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Observational Studies 2 (2016) 134-146 Submitted 8/16; Published 12/16 The Choice of Neighborhood in Regression Discontinuity Designs Matias D. Cattaneo Department of Economics and Department of Statistics University of Michigan Ann Arbor, MI 48104, US Gonzalo Vazquez-Bare Department of Economics University of Michigan Ann Arbor, MI 48104, US This version: January 22, 2017 The seminal paper of Thistlethwaite and Campbell (1960) is one of the greatest breakthroughs in program evaluation and causal inference for observational studies. The originally coined Regression-Discontinuity Analysis, and nowadays widely known as the Regression Discontinuity (RD) design, is likely the most credible and internally valid quantitative approach for the analysis and interpretation of non-experimental data. Early reviews and perspectives on RD designs include Cook (2008), Imbens and Lemieux (2008) and Lee and Lemieux (2010); see also Cattaneo and Escanciano (2017) for a contemporaneous edited volume with more recent overviews, discussions, and references. The key design feature in RD is that units have an observable running variable, score or index, and are assigned to treatment whenever this variable exceeds a known cutoff. Empirical work in RD designs seeks to compare the response of units just below the cutoff (control group) to the response of units just above (treatment group) to learn about the treatment effects of interest. It is by now generally recognized that the most important task in practice is to select the appropriate neighborhood near the cutoff, that is, to correctly determine which observations near the cutoff will be used. Localizing near the cutoff is crucial because empirical findings can be quite sensitive to which observations are included in the analysis. Several neighborhood selection methods have been developed in the literature depending on the goal (e.g., estimation, inference, falsification, graphical presentation), the underlying assumptions invoked (e.g., parametric specification, continuity/nonparametric specification, local randomization), the parameter of interest (e.g., sharp, fuzzy, kink), and even the specific design (e.g., single-cutoff, multi-cutoff, geographic). We offer a comprehensive discussion of both deprecated and modern neighborhood selection approaches available in the literature, following their historical as well as methodological evolution over the last decades. We focus on the prototypical case of a continuously distributed running variable for the most part, though we also discuss the discrete-valued case towards the end of the discussion. The bulk of the presentation focuses on neighborhood selection for estimation and inference, outlining different methods and approaches according to, roughly speaking, the size of a typical selected neighborhood in each case, going from the largest to smallest neighborhood. Figure 1 provides a heuristic summary, which we c 2016 Matias D. Cattaneo and Gonzalo Vazquez-Bare. Choice of Neighborhood in RD Designs Figure 1: Choice of neighborhood (single-cutoff sharp RD) discuss in detail throughout this article. This ordering among neighborhood selectors is not strict, but it does reflect typical empirical results and may hold under reasonable assumptions and conditions. Furthermore, this ordering follows roughly the historical evolution in the empirical and methodological RD literatures. To complement the discussion, we also reflect briefly on neighborhood selection for several falsification and validation approaches that have recently been proposed in the RD literature. Our main methodological discussion and recommendations apply not only to the most standard single-cutoff sharp RD design but also more generally to many other RD settings such as fuzzy RD designs (e.g., Hahn et al., 2001), kink RD designs (e.g., Card et al., 2015, 2017), geographic RD designs (e.g., Keele and Titiunik, 2015; Keele et al., 2017), multi-cutoff RD designs (e.g., Cattaneo et al., 2016b), derivative estimation and stability testing (e.g., Dong and Lewbel, 2015; Cerulli et al., 2017), distributional treatment effects (e.g., Shen and Zhang, 2016), and density discontinuity designs (e.g., Jales and Yu, 2017). Adapting the main discussion to these other RD settings is not difficult because our main methodological points are conceptual, and hence not directly tied to any specific RD setup (i.e., only the underlying technicalities or specific features of the problem considered would change, not the general message). The last section summarizes the implications of our methodological points in the form of...


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pp. 134-146
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