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Toward an Inequality-Sensitive Measure of Development: The Unidimensional Case

  • Asis Kumar BanerjeeEmail author
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Part of the Themes in Economics book series (THIE)

Abstract

This book seeks an inequality-sensitive measure of development. In this chapter, we review the standard theory in this regard for the case where there is a single dimension of development (say, income). Part of the theory is concerned with the question how we should measure inequality. However, inequality ranking is only one part of development ranking. The efficiency aspect is also to be taken into account. The important question for us is whether we can arrive at a complete development ranking, i.e. whether we can rank all pairs of economies in terms of development. It turns out that while the answer to the question is, in general, in the negative, for any given pair of economies, it is possible to formulate necessary and sufficient conditions (in terms of the observed data on incomes of the individuals in the economies) under which the two economies can be ranked. The notions of Lorenz dominance and generalized Lorenz dominance play important roles in these conditions. Whenever these conditions are violated, however, there would be ranking failures, i.e. we would be unable to rank the two economies in terms of their levels of development.

References

  1. Anand S (1983) Inequality and poverty in Malaysia. Oxford University Press, OxfordGoogle Scholar
  2. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2(3):244–263CrossRefGoogle Scholar
  3. Ben-Porath E, Gilboa I (1994) Linear measures, the Gini index and the income-equality trade-off. J Econ Theory 64(2):443–467CrossRefGoogle Scholar
  4. Blackorby C, Donaldson D (1978) Measures of relative equality and their meaning in terms of social welfare. J Econ Theory 18(1):59–80CrossRefGoogle Scholar
  5. Bourguignon F (1979) Decomposable income inequality measures. Econometrica 47(4):901–920CrossRefGoogle Scholar
  6. Cowell FA (1980) On the structure of additive inequality measures. Rev Econ Stud 47(3):521–531CrossRefGoogle Scholar
  7. Cowell FA, Kuga K (1981) Additivity and the entropy concept: An axiomatic approach in inequality measurement. J Econ Theory 25(1):131–143CrossRefGoogle Scholar
  8. Dalton H (1920) The measurement of the inequality of incomes. Econ J 30(119):348–361CrossRefGoogle Scholar
  9. Dasgupta P, Sen AK, Starrett D (1973) Nots on the measurement of inequality. J Econ Theory 6(2):180–187CrossRefGoogle Scholar
  10. Fields GS, Fei JCS (1978) On inequality comparisons. Econometrica 46(2):305–316CrossRefGoogle Scholar
  11. Foster JE (1985) Inequality measurement. In: Young PH (ed) Fair allocation. American Mathematical Society, Providence, RI, pp 31–68CrossRefGoogle Scholar
  12. Gastwirth JL (1971) A general definition of the Lorenz curve. Econometrica 39(6):1037–1039CrossRefGoogle Scholar
  13. Gini C (1912) Variabilita e mutabilita. C. Cuppini, BolognaGoogle Scholar
  14. Hardy GH, Littlewood JE, Poliya G (1952) Inequalities, 2nd edn. Cambridge University Press, LondonGoogle Scholar
  15. Kakwani NC (1980) Income inequality and poverty. Oxford University Press, New YorkGoogle Scholar
  16. Kolm S-C (1969) The optimal production of social justice. In: Margolis J, Guitton G (eds) Public economics. Macmillan, London, pp 145–200CrossRefGoogle Scholar
  17. Marshall AW, Olkin I (1979) Inequalities: Theory of majorization and its applications. Academic Press, New YorkGoogle Scholar
  18. Muirhead RF (1902) Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proc Edinburgh Math Soc 21(February):144–157CrossRefGoogle Scholar
  19. Newbery DMG (1970) A theorem on the measurement of inequality. J Econ Theory 2(3):264–266CrossRefGoogle Scholar
  20. Ricci U (1916) L’indice di variabilita e la curve dei redditi. Giorn d Ec 27(9):177–228Google Scholar
  21. Sen AK (1970) The impossibility of a Paretian liberal. J Polit Economy 78(1):152–157CrossRefGoogle Scholar
  22. Sen A (1997) On economic inequality. Oxford University Press, OxfordGoogle Scholar
  23. Sheshinski E (1972) Relation between a social welfare function and the Gini index of inequality. J Econ Theory 4(1):98–100CrossRefGoogle Scholar
  24. Shorrocks AF (1980) The class of additively decomposable inequality measures. Econometrica 48(3):613–625CrossRefGoogle Scholar
  25. Shorrocks AF (1982) Inequality decomposition by factor components. Econometrica 50(1):193–211CrossRefGoogle Scholar
  26. Shorrocks AF (1983) Ranking income distributions. Economica 50(197):3–17CrossRefGoogle Scholar
  27. Shorrocks AF (1984) Inequality decomposition by population subgroups. Econometrica 52(6):1369–1385CrossRefGoogle Scholar
  28. Shorrocks A, Slottje DJ (2002) Approximatng unanimity orderings: an application to Lorenz dominance. J Econ 9(1):91–117CrossRefGoogle Scholar
  29. Sundaram RK (1996) A first course in optimisation theory. Cambridge University Press, New YorkCrossRefGoogle Scholar
  30. Theil H (1967) Economics and information theory. North-Holland, AmsterdamGoogle Scholar
  31. Weymark JA (1981) Generalized Gini inequality indices. Mathl Soc Sci 1(4):409–430CrossRefGoogle Scholar
  32. Yitzhaki S, Schechtman E (2013) The Gini mehodology. Springer, New YorkCrossRefGoogle Scholar
  33. Yntema DB (1933) Measures of the inequality in the personal distribution of wealth and income. J Am Stat Assoc 28(184):423–433CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.University of CalcuttaKolkataIndia

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