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Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models

Author

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  • Victor Chernozhukov
  • Iván Fernández-Val
  • Whitney Newey
  • Sami Stouli
  • Francis Vella

Abstract

This paper introduces two classes of semiparametric triangular systems with nonadditively separable unobserved heterogeneity. They are based on distribution and quantile regression modeling of the reduced-form conditional distributions of the endogenous variables. We show that these models are flexible and identify the average, distribution and quantile structural functions using a control function approach that does not require a large support condition. We propose a computationally attractive three-stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. We illustrate the implementation and applicability of our methods with numerical simulations and an empirical application to demand analysis.

Suggested Citation

  • Victor Chernozhukov & Iván Fernández-Val & Whitney Newey & Sami Stouli & Francis Vella, 2017. "Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models," Bristol Economics Discussion Papers 17/690, School of Economics, University of Bristol, UK.
    • Handle: RePEc:bri:uobdis:17/690
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    References listed on IDEAS

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    Cited by:

    1. Romuald Meango & Esther Mirjam Girsberger, 2023. "Identification of Ex ante Returns Using Elicited Choice Probabilities: an Application to Preferences for Public-sector Jobs," Papers 2303.03009, arXiv.org, revised Jun 2024.
    2. Jayeeta Bhattacharya, 2020. "Quantile regression with generated dependent variable and covariates," Papers 2012.13614, arXiv.org.
    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. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    5. 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.
    6. Fernández-Val, Ivan & van Vuuren, Aico & Vella, Francis, 2024. "Nonseparable sample selection models with censored selection rules," Journal of Econometrics, Elsevier, vol. 240(2).
    7. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    8. Christian Gische & Manuel C. Voelkle, 2022. "Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 868-901, September.
    9. Richard Spady & Sami Stouli, 2020. "Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions," Papers 2011.06416, arXiv.org.
    10. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    11. Bruneel-Zupanc, Christophe Alain, 2021. "Discrete-Continuous Dynamic Choice Models: Identification and Conditional Choice Probability Estimation," TSE Working Papers 21-1185, Toulouse School of Economics (TSE).
    12. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.
    13. Iv'an Fern'andez-Val & Franco Peracchi & Aico van Vuuren & Francis Vella, 2018. "Selection and the Distribution of Female Hourly Wages in the U.S," Papers 1901.00419, arXiv.org, revised Jan 2022.
    14. Nir Billfeld & Moshe Kim, 2024. "Context-dependent Causality (the Non-Nonotonic Case)," Papers 2404.05021, arXiv.org.
    15. Nagasawa, Kenichi, 2020. "Identification and Estimation of Group-Level Partial Effects," The Warwick Economics Research Paper Series (TWERPS) 1243, University of Warwick, Department of Economics.
    16. Romauld Méango, 2023. "Identification of ex ante returns using elicited choice probabilities," Economics Series Working Papers 1007, University of Oxford, Department of Economics.
    17. Iván Fernández‐Val & Aico van Vuuren & Francis Vella & Franco Peracchi, 2023. "Selection and the distribution of female real hourly wages in the United States," Quantitative Economics, Econometric Society, vol. 14(2), pages 571-607, May.

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