In statistics, econometrics, political science, epidemiology, and related disciplines, a regression discontinuity design (RDD) is a quasi-experimental pretest–posttest design that aims to determine the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned.

The standard RD model is a subset of this broader model, which assumes no always-assigned units. Identifying assumption: manipulation occurs through one-sided selection. The approach does not make a binary decision on manipulation in RD designs but assesses its extent and worst-case impact.

13.2 Basic idea of RDD. The basic idea of regression discontinuity RDD is the following: Observations (e.g. firm, individual, etc.) are “treated” based on a known cutoff rule. The cutoff is what creates the discontinuity. Researcher is interested in how this treatment affects outcome variable of interest, \(y\). Examples of RDD settings

The key feature of RDD is that there is a continuous variable Xi that determines who gets treatment, denoted by Di (1 if treated). By convention X is called the running variable, the assignment variable or the forcing variable In sharp RDD, a unit is treated if …

在 RD 中，每个个体拥有一个得分 (或称为驱动变量 running variable, 或指标 index)，并且处理取决于得分是否高于断点。 引入一些符号，假设有 n 个个体，使用 i=1,2,3, \cdots, n 标注，每个个体的得分表示为 X_ {i}, c 是一个已知的断点。 当 X_ {i} \geq c 时, 个体接受处理，否则不接受处理。 处理状态可以表示为 T_ {i}=\mathbb {I}\left (X_ {i} \geq c\right), 该形式为示性函数。因此, 知道 个体得分，就知道个体处理状态，即处理的概率是得分的函数。 但是满足处理条件并不意味着 …

A regression discontinuity design (RDD, for short) arises when the selection of a unit into a treatment group depends on a covariate score that creates some discontinuity in the probability of receiving the treatment. In this lecture we will consider both “sharp” and “fuzzy” RDDs.

Regression discontinuity design (RDD) is another quasi-experimental technique. Unlike natural experiments, assignment to treatment and control groups in a RDD is not random. Instead, RDD takes advantage of a known cut-off or threshold determining treatment assignment or the probability of receiving treatment.

• Regression discontinuity design (RDD): Compare shareholder proposals that pass or fail by small margin of votes. • Identifying assumption of the RDD: Around majority threshold, outcome of vote is as good as random. • Two standard tests of this assumption (akin to tests of randomization in randomized experiments):

Let’s estimate an RDD model using the data from a 2009 paper by Carpenter and Dobkin about the effect of increasing the drinking age on mortality rates. Carpenter, Christopher and Carlos Dobkin. “The Effects of Alcohol Consumption on Mortality: Regression Discontinuity from the Minimum Drinking Age,” American Economic Journal: Applied ...

RDestimate supports both sharp and fuzzy RDD utilizing the AER package for 2SLS regression under the fuzzy design. Local linear regressions are performed to either side of the cutpoint using