distributions in their whole range. This effect is explained by the existence of different mechanisms yielding to low-medium and high incomes. While more than 97% of the distributions can be described by exponential or log-normal models, high incomes (about 3% or less) are in agreement with the power law.

Purpose of the article: The aim of this paper is an analysis of the structure of the household income distributions in Poland. We verify the hypothesis about two-part structure of those distributions by using log-normal and Pareto models.

Methods: The studies are based on the households’ budgets microdata for years 2004–2012. The two-component models are used to describe the income distributions. The major parts of the distributions are described by the two parametric log-normal model. The highest incomes are described by the Pareto model. We also investigate the agreement with data of the more complex models, like Dagum, and Singh-Madalla.

Findings & Value added: One has showed that two or three parametric models explain from about 95% to more than 99% of income distributions. The poorest agreement with data is for the log-normal model, while the best agreement has been obtained for the Dagum model. However, two-part model: log-normal for low-middle incomes and Pareto model for the highest incomes describes almost the whole range of income distributions very well.

## Article Details

*Equilibrium. Quarterly Journal of Economics and Economic Policy*,

*13*(4), 603-622. https://doi.org/10.24136/eq.2018.029

This work is licensed under a Creative Commons Attribution 4.0 International License.

## References

Bandourian, R., McDonald, J., & Turley, R. S. (2002). A comparison of parametric models of income distribution across countries and over time. Luxembourg Income Study Working Paper, 305. doi: 10.2139/ssrn.324900.

Brzeziński, M. (2014). Empirical modeling of the impact factor distribution. Journal of Informetrics, 8. doi: 10.1016/j.joi.2014.01.009.

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. Springer-Verlag. doi: 10.1007/88-470-0389-X_1.

Clementi, F., & Gallegati, M. (2005). Power law tails in the Italian personal income distribution. Physica A, 350. doi: 10.1016/j.physa.2004.11.038.

Dagum, C. (2008). A new model of personal income distribution: specification and estimation. In D. Chotikapanich (Ed.). Modeling income distributions and Lorenz curves. Springer. doi: 10.1007/978-0-387-72796-7_1.

Dagum, C., & Lemmi, A. (1989). A contribution to the analysis of income distribution and income inequality and a case study: Italy. In D. J. Slottjee (Ed.). Research on economic inequality, 1. Greenwich CT: JAI Press.

Dagum, C. (2006). Wealth distribution models: analysis and applications. Statistica, 61(3).

Dragulescu, A. 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, 299. doi: 10.1016/S0378-4371(01)00298-9.

Jagielski, M., & Kutner R. (2010). Study of households’ income in Poland by using the statistical physics approach. Acta Physica Polonica A, 117(4). doi: 10.12693/APhysPolA.117.615.

Jagielski, M., & Kutner, R. (2013). Modelling of income distribution in the European Union with the Fokker–Planck equation. Physica A, 392(9). doi: 10.1016/j.physa.2013.01.028.

Kleiber, C. (1996). Dagum vs. Singh-Maddala income distributions. Economics Letter, 53(3). doi: 10.1016/S0165-1765(96)00937-8.

Levy, M., & Solomon, S. (1997). New evidence for the power-law distribution of wealth. Physica A, 242. doi: 10.1016/S0378-4371(97)00217-3.

Łukasiewicz, P., & Orłowski A. J. (2004). Probabilistic models of income distributions. Physica A, 344(1-2). doi: 10.1016/j.physa.2004.06.106.

Łukasiewicz, P., & Orłowski, A. J. (2003). Probabilistic models of income distributions of Polish households. Quantitative Methods in Economic Research III.

Łukasiewicz, P., Karpio, K., & Orłowski, A. J. (2012). The models of personal incomes in USA. Acta Physica Polonica A, 121(2B). doi: 10.12693/APhysPol A.121.B-82.

McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52(3). doi: 10.2307/1913469.

McDonald, J. B., & Xu, Y. J. (1995). A generalization of the beta distribution with applications. Journal of Econometrics, 66(1-2). doi: 10.1016/0304-4076(94) 01612-4.

Nirei, M., & Souma, W. (2004). Income distribution and stochastic multiplicative process with reset events. In M. Gallegati, A. P. Kirman & M. Marsili (Eds.). The complex dynamics of economic interaction. Berlin, Heidelberg: Springer. doi: 10.1007/978-3-642-17045-4_9.

Nirei, M., & Souma, W. (2007). A two factor model of income distribution dynamics. Review of Income and Wealth, 53(3). doi: 10.1111/j.1475-4991.2007. 00242.x.

Okuyama, K., Takayasu, M., & Takayasu, H. (1999). Zipf's law in income distribution of companies. Physica A, 269. doi: 10.1016/S0378-4371(99)00086-2.

Pareto, V. (1896-97). Cours d’Economie Politique. Lausanne: F. Rouge.

Quintano, C., & D’Agostino, A. (2006). Studying inequality in income distribution of single-person households in four developed countries. Review of Income and Wealth, 52(4). doi: 10.1111/j.1475-4991.2006.00206.x.

Silva, A. C., & Yakovenko, V. M. (2005). Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001. Europhysics Letters, 69(2). doi: 10.1209/epl/i2004-10330-3.

Singh, S. K., & Manddala, G. S. (1976). A function for size distribution of incomes. Econometrica, 44(5). doi: 10.2307/1911538.

Suoma, W. (2001). Universal structure of the personal income distribution. Fractals, 09(04). doi: 10.1142/S0218348X01000816.