IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v27y2011i03p663-671_00.html
   My bibliography  Save this article

Identification In Triangular Systems Using Control Functions

Author

Listed:
  • Kasy, Maximilian

Abstract

This note discusses identification in nonparametric, continuous triangular systems. It provides conditions that are both necessary and sufficient for the existence of control functions satisfying conditional independence and support requirements. Confirming a commonly noticed pattern, these conditions restrict the admissible dimensionality of unobserved heterogeneity in the first-stage structural relation, or more generally the dimensionality of the family of conditional distributions of second-stage heterogeneity given explanatory variables and instruments. These conditions imply that no such control function exists without assumptions that seem hard to justify in most applications. In particular, none exists in the context of a generic random coefficient model.

Suggested Citation

  • Kasy, Maximilian, 2011. "Identification In Triangular Systems Using Control Functions," Econometric Theory, Cambridge University Press, vol. 27(3), pages 663-671, June.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:03:p:663-671_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466610000460/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    2. Mourifié, Ismael, 2015. "Sharp bounds on treatment effects in a binary triangular system," Journal of Econometrics, Elsevier, vol. 187(1), pages 74-81.
    3. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    4. Ming Li, 2021. "A Time-Varying Endogenous Random Coefficient Model with an Application to Production Functions," Papers 2110.00982, arXiv.org.
    5. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    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. Jun, Sung Jae & Pinkse, Joris, 2020. "Counterfactual prediction in complete information games: Point prediction under partial identification," Journal of Econometrics, Elsevier, vol. 216(2), pages 394-429.
    8. Kasy, Maximilian, 2022. "Who wins, who loses? Identification of conditional causal effects, and the welfare impact of changing wages," Journal of Econometrics, Elsevier, vol. 226(1), pages 155-170.
    9. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    10. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    11. Kim Kyoo il & Petrin Amil, 2022. "A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 91-125, January.
    12. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2023. "Nonparametric difference-in-differences in repeated cross-sections with continuous treatments," Journal of Econometrics, Elsevier, vol. 234(2), pages 664-690.
    13. Denis Chetverikov & Daniel Wilhelm, 2016. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 48/16, Institute for Fiscal Studies.
    14. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    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. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    17. Carlson, Alyssa, 2023. "Relaxing conditional independence in an endogenous binary response model," Journal of Econometrics, Elsevier, vol. 232(2), pages 490-500.
    18. 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.
    19. Stefan Hoderlein & Hajo Holzmann & Maximilian Kasy & Alexander Meister, 2015. "Erratum regarding “Instrumental variables with unrestricted heterogeneity and continuous treatment”," Boston College Working Papers in Economics 896, Boston College Department of Economics, revised 01 Feb 2016.
    20. Amaresh K Tiwari, 2021. "A Control Function Approach to Estimate Panel Data Binary Response Model," Papers 2102.12927, arXiv.org, revised Sep 2021.
    21. Tsionas, Mike G., 2022. "Convex non-parametric least squares, causal structures and productivity," European Journal of Operational Research, Elsevier, vol. 303(1), pages 370-387.
    22. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 39/15, Institute for Fiscal Studies.
    23. David Powell, 2020. "Quantile Treatment Effects in the Presence of Covariates," The Review of Economics and Statistics, MIT Press, vol. 102(5), pages 994-1005, December.

    More about this item

    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:cup:etheor:v:27:y:2011:i:03:p:663-671_00. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.