Model of income distribution on the basis of a finite functional sequence and its application for inequality analysis

Abstract

The paper develops the results presented in the author's previously published articles on the elaboration of a new model of income distribution described by a finite functional sequence. The model provides a good accuracy of approximation of the distribution of income for equal groups of the population that is confirmed by the results of empirical studies and is justified theoretically. The introduction of a new indicator of inequality that is correlated with Gini coefficient as well as with the quintile and decile dispersion ratios makes it possible to estimate theoretically the income shares of 20 and 10% groups (quintiles and deciles) for different levels of inequality. The results obtained allow identifying the specific features of changes in the share of income of these groups with the growth of inequality. The model also makes it possible to consider certain ratios between the incomes of some population groups that are typical of different inequality levels as well as to obtain for them an analytical expression; for example, such expression is obtained for the Palm ratio. These ratios can serve to some extent as some normatives for the development of the inequality reducing policy. The developed model allows also justifying the optimal (harmonious) level of inequality. In the annex the results of the estimation of the new inequality indicator for 18 countries are given.