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Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables

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  • Huang, Liquan
  • Khalil, Umair
  • Yıldız, Neşe

Abstract

We develop a novel identification method for a partially linear model with multiple endogenous variables of interest but a single instrumental variable, which could even be binary. We present an easy-to-implement consistent estimator for the parametric part. This estimator retains n-convergence rate and asymptotic normality even though we have a generated regressor in our setup. The nonparametric part of the model is also identified. We also outline how our identification strategy can be extended to a fully non-parametric model. Finally, we use our methods to assess the impact of smoking during pregnancy on birth weight.

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  • Huang, Liquan & Khalil, Umair & Yıldız, Neşe, 2019. "Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables," Journal of Econometrics, Elsevier, vol. 208(2), pages 346-366.
    • Handle: RePEc:eee:econom:v:208:y:2019:i:2:p:346-366
    DOI: 10.1016/j.jeconom.2017.10.009
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    Cited by:

    1. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Dec 2024.
    2. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Carolina Caetano & Gregorio Caetano & Juan Carlos Escanciano, 2023. "Regression discontinuity design with multivalued treatments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 840-856, September.
    4. Salanié, Bernard & Lee, Sokbae, 2020. "Filtered and Unfiltered Treatment Effects with Targeting Instruments," CEPR Discussion Papers 15092, C.E.P.R. Discussion Papers.
    5. Sokbae (Simon) Lee & Bernard Salanie, 2024. "Treatment effects with targeting instruments," CeMMAP working papers 23/24, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Identification; Multiple endogenous variables; Control function approach;
    All these keywords.

    JEL classification:

    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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