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What Do Quantile Regressions Identify For General Structural Functions?

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  • Sasaki, Yuya

Abstract

This paper shows what quantile regressions identify for general structural functions. Under fairly mild conditions, the quantile partial derivative identifies a weighted average of heterogeneous structural partial effects among the subpopulation of individuals at the conditional quantile of interest. This result justifies the use of quantile regressions as means of measuring heterogeneous causal effects for a general class of structural functions with multiple unobservables.

Suggested Citation

  • Sasaki, Yuya, 2015. "What Do Quantile Regressions Identify For General Structural Functions?," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1102-1116, October.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:05:p:1102-1116_00
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    References listed on IDEAS

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    Cited by:

    1. Carolina Caetano & Gregorio Caetano & Leonard Goff & Eric Nielsen, 2025. "Identification of Causal Effects with a Bunching Design," Papers 2507.05210, arXiv.org.
    2. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    3. Chalak, Karim, 2019. "A note on the robustness of quantile treatment effect estimands," Economics Letters, Elsevier, vol. 185(C).
    4. Victor Chernozhukov & Iván Fernández‐Val & Ye Luo, 2018. "The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages," Econometrica, Econometric Society, vol. 86(6), pages 1911-1938, November.
    5. Creemers, Sarah & Peeters, Ludo & Quiroz Castillo, Juan Luis & Vancauteren, Mark & Voordeckers, Wim, 2023. "Family firms and the labor productivity controversy: A distributional analysis of varying labor productivity gaps," Journal of Family Business Strategy, Elsevier, vol. 14(2).
    6. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    7. Leonard Goff, 2022. "Identifying causal effects with subjective ordinal outcomes," Papers 2212.14622, arXiv.org, revised Jan 2025.
    8. Xiaohong Chen & Wayne Yuan Gao, 2025. "Semiparametric Learning of Integral Functionals on Submanifolds," Cowles Foundation Discussion Papers 2450, Cowles Foundation for Research in Economics, Yale University.
    9. Xie, Haitian, 2024. "Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment," Journal of Econometrics, Elsevier, vol. 242(1).
    10. Chiang, Harold D. & Sasaki, Yuya, 2019. "Causal inference by quantile regression kink designs," Journal of Econometrics, Elsevier, vol. 210(2), pages 405-433.
    11. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Estimation of Heterogeneous Treatment Effects Using Quantile Regression with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 13/22, Monash University, Department of Econometrics and Business Statistics.
    12. Chernozhukov, Victor & Fernández-Val, Iván & Newey, Whitney K., 2019. "Nonseparable multinomial choice models in cross-section and panel data," Journal of Econometrics, Elsevier, vol. 211(1), pages 104-116.
    13. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon–Jae Whang, 2025. "Quantile random-coefficient regression with interactive fixed effects: Heterogeneous group-level policy evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 44(5), pages 630-648, May.
    14. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, vol. 4(1), pages 1-14, December.
    15. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.
    16. Xiaohong Chen & Wayne Yuan Gao, 2025. "Thin Sets Are Not Equally Thin: Minimax Learning of Submanifold Integrals," Papers 2507.12673, arXiv.org, revised Mar 2026.
    17. Xiaohong Chen & Wayne Yuan Gao, 2026. "Thin Sets Are Not Equally Thin: Minimax Learning of Submanifold Integrals," Cowles Foundation Discussion Papers 2450R1, Cowles Foundation for Research in Economics, Yale University.

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