Binned scatter plots, or binscatters, have become a popular and convenient tool in applied microeconomics for visualizing bivariate relations and conducting informal specification testing. However, a binscatter, on its own, is very limited in what it can characterize about the conditional mean. We introduce a suite of formal and visualization tools based on binned scatter plots to restore, and in some dimensions surpass, the visualization benefits of the classical scatter plot. We deliver a comprehensive toolkit for applications, including estimation of conditional mean and quantile functions, visualization of variance and precise quantification of uncertainty, and formal tests of substantive hypotheses such as linearity or monotonicity, and an extension to testing differences across groups. To do so we give an extensive theoretical analysis of binscatter and related partition-based methods, accommodating nonlinear and potentially nonsmooth models, which allows us to treat binary, count, and other discrete outcomes as well. We also correct a methodological mistake related to covariate adjustment present in prior implementations, which yields an incorrect shape and support of the conditional mean. All of our results are implemented in publicly available software, and showcased with three substantive empirical illustrations. Our empirical results are dramatically different when compared to those obtained using the prevalent methods in the literature.
Joint paper with Richard K. Crump, Max H. Farrell and Yingjie Feng.