Home Poverty Orderings with Asymmetric Attributes
Article
Licensed
Unlicensed Requires Authentication

Poverty Orderings with Asymmetric Attributes

  • Rocio Garcia-Diaz EMAIL logo
Published/Copyright: June 21, 2013
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 13 Issue 1

Abstract

We provide a theorem that lists the necessary and sufficient dominance conditions for the poverty comparisons of the bivariate distributions function when considering an asymmetric treatment of attributes. The normative justification for an asymmetric treatment is based on the compensation principle proposed by Muller and Trannoy (2012), under which it makes sense to use one attribute to compensate another. The formulation results in a generalization of the needs approach in poverty analysis proposed by Atkinson (1992). The dominance conditions we found lie between those obtained by Bourguignon and Chakravarty (2002) and Duclos, Sahn, and Younger (2006a) when attributes are symmetric and those obtained within the needs framework by Atkinson (1992) and Jenkins and Lambert (1993) when attributes are asymmetric, but one is of discrete nature.

Keywords: multidimensional poverty orderings; sequential stochastic dominance; asymmetric treatment of attributes; compensation theory

Appendix

Derivation of formula [7]. To derive the conditions, this section is formulated in terms of a continuum of population, the suffix in the vector and is dropped. We start with the definition of the dominance condition

[9]
[9]

We integrate by parts eq. [9], and consider first the inner integral and integrate with respect to . This yields

[10]
[10]

After evaluating the first square bracketed term, we get

[11]
[11]

Then we substitute eq. [11] into eq. [9], we obtain

[12]
[12]

Integrating by parts, the first part of eq. [12] and evaluating the first term, we get

[13]
[13]

By using the definition of a conditional probability distribution, it reduces to

[14]
[14]

Integrating by parts, the second part of eq. [12] and evaluating the first term, we get

[15]
[15]

By using the definition of a conditional probability distribution (3), it reduces to

[16]
[16]

By substituting eqs. [14] and [16] into eq. [12], we obtain

[17]
[17]

The first term reduces to zero by the definition of a distribution function, and when we insert and , the whole expression reduces to

[18]
[18]

Let us now take into account the following properties implied by the focus definition:

These conditions are sufficient to replace the bounds and in eq. [18] by the poverty thresholds and . Therefore, we get

References

Alkire, S., and J. Foster. 2011. “Counting and Multidimensional Poverty Measurement.” Journal of Public Economics 95(7):476–87.10.1016/j.jpubeco.2010.11.006Search in Google Scholar

Anand, S., and A. Sen. 2000. “Human Development and Economic Sustainability.” World Development 28:2029–49.10.1016/S0305-750X(00)00071-1Search in Google Scholar

Atkinson, A. B. 1987. “On the Measurement of Poverty.” Econometrica 55:749–64.10.2307/1911028Search in Google Scholar

Atkinson, A. B. 1992. “Measuring Poverty and Differences in Family Composition.” Economica 59(233):1–16.10.2307/2555062Search in Google Scholar

Atkinson, A. B. 2003. “Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches.” Journal of Economic Inequality 1(1):51–65.10.1023/A:1023903525276Search in Google Scholar

Atkinson, A. B., and F. Bourguignon 1987. “Income Distributions and Differences in Needs.” In Arrow and the Foundations of the Theory of Economic Policy, edited by G. F. Feiwell, 350–70. London: Macmillan, 1987.10.1007/978-1-349-07357-3_13Search in Google Scholar

Bazen, S., and P. Moyes. 2003 “International Comparisons of Income Distributions.” Research on Economic Inequality 9:85–104.10.1016/S1049-2585(03)09006-9Search in Google Scholar

Bibi, S., and A. R. El Lahga. 2008. “Robust Ordinal Comparisons of Multidimensional Poverty Between South Africa and Egypt.” Revue D’économie Du Développement 22(5):37.Search in Google Scholar

