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Attention Overload

注意力过载

We introduce an Attention Overload Model (AOM) in which alternatives compete for attention, so each alternative's consideration probability weakly decreases as the choice problem expands. This nonparametric restriction has a search-capacity foundation. We identify exactly which preference rankings are compatible with observed choices and establish sharp bounds on latent attention. We then consider heterogeneous preferences in settings where alternatives are presented in a…

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Nonlinear Binscatter Methods

非线性分箱散点图方法

Binscatters are a powerful tool for empirical work in the social, behavioral, and biomedical sciences. Available tools rely on least squares estimation of the conditional mean. We introduce novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation, covering generalized linear, robust, and quantile regression models. We provide theoretical results and practical tools, including optimal bin selection, confidence bands, and statistical tests regarding…

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Uniform Estimation and Inference for Nonparametric Partitioning-Based M-Estimators

非参数分割型 M 估计的一致估计与统一推断

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions; (ii) rate-optimal uniform Bahadur representations; (iii) rate-optimal uniform (and mean square) convergence rates; (iv) valid strong approximations and feasible uniform inference methods; and (v) extensions to functional transformations of…

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Accuracy Limits of Causal Trees for Individualized Treatment Effects

因果树估计个体化处理效应的精度极限

Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning, with splitting criteria designed to identify variation in treatment effects across covariate-defined subgroups. We study causal tree estimators based on adaptive recursive partitioning and establish lower bounds on their estimation accuracy. The class we analyze…

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rd2d: Causal Inference in Boundary Discontinuity Designs

rd2d:边界断点设计中的因果推断软件

Boundary Discontinuity (BD) designs are used in empirical research to learn about causal treatment effects along a continuous assignment boundary defined by a bivariate score. These designs are also known as multi-score regression discontinuity (RD) designs, and include geographic RD designs as a prominent example. This article introduces \pkg{rd2d}, a statistical software package for \proglang{R}, \proglang{Python}, and \proglang{Stata} that implements local polynomial…

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Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods

边界不连续设计中的估计与推断:基于距离的方法

We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We establish identification, estimation, and inference results both pointwise and uniformly along the treatment assignment boundary. We show that the geometric regularity of the boundary, a one-dimensional manifold, plays a central role in…

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Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods

边界断点设计的估计与推断:基于位置的方法

Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well…

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Randomization Inference for Before-and-After Studies with Multiple Units: An Application to a Criminal Procedure Reform in Uruguay

多单位前后比较研究的随机化推断:乌拉圭刑事程序改革应用

Learning about the immediate causal effects of large-scale policy interventions poses a significant challenge for quasi-experimental methods that rely on long-term trends or parametric modeling assumptions. As an alternative, we develop a randomization inference framework for before-and-after studies with multiple units, designed specifically for short-term causal inference and allowing for general assignment mechanisms. The method provides finite-sample-valid statistical…

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The Regression Discontinuity Design in Medical Science

医学研究中的回归不连续设计

This article provides an introduction to the Regression Discontinuity (RD) design, and its application to empirical research in the medical sciences. While the main focus of this article is on causal interpretation, key concepts of estimation and inference are also briefly mentioned. A running medical empirical example is provided.

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Leveraging Covariates in Regression Discontinuity Designs

在回归不连续设计中有效利用协变量

It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis and conclusions. Typically implemented via local least squares regressions, covariate adjustment can serve three main distinct purposes: (i) improving the efficiency of RD average causal effect estimators, (ii) learning about heterogeneous…

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Treatment Effect Heterogeneity in Regression Discontinuity Designs

断点回归设计中的处理效应异质性

Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates, even though no formal statistical methods exist for such analyses. This has led to the widespread use of ad hoc approaches in applications. Motivated by common empirical practice, we develop a unified, theoretically grounded framework for RD heterogeneity analysis. We show that a fully interacted local linear (in functional parameters)…

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rdhte: Conditional Average Treatment Effects in RD Designs

rdhte:断点回归设计中的条件平均处理效应

Understanding causal heterogeneous treatment effects based on pretreatment covariates is a crucial aspect of empirical work. Building on Calonico, Cattaneo, Farrell, Palomba, and Titiunik (2025), this article discusses the software package rdhte for estimation and inference of heterogeneous treatment effects in sharp regression discontinuity (RD) designs. The package includes three main commands: rdhte conducts estimation and robust bias-corrected inference for heterogeneous…

