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Averaging Lorenz Curves

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  • Duangkamon Chotikapanich

    ()

  • William E. Griffiths

Abstract

A large number of functional forms have been suggested in the literature for estimating Lorenz curves that describe the relationship between income and population shares. One way of choosing a particular functional form is to pick the one that best fits the data in some sense. Another approach, and the one followed here, is to use Bayesian model averaging to average the alternative functional forms. In this averaging process, the different Lorenz curves are weighted by their posterior probabilities of being correct. Unlike a strategy of picking the best-fitting function, Bayesian model averaging gives posterior standard deviations that reflect the functional form uncertainty. Building on our earlier work (Chotikapanich and Griffiths 2002), we construct likelihood functions using the Dirichlet distribution and estimate a number of Lorenz functions for Australian income units. Prior information is formulated in terms of the Gini coefficient and the income shares of the poorest 10% and poorest 90% of the population. Posterior density functions for these quantities are derived for each Lorenz function and are averaged over all the Lorenz functions.

Suggested Citation

  • Duangkamon Chotikapanich & William E. Griffiths, 2003. "Averaging Lorenz Curves," Monash Econometrics and Business Statistics Working Papers 22/03, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2003-22
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp22-03.pdf
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    References listed on IDEAS

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    1. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    2. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
    3. Kakwani, Nanak C & Podder, N, 1976. "Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations," Econometrica, Econometric Society, vol. 44(1), pages 137-148, January.
    4. Kakwani, Nanak, 1980. "On a Class of Poverty Measures," Econometrica, Econometric Society, vol. 48(2), pages 437-446, March.
    5. Datt, Gaurav, 1998. "Computational tools for poverty measurement and analysis," FCND discussion papers 50, International Food Policy Research Institute (IFPRI).
    6. Basmann, R. L. & Hayes, K. J. & Slottje, D. J. & Johnson, J. D., 1990. "A general functional form for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 77-90.
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    Citations

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    Cited by:

    1. Genya Kobayashi & Kazuhiko Kakamu, 2019. "Approximate Bayesian computation for Lorenz curves from grouped data," Computational Statistics, Springer, vol. 34(1), pages 253-279, March.
    2. Andrew C. Chang & Phillip Li & Shawn M. Martin, 2018. "Comparing cross‐country estimates of Lorenz curves using a Dirichlet distribution across estimators and datasets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 473-478, April.
    3. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    4. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Working Papers halshs-02320110, HAL.
    5. Anwar Shaikh, 2018. "Some Universal Patterns in Income Distribution: An Econophysics Approach," Working Papers 1808, New School for Social Research, Department of Economics.

    More about this item

    Keywords

    Gini coefficient; Bayesian inference; Dirichlet distribution.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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