Authors: Matias D. Cattaneo, Richard K. Crump, Max H. Farrell, and Yingjie Feng
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Staff Reports
Nonlinear Binscatter Methods
Number 1110
August 2024 Revised August 2026
August 2024 Revised August 2026
JEL classification: C14, C18, C21
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.
Author Disclosure Statement(s)
Matias D. Cattaneo
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Max Farrell and Yingjie Feng.
Richard K. Crump
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Matias Cattaneo, Max Farrell and Yingjie Feng.
Max H. Farrell
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Matias Cattaneo, and Yingjie Feng.
Yingjie Feng
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Matias Cattaneo, and Max Farrell.
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Max Farrell and Yingjie Feng.
Richard K. Crump
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Matias Cattaneo, Max Farrell and Yingjie Feng.
Max H. Farrell
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Matias Cattaneo, and Yingjie Feng.
Yingjie Feng
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Nonlinear Binscatter Methods,” joint with Richard Crump, Matias Cattaneo, and Max Farrell.
Suggested Citation:
Cattaneo, Matias D., Richard K. Crump, Max H. Farrell, and Yingjie Feng. 2024. “Nonlinear Binscatter Methods.” Federal Reserve Bank of New York Staff Reports, no. 1110, revised August 2026. https://doi.org/10.59576/sr.1110
Cattaneo, Matias D., Richard K. Crump, Max H. Farrell, and Yingjie Feng. 2024. “Nonlinear Binscatter Methods.” Federal Reserve Bank of New York Staff Reports, no. 1110, revised August 2026. https://doi.org/10.59576/sr.1110
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