Information theoretic approaches to income density estimation with an application to the U.S. income data

  • Sung Y. Park
  • Anil K. Bera


The size distribution of income is the basis of income inequality measures which in turn are needed for evaluation of social welfare. Therefore, proper specification of the income density function is of special importance. In this paper, using information theoretic approach, first, we provide a maximum entropy (ME) characterization of some well-known income distributions. Then, we suggest a class of flexible parametric densities which satisfy certain economic constraints and stylized facts of personal income data such as the weak Pareto law and a decline of the income-share elasticities. Our empirical results using the U.S. family income data show that the ME principle provides economically meaningful and a very parsimonious and, at the same time, flexible specification of the income density function.


Income density estimation Information theoretic approach Maximum entropy Weak Pareto law 


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We are grateful to three anonymous referees, and especially the editor for many pertinent comments and helpful suggestions. We would also like to thank Duncan Foley, Essie Maasoumi, Roger Koenker, Zhongjun Qu and Ximing Wu for their comments on an earlier version of the paper. However, we retain the responsibility for any remaining errors. Financial support from the Research Board, University of Illinois at Urbana-Champaign is gratefully acknowledged.


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Authors and Affiliations

  1. 1.School of EconomicsChung-Ang UniversitySeoulKorea
  2. 2.Department of EconomicsUniversity of IllinoisUrbanaUSA

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