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

Abstract

Regression discontinuity (RD) designs are commonly used for program evaluation with continuous treatment assignment variables. But in practice, treatment assignment is frequently based on ordinal variables. In this study, we propose an RD design with an ordinal running variable to assess the effects of extended time accommodations (ETA) for English-language learners (ELLs). 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 (ATE), intent-to-treat effect, and the local ATE 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 remaining confounding.

Fuzzy Regression Discontinuity Designs with Multiple Control Groups Under One-Sided Noncompliance: Evaluating Extended Time Accommodations

“…These variables partially explained why some eligible students did not use ETA. Following Suk et al (2022), we mapped the ordinal ELL English categories onto their ranks, assuming that the performance differences between consecutive categories were approximately equidistant. For a complete list of variables used in this study, see Appendix G.…”

“…For example, in our empirical data, ELL English proficiency is indeed discretized into six categories, ranging from the No Proficiency level to the Never ELL level. To identify and estimate the LATE at the cutoff in fuzzy RD designs with a discrete running variable, parametric modeling assumptions on the outcome and treatment are required instead of the continuity assumption (Lee & Card, 2008;Suk et al, 2022). For more details on causal identification and estimation on fuzzy RD designs with a discrete running variable, see Appendix A.…”

Regression Discontinuity Designs in Education: A Practitioner's Guide

“…Setting Angrist and Rokkanen (2015) Selective public schools Bergolo and Galván (2018) Cash transfer programs Brunner et al (2023) Selective public schools Carlson and Knowles (2016) English language learner reclassification Coyne et al (2018) Reading programs Figlio et al (2018) Literacy programs Figlio and Özek (2023) Test-based remediation Heissel and Ladd (2018) School turnaround programs M. G. Lee and Soland (2022) English language learner reclassification McEachin et al (2020) Algebra courses Melguizo et al (2015) Subsidized loan programs Nomi and Raudenbush (2016) Algebra courses Schwerdt et al (2017) Test-based retention Suk et al (2022) Testing accommodations…”

“…. , F , as illustrated in Figure 3b) and English proficiency levels of English language learners (Suk et al, 2022), bond ratings (Li et al, 2021), and inmate classification scores (Hjalmarsson, 2009). Using an ordinal running variable presents challenges due to the lack of a meaningful scale of distance.…”

“…notably discussed inSuk et al (2022) andLi et al (2021) Suk et al (2022). employ a scale function to map the ordinal running variable onto a numeric scale and incorporate parametric modeling assumptions on the outcome (and treatment) for causal identification in RD settings.…”