On Binscatter

44 Pages Posted: 1 Mar 2019

See all articles by Matias D. Cattaneo

Matias D. Cattaneo

University of Michigan at Ann Arbor - Department of Economics

Richard K. Crump

Federal Reserve Banks - Federal Reserve Bank of New York

Max Farrell

University of Chicago - Booth School of Business - Econometrics and Statistics

Yingjie Feng

University of Michigan, College of Literature, Science and the Arts, Department of Economics, Students

Date Written: February 2019

Abstract

Binscatter is very popular in applied microeconomics. It provides a flexible, yet parsimonious way of visualizing and summarizing “big data” in regression settings, and it is often used for informal testing of substantive hypotheses such as linearity or monotonicity of the regression function. This paper presents a foundational, thorough analysis of binscatter: We give an array of theoretical and practical results that aid both in understanding current practices (that is, their validity or lack thereof) and in offering theory-based guidance for future applications. Our main results include principled number of bins selection, confidence intervals and bands, hypothesis tests for parametric and shape restrictions of the regression function, and several other new methods, applicable to canonical binscatter as well as higher-order polynomial, covariate-adjusted, and smoothness-restricted extensions thereof. In particular, we highlight important methodological problems related to covariate adjustment methods used in current practice. We also discuss extensions to clustered data. Our results are illustrated with simulated and real data throughout. Companion general-purpose software packages for Stata and R are provided. Finally, from a technical perspective, new theoretical results for partitioning-based series estimation are obtained that may be of independent interest.

Keywords: binned scatter plot, regressogram, piecewise polynomials, splines, partitioning estimators, nonparametric regression, robust bias correction, uniform inference, binning selection

JEL Classification: C14, C18, C21

Suggested Citation

Cattaneo, Matias D. and Crump, Richard K. and Farrell, Max and Feng, Yingjie, On Binscatter (February 2019). FRB of New York Staff Report No. 881, Available at SSRN: https://ssrn.com/abstract=3344739 or http://dx.doi.org/10.2139/ssrn.3344739

Matias D. Cattaneo

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
734-763-1306 (Phone)

HOME PAGE: http://www.umich.edu/~cattaneo/

Richard K. Crump (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

Max Farrell

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States

Yingjie Feng

University of Michigan, College of Literature, Science and the Arts, Department of Economics, Students ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States

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