IDEAS home Printed from https://ideas.repec.org/a/bla/jpbect/v23y2021i2p228-247.html
   My bibliography  Save this article

Stochastic dominance and decomposable measures of inequality and poverty

Author

Listed:
  • Buhong Zheng

Abstract

In this paper, we characterize some new links between stochastic dominance and the measurement of inequality and poverty. We show that: for second‐degree normalized stochastic dominance (NSD), the weighted area between the NSD curve of a distribution and that of the equalized distribution is a decomposable inequality measure; for first‐degree and second‐degree censored stochastic dominance (CSD), the weighted area between the CSD curve of a distribution and that of the zero‐poverty distribution is a decomposable poverty measure. These characterizations provide graphical representations for decomposable inequality and poverty measures in the same manner as Lorenz curve does for the Gini index. The extensions of the links to higher degrees of stochastic dominance are also investigated.

Suggested Citation

  • Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    • Handle: RePEc:bla:jpbect:v:23:y:2021:i:2:p:228-247
    DOI: 10.1111/jpet.12496
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jpet.12496
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jpet.12496?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Formby, John P. & Smith, W. James & Zheng, Buhong, 1999. "The coefficient of variation, stochastic dominance and inequality: A new interpretation," Economics Letters, Elsevier, vol. 62(3), pages 319-323, March.
    2. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    3. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    4. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    6. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    7. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    8. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
    9. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    10. Anthony Shorrocks & Daniel Slottje, 2002. "Approximating unanimity orderings: An application to Lorenz dominance," Journal of Economics, Springer, vol. 77(1), pages 91-117, December.
    11. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    12. Buhong Zheng, 2007. "Unit‐Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, February.
    13. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    14. Dominique Thon, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    15. Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 415-435, October.
    16. repec:zbw:hohpro:325 is not listed on IDEAS
    17. Zheng, Buhong, 2017. "A class of generalized Sen poverty indices," Economics Letters, Elsevier, vol. 159(C), pages 100-103.
    18. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    19. Zheng, Buhong, et al, 2000. "Inequality Orderings, Normalized Stochastic Dominance, and Statistical Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 479-488, October.
    20. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    21. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    22. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    23. repec:bla:jecsur:v:11:y:1997:i:2:p:123-62 is not listed on IDEAS
    24. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
    25. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
    26. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    27. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    28. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    29. repec:bla:revinw:v:25:y:1979:i:4:p:429-39 is not listed on IDEAS
    30. Bosmans, Kristof & Cowell, Frank A., 2010. "The class of absolute decomposable inequality measures," Economics Letters, Elsevier, vol. 109(3), pages 154-156, December.
    31. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    32. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    33. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    34. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    35. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    36. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    37. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    38. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
    39. Buhong Zheng, 1999. "On the power of poverty orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 349-371.
    40. Buhong Zheng, 2018. "Almost Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 51-63, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chan, Terence, 2024. "Coherence of inequality measures with respect to partial orderings of income distributions," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 90-99.
    2. Chan, Terence, 2022. "On a new class of continuous indices of inequality," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 8-23.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    2. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    3. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    4. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    5. Jean–Yves Duclos & Phillipe Grégoire, 2002. "Absolute and Relative Deprivation and the Measurement of Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(4), pages 471-492, December.
    6. Ottó Hajdu, 2021. "A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 158(3), pages 839-861, December.
    7. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    8. Jean‐Yves Duclos & Paul Makdissi, 2004. "Restricted and Unrestricted Dominance for Welfare, Inequality, and Poverty Orderings," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(1), pages 145-164, February.
    9. Bibi, Sami & Duclos, Jean-Yves, 2007. "Equity and policy effectiveness with imperfect targeting," Journal of Development Economics, Elsevier, vol. 83(1), pages 109-140, May.
    10. Sean Higgins & Nora Lustig, 2015. "Can Poverty-Reducing and Progressive Tax and Transfer System Hurt the Poor?," Commitment to Equity (CEQ) Working Paper Series 1333, Tulane University, Department of Economics.
    11. Suman Seth, Sabina Alkire, 2014. "Measuring and Decomposing Inequality among the Multidimensionally Poor Using Ordinal Data: A Counting Approach," OPHI Working Papers 68, Queen Elizabeth House, University of Oxford.
    12. Higgins, Sean & Lustig, Nora, 2016. "Can a poverty-reducing and progressive tax and transfer system hurt the poor?," Journal of Development Economics, Elsevier, vol. 122(C), pages 63-75.
    13. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(3), pages 253-277, December.
    14. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    15. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2021. "Ranking intersecting distribution functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 639-662, September.
    16. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    17. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    18. Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 415-435, October.
    19. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    20. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jpbect:v:23:y:2021:i:2:p:228-247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/apettea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.