Nonlinear Binscatter Methods

Matias Cattaneo, Richard Crump, Max Farrell and Yingjie Feng

No 1110, Staff Reports from Federal Reserve Bank of New York

Abstract: 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.

Keywords: partition-based semi-linear estimators; Linear models; quantile regression; robust bias correction; uniform inference; binning selection; treatment effect estimation (search for similar items in EconPapers)
JEL-codes: C14 C18 C21 (search for similar items in EconPapers)
Pages: 104
Date: 2024-08-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Working Paper: Nonlinear Binscatter Methods (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fednsr:98622

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DOI: 10.59576/sr.1110

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