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
August 2024
JEL classification: C14, C18, C21
Binned scatter plots are a powerful statistical tool for empirical work in the social, behavioral, and biomedical sciences. Available methods rely on a quantile-based partitioning estimator of the conditional mean regression function to primarily construct flexible yet interpretable visualization methods, but they can also be used to estimate treatment effects, assess uncertainty, and test substantive domain-specific hypotheses. This paper introduces novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation methods, covering generalized linear, robust, and quantile regression models. We provide a host of theoretical results and practical tools for local constant estimation along with piecewise polynomial and spline approximations, including (i) optimal tuning parameter (number of bins) selection, (ii) confidence bands, and (iii) formal statistical tests regarding functional form or shape restrictions. Our main results rely on novel strong approximations for general partitioning-based estimators covering random, data-driven partitions, which may be of independent interest. We demonstrate our methods with an empirical application studying the relation between the percentage of individuals without health insurance and per capita income at the zip-code level. We provide general-purpose software packages implementing our methods in Python, R, and Stata.
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, August. 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, August. https://doi.org/10.59576/sr.1110
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