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The first moment of income density functions and estimation of single-parametric Lorenz curves

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  • Liang Frank Shao

Abstract

This paper discusses the first moment, i.e., the mean income point, of income density functions and the estimation of single-parametric Lorenz curves. The mean income point is implied by an income density function and associated with a single-parametric Lorenz function. The boundary of the mean income point can show the flexibility of a parametric Lorenz function. I minimize the sum of squared errors in fitting both grouped income data and the mean income point and identify the best parametric Lorenz function using a large panel dataset. I find that each parametric Lorenz function may do a better job than others in fitting particular grouped data; however, a zero- and unit-modal single-parametric Lorenz function is identified to be the best of eight typical optional functions in fitting most (666 out of 969) observations of a large panel dataset. I perform a Monte Carlo simulation as a robustness check of the empirical estimation.

Suggested Citation

  • Liang Frank Shao, 2022. "The first moment of income density functions and estimation of single-parametric Lorenz curves," PLOS ONE, Public Library of Science, vol. 17(6), pages 1-24, June.
    • Handle: RePEc:plo:pone00:0267828
    DOI: 10.1371/journal.pone.0267828
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