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Minimizing Sensitivity to Model Misspecification

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  • St'ephane Bonhomme
  • Martin Weidner

Abstract

We propose a framework for estimation and inference when the model may be misspecified. We rely on a local asymptotic approach where the degree of misspecification is indexed by the sample size. We construct estimators whose mean squared error is minimax in a neighborhood of the reference model, based on one-step adjustments. In addition, we provide confidence intervals that contain the true parameter under local misspecification. As a tool to interpret the degree of misspecification, we map it to the local power of a specification test of the reference model. Our approach allows for systematic sensitivity analysis when the parameter of interest may be partially or irregularly identified. As illustrations, we study three applications: an empirical analysis of the impact of conditional cash transfers in Mexico where misspecification stems from the presence of stigma effects of the program, a cross-sectional binary choice model where the error distribution is misspecified, and a dynamic panel data binary choice model where the number of time periods is small and the distribution of individual effects is misspecified.

Suggested Citation

  • St'ephane Bonhomme & Martin Weidner, 2018. "Minimizing Sensitivity to Model Misspecification," Papers 1807.02161, arXiv.org, revised Oct 2021.
  • Handle: RePEc:arx:papers:1807.02161
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    3. Jiaming Mao & Zhesheng Zheng, 2020. "Structural Regularization," Papers 2004.12601, arXiv.org, revised Jun 2020.
    4. Stéphane Bonhomme & Martin Weidner, 2020. "Posterior average effects," CeMMAP working papers CWP49/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    7. Matthew A. Masten & Alexandre Poirier, 2021. "Salvaging Falsified Instrumental Variable Models," Econometrica, Econometric Society, vol. 89(3), pages 1449-1469, May.
    8. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust decision-making under risk and ambiguity," Papers 2104.12573, arXiv.org, revised Oct 2021.
    9. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Oct 2024.
    10. Eliaz, Kfir & Spiegler, Ran & Weiss, Yair, 2019. "Cheating with (recursive) models," CEPR Discussion Papers 14100, C.E.P.R. Discussion Papers.
    11. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    12. St'ephane Bonhomme & Martin Weidner, 2019. "Posterior Average Effects," Papers 1906.06360, arXiv.org, revised Sep 2021.
    13. Timothy B. Armstrong & Michal Kolesár, 2021. "Sensitivity analysis using approximate moment condition models," Quantitative Economics, Econometric Society, vol. 12(1), pages 77-108, January.
    14. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    15. Maximilian Blesch & Philipp Eisenhauer, 2023. "Robust Decision-Making under Risk and Ambiguity," Rationality and Competition Discussion Paper Series 463, CRC TRR 190 Rationality and Competition.
    16. Raffaella Giacomini & Toru Kitagawa & Harald Uhlig, 2019. "Estimation Under Ambiguity," CeMMAP working papers CWP24/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Pietro Emilio Spini, 2021. "Robustness, Heterogeneous Treatment Effects and Covariate Shifts," Papers 2112.09259, arXiv.org, revised Aug 2024.
    18. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    19. Bo E. Honoré & Thomas Jorgensen & Áureo de Paula, 2019. "Sensitivity of Estimation Precision to Moments with an Application to a Model of Joint Retirement Planning of Couples," CeMMAP working papers CWP36/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Robust Bayesian Analysis for Econometrics," Working Paper Series WP-2021-11, Federal Reserve Bank of Chicago.
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    23. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.

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