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Variance estimation for richness measures

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  • Michał Brzeziński

    () (Faculty of Economic Sciences, University of Warsaw)

Abstract

Richness indices are distributional statistics used to measure the incomes, earnings, or wealth of the rich. This paper uses a linearization method to derive the sampling variances for recently introduced distributionally-sensitive richness measures when estimated from survey data. The results are derived for two cases: (1) when the richness line is known, and (2) when it has to be estimated from the sample. The proposed approach enables easy consideration of the effects of a complex sampling design. Monte Carlo results suggest that the proposed approach allows for reliable inference in case of “concave” richness indices, but that it is not satisfactory in case of “convex” richness measures.

Suggested Citation

  • Michał Brzeziński, 2013. "Variance estimation for richness measures," Working Papers 2013-03, Faculty of Economic Sciences, University of Warsaw.
  • Handle: RePEc:war:wpaper:2013-03
    as

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    File URL: http://www.wne.uw.edu.pl/inf/wyd/WP/WNE_WP88.pdf
    File Function: First version, 2013
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    richness; affluence; distributional indices; variance estimation; statistical inference;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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