Explanations of the internal validity of regression discontinuity designs (RDD) generally appeal to the idea that RDDs are ``as good as" random near the treatment cut point. Cattaneo, Frandsen, and Titiunik (2015) are the first to take this justification to its full conclusion and propose estimating the RDD local average treatment effect (LATE) the same as one would a randomized experiment. This paper explores the implications of analyzing an RDD as a local random experiment when the running variable is a test score. I derive a formula for the bias in the LATE estimate estimated using the local randomization method, $a\rho\Delta$. Where $a$ is the relationship between latent proficiency and the potential outcome absent treatment, $\rho$ is the test reliability, and $\Delta$ is the distance between the treatment and control running variable value. I use this quantification of the bias to demonstrate that local randomization and related design based methods for estimating RDDs are problematic when the running variable is test score or other human developed measure (e.g., medical tests).
翻译:回归不连续设计(RDD) 的内部有效性解释通常对RDD在治疗切切点附近“与随机性一样”的“好”概念有吸引力。 Cattaneo, Frandsen和Titiunik(2015年)是第一个提出充分结论的理由,并提议估算RDD当地平均治疗效果(LATE)与随机实验一样。本文探讨了在运行变量为测试分时将RDD分析为局部随机实验的影响。我为LATE估计的偏差得出了一个公式,使用本地随机化方法估算,即$a\rho\Delta$。$a$是潜在熟练程度与没有治疗的潜在结果之间的关系,美元是测试可靠性,$\rho$是治疗和控制运行可变值之间的距离。我用这种偏差量化方法来证明,当运行变量为测试分或其他人类开发措施(例如,医学测试)时,用于估算RDDDDD的本地随机化和相关设计方法有问题。