Regression Discontinuity Designs With an Ordinal Running Variable: Evaluating the Effects of Extended Time Accommodations for English-Language Learners

Regression discontinuity designs are commonly used for program evaluation with continuous treatment assignment variables. But in practice, treatment assignment is frequently based on discrete or ordinal variables. In this study, we propose a regression discontinuity design with an ordinal running variable to assess the effects of extended time accommodations (ETA) for English language learners (ELL). ETA eligibility is determined by ordinal ELL English proficiency categories of National Assessment of Educational Progress data. We discuss the identification and estimation of the average treatment effect, intent-to-treat effect, and the local average treatment effect at the cutoff. We also propose a series of sensitivity analyses to probe the effect estimates' robustness to the choices of scaling functions and cutoff scores, and unmeasured confounding.