IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.15276.html

Nonlinear Binscatter Methods

Author

Listed:
  • Matias D. Cattaneo
  • Richard K. Crump
  • Max H. Farrell
  • Yingjie Feng

Abstract

Binscatters are a powerful tool for empirical work in the social, behavioral, and biomedical sciences. Available tools rely on least squares estimation of the conditional mean. We introduce novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation, covering generalized linear, robust, and quantile regression models. We provide theoretical results and practical tools, including optimal bin selection, confidence bands, and statistical tests regarding functional form or shape restrictions. We demonstrate our methods by studying the relationship of income and (lack of) health insurance. We provide software for Python, R, and Stata. Our technical results may be of independent interest.

Suggested Citation

  • Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Yingjie Feng, 2024. "Nonlinear Binscatter Methods," Papers 2407.15276, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2407.15276
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2407.15276
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    2. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    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. Crump, Richard K. & Eusepi, Stefano & Giannoni, Marc & Şahin, Ayşegül, 2024. "The unemployment–inflation trade-off revisited: The Phillips curve in COVID times," Journal of Monetary Economics, Elsevier, vol. 145(S).

    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. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    2. Mona Azadkia & Leihao Chen & Fang Han, 2025. "Bias correction for Chatterjee's graph-based correlation coefficient," Papers 2508.09040, arXiv.org, revised Jan 2026.
    3. Li, Jia & Liao, Zhipeng & Zhou, Wenyu, 2025. "A general test for functional inequalities," Journal of Econometrics, Elsevier, vol. 251(C).
    4. Haoze Hou & Wei Huang & Zheng Zhang, 2025. "Non-parametric Quantile Regression and Uniform Inference with Unknown Error Distribution," Papers 2504.01761, arXiv.org.
    5. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    6. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    7. Jia-Young Michael Fu & Joel L. Horowitz & Matthias Parey, 2015. "Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions," CeMMAP working papers 68/15, Institute for Fiscal Studies.
    8. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    9. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    11. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    12. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    13. Damian Kozbur, 2013. "Inference in additively separable models with a high-dimensional set of conditioning variables," ECON - Working Papers 284, Department of Economics - University of Zurich, revised Apr 2018.
    14. Xiaohong Chen & Wayne Yuan Gao & Likang Wen, 2025. "ReLU-Based and DNN-Based Generalized Maximum Score Estimators," Papers 2511.19121, arXiv.org.
    15. Xiaohong Chen & Elie Tamer & Qingsong Yao, 2026. "Fast Online Inference on Semiparametric Models," Papers 2603.08614, arXiv.org, revised Jul 2026.
    16. Yukun Ma & Pedro H. C. Sant'Anna & Yuya Sasaki & Takuya Ura, 2023. "Doubly Robust Estimators with Weak Overlap," Papers 2304.08974, arXiv.org, revised Apr 2026.
    17. Victor Chernozhukov & Vira Semenova, 2018. "Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions," CeMMAP working papers CWP40/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Nan Liu & Yanbo Liu & Yuya Sasaki & Yuanyuan Wan, 2025. "Nonparametric Uniform Inference in Binary Classification and Policy Values," Working Papers tecipa-811, University of Toronto, Department of Economics.
    19. Adam Lee, 2024. "Locally Regular and Efficient Tests in Non-Regular Semiparametric Models," Papers 2403.05999, arXiv.org, revised Dec 2024.
    20. Christoph Breunig & Peter Haan, 2018. "Nonparametric Regression with Selectively Missing Covariates," Papers 1810.00411, arXiv.org, revised Oct 2020.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    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:arx:papers:2407.15276. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.