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度量统计视角下的随机集AI 解读

Since the seminal work by Beresteanu and Molinari(2008), the random set theory and related inference methods have been widely applied in partially identified econometric models. Meanwhile, there is an emerging field in statistics for studying random objects in metric spaces, called metric statistics. This paper clarifies a relationship between two fundamental concepts in these literatures, the Aumann and Fréchet means, and presents some applications of metric statistics to…

随机阈值设计中的政策评估：对回归不连续设计的警示AI 解读

Many policies assign treatment according to whether a score crosses a cutoff. Regression discontinuity (RD) designs identify the effect of treatment assignment, but the threshold policy itself may also reshape individuals' incentives, inducing behavioral responses that affect outcomes even holding treatment status fixed---a channel that conventional RD designs cannot capture. We develop a framework that exploits randomized variation in policy thresholds, together with…

断点回归设计中外推治疗效应的界AI 解读

External validity is a central concern in regression discontinuity (RD) designs. To assess treatment effect heterogeneity and the representativeness of the conventional RD estimand, this paper studies the identifying content of monotonicity and smoothness restrictions for treatment effects away from the cutoff in both canonical and multi-cutoff RD designs. In the canonical design, monotonicity in the running variable alone has limited identifying power and generally yields…

随机对象的单调处理反应与部分识别AI 解读

Monotone treatment response (MTR), monotone treatment selection (MTS), and monotone instrumental variable (MIV) assumptions are widely used to partially identify counterfactual mean outcomes, but existing analyses have focused almost exclusively on scalar outcomes. We develop a unified framework for partial identification with outcomes that take values in a general metric space under these monotonicity restrictions by embedding the metric space into an $L^2$ space and…

无限维部分识别参数的一致置信带AI 解读

Infinite-dimensional parameters are ubiquitous in empirical economics. This paper develops an Imbens--Manski--Stoye type confidence band for infinite-dimensional partially identified parameters. In particular, we propose multiplier bootstrap-based construction of a uniform confidence band. By employing approximation theorems for suprema of non-centered empirical processes indexed by possibly non-Donsker classes \citep{chernozhukov2016empirical}, we confirm the uniform…

断点回归效应及其外部有效性的联合推断AI 解读

The external validity of regression discontinuity designs is crucial for informing policy but is rarely examined in applied work. To advance empirical practice, we propose a joint inference procedure for the treatment effect and its local external validity, captured by the treatment effect derivative (TED), within a robust bias correction framework. We further introduce a locally linear treatment effects assumption, which extends the scope of the TED and enables…

随机对象的 Lee 界AI 解读

In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as compositional and distributional data. By exploiting a representation of the Fréchet mean of the potential outcome via embedding in an Euclidean or Hilbert space, we present a feasible characterization of the identified set of the causal…

边界处局部多项式密度估计的核函数选择AI 解读

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and empirical evidence indicate that the popular triangular kernel delivers large mean squared error, wide confidence intervals, and limited power for detecting discontinuities. Moreover, small-sample variance can explode because the…

区间数据下的双重差分AI 解读

Difference-in-differences (DID) is one of the most popular tools used to evaluate causal effects of policy interventions. This paper extends the DID methodology to accommodate interval outcomes, which are often encountered in empirical studies using survey or administrative data. We point out that a naive application or extension of the conventional parallel trends assumption may yield uninformative or counterintuitive results, and present a suitable identification strategy,…

增强 Lee 界的稳健性并收紧区间：随机单调性与对称性下的样本选择模型AI 解读

In the presence of sample selection, Lee's (2009) nonparametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, whose empirical validity is sometimes unclear. Furthermore, the bounds are often regarded to be wide and less informative even under monotonicity. To address these issues, this study introduces a stochastic version of the monotonicity assumption alongside a nonparametric distributional shape…