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A Simple Consistent Nonparametric Estimator of the Lorenz Curve

In: Essays in Honor of Aman Ullah

Author

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  • Yu Yvette Zhang
  • Ximing Wu
  • Qi Li

Abstract

We propose a nonparametric estimator of the Lorenz curve that satisfies its theoretical properties, including monotonicity and convexity. We adopt a transformation approach that transforms a constrained estimation problem into an unconstrained one, which is estimated nonparametrically. We utilize the splines to facilitate the numerical implementation of our estimator and to provide a parametric representation of the constructed Lorenz curve. We conduct Monte Carlo simulations to demonstrate the superior performance of the proposed estimator. We apply our method to estimate the Lorenz curve of the U.S. household income distribution and calculate the Gini index based on the estimated Lorenz curve.

Suggested Citation

  • Yu Yvette Zhang & Ximing Wu & Qi Li, 2016. "A Simple Consistent Nonparametric Estimator of the Lorenz Curve," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 635-653, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320160000036028
    DOI: 10.1108/S0731-905320160000036028
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    Citations

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    Cited by:

    1. Lina M Cortés & Juan M Lozada & Javier Perote, 2021. "Firm size and economic concentration: An analysis from a lognormal expansion," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-21, July.
    2. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    3. Lina Cortés & Juan M. Lozada & Javier Perote, 2019. "Firm size and concentration inequality: A flexible extension of Gibrat’s law," Documentos de Trabajo de Valor Público 17205, Universidad EAFIT.
    4. Dong Li & Luya Wang & Ximing Wu, 2021. "Bayesian estimation of bidding process and bidder’s preference under shape restrictions," Empirical Economics, Springer, vol. 60(1), pages 157-176, January.

    More about this item

    Keywords

    Lorenz curve; spline estimation; monotonicity; convexity; Gini index; C14; C52; D63;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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