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Nonparametric estimation of triangular simultaneous equations models under weak identification

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  • Sukjin Han

Abstract

This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then nonparametric weak instruments are defined as a sequence of reduced‐form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized as concurvity, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments and shows that it achieves desirable asymptotic properties. A data‐driven procedure is proposed for the choice of the penalization parameter. The findings of this paper provide useful implications for empirical work. To illustrate them, Monte Carlo results are presented and an empirical example is given in which the effect of class size on test scores is estimated nonparametrically.

Suggested Citation

  • Sukjin Han, 2020. "Nonparametric estimation of triangular simultaneous equations models under weak identification," Quantitative Economics, Econometric Society, vol. 11(1), pages 161-202, January.
    • Handle: RePEc:wly:quante:v:11:y:2020:i:1:p:161-202
    DOI: 10.3982/QE975
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    Cited by:

    1. Otsu, Taisuke & Sunada, Keita, 2024. "On large market asymptotics for spatial price competition models," Economics Letters, Elsevier, vol. 234(C).
    2. Han, Sukjin & Yang, Shenshen, 2024. "A computational approach to identification of treatment effects for policy evaluation," Journal of Econometrics, Elsevier, vol. 240(1).
    3. Javier Alejo & Antonio F. Galvao & Julian Martinez-Iriarte & Gabriel Montes-Rojas, 2024. "Endogenous Heteroskedasticity in Linear Models," Papers 2412.02767, arXiv.org, revised Dec 2025.
    4. Dakyung Seong, 2025. "Binary Response Model With Many Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(2), pages 214-230, March.
    5. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    6. Edvard Bakhitov & Amandeep Singh, 2021. "Causal Gradient Boosting: Boosted Instrumental Variable Regression," Papers 2101.06078, arXiv.org.
    7. Otsu, Taisuke & Sunada, Keita, 2024. "On large market asymptotics for spatial price competition models," LSE Research Online Documents on Economics 120588, London School of Economics and Political Science, LSE Library.
    8. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.

    More about this item

    JEL classification:

    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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