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A Symmetric Information-Theoretic Index For The Measurement of Inequality

The application of information theory to the measurement of income inequality has yielded an impressive array of measurement techniques known as Generalized Entropy (GE) measures. Special cases of this class of index include Theil’s T and L measures which are considered axiomatically superior to other types of metrics including the popular Gini coefficient. In this paper we show that the parallel between information theory and inequality measurement has not yet been fully explored and propose a new inequality measure based upon this concept. The proposed measure is already established as a tool for use in statistical classification and signal processing problems and is known in these fields as the J-Divergence or Symmetric Kullback-Leibler Divergence. As an inequality metric the measure is shown to be axiomatically complete and is in possession of an additional property allowing for an alternate type of decomposition analysis. The new type of decomposition makes the contribution of any individual or subgroup to the inequality metric directly observable such that the overall index may be reconciled with a weighted sum of each group contribution. We illustrate with an example using income micro-data from the United States where we evaluate the contributions of various racial groups to overall inequality. We also provide a standard decomposition of the inequalities between and within the racial groups to contrast the techniques. and within the racial groups to contrast the techniques.

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Paper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 398.

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Date of creation: 2009
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Handle: RePEc:qld:uq2004:398
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  1. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  2. Michael Rothschild & Joseph E. Stiglitz, 1972. "Some Further Results on the Measurement of Inequality," Cowles Foundation Discussion Papers 344, Cowles Foundation for Research in Economics, Yale University.
  3. Branko milanovic, 2003. "True world income distribution, 1988 and 1993: First calculation based on household surveys alo," HEW 0305002, EconWPA.
  4. Xavier Sala-i-Martin, 2006. "The World Distribution of Income: Falling Poverty and ... Convergence, Period," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 351-397, May.
  5. Chotikapanich, Duangkamon & Valenzuela, Rebecca & Rao, D S Prasada, 1997. "Global and Regional Inequality in the Distribution of Income: Estimation with Limited and Incomplete Data," Empirical Economics, Springer, vol. 22(4), pages 533-46.
  6. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March.
  7. Xavier Sala-i-Martin, 2002. "The Disturbing "Rise" of Global Income Inequality," NBER Working Papers 8904, National Bureau of Economic Research, Inc.
  8. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  9. 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.
  10. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  11. Cowell, Frank A. & Kuga, Kiyoshi, 1981. "Additivity and the entropy concept: An axiomatic approach to inequality measurement," Journal of Economic Theory, Elsevier, vol. 25(1), pages 131-143, August.
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