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Non-separable Models with High-dimensional Data

Author

Listed:
  • Liangjun Su

    (School of Economics, Singapore Management University)

  • Takuya Ura

    (Department of Economics, University of California Davis)

  • Yichong Zhang

    (School of Economics, Singapore Management University)

Abstract

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and penalized conditional density estimation, respectively, where control variables are selected via a localized method of L1-penalization at each value of the continuous treatment. In the second stage we estimate the average and the marginal distribution of the potential outcome via the plug-in principle. In the third stage, we estimate the quantile and marginal treatment effects by inverting the estimated distribution function and using the local linear regression, respectively. We study the asymptotic properties of these estimators and propose a weighted-bootstrap method for inference. Using simulated and real datasets, we demonstrate the proposed estimators perform well in finite samples.

Suggested Citation

  • Liangjun Su & Takuya Ura & Yichong Zhang, 2017. "Non-separable Models with High-dimensional Data," Economics and Statistics Working Papers 15-2017, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2017_015
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    2. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    3. Ying-Ying Lee & Chu-An Liu, 2024. "Lee Bounds with a Continuous Treatment in Sample Selection," Papers 2411.04312, arXiv.org, revised Oct 2025.
    4. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity," Papers 2310.08063, arXiv.org, revised Jun 2024.
    5. Zeqi Wu & Meilin Wang & Wei Huang & Zheng Zhang, 2025. "A New and Efficient Debiased Estimation of General Treatment Models by Balanced Neural Networks Weighting," Papers 2507.04044, arXiv.org.
    6. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    7. Alexander Krei{ss} & Christoph Rothe, 2021. "Inference in Regression Discontinuity Designs with High-Dimensional Covariates," Papers 2110.13725, arXiv.org, revised May 2022.
    8. Qingliang Fan & Yu-Chin Hsu & Robert P. Lieli & Yichong Zhang, 2022. "Estimation of Conditional Average Treatment Effects With High-Dimensional Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 313-327, January.
    9. Yizhen Xu & Numair Sani & AmirEmad Ghassami & Ilya Shpitser, 2021. "Multiply Robust Causal Mediation Analysis with Continuous Treatments," Papers 2105.09254, arXiv.org, revised Oct 2024.
    10. Alexander Kreiss & Christoph Rothe, 2023. "Inference in regression discontinuity designs with high-dimensional covariates," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 105-123.
    11. Xie, Haitian, 2024. "Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment," Journal of Econometrics, Elsevier, vol. 242(1).
    12. Sylvia Klosin, 2021. "Automatic Double Machine Learning for Continuous Treatment Effects," Papers 2104.10334, arXiv.org.
    13. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-Driven Policy Learning for Continuous Treatments," Papers 2402.02535, arXiv.org, revised Dec 2025.
    14. Ta-Wei Huang & Eva Ascarza, 2024. "Doing More with Less: Overcoming Ineffective Long-Term Targeting Using Short-Term Signals," Marketing Science, INFORMS, vol. 43(4), pages 863-884, July.
    15. Yikun Zhang & Yen-Chi Chen, 2025. "Doubly Robust Inference on Causal Derivative Effects for Continuous Treatments," Papers 2501.06969, arXiv.org, revised Apr 2025.
    16. Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves," Papers 2010.04855, arXiv.org, revised Oct 2022.
    17. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    18. Lucas Z. Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org, revised Dec 2025.
    19. Cheuk Hang Leung & Yijun Li & Qi Wu, 2025. "Distribution-valued Causal Machine Learning: Implications of Credit on Spending Patterns," Papers 2509.03063, arXiv.org.
    20. Tübbicke Stefan, 2022. "Entropy Balancing for Continuous Treatments," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 71-89, January.

    More about this item

    Keywords

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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • I19 - Health, Education, and Welfare - - Health - - - Other

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