Bosmans, K., L. Lauwers, and E. Ooghe. 2009. “A Consistent Multidimensional Pigou–Dalton Transfer Principle.” Journal of Economic Theory 144(3):1358–71.10.1016/j.jet.2009.01.003Search in Google Scholar

Bourguignon, F. 1989. “Family Size and Social Utility: Income Distribution Dominance Criteria.” Journal of Econometrics 42(1):67–80.10.1016/0304-4076(89)90076-6Search in Google Scholar

Bourguignon, F., and S. R. Chakravarty. 2002. “Multidimensional Poverty Orderings.” DELTA, working paper No 2002–22.Search in Google Scholar

Bourguignon, F., and S. R. Chakravarty. 2003. “The Measurement of Multidimensional Poverty.” Journal of Economic Inequality 1(1):25–49.10.1023/A:1023913831342Search in Google Scholar

Chambaz, C., and E. Maurin. 1998. “Atkinson and Bourguignon’s Dominance Criteria: Extended and Applied to the Measurement of Poverty in France.” Review of Income and Wealth 44(4):497–513.10.1111/j.1475-4991.1998.tb00295.xSearch in Google Scholar

Decancq, K., and M. A. Lugo. 2012. “Weights in Multidimensional Indices of Wellbeing: An Overview.” Econometric Reviews 32(1):7–34.10.1080/07474938.2012.690641Search in Google Scholar

Duclos, J. Y., and P. Makdissi. 2005. “Sequential Stochastic Dominance and the Robustness of Poverty Orderings.” Review of Income and Wealth 51(1):63–87.10.1111/j.1475-4991.2005.00145.xSearch in Google Scholar

Duclos, J. Y., and M. Mercader-Prats. 1999. “Household Needs and Poverty: With Application to Spain and the UK.” Review of Income and Wealth 45(1):77–98.10.1111/j.1475-4991.1999.tb00313.xSearch in Google Scholar

Duclos, J. Y., D. E. Sahn, and S. D. Younger. 2006a. “Robust Multidimensional Poverty Comparisons.” The Economic Journal 116(514):943–68.10.1111/j.1468-0297.2006.01118.xSearch in Google Scholar

Duclos, J., D. Sahn, and S. D. Younger. 2006b. “Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda.” The World Bank Economic Review 20:91–113.10.1093/wber/lhj005Search in Google Scholar

Esposito, L., and E. Chiappero-Martinetti. 2010. “Multidimensional Poverty Measurement: Restricted and Unrestricted Hierarchy Among Poverty Dimensions.” Journal of Applied Economics 13(2):181–204.10.1016/S1514-0326(10)60009-8Search in Google Scholar

Fleurbaey, M. 1995. “Three Solutions for the Compensation Problem.” Journal of Economic Theory 65:505–21.10.1006/jeth.1995.1018Search in Google Scholar

Fleurbaey, M., and F. Maniquet. 2006. “Compensation and Responsibility.” In Handbook of Social Choice and Welfare, edited by K. Arrow, K. Sen, and K. Suzumura, 507–598. New York: Elsevier.Search in Google Scholar

Gordon, A., I. Crawford, and A. Leicester. 2011. “Welfare Rankings from Multivariate Data, a Nonparametric Approach.” Journal of Public Economics 95(3–4):247–52.Search in Google Scholar

Gravel, N., P. Moyes, and T. Benoit. 2009. “Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods.” Economica 76:432–61.10.1111/j.1468-0335.2008.00688.xSearch in Google Scholar

Gravel, N., and A. Mukhopadhyay. 2010. “Is India Better Off Today Than 15 Years Ago? A Robust Multidimensional Answer.” Journal of Economic Inequality 8(2):173–95.10.1007/s10888-009-9112-9Search in Google Scholar

Jenkins, S. P., and P. J. Lambert. 1993. “Ranking Income Distributions When Needs Differ.” Review of Income and Wealth 39(4):337–56.10.1111/j.1475-4991.1993.tb00466.xSearch in Google Scholar

