Background/Context: Observational studies often employ regression discontinuity (RD) designs and multiple control-group designs to explore the causal quantities of interest. RD designs assess policy and program effectiveness by assigning subjects to treatment based on whether they exceed a pre-defined cutoff. RD designs are classified into two…

Background/Context: Some observational studies involve multiple layers of treatment selection, specifically in the context of the extended time accommodation (ETA) for English language learners (ELLs). In ETA settings, the first selection occurs due to the eligibility rule, where students whose ELL English proficiency is below a certain threshold…