Income Thresholds and Income Classes

This paper proposes a method for detecting income classes based on the change-point problem. There is an increasing demand for such a method in the literature. Computation of polarization indices requires a pre-grouping of the incomes. Similarly, indices of social exclusion and sometimes indices of income inequality require detection of thresholds. The estimation procedure is implemented using a bootstrap technique. Finally, an application of the method to EU member states and to the United States is also considered.income distribution, change-point, thresholds.

Target Shortfall Orderings and Indices

Given any income distribution, to each income we associate a subgroup containing all persons whose incomes are not higher than this income and a person's target shortfall in a subgroup is the gap between the subgroup highest income and his own income. We then develop an absolute target shortfall ordering, which, under constancy of population size and total income, implies the Lorenz and Cowell-Ebert complaint orderings. Under the same restrictions, one distribution dominates the other by this ordering if and only if the dominated distribution can be obtained from the dominant one by a sequence of rank preserving progressive transfers, where each transfer is shared equally by all persons poorer than the donor of the transfer. The relationship of the ordering with the absolute deprivation and differential orderings, and its consistency with ranking of distributions by absolute target shortfall indices are explored. Well-known inequality indices like the absolute Gini index and the standard deviation are interpreted as absolute target shortfall indices. Finally, the possibility of a relative target shortfall ordering is also discussed.Target shortfall orderings, transfer, indices

An urn-based Bayesian block bootstrap

Block bootstrap has been introduced in the literature for resampling dependent data, i.e. stationary processes. One of the main assumptions in block bootstrapping is that the blocks of observations are exchangeable, i.e. their joint distribution is immune to permutations. In this paper we propose a new Bayesian approach to block bootstrapping, starting from the construction of exchangeable blocks. Our sampling mechanism is based on a particular class of reinforced urn processe

A class of neutral to the right priors induced by superposition of beta processes

A random distribution function on the positive real line which belongs to the class of neutral to the right priors is defined. It corresponds to the superposition of independent beta processes at the cumulative hazard level. The definition is constructive and starts with a discrete time process with random probability masses obtained from suitably defined products of independent beta random variables. The continuous time version is derived as the corresponding infinitesimal weak limit and is described in terms of completely random measures. It takes the interpretation of the survival distribution resulting from independent competing failure times. We discuss prior specification and illustrate posterior inference on a real data example.Bayesian nonparametrics; beta process; beta-Stacy process; completely random measures; neutral to the right priors; survival analysis

Income and Wealth Distributions in a Population of Heterogeneous Agents

This paper develops a simple framework to characterize the distribution of income and wealth in a real business cycle model. Agents are of two types depending on the human factor of production they own and they are located in separated markets, cities. In each city the two types of agent match to produce a composite factor, human service. We show that if the population is an exchangeable sequence of agents' types generated according to a Pòlya urn then (i) the share of agents' type follows a Beta distribution and (ii) the functional form of the matching function belongs to the family of the constant elasticity of substitution, with agent shares that depend on the composition of the population. We nest this structure into a standard Bewley economy, in which the aggregate supply of human service is combined with physical capital to produce the homogeneous output. Given the results (i)-(ii) we perform the exact aggregation of income, consumption and asset holding across agents, leading to the solution of the real business cycle model with heterogeneous agents. Our framework predicts that the theoretical distributions of income and wealth are known real valued transformations of a Beta distribution. This result provides a simple way to characterize the equilibrium of macroeconomic models with heterogeneous agents