Bayesian Inference for Multidimensional Welfare Comparisons

TL;DR

This paper demonstrates how Bayesian inference, combined with stochastic dominance and copula methods, can be used to compare multidimensional welfare across time using survey data.

Contribution

It introduces a Bayesian framework for multivariate welfare comparison incorporating multiple attributes and utility functions, advancing welfare analysis methods.

Findings

Bayesian methods effectively estimate multidimensional well-being distributions.

Posterior probabilities of stochastic dominance reveal welfare improvements over time.

Different utility function classes influence dominance conditions and results.

Abstract

Using both single-index measures and stochastic dominance concepts, we show how Bayesian inference can be used to make multivariate welfare comparisons. A four-dimensional distribution for the well-being attributes income, mental health, education, and happiness are estimated via Bayesian Markov chain Monte Carlo using unit-record data taken from the Household, Income and Labour Dynamics in Australia survey. Marginal distributions of beta and gamma mixtures and discrete ordinal distributions are combined using a copula. Improvements in both well-being generally and poverty magnitude are assessed using posterior means of single-index measures and posterior probabilities of stochastic dominance. The conditions for stochastic dominance depend on the class of utility functions that is assumed to define a social welfare function and the number of attributes in the utility function. Three classes of utility functions are considered, and posterior probabilities of dominance are computed for one, two, and four-attribute utility functions for three time intervals within the period 2001 to 2019.