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Bayesian assessment of Lorenz and stochastic dominance

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Listed:
  • David Lander
  • David Gunawan
  • William Griffiths
  • Duangkamon Chotikapanich

Abstract

We 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. Évaluation 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.

Suggested Citation

  • David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
  • Handle: RePEc:wly:canjec:v:53:y:2020:i:2:p:767-799
    DOI: 10.1111/caje.12443
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    Cited by:

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    2. David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2021. "Posterior Probabilities for Lorenz and Stochastic Dominance of Australian Income Distributions," The Economic Record, The Economic Society of Australia, vol. 97(319), pages 504-524, December.
    3. Michel Lubrano & Zhou Xun, 2023. "The Bayesian approach to poverty measurement," Post-Print hal-04347292, HAL.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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