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Control variables, discrete instruments, and identification of structural functions

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  • Newey, Whitney
  • Stouli, Sami

Abstract

Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identification results under a variety of restrictions on the way the endogenous variable and the control variables affect the outcome. We consider many structural objects of interest, such as average or quantile treatment effects. We illustrate our results with an empirical application to Engel curve estimation.

Suggested Citation

  • Newey, Whitney & Stouli, Sami, 2021. "Control variables, discrete instruments, and identification of structural functions," Journal of Econometrics, Elsevier, vol. 222(1), pages 73-88.
    • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:73-88
    DOI: 10.1016/j.jeconom.2020.07.027
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    1. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
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    11. Victor Chernozhukov & Iván Fernández‐Val & Whitney Newey & Sami Stouli & Francis Vella, 2020. "Semiparametric estimation of structural functions in nonseparable triangular models," Quantitative Economics, Econometric Society, vol. 11(2), pages 503-533, May.
    12. Iv'an Fern'andez-Val & Aico van Vuuren & Francis Vella, 2018. "Nonseparable Sample Selection Models with Censored Selection Rules," Papers 1801.08961, arXiv.org, revised Sep 2020.
    13. R H Spady & S Stouli, 2018. "Dual regression," Biometrika, Biometrika Trust, vol. 105(1), pages 1-18.
    14. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    15. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    16. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    17. Fernández-Val, Iván & van Vuuren, Aico & Vella, Francis, 2018. "Nonseparable Sample Selection Models with Censored Selection Rules: An Application to Wage Decompositions," IZA Discussion Papers 11294, Institute of Labor Economics (IZA).
    18. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    20. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
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    Cited by:

    1. Victor Chernozhukov & Iván Fernández‐Val & Whitney Newey & Sami Stouli & Francis Vella, 2020. "Semiparametric estimation of structural functions in nonseparable triangular models," Quantitative Economics, Econometric Society, vol. 11(2), pages 503-533, May.
    2. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    3. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    4. Osama Khassawneh & Hamzah Elrehail, 2022. "The Effect of Participative Leadership Style on Employees’ Performance: The Contingent Role of Institutional Theory," Administrative Sciences, MDPI, vol. 12(4), pages 1-13, December.
    5. Christophe Bruneel-Zupanc, 2023. "Don't (fully) exclude me, it's not necessary! Identification with semi-IVs," Papers 2303.12667, arXiv.org, revised Jul 2023.

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    More about this item

    Keywords

    Control variables; Discrete instruments; Structural functions; Endogeneity; Partially nonparametric; Nonseparable models; Identification; Treatment effects;
    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

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