Modelling Income Mobility in Russia

This paper focuses on the application of (relatively novel) method which employs finite mixture of lognormal distributions with the mixture proportions modelled via concomitant variables. Along with that, the component-specific distributional parameters are being conditional on some independent variables, and therefore the considered method is a combination of model-based clustering and finite mixture of regressions. Based on the theory of continuous proportionate effect, it is easily shown that the employed approach is a natural feasible simplification of compound lognormal distribution with lognormal mixing function, which describes the overall distribution of individual income-receivers. Mixture model with concomitant variables allows to identify relatively homogeneous components inside the distribution. This, in turn, will allow to analyse the dynamics of separate groups of income-receiving units, to detect the between-group mobility and to have more precise estimates of predictors' effects on income not for the whole population, but for smaller and more homogeneous clusters inside it. It is shown that for all federal districts in Russia the probability mass of income distribution tends to concentrate in the left tail, which results in the density curves being more leptokurtic. For the sake of better intuition, it was chosen to have three mixture components which naturally correspond to the three income classes. Based on this partition, the intergroup mobility pattern was revealed, and also the effect of households' individual features on the relative probabilities of belonging to a more high-income class. Based on the the decomposition, a mixture of regressions was also estimated, where each component's parameters are being dependent on the features such as household head's age, education level, marital status and population of the area the household resides in. This allows to identify how different predictors' effects vary across different income classes.