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Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects

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  • Whitney K. Newey
  • Sami Stouli

Abstract

Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. We consider heterogenous coefficients models where the outcome is a linear combination of known functions of treatment and heterogenous coefficients. We use control variables to obtain identification results for average treatment effects. With discrete instruments in a triangular model we find that average treatment effects cannot be identified when the number of support points is less than or equal to the number of coefficients. A sufficient condition for identification is that the second moment matrix of the treatment functions given the control is nonsingular with probability one. We relate this condition to identification of average treatment effects with multiple treatments.

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  • Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    • Handle: RePEc:arx:papers:1811.09837
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    1. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    2. 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.
    3. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
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    5. Newey, Whitney & Stouli, Sami, 2021. "Control variables, discrete instruments, and identification of structural functions," Journal of Econometrics, Elsevier, vol. 222(1), pages 73-88.
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    7. 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.
    8. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
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    Cited by:

    1. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2024. "Testing and relaxing the exclusion restriction in the control function approach," Journal of Econometrics, Elsevier, vol. 240(2).
    2. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Newey, Whitney & Stouli, Sami, 2021. "Control variables, discrete instruments, and identification of structural functions," Journal of Econometrics, Elsevier, vol. 222(1), pages 73-88.
    4. W K Newey & S Stouli, 2022. "Heterogeneous coefficients, control variables and identification of multiple treatment effects [Multivalued treatments and decomposition analysis: An application to the WIA program]," Biometrika, Biometrika Trust, vol. 109(3), pages 865-872.

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