Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design

研究问题: 断点附近有效样本很少时，如何检验基线协变量的整个分布在阈值处连续，从而为断点回归设计的可信性提供诊断？
方法与思路: 作者基于诱导次序统计量提出置换检验，令局部观测数 $q$ 在 $n\to \infty$ 时固定，以渐近框架逼近阈值附近的小样本现象。作者基于诱导次序统计量提出置换检验，令局部观测数$q$在$n\to \infty$时固定，以渐近框架逼近阈值附近的小样本现象。
材料陈述的贡献: 摘要称，检验在较弱条件下渐近有效、更强条件下有限样本有效，相对均值检验具有良好功效，并提供模拟和选举应用。
阅读关注点: 应核对固定 $q$ 框架中局部观测的选取、渐近与有限样本有效性的不同条件，以及分布检验相对均值检验的功效比较范围。应核对固定$q$框架中局部观测的选取、渐近与有限样本有效性的不同条件，以及分布检验相对均值检验的功效比较范围。
阅读边界: 摘要未列明两类有效性条件或模拟设定；协变量连续性检验是设计诊断，不能单凭不拒绝原假设就确认断点因果识别成立。

GPT-6.1 Sol · 高 · 2026-10-15

原文摘要

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing whether the means of baseline covariates do not change at the cut-off (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cut-off. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cut-off; and introduce a novel asymptotic framework to analyse its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number $n$ of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as $n\to \infty$ , our framework keeps the number $q$ of observations local to the cut-off fixed as $n\to \infty$ . The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favourable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing whether the means of baseline covariates do not change at the cut-off (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cut-off. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cut-off; and introduce a novel asymptotic framework to analyse its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number $n$ of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as $n\to \infty$, our framework keeps the number $q$ of observations local to the cut-off fixed as $n\to \infty$. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favourable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

摘要来源：RePEc · 出版社摘要

笔记与分组

分类依据与纠错

Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design

代码、数据与补充材料

断点回归中的近似置换检验与诱导次序统计量

原文摘要

同方向的基础文献

同方向的基础文献