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Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments

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  • JoonHwan Cho
  • Thomas M. Russell

Abstract

This paper considers uniformly valid inference for linear functionals and scalar subvectors of partially identified parameters defined by linear moment inequalities. Our proposed procedure amounts to bootstrapping the value functions of four carefully constructed "perturbed" linear programming problems, and does not require the researcher to grid over the parameter space. Our low-level conditions for uniform validity rely on a novel application of Sard's Theorem from differential topology, and may be of substantial separate interest. Our procedure is asymptotically conservative for the true partially identified parameter, but draws its appeal from the fact that it is valid under weak assumptions, it performs well in finite samples, and is computationally simple to implement.

Suggested Citation

  • JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised Dec 2020.
  • Handle: RePEc:arx:papers:1810.03180
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    References listed on IDEAS

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    1. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    2. Xiaohong Chen & Timothy Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2016.
    3. Maximilian Kasy, 2016. "Partial Identification, Distributional Preferences, and the Welfare Ranking of Policies," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 111-131, March.
    4. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190.
    5. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    6. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    7. Shi, Xiaoxia & Shum, Matthew, 2015. "Simple Two-Stage Inference For A Class Of Partially Identified Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 493-520, June.
    8. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    9. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    10. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2017. "Inference for subvectors and other functions of partially identified parameters in moment inequality models," Quantitative Economics, Econometric Society, vol. 8(1), pages 1-38, March.
    11. Kasy Maximilian, 2019. "Uniformity and the Delta Method," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-19, January.
    12. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    13. Gafarov, Bulat & Meier, Matthias & Montiel Olea, José Luis, 2018. "Delta-method inference for a class of set-identified SVARs," Journal of Econometrics, Elsevier, vol. 203(2), pages 316-327.
    14. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701.
    15. 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, January.
    16. 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, January.
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    Cited by:

    1. Isaiah Andrews & Jonathan Roth & Ariel Pakes, 2019. "Inference for Linear Conditional Moment Inequalities," NBER Working Papers 26374, National Bureau of Economic Research, Inc.

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