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Sensitivity Analysis in Semiparametric Likelihood Models

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    Abstract

    We provide methods for inference on a finite dimensional parameter of interest, theta in Re^{d_theta}, in a semiparametric probability model when an infinite dimensional nuisance parameter, g, is present. We depart from the semiparametric literature in that we do not require that the pair (theta, g) is point identified and so we construct confidence regions for theta that are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates of theta to specification of g in a likelihood setup. To construct these confidence regions for theta, we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null distribution of this profiled sieve LR, which is nonstandard when theta is not point identified (but is chi^2 distributed under point identification). We show that a simple weighted bootstrap procedure consistently estimates this complicated distribution's quantiles. Monte Carlo studies of a semiparametric dynamic binary response panel data model indicate that our weighted bootstrap procedures performs adequately in finite samples. We provide three empirical illustrations to contrast our procedure to the ones obtained using standard (less robust) methods.

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    File URL: http://cowles.econ.yale.edu/P/cd/d18a/d1836.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1836.

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    Length: 58 pages
    Date of creation: Nov 2011
    Date of revision:
    Handle: RePEc:cwl:cwldpp:1836

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    Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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    Web page: http://cowles.econ.yale.edu/
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    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

    Related research

    Keywords: Semiparametric models; Partial identification; Irregular functionals; Sieve likelihood ratio; Weighted bootstrap;

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    1. Donald W.K. Andrews & Xu Cheng, 2010. "Estimation and Inference with Weak, Semi-strong, and Strong Identification," Cowles Foundation Discussion Papers 1773, Cowles Foundation for Research in Economics, Yale University.
    2. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2012. "Intersection bounds: estimation and inference," CeMMAP working papers CWP33/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Michael P. Keane & Kenneth I. Wolpin, 1995. "The career decisions of young men," Working Papers 559, Federal Reserve Bank of Minneapolis.
    5. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    6. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
    7. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
    8. Monique De Haan & Erik Plug, 2011. "Estimating intergenerational schooling mobility on censored samples: consequences and remedies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 151-166, January/F.
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