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Inference in semiparametric conditional moment models with partial identification

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  • Hong, Shengjie

Abstract

This paper develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. For a conjectured restriction on the parameter, we consider testing the hypothesis that the restriction is satisfied by at least one element of the identified set. We propose using the sieve minimum of a Kolmogorov–Smirnov type statistic as the test statistic, derive its asymptotic distribution, and provide consistent bootstrap critical values. In this way a broad family of restrictions can be consistently tested, making the proposed procedure applicable to testing the model specification and constructing confidence set for any given component or some feature of the parameter. Our methods are robust to partial identification, and allow for the moment functions to be nonsmooth. As an illustration, we apply the proposed inference methods to study the quantile instrumental variable Engel curves for gasoline in Brazil. A Monte Carlo study demonstrates finite sample performance.

Suggested Citation

  • Hong, Shengjie, 2017. "Inference in semiparametric conditional moment models with partial identification," Journal of Econometrics, Elsevier, vol. 196(1), pages 156-179.
  • Handle: RePEc:eee:econom:v:196:y:2017:i:1:p:156-179
    DOI: 10.1016/j.jeconom.2016.09.014
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    Cited by:

    1. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    2. Chen, Qihui, 2021. "Robust and optimal estimation for partially linear instrumental variables models with partial identification," Journal of Econometrics, Elsevier, vol. 221(2), pages 368-380.
    3. Isaac Loh, 2024. "Inference under partial identification with minimax test statistics," Papers 2401.13057, arXiv.org, revised Apr 2024.
    4. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    5. Loh, Isaac, 2023. "Nonparametric identification and estimation with discrete instruments and regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1257-1279.
    6. Fan, Yanqin & Shi, Xuetao & Tao, Jing, 2023. "Partial identification and inference in moment models with incomplete data," Journal of Econometrics, Elsevier, vol. 235(2), pages 418-443.

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    More about this item

    Keywords

    Conditional moment equalities; Identified set; Sieve space; Bootstrap;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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