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Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference

处理分配存在干扰时直接平均处理效应的稳健推断

This paper develops methods for uncertainty quantification in causal inference settings with random network interference. We study the large-sample distributional properties of the classical difference-in-means Hajek treatment effect estimator, and propose a robust inference procedure for the (conditional) direct average treatment effect. Our framework allows for cross-unit interference in both the outcome equation and the treatment assignment mechanism. Drawing from…

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lpcde: Estimation and Inference for Local Polynomial Conditional Density Estimators

lpcde:局部多项式条件密度估计与推断

This paper discusses the R package lpcde, which stands for local polynomial conditional density estimation. It implements the kernel-based local polynomial smoothing methods introduced in Cattaneo, Chandak, Jansson, Ma (2024) for statistical estimation and inference of conditional distributions, densities, and derivatives thereof. The package offers mean square error optimal bandwidth selection and associated point estimators, as well as uncertainty quantification based on…

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Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

错位处理采用下合成控制的不确定性量化

We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly…

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Binscatter Regressions

分箱散点回归与 Binsreg 软件包

We introduce the package Binsreg, which implements the binscatter methods developed by Cattaneo, Crump, Farrell, and Feng (2024b,a). The package includes seven commands: binsreg, binslogit, binsprobit, binsqreg, binstest, binspwc, and binsregselect. The first four commands implement binscatter plotting, point estimation, and uncertainty quantification (confidence intervals and confidence bands) for least squares linear binscatter regression (binsreg) and for nonlinear…

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A Practical Introduction to Regression Discontinuity Designs: Extensions

断点回归设计实用导论:扩展篇

This monograph, together with its accompanying first part Cattaneo, Idrobo and Titiunik (2020), collects and expands the instructional materials we prepared for more than $50$ short courses and workshops on Regression Discontinuity (RD) methodology that we taught between 2014 and 2023. In this second monograph, we discuss several topics in RD methodology that build on and extend the analysis of RD designs introduced in Cattaneo, Idrobo and Titiunik (2020). Our first goal is…

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Protocols for Observational Studies: An Application to Regression Discontinuity Designs

观察性研究方案:回归不连续设计的应用

In his 2022 IMS Medallion Lecture delivered at the Joint Statistical Meetings, Prof. Dylan S. Small eloquently advocated for the use of protocols in observational studies. We discuss his proposal and, inspired by his ideas, we develop a protocol for the regression discontinuity design.

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On Rosenbaum's Rank-based Matching Estimator

论 Rosenbaum 基于秩的匹配估计量

In two influential contributions, Rosenbaum (2005, 2020) advocated for using the distances between component-wise ranks, instead of the original data values, to measure covariate similarity when constructing matching estimators of average treatment effects. While the intuitive benefits of using covariate ranks for matching estimation are apparent, there is no theoretical understanding of such procedures in the literature. We fill this gap by demonstrating that Rosenbaum's…

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Uniform Inference for Kernel Density Estimators with Dyadic Data

成对关系数据核密度估计的一致推断

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of uniformly estimating a dyadic Lebesgue density function, focusing on nonparametric kernel-based estimators taking the form of dyadic empirical processes. Our main contributions include the minimax-optimal uniform convergence rate of the dyadic…

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Context-Dependent Heterogeneous Preferences: A Comment on Barseghyan and Molinari (2023)

依赖情境的异质性偏好:对 Barseghyan 与 Molinari(2023)的评论

Barseghyan and Molinari (2023) give sufficient conditions for semi-nonparametric point identification of parameters of interest in a mixture model of decision-making under risk, allowing for unobserved heterogeneity in utility functions and limited consideration. A key assumption in the model is that the heterogeneity of risk preferences is unobservable but context-independent. In this comment, we build on their insights and present identification results in a setting where…

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A Guide to Regression Discontinuity Designs in Medical Applications

医学应用中的回归不连续设计指南

We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity-based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias-corrected…

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scpi: Uncertainty Quantification for Synthetic Control Methods

scpi:合成控制方法的不确定性量化

The synthetic control method offers a way to quantify the effect of an intervention using weighted averages of untreated units to approximate the counterfactual outcome that the treated unit(s) would have experienced in the absence of the intervention. This method is useful for program evaluation and causal inference in observational studies. We introduce the software package scpi for prediction and inference using synthetic controls, implemented in Python, R, and Stata. For…

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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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