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Identification in Multiple Treatment Models under Discrete Variation

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  • Vishal Kamat
  • Samuel Norris
  • Matthew Pecenco

Abstract

We develop a method to learn about treatment effects in multiple treatment models with discrete-valued instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that permits multidimensional unobserved heterogeneity. Under a semi-parametric restriction on the distribution of unobserved heterogeneity, we show how a sequence of linear programs can be used to compute sharp bounds for a number of treatment effect parameters when the marginal treatment response functions underlying them remain nonparametric or are additionally parameterized.

Suggested Citation

  • Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
  • Handle: RePEc:arx:papers:2307.06174
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    File URL: http://arxiv.org/pdf/2307.06174
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    References listed on IDEAS

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    1. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    4. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    5. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    6. 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.
    7. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    8. Jack Mountjoy, 2022. "Community Colleges and Upward Mobility," American Economic Review, American Economic Association, vol. 112(8), pages 2580-2630, August.
    9. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    10. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2008. "Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case," Annals of Economics and Statistics, GENES, issue 91-92, pages 151-174.
    11. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    12. Vishal Kamat, 2017. "Identifying the Effects of a Program Offer with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Aug 2023.
    13. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Dec 2024.
    14. Poirier, Dale J., 1980. "Partial observability in bivariate probit models," Journal of Econometrics, Elsevier, vol. 12(2), pages 209-217, February.
    15. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    16. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    17. Carolina Arteaga, 2021. "Parental Incarceration and Children's Educational Attainment," Working Papers tecipa-703, University of Toronto, Department of Economics.
    18. Mogstad, Magne & Torgovitsky, Alexander & Walters, Christopher R., 2024. "Policy evaluation with multiple instrumental variables," Journal of Econometrics, Elsevier, vol. 243(1).
    19. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    20. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    21. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    22. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 200-216, January.
    23. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    24. Toshiki Tsuda, 2022. "Treatment Effects with Multidimensional Unobserved Heterogeneity: Identification of the Marginal Treatment Effect," Papers 2209.11444, arXiv.org, revised Jan 2024.
    25. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
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