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

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  • Toru Kitagawa

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    (Institute for Fiscal Studies and UCL)

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    Abstract

    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.

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    File URL: http://cemmap.ifs.org.uk/wps/cwp1611.pdf
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    Bibliographic Info

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

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    Date of creation: May 2011
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    Handle: RePEc:ifs:cemmap:16/11

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    1. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    2. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07.
    3. 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.
    4. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, 01.
    5. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-36, May.
    6. 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.
    7. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(04), pages 483-509, August.
    8. 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.
    9. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    10. 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.
    11. 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.
    12. Alfred Galichon & Marc Henry, 2006. "Inference in Incomplete Models," Discussion Papers 0506-28, Columbia University, Department of Economics.
    13. 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.
    14. 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.
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