Abstract
Although Cattaneo et al. (2019) provided a data-driven framework for power computations for Regression Discontinuity Designs in line with rdrobust Stata and R commands, which allows higher-order functional forms for the score variable when using the non-parametric local polynomial estimation, analogous advancements in their parametric estimation have been lagging. This study extends power formulas for Cluster-level Regression Discontinuity (CRD) designs beyond the linear form specification proposed by Schochet (2009). Results reveal that, with symmetric truncation intervals and symmetric distributions, a linear form, linear form with interactions, or quadratic form all require the same sample size. However, quadratic form with interactions requires larger sample sizes to reach the same level of precision as the other functional forms. In comparison, with asymmetric truncation intervals or asymmetric distributions, even a slight change in the functional form can alter sample size requirements. CRD design effects are usually inflated when interactions are introduced, but they hardly vary as a function of treatment group sampling rate, especially with the truncated normal or uniform distributions. Formulas and the extended empirical framework are implemented in the cosa R package and the companion web application.
Published Version
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