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Microeconometrics with partial identification

In: Handbook of Econometrics

Author

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  • Molinari, Francesca

Abstract

This chapter reviews the microeconometrics literature on partial identification, focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions may yield much information about a parameter of interest, even if they do not reveal it exactly. Special attention is devoted to discussing the challenges associated with, and some of the solutions put forward to, (1) obtain a tractable characterization of the values for the parameters of interest which are observationally equivalent, given the available data and maintained assumptions; (2) estimate this set of values; (3) conduct test of hypotheses and make confidence statements. The chapter reviews advances in partial identification analysis both as applied to learning (functionals of) probability distributions that are well-defined in the absence of models, as well as to learning parameters that are well-defined only in the context of particular models. A simple organizing principle is highlighted: the source of the identification problem can often be traced to a collection of random variables that are consistent with the available data and maintained assumptions. This collection may be part of the observed data or be a model implication. In either case, it can be formalized as a random set. Random set theory is then used as a mathematical framework to unify a number of special results and produce a general methodology to carry out partial identification analysis.

Suggested Citation

  • Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
  • Handle: RePEc:eee:ecochp:7a-355
    DOI: 10.1016/bs.hoe.2020.05.002
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    Citations

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    Cited by:

    1. Kim, Dongwoo, 2023. "Partially identifying competing risks models: An application to the war on cancer," Journal of Econometrics, Elsevier, vol. 234(2), pages 536-564.
    2. Giustinelli, Pamela & Manski, Charles F. & Molinari, Francesca, 2022. "Tail and center rounding of probabilistic expectations in the Health and Retirement Study," Journal of Econometrics, Elsevier, vol. 231(1), pages 265-281.
    3. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Daniel Kaliski, 2023. "Identifying the impact of health insurance on subgroups with changing rates of diagnosis," Health Economics, John Wiley & Sons, Ltd., vol. 32(9), pages 2098-2112, September.
    5. Lixiong Li & Désiré Kédagni & Ismaël Mourifié, 2024. "Discordant relaxations of misspecified models," Quantitative Economics, Econometric Society, vol. 15(2), pages 331-379, May.
    6. Nathan Canen & Kristopher Ramsay, 2024. "Quantifying theory in politics: Identification, interpretation, and the role of structural methods," Journal of Theoretical Politics, , vol. 36(4), pages 301-327, October.
    7. Bloem, Jeffrey R. & Rahman, Khandker Wahedur, 2024. "What I say depends on how you ask: Experimental evidence of the effect of framing on the measurement of attitudes," Economics Letters, Elsevier, vol. 238(C).
    8. Chalak, Karim, 2024. "Nonparametric Gini-Frisch bounds," Journal of Econometrics, Elsevier, vol. 238(1).
    9. Aibo Gong, 2021. "Bounds for Treatment Effects in the Presence of Anticipatory Behavior," Papers 2111.06573, arXiv.org, revised Dec 2022.
    10. Jeff Dominitz & Charles F. Manski, 2024. "Using Total Margin of Error to Account for Non-Sampling Error in Election Polls: The Case of Nonresponse," Papers 2407.19339, arXiv.org, revised Oct 2024.
    11. Marcoux, Mathieu & Russell, Thomas M. & Wan, Yuanyuan, 2024. "A simple specification test for models with many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 242(1).
    12. Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org, revised Nov 2024.
    13. Charles F. Manski, 2022. "Identification and Statistical Decision Theory," Papers 2204.11318, arXiv.org, revised Mar 2024.
    14. Sarah Moon, 2024. "Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model," Papers 2403.07236, arXiv.org, revised May 2024.
    15. Koh, Paul S., 2023. "Stable outcomes and information in games: An empirical framework," Journal of Econometrics, Elsevier, vol. 237(1).
    16. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).

    More about this item

    Keywords

    Partial identification; Random sets; Incomplete data and models; Discrete choice models; Auction models; Moment inequalities; Support function approach; Criterion function approach; Model misspecification; Computational methods;
    All these keywords.

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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