Minimum Detectable Effect Size Computations for Cluster-Level Regression Discontinuity: Quadratic Functional Form and Beyond
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Although Cattaneo, Titiunik, and Vazquez-Bare (2019) provides an ex-post data-driven framework for power computations in line with rdrobust Stata and R commands, which allows higher-order functional form of the score variable in non-parametric local polynomial estimation, ex-ante definitions for power computations are less clear and conventional definition of optimal design is not straightforward in cluster-level regression discontinuity (CRD) studies. This study extends power formulas proposed by Schochet (2008) assuming that the cluster-level score variable follows quadratic functional form. Results reveal that we need not be concerned with treatment by linear term interaction, and polynomial degree up to second order for symmetric truncation intervals. In comparison, every slight change in the functional form alters sample size requirements for asymmetric truncation intervals. Finally, an empirical framework beyond quadratic functional form is provided when the asymptotic variance of the treatment effect is untraceable. In this case, the CRD design effect is either computed from moments of the sample or approximate population moments via simulation. Formulas for quadratic functional form and the extended empirical framework are implemented in the cosa R package and companion Shiny web application.
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