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Log-Transform Kernel Density Estimation of Income Distribution

Author

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  • Arthur Charpentier

    (UQAM - Université du Québec à Montréal = University of Québec in Montréal)

  • Emmanuel Flachaire

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

Standard kernel density estimation methods are very often used in practice to estimate density function. 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

  • Arthur Charpentier & Emmanuel Flachaire, 2014. "Log-Transform Kernel Density Estimation of Income Distribution," Working Papers halshs-01115988, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01115988
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01115988
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    References listed on IDEAS

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    6. 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.
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    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    14. Arthur Charpentier & Abder Oulidi, 2010. "Beta kernel quantile estimators of heavy-tailed loss distributions," Post-Print halshs-00425566, HAL.
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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. 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.
    3. 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.
    4. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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    More about this item

    Keywords

    nonparametric density estimation; heavy-tail; income distribution; data transformation; lognormal kernel;
    All these keywords.

    JEL classification:

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

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