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Control variables, discrete instruments, and identification of structural functions

Author

Listed:
  • Whitney K. Newey

    (Institute for Fiscal Studies and MIT)

  • Sami Stouli

    (Institute for Fiscal Studies and University of Bristol)

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 identi cation 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

  • Whitney K. Newey & Sami Stouli, 2018. "Control variables, discrete instruments, and identification of structural functions," CeMMAP working papers CWP55/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:55/18
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    References listed on IDEAS

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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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    6. 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.
    7. Matthew A. Masten & Alexander Torgovitsky, 2016. "Identification of Instrumental Variable Correlated Random Coefficients Models," The Review of Economics and Statistics, MIT Press, vol. 98(5), pages 1001-1005, December.
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    9. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
    10. Jerry A. Hausman & Whitney K. Newey, 2016. "Individual Heterogeneity and Average Welfare," Econometrica, Econometric Society, vol. 84, pages 1225-1248, May.
    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.
    19. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    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. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    3. 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.
    4. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    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

    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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