Dynamics of Income Distribution — A Diffusion Analysis
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Abstract
The study is motivated by the observation that the distribution of income across countries varies as a function of time. It would not be unreasonable to assume that there exists a statistical equilibrium distribution of income with a certain mean and variance, towards which the ensemble of countries considered tend to converge, and there is a speed of adjustment towards this said equilibrium. In order to quantify this process, the evolution through time of income around its trend is modeled using a classic stochastic differential equation. The model describes the diffusion of shocks across space, via an income adjustment process with noise. The dynamics rely on two opposing flows: (i) a factor equalization process, and (ii) a counteracting diffusion process. It is hypothesized that these flows follow simple evolutionary laws that can be described with five parameters — parameters that can be estimated from historical data with some accuracy. The dynamic behavior of the model is analytically derived. Both the extent and speed of adjustment of income are analyzed. An empirical application of the proposed model to the evolution of the distribution of income for 25 countries in the European Union tests the validity of the proposed method and suggests that diffusion may be a preferable technique for the analysis of income dynamics.
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