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Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models

Author

Listed:
  • Victor Chernozhukov
  • Iv'an Fern'andez-Val
  • Whitney Newey
  • Sami Stouli
  • Francis Vella
Abstract
Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modelling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution and quantile structural functions are identified in these systems through 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. These results establish the validity of the bootstrap for three-stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis.

Suggested Citation

  • Victor Chernozhukov & Iv'an Fern'andez-Val & Whitney Newey & Sami Stouli & Francis Vella, 2017. "Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models," Papers 1711.02184, arXiv.org, revised Oct 2019.
    • Handle: RePEc:arx:papers:1711.02184
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    References listed on IDEAS

    as
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    Full references (including those not matched with items 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. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    3. 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.
    4. 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.
    5. 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).
    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. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    8. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.
    9. 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.
    10. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous coefficients, discrete instruments, and identification of treatment effects," CeMMAP working papers CWP66/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Richard Spady & Sami Stouli, 2020. "Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions," Papers 2011.06416, arXiv.org.
    12. Nir Billfeld & Moshe Kim, 2024. "Context-dependent Causality (the Non-Nonotonic Case)," Papers 2404.05021, arXiv.org.
    13. 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.
    14. Newey, Whitney & Stouli, Sami, 2021. "Control variables, discrete instruments, and identification of structural functions," Journal of Econometrics, Elsevier, vol. 222(1), pages 73-88.
    15. 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.
    16. Jayeeta Bhattacharya, 2020. "Quantile regression with generated dependent variable and covariates," Papers 2012.13614, arXiv.org.
    17. Romauld Méango, 2023. "Identification of ex ante returns using elicited choice probabilities," Economics Series Working Papers 1007, University of Oxford, Department of Economics.

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