Unidimensional Inequality – Unidimensional Dominance – 2010

Instructor: Maria Emma Santos, OPHI Research Officer 

Class Objectives:

  • The Lorenz Curve and Lorenz Dominance. Atkinson’s theorem.
  • The Generalized Lorenz Curve and Generalized Lorenz Dominance. Generalization of Atkinson’s theorem.
  • The four basic properties of unidimensional inequality measures. Lorenz consistent inequality measures.
  • Other properties (Transfer Sensitivity, Consistency and Decomposability).
  • Unidimensional inequality measures and their properties.
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Download Lecture Slides (pdf)

Unidimensional Inequality & Dominance

Unidimensional Poverty

Poverty Orderings

Exercise Files (zip file)

Unidimensional Inequality Poverty Exercises

Reading List
Suggested basic readings on this topic:
FIELDS, G. (2001): Distribution and Development. New York: Russell Sage Foundation and Cambridge, MA: MIT. Chapter 2.
FOSTER, J. (2008): “Inequality Measurement” in David Clark (ed.) The Elgar Companion to Development Studies . Cheltenham: Edward Elgar.
RAY, D. (1998): Development Economics . New Jersey: Princeton. Chapter 6.

Advanced reading on this topic:
FOSTER, J. E. and A. Sen (1997): “On Economic Inequality: After a Quarter Century”. Annex to the Expanded Edition of A. Sen. On Economic Inequality. Oxford: Clarendon Press. Sections A.2 to A.5.

Further readings:
ATKINSON, A. B. (1970): “On the Measurement of Inequality”, Journal of Economic Theory. 2: 244-263.
BOURGUIGNON, F. (1979): “Decomposable Income Inequality Measures”, Econometrica. 47: 901-20.
COWELL, F. A. (1988): “Inequality Decomposition – Three Bad Measures”, Bulletin of Economic Research. 40: 309-312
COWELL, F. A. (2000): “Measurement of Inequality”, in Anthony B. Atkinson and Francois Bourguignon. Handbook of Income Distribution, Volume 1. Amsterdam: North-Holland. (This is a survey)
DALTON, H. (1920): “The Measurement of Inequality of Incomes”, Economic Journal. 30(119): 348-61.
FOSTER, J. and A. SHNEYEROV. (1999): “A General Class of Additively Decomposable Inequality Measures”, Economic Theory. 14: 89-111.
FOSTER, J. and A. SHNEYEROV. (2000): “Path Independent Inequality Measures”, Journal of Economic Theory. 91: 199-222.
FOSTER, J. E. (1985): “Inequality Measurement” in H. Peyton Young (ed.) Fair Allocation. Providence, RI: American Mathematical Society. (It provided the first proof that “Lorenz consistency” is equivalent to the four basic axioms of inequality measurement.)
FOSTER, J. E. and E. A. OK. (1999): “Lorenz Dominance and the Variance of Logarithms”, Econometrica. 67: 901-908.
FOSTER, J. E. (1983): “An Axiomatic Characterization of the Theil Measure of Income Inequality”, Journal of Economic Theory. 31: 105-121.
SHORROCKS, A. F. (1980): “The Class of Additively Decomposable Inequality Measures”, Econometrica. 48(3): 613-25.
SHORROCKS, A. F. (1982): “Inequality Decomposition by Factor Components”, Econometrica. 50(1): 193-211.
SHORROCKS, A. F. (1983): “Ranking Income Distributions”, Economica. 50(197): 3-17.
SHORROCKS, A. F. (1988): “Aggregation Issues in Inequality Measurement” in W. Eichorn (ed.) Measurement in Economics. New York: Physica-Verlag.
THEIL, H. (1967) Economics and Information Theory. Amsterdam: North-Holland.
WEYMARK, J. A. (1981): “Generalized Gini Inequality Indices”, Mathematical Social Sciences. 1: 409-30.