Donut Regression Discontinuity Designs
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Donut regression discontinuity (RD) designs exclude observations in a neighborhood around the cutoff. They are widely used in empirical work to address concerns about manipulation, sorting, or measurement error in the running variable. Despite their popularity, donut RD estimators are typically implemented heuristically, with limited formal guidance and unclear implications for bias, variance, and statistical inference. This paper provides a theoretical analysis of donut RD designs within the local linear estimation framework. We derive new results for point estimation, inference, and specification testing in donut RD designs. We show that donut trimming affects the bias and variance of the estimator and thus introduces substantial additional uncertainty relative to conventional RD estimators. We further show that recently developed bias-aware confidence intervals accurately account for this additional uncertainty without requiring modifications. Finally, we formalize specification tests based on comparing conventional and donut RD estimators to allow for valid statistical inference. The results are illustrated with two empirical applications.
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非参数回归的稳健经验似然及其断点回归应用
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动态阈值设计中的非参数因果推断
We consider causal inference in dynamic settings where treatment is assigned by thresholding a state variable that can change over time. There is a large literature on regression-discontinuity methods building on the fact that, in the static setting, treatment assignment via threshold crossing induces a quasi-experimental design that enables pragmatic causal inference. But dynamic settings involve challenges not present in the static setting, e.g., past treatments may affect…
模糊断点回归的一类广义有限矩估计量
The standard fuzzy regression discontinuity (FRD) estimator is a ratio of differences of local polynomial estimators. I show that this estimator does not possess any finite integer moments, regardless of local polynomial degree, kernel function, or bandwidth. The estimator is heavy-tailed in small samples or when the treatment probability discontinuity at the cutoff is small. I present a generalized class of FRD estimators which preserves all finite moments from the data,…
聚类数据下回归不连续设计的推断
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and derive high-level conditions under which the standard local linear RD estimator is asymptotically normal. We verify that our high-level assumptions hold across a wide range of empirical designs, including settings of growing cluster sizes. We…