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Two Margins in Difference-in-Differences with a Continuous Treatment

连续处理双重差分中的水平与响应两种边际

This paper studies difference-in-differences with staggered adoption and a continuous, time-invariant dose. Each cohort-time comparison contains two margins. The level margin is the average treatment effect at realized doses. Under level parallel trends it equals the level contrast between the treated cohort and not-yet-treated controls. The response margin is the within-cohort slope of the outcome change on dose. It uses no controls, and its causal interpretation requires a…

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Identification and Inference with Machine-Learned Instruments

机器学习工具变量下的识别与推断

Instrumental-variables estimation increasingly pools many or high-dimensional instruments into a single machine-learned first stage, with rich controls partialled out. The resulting estimand, the partialled-out IV coefficient built from any signal of the instruments, is a signal-weighted average of the heterogeneous effects, which gives an opaque first stage a precise structural meaning. The average is convex whenever a covariance-monotonicity condition holds, and we provide…

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Identification and Estimation of Optimal Continuous Treatment Effects

最优连续处理效应的识别与估计

Estimating continuous treatment effects is hard because average-derivative estimators rely on an ill-posed conditional-density score. Recent work makes a bounded outcome weight the primitive, characterizing a class of weighted average derivative effects without density estimation. In this paper, we develop the identification and estimation theory for the optimally efficient estimands of this class under homoskedasticity and heteroskedasticity. On identification, we show that…

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A Variance-Based Test for Heterogeneous Treatment Effects

基于方差的治疗效应异质性检验

This paper proposes a robust nonparametric hypothesis test for the existence of heterogeneous treatment effects. We focus on the variance of the Conditional Average Treatment Effect (CATE) as a natural omnibus parameter, where a non-zero variance implies the presence of relevant heterogeneity. Standard inference for this parameter faces a fundamental theoretical challenge. On one hand, evaluating variance components on the same sample leads to null degeneracy, where the…

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Sensitivity, Informativeness, and Misspecification in GMM Estimation

GMM 估计中的敏感性、信息含量与模型误设

This paper develops misspecification-robust sensitivity and informativeness diagnostics for GMM estimators, evaluated at pseudo-true values. The sensitivity matrix nests that of Andrews, Gentzkow, and Shapiro (2017) under correct specification. The informativeness $Δ$ measures the share of an estimator's asymptotic variance explained by sampling variation in the moments, a notion of structural efficiency that equals one under correct specification and can fall below one…

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