IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v238y2024i1s030440762300283x.html
   My bibliography  Save this article

Endogeneity in weakly separable models without monotonicity

Author

Listed:
  • Chen, Songnian
  • Khan, Shakeeb
  • Tang, Xun

Abstract

We identify and estimate treatment effects when potential outcomes are weakly separable with a binary endogenous treatment. Vytlacil and Yildiz (2007) proposed an identification strategy that exploits the mean of observed outcomes, but their approach requires a monotonicity condition. In comparison, we exploit full information in the entire outcome distribution, instead of just its mean. As a result, our method does not require monotonicity and is also applicable to general settings with multiple indices. We provide examples where our approach can identify treatment effect parameters of interest whereas existing methods would fail. These include models where potential outcomes depend on multiple unobserved disturbance terms, such as a Roy model, a multinomial choice model, as well as a model with endogenous random coefficients. We establish consistency and asymptotic normality of our estimators.

Suggested Citation

  • Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2024. "Endogeneity in weakly separable models without monotonicity," Journal of Econometrics, Elsevier, vol. 238(1).
    • Handle: RePEc:eee:econom:v:238:y:2024:i:1:s030440762300283x
    DOI: 10.1016/j.jeconom.2023.105567
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440762300283X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.105567?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
    4. Stacey H. Chen & Shakeeb Khan, 2014. "Semi‐Parametric Estimation Of Program Impacts On Dispersion Of Potential Wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 901-919, September.
    5. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    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. Xavier D'Haultfœuille & Philippe Février, 2015. "Identification of Nonseparable Triangular Models With Discrete Instruments," Econometrica, Econometric Society, vol. 83(3), pages 1199-1210, May.
    9. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    10. Matthew A Masten, 2018. "Random Coefficients on Endogenous Variables in Simultaneous Equations Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 1193-1250.
    11. Xiaoxia Shi & Matthew Shum & Wei Song, 2018. "Estimating Semi‐Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity," Econometrica, Econometric Society, vol. 86(2), pages 737-761, March.
    12. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    13. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    14. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(3), pages 804-837, June.
    15. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    16. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    17. 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.
    18. Sung Jae Jun & Joris Pinkse & Haiqing Xu & Neşe Yıldız, 2016. "Multiple Discrete Endogenous Variables in Weakly-Separable Triangular Models," Econometrics, MDPI, vol. 4(1), pages 1-21, February.
    19. Brigham R. Frandsen & Lars J. Lefgren, 2018. "Testing Rank Similarity," The Review of Economics and Statistics, MIT Press, vol. 100(1), pages 86-91, March.
    20. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    21. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
    22. Quang Vuong & Haiqing Xu, 2017. "Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity," Quantitative Economics, Econometric Society, vol. 8(2), pages 589-610, July.
    23. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    24. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
    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. Songnian Chen & Shakeeb Khan & Xun Tang, 2022. "Endogeneity in Weakly Separable Models without Monotonicity," Papers 2208.05047, arXiv.org.
    2. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    3. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    4. 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.
    5. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.
    7. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    8. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    9. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    10. Han, Sukjin & Yang, Shenshen, 2024. "A computational approach to identification of treatment effects for policy evaluation," Journal of Econometrics, Elsevier, vol. 240(1).
    11. Ma, Jun & Marmer, Vadim & Yu, Zhengfei, 2023. "Inference on individual treatment effects in nonseparable triangular models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2096-2124.
    12. 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.
    13. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1614-1636.
    14. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    15. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    16. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2024. "Testing and relaxing the exclusion restriction in the control function approach," Journal of Econometrics, Elsevier, vol. 240(2).
    17. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    18. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    19. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    20. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.

    More about this item

    Keywords

    Weak Separability; Treatment Effects; Monotonicity; Endogeneity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

    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:eee:econom:v:238:y:2024:i:1:s030440762300283x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.