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Microeconometrics with Partial Identification

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  • Francesca Molinari

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.

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  • Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
  • Handle: RePEc:arx:papers:2004.11751
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    4. Manski, Charles F. & Molinari, Francesca, 2021. "Estimating the COVID-19 infection rate: Anatomy of an inference problem," Journal of Econometrics, Elsevier, vol. 220(1), pages 181-192.
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    6. Levon Barseghyan & Maura Coughlin & Francesca Molinari & Joshua C. Teitelbaum, 2021. "Heterogeneous Choice Sets and Preferences," Econometrica, Econometric Society, vol. 89(5), pages 2015-2048, September.
    7. Xavier D'Haultf{oe}uille & Christophe Gaillac & Arnaud Maurel, 2022. "Partially Linear Models under Data Combination," Papers 2204.05175, arXiv.org.
    8. 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.
    9. Xiaohong Chen & Matthew Gentry & Tong Li & Jingfeng Lu, 2020. "Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry," Cowles Foundation Discussion Papers 2257, Cowles Foundation for Research in Economics, Yale University.
    10. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    11. Jörg Stoye, 2022. "Bounding infection prevalence by bounding selectivity and accuracy of tests: with application to early COVID-19 [False-negative results of initial RT-PCR assays for COVID-19: a systematic review]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 1-14.
    12. Aibo Gong, 2021. "Bounds for Treatment Effects in the Presence of Anticipatory Behavior," Papers 2111.06573, arXiv.org.
    13. Charles F. Manski, 2022. "Identification and Statistical Decision Theory," Papers 2204.11318, arXiv.org.
    14. Ryo Okui, 2021. "A moment inequality approach to statistical inference for rankings," The Japanese Economic Review, Springer, vol. 72(2), pages 169-184, April.

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