IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.05177.html

Treatment Effects of Multi-Valued Treatments in Hyper-Rectangle Model

Author

Listed:
  • Xunkang Tian

Abstract

This study investigates the identification of marginal treatment responses within multi-valued treatment models. Extending the hyper-rectangle model introduced by Lee and Salanie (2018), this paper relaxes restrictive assumptions, including the requirement of known treatment selection thresholds and the dependence of treatments on all unobserved heterogeneity. By incorporating an additional ranked treatment assumption, this study demonstrates that the marginal treatment responses can be identified under a broader set of conditions, either point or set identification. The framework further enables the derivation of various treatment effects from the marginal treatment responses. Additionally, this paper introduces a hypothesis testing method to evaluate the effectiveness of policies on treatment effects, enhancing its applicability to empirical policy analysis.

Suggested Citation

  • Xunkang Tian, 2025. "Treatment Effects of Multi-Valued Treatments in Hyper-Rectangle Model," Papers 2509.05177, arXiv.org.
    • Handle: RePEc:arx:papers:2509.05177
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.05177
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    2. Victor Chernozhukov & Mert Demirer & Esther Duflo & Iván Fernández-Val, 2018. "Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, with an Application to Immunization in India," NBER Working Papers 24678, National Bureau of Economic Research, Inc.
    3. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    4. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    2. Arun G. Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2019. "Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap," NBER Working Papers 25593, National Bureau of Economic Research, Inc.
    3. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    4. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    5. repec:cwl:cwldpp:1761rr is not listed on IDEAS
    6. Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, vol. 192(1), pages 269-290.
    7. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    8. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    9. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    10. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    11. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    12. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    13. Armstrong, Timothy B., 2014. "Weighted KS statistics for inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 181(2), pages 92-116.
    14. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers 43/12, Institute for Fiscal Studies.
    15. Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
    16. Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2015. "Sharing Rule Identification for General Collective Consumption Models," Econometrica, Econometric Society, vol. 83(5), pages 2001-2041, September.
    17. Hahn Jinyong & Ridder Geert, 2015. "Non-Standard Tests through a Composite Null and Alternative in Point-Identified Parameters," Journal of Econometric Methods, De Gruyter, vol. 4(1), pages 1-28, January.
    18. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
    19. Thierry Magnac, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258.
    20. Sung Jae Jun & Yoonseok Lee & Youngki Shin, 2016. "Treatment Effects With Unobserved Heterogeneity: A Set Identification Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 302-311, April.
    21. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2509.05177. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.