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Influence functions for distributional statistics


  • B. Essama-Nssah

    (World Bank Group)

  • Peter J. Lambert

    () (University of Oregon)


Social evaluation functions used in policy impact analysis can be viewed as real-valued functionals of the underlying outcome distributions. Influence functions may be used to identify the sources of variation in social outcomes in terms of individual or household characteristics. This paper sets forth in clear terms the definition of the influence function and recentered influence function, and catalogs these functions for a wide range of distributional statistics, including measures of central tendency, inequality and poverty and also measures of the degree of pro-poorness of a shock- or policy-induced change in income levels.

Suggested Citation

  • B. Essama-Nssah & Peter J. Lambert, 2011. "Influence functions for distributional statistics," Working Papers 236, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2011-236

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    References listed on IDEAS

    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
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    3. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
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    7. Ravallion, Martin & Chen, Shaohua, 2003. "Measuring pro-poor growth," Economics Letters, Elsevier, vol. 78(1), pages 93-99, January.
    8. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    9. Chantreuil, F. & Trannoy, A., 1999. "Inequality Decomposition Values: the Trade-Off Between Marginality and Consistency," Papers 99-24, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    11. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
    12. Jenkins, Stephen P & Lambert, Peter J, 1997. "Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends," Oxford Economic Papers, Oxford University Press, vol. 49(3), pages 317-327, July.
    13. B. Essama-Nssah & Peter J. Lambert, 2009. "Measuring Pro-Poorness: A Unifying Approach With New Results," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(3), pages 752-778, September.
    14. Datt, Gaurav & Ravallion, Martin, 1992. "Growth and redistribution components of changes in poverty measures : A decomposition with applications to Brazil and India in the 1980s," Journal of Development Economics, Elsevier, vol. 38(2), pages 275-295, April.
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    Cited by:

    1. Fernandez Sierra, Manuel & Messina, Julián, 2017. "Skill Premium, Labor Supply and Changes in the Structure of Wages in Latin America," IZA Discussion Papers 10718, Institute for the Study of Labor (IZA).
    2. Clementi, Fabio & Molini, Vasco & Schettino, Francesco, 2018. "All that Glitters is not Gold: Polarization Amid Poverty Reduction in Ghana," World Development, Elsevier, vol. 102(C), pages 275-291.
    3. Fernandez Sierra, Manuel & Messina, Julián, 2017. "Skill Premium, Labor Supply and Changes in the Structure of Wages in Latin America," IZA Discussion Papers 10718, Institute for the Study of Labor (IZA).

    More about this item


    Influence function; robust statistic; distributional statistic; inequality; poverty; social evaluation.;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling


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