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

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Listed:
  • Richard Blundell

    () (Institute for Fiscal Studies and IFS and UCL)

  • 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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    Cited by:

    1. 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.
    2. Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(02), pages 231-266, April.
    3. 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.
    4. 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.
    5. Giovanni Forchini, 2012. "Structural Equations and Invariance," School of Economics Discussion Papers 0312, School of Economics, University of Surrey.
    6. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1614-1636.
    7. 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.
    8. 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.

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