A model for analyzing income inequality based on a finite functional sequence (adequacy and application problems)

The paper considers the adequacy of the model developed earlier by the author for the analysis of income inequality and based on an empirically confirmed hypothesis that the relative (to the income of the richest group) income values of 20 % population groups in total income can be represented as a finite functional sequence, each member of which depends on one parameter — a specially defined indicator of inequality. It is shown that in addition to the existing methods of inequality analysis, the model makes it possible to estimate with the help of analytical expressions the income shares of 20 %, 10 % and smaller groups of the population for different levels of inequality, as well as to identify how they change with the growth of inequality, to estimate the level of inequality for known ratios between the incomes of different groups of the population, etc.
The paper provides a more detailed confirmation of the proposed model adequacy in comparison with the previously obtained results of statistical analysis of empirical data on the distribution of income between the 20 % and 10 % population groups. It is based on the analysis of certain ratios between the values of quintiles and deciles according to the proposed model. The verification of these ratios was carried out using a set of data for a large number of countries and the estimates obtained confirm the sufficiently high accuracy of the model.
Data are presented that confirm the possibility of using the model to analyze the dependence of income distribution by population groups on the level of inequality, as well as to estimate the inequality indicator for income ratios between different groups, including variants when the income of the richest 20 % is equal to the income of the poor 60 %, income of the middle class 40 % or income of the rest 80 % of the population, as well as when the income of the richest 10 % is equal to the income of the poor 40 %, 50 % or 60 %, to the income of various middle class groups, etc., as well as for cases, when the distribution of income obeys harmonic proportions and when the quintiles and deciles corresponding to the middle class reach a maximum. It is shown that the income shares of the richest middle class groups are relatively stable and have a maximum at certain levels of inequality.
The results obtained with the help of the model can be used to determine the standards for developing a policy of gradually increasing the level of progressive taxation in order to move to the level of inequality typical of countries with social oriented economy.