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Measuring poverty with the Foster, Greer and Thorbecke indexes based on the Gamma distribution

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  • Fernández-Morales, Antonio

Abstract

The purpose of this paper is the estimation of the Foster, Greer and Thorbecke family of poverty indexes using the Gamma distribution as a continuous representation of the distribution of incomes. The expressions of this family of poverty indexes associated with the Gamma probability model and their asymptotic distributions are derived in the text, both for an exogenous and a relative (to the mean) poverty line. Finally, a Monte Carlo experiment is performed to compare three different methods of estimation for grouped data.

Suggested Citation

  • Fernández-Morales, Antonio, 2016. "Measuring poverty with the Foster, Greer and Thorbecke indexes based on the Gamma distribution," MPRA Paper 69648, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:69648
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    File URL: https://mpra.ub.uni-muenchen.de/69648/1/MPRA_paper_69648.pdf
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    References listed on IDEAS

    as
    1. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    2. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, vol. 42(6), pages 1115-1127, November.
    3. Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
    4. Satya R. Chakravarty & Nachiketa Chattopadhyay & Joseph Deutsh & Zoya Nissanov & Jacques Silber, 2019. "Reference Groups and the Poverty Line: An Axiomatic Approach with an Empirical Illustration," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 39-61, Springer.
    5. Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    6. Giovanni Maria Giorgi & Saralees Nadarajah, 2010. "Bonferroni and Gini indices for various parametric families of distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 23-46.
    7. Satya R. Chakravarty & Nachiketa Chattopadhyay & Joseph Deutsch & Zoya Nissanov & Jacques Silber, 2016. "Reference Groups and the Poverty Line: An Axiomatic Approach with an Empirical Illustration," Research on Economic Inequality, in: John A. Bishop & Juan Gabriel Rodríguez (ed.), Inequality after the 20th Century: Papers from the Sixth ECINEQ Meeting, volume 24, pages 1-27, Emerald Publishing Ltd.
    8. Gholamreza Hajargasht & William E. Griffiths & Joseph Brice & D.S. Prasada Rao & Duangkamon Chotikapanich, 2012. "Inference for Income Distributions Using Grouped Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 563-575, May.
    9. Duangkamon Chotikapanich & William E. Griffiths, 2008. "Estimating Income Distributions Using a Mixture of Gamma Densities," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 16, pages 285-302, Springer.
    10. Maxim Pinkovskiy & Xavier Sala-i-Martin, 2009. "Parametric Estimations of the World Distribution of Income," NBER Working Papers 15433, National Bureau of Economic Research, Inc.
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    12. Carmelo Garcia Perez & Mercedes Prieto Alaiz, 2011. "Using the Dagum model to explain changes in personal income distribution," Applied Economics, Taylor & Francis Journals, vol. 43(28), pages 4377-4386.
    13. McDonald, James B & Ransom, Michael R, 1979. "Functional Forms, Estimation Techniques and the Distribution of Income," Econometrica, Econometric Society, vol. 47(6), pages 1513-1525, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Poverty indexes; Income distribution; Gamma distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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