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

Inference and decision for set identified parameters using posterior lower and upper probabilities

  • Toru Kitagawa

    ()

    (Institute for Fiscal Studies and cemmap and UCL)

Registered author(s):

    This paper develops inference and statistical decision for set-identified parameters from the robust Bayes perspective. When a model is set-identified, prior knowledge for model parameters is decomposed into two parts: the one that can be updated by data (revisable prior knowledge) and the one that never be updated (unrevisable prior knowledge.) We introduce a class of prior distributions that shares a single prior distribution for the revisable, but allows for arbitrary prior distributions for the unrevisable. A posterior inference procedure proposed in this paper operates on the resulting class of posteriors by focusing on the posterior lower and upper probabilities. We analyze point estimation of the set-identified parameters with applying the gamma-minimax criterion. We propose a robustified posterior credible region for the set-identified parameters by focusing on a contour set of the posterior lower probability. Our framework offers a procedure to eliminate set-identified nuisance parameters, and yields inference for the marginalized identified set. For an interval identified parameter case, we establish asymptotic equivalence of the lower probability inference to frequentist inference for the identified set.

    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://cemmap.ifs.org.uk/wps/cwp1611.pdf
    Download Restriction: no

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP16/11.

    as
    in new window

    Length:
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:ifs:cemmap:16/11
    Contact details of provider: Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
    Phone: (+44) 020 7291 4800
    Fax: (+44) 020 7323 4780
    Web page: http://cemmap.ifs.org.uk
    Email:


    More information through EDIRC

    Order Information: Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
    Email:


    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. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
    2. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
    3. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(04), pages 483-509, August.
    4. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
    5. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-36, May.
    6. Alfred Galichon & Marc Henry, 2006. "Inference in Incomplete Models," Discussion Papers 0506-28, Columbia University, Department of Economics.
    7. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January.
    8. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
    9. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(03), pages 931-951, June.
    10. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    11. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    12. Gustafson, Paul, 2009. "What Are the Limits of Posterior Distributions Arising From Nonidentified Models, and Why Should We Care?," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1682-1695.
    13. Donald W.K. Andrews & Gustavo Soares, 2007. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Cowles Foundation Discussion Papers 1631, Cowles Foundation for Research in Economics, Yale University.
    14. Insua David Ríos & Ruggeri Fabrizio & Vidakovic Brani, 1995. "Some Results On Posterior Regret Γ-Μινιμαχ Estimation," Statistics & Risk Modeling, De Gruyter, vol. 13(4), pages 315-332, April.
    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:ifs:cemmap:16/11. 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: (Benita Rajania)

    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.