A Bayesian model of income distribution

The purpose of this study is to build a Bayesian model for the income distribution generating process. Mathematical models of income distribution have been developed in the social sciences field; however, these models lack empirical validity. Human capital approaches have been developed to estimate the effect of individual investment on earnings, but those approaches lack rigorous mathematical consistency with the probability distribution of income. There is no appropriate probability model for testing the empirical validity of the theory that can explain the genesis of the distribution through human capital. To solve the problem, we built a generative income distribution model, expressed as a stochastic model, which formally represents human capital theory and a rigorous micro-macro linkage. Using nationwide survey data in Japan, we estimate the posterior distributions of the parameters of the probabilistic toy model using Markov chain Monte Carlo method. Moreover, we try to check the predictive accuracy of the models using the widely appreciable information criteria and the leave-one-out cross-validation. As a result, we conjecture that the predictive accuracy of the theory-based model is as good as that of the generalized linear model and provides interesting information about latent parameters.