Endogenous Household Classification: Russian Regions

In order to study the structure of society, sociologists usually distinguish several homogeneous social groups, or classes. The most common division consists of three groups: upper, middle and lower classes. Such a partition is traditionally based on a subjective (exogenous) criteria adopted by a particular researcher. In this paper, the distribution of households in Russian federal districts is modeled as a mixture of three lognormal distributions. The mixing proportions (probabilities) of the mixture components and the corresponding distribution parameters are modeled as functions of the individual characteristics of households. The result is an endogenous decomposition of household sample into three clusters (lower, middle, upper). This classification allows analyzing the difference between regions and the patterns of intergroup dynamics in the period 2014—2018. The approach used in this work has demonstrated great flexibility in analyzing the distribution of income, the dynamics of this distribution over time, as well as a migration between relatively homogeneous clusters. The use of mixture density function with endogenously determined probabilities allows for precise detection of the effects of the income heterogeneity determinants within each cluster.