Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/302200 
Year of Publication: 
2024
Series/Report no.: 
Staff Reports No. 1110
Publisher: 
Federal Reserve Bank of New York, New York, NY
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.
Subjects: 
partition-based semi-linear estimators
generalized linear models
quantile regression
robust bias correction
uniform inference
binning selection
treatment effect estimation
JEL: 
C14
C18
C21
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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