Muller, C., and A. Trannoy. 2012. “Multidimensional Inequality Comparisons: A Compensation Perspective.” Journal of Economic Theory 147(4):1427–49.10.1016/j.jet.2011.09.002Search in Google Scholar

Qizilbash, M. 2004. “On the Arbitrariness and Robustness of Multi-Dimensional Poverty Rankings.” Journal of Human Development 5(3):355–75.10.1080/1464988042000277242Search in Google Scholar

Sahn, D. E., and S. D. Younger. 2005. “Improvements in Children’s Health: Does Inequality Matter?” The Journal of Economic Inequality 3(2):125–43.10.1007/s10888-005-4494-9Search in Google Scholar

Tsui, K. 2002. “Multidimensional Poverty Indices.” Social Choice and Welfare 19(1):69–93.10.1007/s355-002-8326-3Search in Google Scholar

  1. 1

    Gravel and Mukhopadhyay (2010) extended these dominance criteria for robust comparisons that involve more than two attributes. The approach is becoming increasingly acknowledged in the empirical applications (see among others, Sahn and Younger (2005); Duclos, Sahn, and Younger (2006b); Bibi and El Lahga (2008)).

Published Online: 2013-6-21
Published in Print: 2013-1-1

©2013 by Walter de Gruyter Berlin / Boston

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Advances
  4. Dependence and Uniqueness in Bayesian Games
  5. Monopolistic Signal Provision†
  6. Multi-task Research and Research Joint Ventures
  7. Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information
  8. A Simple Bargaining Procedure for the Myerson Value
  9. On the Difference between Social and Private Goods
  10. Optimal Use of Rewards as Commitment Device When Bidding Is Costly
  11. Labor Market and Search through Personal Contacts
  12. Contributions
  13. Learning, Words and Actions: Experimental Evidence on Coordination-Improving Information
  14. Are Trust and Reciprocity Related within Individuals?
  15. Optimal Contracting Model in a Social Environment and Trust-Related Psychological Costs
  16. Contract Bargaining with a Risk-Averse Agent
  17. Academia or the Private Sector? Sorting of Agents into Institutions and an Outside Sector
  18. Topics
  19. Poverty Orderings with Asymmetric Attributes
  20. Dictatorial Mechanisms in Constrained Combinatorial Auctions
  21. When Should a Monopolist Improve Quality in a Network Industry?
  22. On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition
  23. Revenue Comparison in Asymmetric Auctions with Discrete Valuations
https://doi.org/10.1515/bejte-2012-0020
Keywords for this article
multidimensional poverty orderings; sequential stochastic dominance; asymmetric treatment of attributes; compensation theory

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Advances
  4. Dependence and Uniqueness in Bayesian Games
  5. Monopolistic Signal Provision†
  6. Multi-task Research and Research Joint Ventures
  7. Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information
  8. A Simple Bargaining Procedure for the Myerson Value
  9. On the Difference between Social and Private Goods
  10. Optimal Use of Rewards as Commitment Device When Bidding Is Costly
  11. Labor Market and Search through Personal Contacts
  12. Contributions
  13. Learning, Words and Actions: Experimental Evidence on Coordination-Improving Information
  14. Are Trust and Reciprocity Related within Individuals?
  15. Optimal Contracting Model in a Social Environment and Trust-Related Psychological Costs
  16. Contract Bargaining with a Risk-Averse Agent
  17. Academia or the Private Sector? Sorting of Agents into Institutions and an Outside Sector
  18. Topics
  19. Poverty Orderings with Asymmetric Attributes
  20. Dictatorial Mechanisms in Constrained Combinatorial Auctions
  21. When Should a Monopolist Improve Quality in a Network Industry?
  22. On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition
  23. Revenue Comparison in Asymmetric Auctions with Discrete Valuations
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 7.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/bejte-2012-0020/html
Scroll to top button