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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
    DOI: 10.3982/ECTA13777
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    11. repec:adr:anecst:y:2008:i:91-92:p:02 is not listed on IDEAS
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    Cited by:

    1. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    2. James J. Heckman & Rodrigo Pinto, 2023. "Econometric Causality: The Central Role of Thought Experiments," NBER Working Papers 31945, National Bureau of Economic Research, Inc.
    3. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    4. Heckman, James J. & Pinto, Rodrigo, 2022. "Causality and Econometrics," IZA Discussion Papers 15081, Institute of Labor Economics (IZA).
    5. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    6. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    7. Vishal Kamat, 2017. "Identifying the Effects of a Program Offer with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Aug 2023.
    8. Federica Braccioli & Paolo Ghinetti & Simone Moriconi & Michele Pellizzari & Costanza Naguib, 2022. "Education expansion, college choice and labour market success," Diskussionsschriften dp2207, Universitaet Bern, Departement Volkswirtschaft.
    9. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2022.
    10. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    11. Balat, Jorge F. & Han, Sukjin, 2023. "Multiple treatments with strategic substitutes," Journal of Econometrics, Elsevier, vol. 234(2), pages 732-757.
    12. Manu Navjeevan & Rodrigo Pinto & Andres Santos, 2023. "Identification and Estimation in a Class of Potential Outcomes Models," Papers 2310.05311, arXiv.org.
    13. Yu-Chang Chen & Haitian Xie, 2020. "Global Representation of the Conditional LATE Model: A Separability Result," Papers 2007.08106, arXiv.org, revised Mar 2022.
    14. James J. Heckman & Rodrigo Pinto, 2022. "Causal Inference of Social Experiments Using Orthogonal Designs," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 7-30, September.
    15. Federica Braccioli & Paolo Ghinetti & Simone Moriconi & Costanza Naguib & Michele Pellizzari, 2023. "Education Expansion, College Choice and Labour Market Success," CESifo Working Paper Series 10842, CESifo.
    16. Haitian Xie, 2020. "Efficient and Robust Estimation of the Generalized LATE Model," Papers 2001.06746, arXiv.org, revised Feb 2022.
    17. Michael Mueller-Smith & Benjamin Pyle & Caroline Walker, 2023. "Estimating the Impact of the Age of Criminal Majority: Decomposing Multiple Treatments in a Regression Discontinuity Framework," Working Papers 23-01, Center for Economic Studies, U.S. Census Bureau.
    18. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    19. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
    20. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.
    21. Choi, Jin-young & Lee, Myoung-jae, 2023. "Complier and monotonicity for Fuzzy Multi-score Regression Discontinuity with partial effects," Economics Letters, Elsevier, vol. 228(C).
    22. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.
    23. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.

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    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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