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On Binscatter

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Document pages: 94 pages

Abstract: Binscatter is very popular in applied microeconomics. It provides a flexible,yet parsimonious way of visualizing and summarizing large data sets inregression settings, and it is often used for informal evaluation ofsubstantive hypotheses such as linearity or monotonicity of the regressionfunction. This paper presents a foundational, thorough analysis of binscatter:we give an array of theoretical and practical results that aid both inunderstanding current practices (i.e., their validity or lack thereof) and inoffering theory-based guidance for future applications. Our main resultsinclude principled number of bins selection, confidence intervals and bands,hypothesis tests for parametric and shape restrictions of the regressionfunction, and several other new methods, applicable to canonical binscatter aswell as higher-order polynomial, covariate-adjusted and smoothness-restrictedextensions thereof. In particular, we highlight important methodologicalproblems related to covariate adjustment methods used in current practice. Wealso discuss extensions to clustered data. Our results are illustrated withsimulated and real data throughout. Companion general-purpose software packagesfor texttt{Stata} and texttt{R} are provided. Finally, from a technicalperspective, new theoretical results for partitioning-based series estimationare obtained that may be of independent interest.

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