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Sensitivity Analysis in Semiparametric Likelihood Models




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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  • Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1836

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    References listed on IDEAS

    1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    2. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    3. 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.
    4. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    5. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    6. 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.
    7. 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.
    8. 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, March.
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    Cited by:

    1. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2017. "Monte Carlo confidence sets for identified sets," CeMMAP working papers CWP43/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Manuel Arellano & Stéphane Bonhomme, 2017. "Nonlinear Panel Data Methods for Dynamic Heterogeneous Agent Models," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 471-496, September.
    3. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "Monte Carlo Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R2, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.
    4. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Paul L. E. Grieco, 2014. "Discrete games with flexible information structures: an application to local grocery markets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 303-340, June.
    6. Arkadiusz Szydlowski, 2015. "Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance," Discussion Papers in Economics 15/06, Department of Economics, University of Leicester.
    7. Kaido, Hiroaki & White, Halbert, 2014. "A two-stage procedure for partially identified models," Journal of Econometrics, Elsevier, vol. 182(1), pages 5-13.
    8. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "Monte Carlo Confidence Sets for Identified Sets," Papers 1605.00499,, revised Sep 2017.
    9. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.

    More about this item


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

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