IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Inference for Inverse Stochastic Dominance

  • Francesco Andreoli

    ()

    (THEMA University of Cergy-Pontoise and University of Verona)

Registered author(s):

    This note presents an innovative inference procedure for assessing if a pair of distributions can be ordered according to inverse stochastic dominance (ISD). At order 1 and 2, ISD coincides respectively with rank and generalized Lorenz dominance and it selects the preferred distribution by all social evaluation functions that are monotonic and display inequality aversion. At orders higher than the second, ISD is associated with dominance for classes of linear rank dependent evaluation functions. This paper focuses on the class of conditional single parameters Gini social evaluation functions and illustrates that these functions can be linearly decomposed into their empirically tractable influence functions. This approach gives estimators for ISD that are asymptotically normal with a variancecovariance structure which is robust to non-simple randomization sampling schemes, a common case in many surveys used in applied distribution analysis. One of these surveys, the French Labor Force Survey, is selected to test the robustness of Equality of Opportunity evaluations in France through ISD comparisons at order 3. The ISD tests proposed in this paper are operationalized through the user-written “isdtest” Stata routine.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.ecineq.org/milano/WP/ECINEQ2013-295.pdf
    Download Restriction: no

    Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 295.

    as
    in new window

    Length: 25 pages
    Date of creation: Apr 2013
    Date of revision:
    Handle: RePEc:inq:inqwps:ecineq2013-295
    Contact details of provider: Web page: http://www.ecineq.org
    Email:


    More information through EDIRC

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 9(1), pages 119-161, December.
    2. Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 723-35, October.
    3. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    4. Buhong Zheng, 2002. "Testing Lorenz Curves with Non-Simple Random Samples," Econometrica, Econometric Society, vol. 70(3), pages 1235-1243, May.
    5. Rolf Aaberge, 2004. "Ranking Intersecting Lorenz Curves," CEIS Research Paper 45, Tor Vergata University, CEIS.
    6. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    7. Arnaud LEFRANC, Nicolas PISTOLESI, Alain TRANNOY, 2009. "Equality of opportunity and luck: De nitions and testable conditions, with an application to income in France," THEMA Working Papers 2009-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    9. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
    10. Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
    11. Rolf Aaberge, 2006. "Gini’s Nuclear Family," Discussion Papers 491, Research Department of Statistics Norway.
    12. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
    13. Buhong Zheng, 1999. "Statistical Inferences for Testing Marginal Rank and (Generalized) Lorenz Dominances," Southern Economic Journal, Southern Economic Association, vol. 65(3), pages 557-570, January.
    14. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    15. Fleurbaey, Marc, 2012. "Fairness, Responsibility, and Welfare," OUP Catalogue, Oxford University Press, number 9780199653591, March.
    16. DONALDSON, David & WEYMARK, John A., . "Ethically flexible Gini indices for income distributions in the continuum," CORE Discussion Papers RP -520, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
    18. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    19. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-86, September.
    20. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    21. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:inq:inqwps:ecineq2013-295. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maria Ana Lugo)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.