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Unordered Monotonicity

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  • James J. Heckman
  • Rodrigo Pinto

Abstract

This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogeneous agents, and discrete†valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.

Suggested Citation

  • James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
  • Handle: RePEc:wly:emetrp:v:86:y:2018:i:1:p:1-35
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    File URL: https://doi.org/10.3982/ECTA13777
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    References listed on IDEAS

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    1. Jason R. Blevins, 2014. "Nonparametric identification of dynamic decision processes with discrete and continuous choices," Quantitative Economics, Econometric Society, vol. 5(3), pages 531-554, November.
    2. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
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    Cited by:

    1. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    2. Vishal Kamat, 2017. "Identification with Latent Choice Sets," Papers 1711.02048, arXiv.org, revised Aug 2019.
    3. Tadao Hoshino & Takahide Yanagi, 2018. "Treatment Effect Models with Strategic Interaction in Treatment Decisions," Papers 1810.08350, arXiv.org, revised Oct 2019.

    More about this item

    JEL classification:

    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • J15 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination

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