TEL  Vol.2 No.5 , December 2012
A Decomposition of the Atkinson Index through the Shapley Value
ABSTRACT
This paper studies the economic inequality as a phenomenon resulting from two variables: The variable of responsibility which depends on the agents’ performance in the economy, and the variable of opportunity which is independent of the individuals’ performance in the economy. Identifying the contribution of the inequality of opportunity in the total inequality as the problem to be measured, we propose a decomposition of the Atkinson inequality index, by using one of the central solution concepts of cooperative game theory, called the Shapley value.

Cite this paper
J. Sánchez-Pérez, "A Decomposition of the Atkinson Index through the Shapley Value," Theoretical Economics Letters, Vol. 2 No. 5, 2012, pp. 539-544. doi: 10.4236/tel.2012.25100.
References
[1]   A. K. Sen, “The Economic Inequality,” Fondo de Cultura Económica, México City, 2001.

[2]   A. Bergson-Samuelson, “A Reformulation of Certain Aspects of Welfare Economics,” Journal of Economics, Vol. 52, No. 2, 1938, pp. 310-334. doi:10.2307/1881737

[3]   A. B. Atkinson, “On the Measurement of Inequality,” Journal of Economic Theory, Vol. 2, No. 3, 1970, pp. 244-263.

[4]   J. Levy, S. Chemerynski and J. Tuchmann, “Incorporating Concepts of Inequality and Inequity into Health Benefits Analysis,” International Journal for Equity in Health, Vol. 5, 2006, p. 2.

[5]   A. F. Shorrocks, “Decomposition Procedures for Distributional Analysis: A Unified Framework Based on the Shapley Value,” University of Essex, Colchester, UK.

[6]   M. Sastre and A. Trannoy, “Shapley Inequality Decomposition by Factor Components: Some Methodological Issues,” Journal of Economics, Vol. 9, No. 1, 2002, pp. 51-90. doi:10.1007/BF03052500

[7]   V. Peragine, “Measuring and Implementing Equality of Opportunity for Income,” Social Choice and Welfare, Vol. 22, No. 1, 2004, pp. 187-210. doi:10.1007/s00355-003-0282-2

[8]   T. Driessen, “Cooperative Games, Solutions and Applications,” Springer-Verlag, Dordrecht, 1988.

[9]   L. S. Shapley, “A Value for n-person Games,” In: H. W. Kuhn and A. W. Tucker, Eds., Annals of Mathematic Studies, Princeton University Press, Princeton, 1953, pp. 307-317.

[10]   M. C. Lasso de la Vega and A. M. Urrutia, “A New Factorial Decomposition for the Atkinson Measure,” Economics Bulletin, Vol. 4, No. 29, 2003, pp. 1-12.

 
 
Top