Optimal Data-Driven Regression Discontinuity Plots

By Sebastian Calonico, M. D. Cattaneo, R. Titiunik. 2015

434 citations recorded by the source corpus.

Exploratory data analysis plays a central role in applied statistics and econometrics. In the popular regression-discontinuity (RD) design, the use of graphical analysis has been strongly advocated because it provides both easy presentation and transparent validation of the design. RD plots are nowadays widely used in applications, despite its formal properties being unknown: these plots are typically presented employing ad hoc choices of tuning parameters, which makes these procedures less automatic and more subjective. In this article, we formally study the most common RD plot based on an evenly spaced binning of the data, and propose several (optimal) data-driven choices for the number of bins depending on the goal of the researcher. These RD plots are constructed either to approximate the underlying unknown regression functions without imposing smoothness in the estimator, or to approximate the underlying variability of the raw data while smoothing out the otherwise uninformative scatterplot of the data. In addition, we introduce an alternative RD plot based on quantile spaced binning, study its formal properties, and propose similar (optimal) data-driven choices for the number of bins. The main proposed data-driven selectors employ spacings estimators, which are simple and easy to implement in applications because they do not require additional choices of tuning parameters. Altogether, our results offer an array of alternative RD plots that are objective and automatic when implemented, providing a reliable benchmark for graphical analysis in RD designs. We illustrate the performance of our automatic RD plots using several empirical examples and a Monte Carlo study. All results are readily available in R and STATA using the software packages described in Calonico, Cattaneo, and Titiunik. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/400b960e9fd832ccbd6df12f209886769888e4cf

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Citations in the corpus

External Validity in Fuzzy Regression Discontinuity Designs (2019, positive): “In this section, we remake the conditional mean plots in Figures 1 and 2 following the optimal data-driven plots of Calonico, Cattaneo, and Titiunik (2015).”
Are Foreign Investors Locusts? The Long-Term Effects of Foreign Institutional Ownership (2017, methodology): “The dots correspond to the sample means of the two variables in each bin, in which the number of bins is selected to mimic the variability of the data using Calonico et al. (2015) estimator.”
Rdrobust: Software for Regression-discontinuity Designs (2017, methodology): “When-ever When-ever possible, we retain the same syntax as in the previous version of this command (Calonico, Cattaneo, and Titiunik 2014a, 2015b).”
Econometric Methods for Program Evaluation (2018, methodology): “, Card 1990, Card & Krueger 1994). For example, Card (1990) estimates the effect of the Mariel Boatlift, a large and sudden influx of immigrants to Miami, on the labor market outcomes of native workers in Miami.”
The Effect of Institutional Ownership on Firm Transparency and Information Production (2015, positive): “8 The analyses use the optimal rule of thumb bandwidth selection procedure prescribed in Calonico et al. (2014b), which corrects for the non-negligible bias in the distributional approximation of subjective bandwidth choices.”
Power calculations for regression-discontinuity designs (2019, methodology): “See Calonico, Cattaneo, and Titiunik (2014a, 2015b) and Calonico et al. (2017) for an introduction to the commands rdrobust, rdbwselect, and rdplot for graphical presentation, estimation, and inference in RD designs using nonparametric local polynomial techniques.”
Regression Discontinuity Designs (2021, methodology): “Keele and Titiunik (2015) and Cattaneo, Keele, Titiunik, and Vazquez-Bare (2016) discuss a causal link between the normalized- and-pooled RD treatment effect and the RD treatment effects along the treatment assignment curve or at multiple cutoffs.”
Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs (2018, background): “The latter case is of interest in, for example, Card et al. (2015, 2017), Dong and Lewbel (2015), Cerulli et al. (2017), and Ganong and Jäger (2018).”