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Log-Transform Kernel Density Estimation Of Income Distribution

Author

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  • Charpentier, Arthur

    (Université du Québec à Montréal)

  • Flachaire, Emmanuel

    (HEC Montréal)

Abstract

Standard kernel density estimation methods are very often used in practice to estimate density functions. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

Suggested Citation

  • Charpentier, Arthur & Flachaire, Emmanuel, 2015. "Log-Transform Kernel Density Estimation Of Income Distribution," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 141-159, Mars-Juin.
    • Handle: RePEc:ris:actuec:0116
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    1. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    2. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    3. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
    4. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen VK, 2010. "Nonparametric density estimation for multivariate bounded data," LIDAM Reprints CORE 2301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    6. Frank A. Cowell, 2008. "Income Distribution and Inequality," Chapters, in: John B. Davis & Wilfred Dolfsma (ed.), The Elgar Companion to Social Economics, chapter 13, Edward Elgar Publishing.
    7. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    8. Arthur Charpentier & Abder Oulidi, 2010. "Beta kernel quantile estimators of heavy-tailed loss distributions," Post-Print halshs-00425566, HAL.
    9. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    10. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    11. Marron, J.S. & Schmitz, H.-P., 1992. "Simultaneous Density Estimation of Several Income Distributions," Econometric Theory, Cambridge University Press, vol. 8(4), pages 476-488, December.
    12. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(2), pages 390-412, April.
    13. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    14. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    15. Ahamada, Ibrahim & Flachaire, Emmanuel, 2010. "Non-Parametric Econometrics," OUP Catalogue, Oxford University Press, number 9780199578009.
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    Cited by:

    1. Edwin Fourrier-Nicolaï & Michel Lubrano, 2021. "Bayesian Inference for Parametric Growth Incidence Curves," Research on Economic Inequality, in: Research on Economic Inequality: Poverty, Inequality and Shocks, volume 29, pages 31-55, Emerald Group Publishing Limited.
    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Surya Bhushan, 2021. "Labour Productivity Dynamics in Indian Agriculture: 2000–2016," The Indian Journal of Labour Economics, Springer;The Indian Society of Labour Economics (ISLE), vol. 64(2), pages 371-388, June.
    4. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.

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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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