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Robust income distribution estimation with missing data

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  • Victoria-Feser, Maria-Pia

Abstract

With income distributions it is common to encounter the problem of missing data. When a parametric model is fitted to the data, the problem can be overcome by specifying the marginal distribution of the observed data. With classical methods of estimation such as the maximum likelihood (ML) an estimator of the parameters can be obtained in a straightforward manner. Unfortunately, it is well known that ML estimators are not robust estimators in the presence of contaminated data. In this paper, we propose a robust alternative to the ML estimator with truncated data, namely one based on M-estimators that we call the EMM estimator. We present an extensive simulation study where the EMM estimator based on optimal B-robust estimators (OBRE) is compared to a more conservative approach based on marginal density (MD) for truncated data, and show that the difference lies in the way the weights associated to each observation are computed. Finally, we also compare the EMM estimator based on the OBRE with the classical ML estimator when the data are contaminated, and show that contrary to the former, the latter can be seriously biased.

Suggested Citation

  • Victoria-Feser, Maria-Pia, 2001. "Robust income distribution estimation with missing data," LSE Research Online Documents on Economics 6561, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:6561
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    File URL: http://eprints.lse.ac.uk/6561/
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    References listed on IDEAS

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    1. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
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    More about this item

    Keywords

    M-estimators; influence function; EM algorithm; truncated data.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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