IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v168y2018icp48-62.html
   My bibliography  Save this article

Joint sufficient dimension reduction for estimating continuous treatment effect functions

Author

Listed:
  • Huang, Ming-Yueh
  • Chan, Kwun Chuen Gary

Abstract

The estimation of continuous treatment effect functions using observational data often requires parametric specification of the effect curves, the conditional distributions of outcomes and treatment assignments given multi-dimensional covariates. While nonparametric extensions are possible, they typically suffer from the curse of dimensionality. Dimension reduction is often inevitable and we propose a sufficient dimension reduction framework to balance parsimony and flexibility. The joint central subspace can be estimated at a n1∕2-rate without fixing its dimension in advance, and the treatment effect function is estimated by averaging local estimates of a reduced dimension. Asymptotic properties are studied. Unlike binary treatments, continuous treatments require multiple smoothing parameters of different asymptotic orders to borrow different facets of information, and their joint estimation is proposed by a non-standard version of the infinitesimal jackknife.

Suggested Citation

  • Huang, Ming-Yueh & Chan, Kwun Chuen Gary, 2018. "Joint sufficient dimension reduction for estimating continuous treatment effect functions," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 48-62.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:48-62
    DOI: 10.1016/j.jmva.2018.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17307273
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2018.07.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    2. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    3. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    4. Wei Luo & Yeying Zhu & Debashis Ghosh, 2017. "On estimating regression-based causal effects using sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 104(1), pages 51-65.
    5. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    6. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    7. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2017. "Joint sufficient dimension reduction and estimation of conditional and average treatment effects," Biometrika, Biometrika Trust, vol. 104(3), pages 583-596.
    8. Antonio F. Galvao & Liang Wang, 2015. "Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1528-1542, December.
    9. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    10. Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
    11. Edward H. Kennedy & Zongming Ma & Matthew D. McHugh & Dylan S. Small, 2017. "Non-parametric methods for doubly robust estimation of continuous treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1229-1245, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Feng, Sanying & Kong, Kaidi & Kong, Yinfei & Li, Gaorong & Wang, Zhaoliang, 2022. "Statistical inference of heterogeneous treatment effect based on single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
    2. Wei Huang & Oliver Linton & Zheng Zhang, 2021. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Papers 2102.08063, arXiv.org, revised Sep 2021.
    3. Yukitoshi Matsushita & Taisuke Otsu & Keisuke Takahata, 2022. "Estimating density ratio of marginals to joint: Applications to causal inference," STICERD - Econometrics Paper Series 619, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    5. Martin Huber & Yu‐Chin Hsu & Ying‐Ying Lee & Layal Lettry, 2020. "Direct and indirect effects of continuous treatments based on generalized propensity score weighting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 814-840, November.
    6. 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.
    7. Tübbicke Stefan, 2022. "Entropy Balancing for Continuous Treatments," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 71-89, January.
    8. Ai, Chunrong & Linton, Oliver & Zhang, Zheng, 2022. "Estimation and inference for the counterfactual distribution and quantile functions in continuous treatment models," Journal of Econometrics, Elsevier, vol. 228(1), pages 39-61.
    9. Edward H. Kennedy & Zongming Ma & Matthew D. McHugh & Dylan S. Small, 2017. "Non-parametric methods for doubly robust estimation of continuous treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1229-1245, September.
    10. Zhang, Xiaoke & Xue, Wu & Wang, Qiyue, 2021. "Covariate balancing functional propensity score for functional treatments in cross-sectional observational studies," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    11. Jiang, Qingshan & Xu, Li & Huang, Can, 2022. "Covariates distributions balancing for continuous treatment," Economics Letters, Elsevier, vol. 217(C).
    12. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    14. W K Newey & S Stouli, 2022. "Heterogeneous coefficients, control variables and identification of multiple treatment effects [Multivalued treatments and decomposition analysis: An application to the WIA program]," Biometrika, Biometrika Trust, vol. 109(3), pages 865-872.
    15. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Carina Steckenleiter & Michael Lechner & Tim Pawlowski & Ute Schüttoff, 2023. "Do local expenditures on sports facilities affect sports participation?," Economic Inquiry, Western Economic Association International, vol. 61(4), pages 1103-1128, October.
    17. repec:jdm:journl:v:17:y:2022:i:6:p:1176-1207 is not listed on IDEAS
    18. Steckenleiter, Carina & Lechner, Michael & Pawlowski, Tim & Schüttoff, Ute, 2019. "Do local public expenditures on sports facilities affect sports participation in Germany?," Economics Working Paper Series 1905, University of St. Gallen, School of Economics and Political Science.
    19. Flores, Carlos A. & Mitnik, Oscar A., 2009. "Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data," IZA Discussion Papers 4451, Institute of Labor Economics (IZA).
    20. repec:cup:judgdm:v:17:y:2022:i:6:p:1176-1207 is not listed on IDEAS
    21. Jie Zhu & Blanca Gallego, 2021. "Continuous Treatment Recommendation with Deep Survival Dose Response Function," Papers 2108.10453, arXiv.org, revised Sep 2023.
    22. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:48-62. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.