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Unordered Monotonicity

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  • Heckman, James J.

    (University of Chicago)

  • Pinto, Rodrigo

    (University of California, Los Angeles)

Abstract

This paper presents a new monotonicity condition for unordered discrete choice models with multiple treatments. Unlike a less general version of monotonicity in binary and ordered choice models, monotonicity in unordered discrete choice models along with other standard assumptions does not necessarily identify causal effects defined by variation in instruments, although in some cases it does. Our condition implies and is implied by additive separability of the choice equations in terms of observables and unobservables. 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 represent IV estimators of counterfactuals as solutions to discrete mixture problems.

Suggested Citation

  • Heckman, James J. & Pinto, Rodrigo, 2017. "Unordered Monotonicity," IZA Discussion Papers 10821, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp10821
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    3. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    4. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706.
    5. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    6. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    7. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    8. 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.
    9. 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.
    10. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    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, 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.
    3. James J. Heckman & Rodrigo Pinto, 2023. "Econometric Causality: The Central Role of Thought Experiments," NBER Working Papers 31945, National Bureau of Economic Research, Inc.
    4. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    5. Heckman, James J. & Pinto, Rodrigo, 2022. "Causality and Econometrics," IZA Discussion Papers 15081, Institute of Labor Economics (IZA).
    6. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    7. 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.
    8. Haitian Xie, 2020. "Efficient and Robust Estimation of the Generalized LATE Model," Papers 2001.06746, arXiv.org, revised Feb 2022.
    9. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    10. Vishal Kamat, 2017. "Identifying the Effects of a Program Offer with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Aug 2023.
    11. 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.
    12. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2022.
    13. 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.
    14. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    15. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    16. Balat, Jorge F. & Han, Sukjin, 2023. "Multiple treatments with strategic substitutes," Journal of Econometrics, Elsevier, vol. 234(2), pages 732-757.
    17. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
    18. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.
    19. 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).
    20. 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.
    21. Manu Navjeevan & Rodrigo Pinto & Andres Santos, 2023. "Identification and Estimation in a Class of Potential Outcomes Models," Papers 2310.05311, arXiv.org.
    22. Yu-Chang Chen & Haitian Xie, 2020. "Global Representation of the Conditional LATE Model: A Separability Result," Papers 2007.08106, arXiv.org, revised Mar 2022.
    23. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.
    24. Luis Antonio Fantozzi Alvarez & Rodrigo Toneto, 2024. "The interpretation of 2SLS with a continuous instrument: a weighted LATE representation," Working Papers, Department of Economics 2024_11, University of São Paulo (FEA-USP).

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    More about this item

    Keywords

    identification; selection bias; instrumental variables; monotonicity; revealed preference; Generalized Roy Model; binary matrices; discrete choice; discrete mixtures;
    All these keywords.

    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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