Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models
证明在回归不连续设计中，处理效应关于运行变量的导数（TED）可非参数识别，并在局部政策不变假设下等于阈值边际变化带来的处理效应变化（MTTE），有助于检验外部有效性和外推LATE。
Regression discontinuity models are commonly used to nonparametrically identify and estimate a local average treatment effect (LATE).We show that the derivative of the treatment effect with respect to the running variable at the cutoff, referred to as the treatment effect derivative (TED), is nonparametrically identified, easily estimated, and has implications for testing external validity and extrapolating the estimated LATE away from the cutoff. Given a local policy invariance assumption, we further show this TED equals the change in the treatment effect that would result from a marginal change in the threshold, which we call the marginal threshold treatment effect (MTTE). We apply these results to Goodman (2008), who estimates the effect of a scholarship program on college choice. MTTE in this case identifies how this treatment effect would change if the test score threshold to qualify for a scholarship were changed, even though no such change in threshold is actually observed.