Nonlinear Binscatter Methods

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Cattaneo, Matias D., Crump, Richard K., Farrell, Max H., Feng, Yingjie
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911963812986880
author Cattaneo, Matias D.
Crump, Richard K.
Farrell, Max H.
Feng, Yingjie
author_facet Cattaneo, Matias D.
Crump, Richard K.
Farrell, Max H.
Feng, Yingjie
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_15276
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nonlinear Binscatter Methods
Cattaneo, Matias D.
Crump, Richard K.
Farrell, Max H.
Feng, Yingjie
Methodology
Econometrics
Statistics Theory
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.
title Nonlinear Binscatter Methods
topic Methodology
Econometrics
Statistics Theory
url https://arxiv.org/abs/2407.15276