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Control functions in nonseparable simultaneous equations models

Author

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  • Richard Blundell
  • Rosa L. Matzkin

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 paper, 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 L. Matzkin, 2014. "Control functions in nonseparable simultaneous equations models," Quantitative Economics, Econometric Society, vol. 5, pages 271-295, July.
    • Handle: RePEc:wly:quante:v:5:y:2014:i::p:271-295
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    File URL: http://hdl.handle.net/10.1111/quan.2014.5.issue-2.x
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    Cited by:

    1. Atila Abdulkadiroğlu & Parag A. Pathak & Jonathan Schellenberg & Christopher R. Walters, 2020. "Do Parents Value School Effectiveness?," American Economic Review, American Economic Association, vol. 110(5), pages 1502-1539, May.
    2. Jerry A. Hausman & Whitney K. Newey, 2016. "Individual Heterogeneity and Average Welfare," Econometrica, Econometric Society, vol. 84, pages 1225-1248, May.
    3. Soren Blomquist & Anil Kumar & Che-Yuan Liang & Whitney K. Newey, 2014. "Individual heterogeneity, nonlinear budget sets, and taxable income," CeMMAP working papers 21/14, Institute for Fiscal Studies.
    4. Steven T. Berry & Philip A. Haile, 2018. "Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure," Econometrica, Econometric Society, vol. 86(1), pages 289-315, January.
    5. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    7. Patrick Kline & Christopher R. Walters, 2019. "On Heckits, LATE, and Numerical Equivalence," Econometrica, Econometric Society, vol. 87(2), pages 677-696, March.
    8. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    9. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    10. Victor Chernozhukov & Jerry Hausman & Whitney K. Newey, 2019. "Demand analysis with many prices," CeMMAP working papers CWP59/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Soren Blomquist & Anil Kumar & Che-Yuan Liang & Whitney K. Newey, 2022. "Nonlinear Budget Set Regressions for the Random Utility Model," Working Papers 2219, Federal Reserve Bank of Dallas.
    12. Steven T. Berry & Philip A. Haile, 2020. "Nonparametric Identification of Differentiated Products Demand Using Micro Data," NBER Working Papers 27704, National Bureau of Economic Research, Inc.
    13. Cheuk Yin Ho, 2016. "Better Health With More Friends: The Role of Social Capital in Producing Health," Health Economics, John Wiley & Sons, Ltd., vol. 25(1), pages 91-100, January.
    14. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," NBER Working Papers 29305, National Bureau of Economic Research, Inc.
    15. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    16. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers CWP60/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    18. C. Aina & D. Sonedda, 2018. "Investment in education and household consumption," Working Paper CRENoS 201806, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    19. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    20. Nir Billfeld & Moshe Kim, 2024. "Context-dependent Causality (the Non-Nonotonic Case)," Papers 2404.05021, arXiv.org.
    21. Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    22. Carmen Aina & Daniela Sonedda, 2022. "Sooner or later? The impact of child education on household consumption," Empirical Economics, Springer, vol. 63(4), pages 2071-2099, October.
    23. Jerry Hausman & Whitney K. Newey, 2014. "Individual Heterogeneity and Average Welfare," CeMMAP working papers 42/14, Institute for Fiscal Studies.
    24. Maes, Sebastiaan & Malhotra, Raghav, 2024. "Robust Hicksian Welfare Analysis under Individual Heterogeneity," CRETA Online Discussion Paper Series 84, Centre for Research in Economic Theory and its Applications CRETA.
    25. Hubner, Stefan, 2023. "Identification of unobserved distribution factors and preferences in the collective household model," Journal of Econometrics, Elsevier, vol. 234(1), pages 301-326.

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