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A discontinuity test for identification in triangular nonseparable models

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  • Caetano, Carolina
  • Rothe, Christoph
  • Yıldız, Neşe

Abstract

This paper presents a test for the validity of control variable approaches to identification in triangular nonseparable models. Assumptions commonly imposed to justify such methods include full independence of instruments and disturbances and existence of a reduced form that is strictly monotonic in a scalar disturbance. We show that if the data has a particular structure, namely that the distribution of the endogenous variable has a mass point at the lower (or upper) boundary of its support, validity of the control variable approach implies a continuity condition on an identified function, which can be tested empirically.

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  • Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:1:p:113-122
    DOI: 10.1016/j.jeconom.2016.01.007
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    Cited by:

    1. Fernández-Val, Ivan & van Vuuren, Aico & Vella, Francis, 2024. "Nonseparable sample selection models with censored selection rules," Journal of Econometrics, Elsevier, vol. 240(2).
    2. 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.
    3. Carolina Caetano & Gregorio Caetano & Hao Fe & Eric R. Nielsen, 2021. "A Dummy Test of Identification in Models with Bunching," Finance and Economics Discussion Series 2021-068, Board of Governors of the Federal Reserve System (U.S.).
    4. 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).
    5. Khalil, Umair & Yıldız, Neşe, 2022. "A test of the selection on observables assumption using a discontinuously distributed covariate," Journal of Econometrics, Elsevier, vol. 226(2), pages 423-450.
    6. 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

    Keywords

    Nonseparable model; Triangular systems; Control variable; Instrument validity; Nonparametric identification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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