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Conditions for the existence of control functions in nonseparable simultaneous equations models

Author

Listed:
  • Richard Blundell

    (Institute for Fiscal Studies and University College London)

  • Rosa Matzkin

    (Institute for Fiscal Studies and UCLA)

Abstract
The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this note, we define a new property of functions called control function separability and show it provides a complete characterization of the structural systems of simultaneous equations in which the control function procedure is valid.

Suggested Citation

  • Richard Blundell & Rosa Matzkin, 2010. "Conditions for the existence of control functions in nonseparable simultaneous equations models," CeMMAP working papers CWP28/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:28/10
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    File URL: http://cemmap.ifs.org.uk/wps/cwp2810.pdf
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    Citations

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    Cited by:

    1. Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(2), pages 231-266, April.
    2. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    3. Jeremy T. Fox & Amit Gandhi, 2011. "Identifying Demand with Multidimensional Unobservables: A Random Functions Approach," NBER Working Papers 17557, National Bureau of Economic Research, Inc.
    4. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    5. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    6. Giovanni Forchini, 2012. "Structural Equations and Invariance," School of Economics Discussion Papers 0312, School of Economics, University of Surrey.
    7. Stefan Hoderlein & Anne Vanhems, 2018. "Estimating the distribution of welfare effects using quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 52-72, January.
    8. Julia Pullbeck & Firmin Doko Tchatoka, 2020. "Inherent effects of corruption on the erosion of political trust in developing countries:Evidence from Ghana," School of Economics and Public Policy Working Papers 2020-01, University of Adelaide, School of Economics and Public Policy.
    9. repec:cwl:cwldpp:1787rr is not listed on IDEAS
    10. Daniel Gutknecht, 2013. "Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function," Economics Series Working Papers 673, University of Oxford, Department of Economics.
    11. 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.
    12. Steven T. Berry & Philip A. Haile, 2011. "Identification in a Class of Nonparametric Simultaneous Equations Models," Cowles Foundation Discussion Papers 1787, Cowles Foundation for Research in Economics, Yale University.
    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. Pereira, Pedro & Ribeiro, Tiago & Vareda, João, 2013. "Delineating markets for bundles with consumer level data: The case of triple-play," International Journal of Industrial Organization, Elsevier, vol. 31(6), pages 760-773.

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