Bayesian assessment of Lorenz and stochastic dominance
Corresponding Author
William Griffiths
University of Melbourne
Corresponding author: William Griffiths, wegrif@unimelb.edu.auSearch for more papers by this authorCorresponding Author
William Griffiths
University of Melbourne
Corresponding author: William Griffiths, wegrif@unimelb.edu.auSearch for more papers by this authorAbstract
enWe introduce a Bayesian approach for assessing Lorenz and stochastic dominance. For two income distributions, say X and Y, estimated via Markov chain Monte Carlo, we describe how to compute posterior probabilities for: (i) X dominates Y, (ii) Y dominates X and (iii) neither Y nor X dominates. The proposed approach is applied to Indonesian income distributions using mixtures of gamma densities that ensure flexible modelling. Probability curves depicting the probability of dominance at each population proportion are used to explain changes in dominance probabilities over restricted ranges relevant for poverty orderings. They also explain some seemingly contradictory outcomes from the p-values of some sampling theory tests.
Résumé
frÉvaluation bayésienne des dominances stochastiques et de Lorenz. Dans cet article, nous présentons une approche bayésienne pour évaluer les dominances stochastiques et de Lorenz. Pour deux distributions de revenus estimées par la méthode de Monte-Carlo par chaînes de Markov, X et Y par exemple, nous décrivons la fac¸on de calculer les probabilités à posteriori lorsque (i) X domine Y, (ii) Y domine X et (iii) ni Y ni X ne sont dominants. Nous avons appliqué l’approche proposée à la distribution des revenus en Indonésie en utilisant une variété de densités gamma pour garantir une modélisation flexible. Des courbes de probabilité illustrant la probabilité de dominance sur chaque proportion de population sont utilisées pour expliquer les changements de probabilité de dominance sur des fourchettes restreintes nécessaires à l’évaluation des niveaux de pauvreté. Ces courbes permettent également d’expliquer les résultats apparemment contradictoires des valeurs p de certains tests théoriques en matière d’échantillonnage.
Supporting Information
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Supplementary material accompanies the online version of this article. The data and code that support the findings of this study are available in the Canadian Journal of Economics Dataverse at https://doi.org/10.5683/SP3/Q817DH. |
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