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Matching Points: Supplementing Instruments with Covariates in Triangular Models

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  • Junlong Feng

Abstract

Models with a discrete endogenous variable are typically underidentified when the instrument takes on too few values. This paper presents a new method that matches pairs of covariates and instruments to restore point identification in this scenario in a triangular model. The model consists of a structural function for a continuous outcome and a selection model for the discrete endogenous variable. The structural outcome function must be continuous and monotonic in a scalar disturbance, but it can be nonseparable. The selection model allows for unrestricted heterogeneity. Global identification is obtained under weak conditions. The paper also provides estimators of the structural outcome function. Two empirical examples of the return to education and selection into Head Start illustrate the value and limitations of the method.

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  • Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1904.01159
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    References listed on IDEAS

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    Cited by:

    1. Loh, Isaac, 2023. "Nonparametric identification and estimation with discrete instruments and regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1257-1279.
    2. Salanié, Bernard & Lee, Sokbae, 2020. "Filtered and Unfiltered Treatment Effects with Targeting Instruments," CEPR Discussion Papers 15092, C.E.P.R. Discussion Papers.
    3. 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).
    4. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.
    5. Leonard Goff, 2020. "A Vector Monotonicity Assumption for Multiple Instruments," Papers 2009.00553, arXiv.org, revised Mar 2024.
    6. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Dec 2024.
    7. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    8. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2024. "Endogeneity in weakly separable models without monotonicity," Journal of Econometrics, Elsevier, vol. 238(1).
    9. Songnian Chen & Shakeeb Khan & Xun Tang, 2022. "Endogeneity in Weakly Separable Models without Monotonicity," Papers 2208.05047, arXiv.org.

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