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断点回归:精确与模糊断点、回归折点设计。
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Covariate Adjustment in Regression Discontinuity Designs

断点回归设计中的协变量调整

The Regression Discontinuity (RD) design is a widely used non-experimental method for causal inference and program evaluation. While its canonical formulation only requires a score and an outcome variable, it is common in empirical work to encounter RD analyses where additional variables are used for adjustment. This practice has led to misconceptions about the role of covariate adjustment in RD analysis, from both methodological and empirical perspectives. In this chapter,…

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Regression discontinuity design in perinatal epidemiology and birth cohort research

围产期流行病学与出生队列研究中的断点回归设计

Regression discontinuity design (RDD) is a quasi-experimental approach to study the causal effects of an intervention/treatment on later health outcomes. It exploits a continuously measured assignment variable with a clearly defined cut-off above or below which the population is at least partially assigned to the intervention/treatment. We describe the RDD and outline the applications of RDD in the context of perinatal epidemiology and birth cohort research. There is an…

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Nonlinear and Nonseparable Structural Functions in Fuzzy Regression Discontinuity Designs

模糊断点回归中的非线性与非可分结构函数

Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be…

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Causal Estimation of Position Bias in Recommender Systems Using Marketplace Instruments

利用平台工具变量因果估计推荐系统的位置偏差

Information retrieval systems, such as online marketplaces, news feeds, and search engines, are ubiquitous in today's digital society. They facilitate information discovery by ranking retrieved items on predicted relevance, i.e. likelihood of interaction (click, share) between users and items. Typically modeled using past interactions, such rankings have a major drawback: interaction depends on the attention items receive. A highly-relevant item placed outside a user's…

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Inference in Regression Discontinuity Designs with High-Dimensional Covariates

具有高维协变量的断点回归设计推断

We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator which first selects a small number of "important" covariates through a localized Lasso-type procedure, and then, in a second step, estimates the treatment effect by including the selected covariates linearly into the usual local linear…

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Hierarchical Gaussian Process Models for Regression Discontinuity/Kink under Sharp and Fuzzy Designs

清晰与模糊断点及折点设计中的层级高斯过程模型

We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) under sharp and fuzzy designs. Our estimators are based on Gaussian Process (GP) regression and classification. The GP methods are powerful probabilistic machine learning approaches that are advantageous in terms of derivative estimation and uncertainty quantification, facilitating RK estimation and inference of RD/RK models. These estimators are extended to…

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Regression Discontinuity Designs

断点回归设计

The Regression Discontinuity (RD) design is one of the most widely used non-experimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and matured, and there is now a large number of methodological results for RD identification, estimation, inference, and validation. We offer a curated review of this methodological literature organized around the two most popular frameworks…

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Optimized Inference in Regression Kink Designs

回归折点设计中的优化推断

We propose a method to remedy finite sample coverage problems and improve upon the efficiency of commonly employed procedures for the construction of nonparametric confidence intervals in regression kink designs. The proposed interval is centered at the half-length optimal, numerically obtained linear minimax estimator over distributions with Lipschitz constrained conditional mean function. Its construction ensures excellent finite sample coverage and length properties which…

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Nonparametric Estimation of Truncated Conditional Expectation Functions

截断条件期望函数的非参数估计

Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk management, and impact evaluation. They typically involve truncating the outcome variable above or below certain quantiles of its conditional distribution. In this paper, based on local linear methods, a novel, two-stage, nonparametric estimator of such functions is proposed. In this estimation problem, the…

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Linear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs

形状约束下非参数推断的线性规划方法:回归折点设计应用

We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a usage of our proposed method with an application to the regression kink design (RKD). Econometric analyses based on the RKD often suffer from wide confidence intervals due to slow convergence rates of nonparametric derivative estimators. We…

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Regression Discontinuity Design with Many Thresholds

具有多个阈值的断点回归设计

Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs, computed over general counterfactual distributions of individuals,…

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The Regression Discontinuity Design

断点回归设计

This handbook chapter gives an introduction to the sharp regression discontinuity design, covering identification, estimation, inference, and falsification methods.

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Analysis of Regression Discontinuity Designs with Multiple Cutoffs or Multiple Scores

多阈值或多评分变量断点回归设计的分析

We introduce the \texttt{Stata} (and \texttt{R}) package \texttt{rdmulti}, which includes three commands (\texttt{rdmc}, \texttt{rdmcplot}, \texttt{rdms}) for analyzing Regression Discontinuity (RD) designs with multiple cutoffs or multiple scores. The command \texttt{rdmc} applies to non-cumulative and cumulative multi-cutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects, and provides robust bias-corrected inference procedures. Post estimation…

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Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

多阈值断点回归设计中的处理效应外推

In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach…

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Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs

断点回归中稳健偏差修正推断的最优带宽选择

Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show they yield suboptimal confidence intervals in terms of coverage error. We establish…

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A Practical Introduction to Regression Discontinuity Designs: Foundations

断点回归设计实用导论:基础

In this Element and its accompanying Element, Matias D. Cattaneo, Nicolas Idrobo, and Rocio Titiunik provide an accessible and practical guide for the analysis and interpretation of Regression Discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. In this Element, the authors discuss the foundations of the canonical Sharp RD design, which has the following features: (i) the score is…

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Simple Local Polynomial Density Estimators

简便的局部多项式密度估计量

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel…

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Regression Discontinuity Designs Using Covariates

使用协变量的回归不连续设计

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements.…

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Optimized Regression Discontinuity Designs

优化回归不连续设计

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models on both sides of a treatment assignment boundary and then reporting plug-in estimates for the effect of interest. In applications, however, it is often difficult to tune the non-parametric regressions in a way that is well calibrated for…

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The State of Applied Econometrics - Causality and Policy Evaluation

应用计量经济学现状:因果关系与政策评估

In this paper we discuss recent developments in econometrics that we view as important for empirical researchers working on policy evaluation questions. We focus on three main areas, where in each case we highlight recommendations for applied work. First, we discuss new research on identification strategies in program evaluation, with particular focus on synthetic control methods, regression discontinuity, external validity, and the causal interpretation of regression…

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