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Omitted Variable Bias in Difference-in-Differences Designs

双重差分设计中的遗漏变量偏误

We study the omitted variable bias (OVB) problem in canonical difference-in-differences (DiD) designs when unobserved confounding induces departures from the parallel trends assumption. Our results provide a novel characterization of the OVB formula for the average treatment effect on the treated (ATT), which is of independent interest. We show how the ATT bias is mainly governed by the strength of confounding in the treatment assignment mechanism and provide alternative…

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Selection and parallel trends

处理选择与平行趋势

We study the role of selection into treatment in difference-in-differences (DiD) designs. We derive necessary and sufficient conditions for parallel trends assumptions under general classes of selection mechanisms. These conditions characterize the empirical content of parallel trends and clarify the trade-offs between assumptions about selection into treatment and restrictions on the time series properties of the potential outcomes required for DiD methods. We use the…

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Was Javert right to be suspicious? Marginal Treatment Effects with Duration Outcomes

冉阿让的警探有理由怀疑吗?持续时间结果的边际处理效应

We identify the distributional and quantile marginal treatment effect functions when the outcome is right-censored. Our method requires a conditionally exogenous instrument and random censoring. We propose asymptotically consistent semi-parametric estimators and valid inferential procedures for the target functions. To illustrate, we evaluate the effect of alternative sentences (fines and community service vs. no punishment) on recidivism in Brazil. Our results highlight…

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Doubly Robust Estimators with Weak Overlap

弱重叠条件下的双重稳健估计量

Doubly robust (DR) estimators guard against model misspecification but remain sensitive to weak covariate overlap. We show that trimming propensity scores reduces variance but eliminates double robustness. We introduce DR estimators that retain double robustness after trimming through bias correction, preserving the original causal targets across unconfoundedness, instrumental variables, and difference-in-differences designs. In four applications, the proposed estimator…

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Difference-in-Differences with a Continuous Treatment

连续处理下的双重差分

This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment-on-the-treated-type parameters are identified under a parallel trends assumption analogous to the binary treatment case. However, comparing these parameters across treatments is challenging because parallel trends does not rule out selection bias. We discuss alternative, typically stronger, assumptions that eliminate selection bias. We further show that popular two-way…

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Beyond Parallel Trends: An Identification-Strategy-Robust Approach to Causal Inference with Panel Data

超越平行趋势:面板因果推断的识别策略稳健方法

In this paper, we propose a new approach to causal inference with panel data. Instead of using panel data to adjust for differences in the distribution of unobserved heterogeneity between the treated and comparison groups, we instead use panel data to search for "close comparison groups" -- groups that are similar to the treated group in terms of pre-treatment outcomes. Then, we compare the outcomes of the treated group to the outcomes of these close comparison groups in…

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Difference-in-Differences with Compositional Changes

存在样本构成变化时的双重差分

This paper studies Difference-in-Differences (DiD) setups with repeated cross-sectional data and potential compositional changes across time periods. We begin our analysis by deriving the efficient influence function and the semiparametric efficiency bound for the average treatment effect on the treated (ATT). We introduce nonparametric estimators that attain the semiparametric efficiency bound under mild rate conditions on the estimators of the nuisance functions,…

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Better Understanding Triple Differences Estimators

更好地理解三重差分估计量

Triple Differences (DDD) designs are widely used in empirical work to relax parallel trends assumptions in Difference-in-Differences (DiD) settings. This paper highlights that common DDD implementations -- such as taking the difference between two DiDs or applying three-way fixed effects regressions -- are generally invalid when identification requires conditioning on covariates. In staggered adoption settings, the common DiD practice of pooling all not-yet-treated units as…

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Efficient Difference-in-Differences and Event Study Estimators

高效的双重差分与事件研究估计量

This paper investigates efficient Difference-in-Differences (DiD) and Event Study (ES) estimation using short panel data sets within the heterogeneous treatment effect framework, free from parametric functional form assumptions and allowing for variation in treatment timing. We provide an equivalent characterization of the DiD potential outcome model using sequential conditional moment restrictions on observables, which shows that the DiD identification assumptions typically…

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Difference-in-Differences Designs: A Practitioner's Guide

双重差分设计:实务指南

Difference-in-differences (DiD) is arguably the most popular quasi-experimental research design. Its canonical form, with two groups and two periods, is well-understood. However, empirical practices can be ad hoc when researchers go beyond that simple case. This article provides an organizing framework for discussing different types of DiD designs and their associated DiD estimators. It discusses covariates, weights, handling multiple periods, and staggered treatments. The…

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Efficient Estimation for Staggered Rollout Designs

交错实施设计中的高效估计

We study estimation of causal effects in staggered rollout designs, i.e. settings where there is staggered treatment adoption and the timing of treatment is as-good-as randomly assigned. We derive the most efficient estimator in a class of estimators that nests several popular generalized difference-in-differences methods. A feasible plug-in version of the efficient estimator is asymptotically unbiased with efficiency (weakly) dominating that of existing approaches. We…

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Specification tests for generalized propensity scores using double projections

利用双重投影检验广义倾向得分模型的设定

This paper proposes a new class of nonparametric tests for the correct specification of models based on conditional moment restrictions, paying particular attention to generalized propensity score models. The test procedure is based on two different projection arguments, leading to test statistics that are suitable to setups with many covariates, and are (asymptotically) invariant to the estimation method used to estimate the nuisance parameters. We show that our proposed…

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What's Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature

双重差分研究的新进展:近期计量文献综述

This paper synthesizes recent advances in the econometrics of difference-in-differences (DiD) and provides concrete recommendations for practitioners. We begin by articulating a simple set of ``canonical'' assumptions under which the econometrics of DiD are well-understood. We then argue that recent advances in DiD methods can be broadly classified as relaxing some components of the canonical DiD setup, with a focus on $(i)$ multiple periods and variation in treatment…

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When Is Parallel Trends Sensitive to Functional Form?

平行趋势何时对函数形式敏感?

This paper assesses when the validity of difference-in-differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger ``parallel trends''-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition for parallel trends to be insensitive to functional form is satisfied if and essentially only…

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Distribution Regression in Duration Analysis: an Application to Unemployment Spells

持续时间分析中的分布回归:失业历程应用

This article proposes inference procedures for distribution regression models in duration analysis using randomly right-censored data. This generalizes classical duration models by allowing situations where explanatory variables' marginal effects freely vary with duration time. The article discusses applications to testing uniform restrictions on the varying coefficients, inferences on average marginal effects, and others involving conditional distribution estimates. Finite…

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Difference-in-Differences with Multiple Time Periods

多时期双重差分

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create…

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The role of parallel trends in event study settings: An application to environmental economics

事件研究中平行趋势的作用:环境经济学应用

Difference-in-Differences (DID) research designs usually rely on variation of treatment timing such that, after making an appropriate parallel trends assumption, one can identify, estimate, and make inference about causal effects. In practice, however, different DID procedures rely on different parallel trends assumptions (PTA), and recover different causal parameters. In this paper, we focus on staggered DID (also referred as event-studies) and discuss the role played by…

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Doubly Robust Difference-in-Differences Estimators

双重稳健的双重差分估计量

This article proposes doubly robust estimators for the average treatment effect on the treated (ATT) in difference-in-differences (DID) research designs. In contrast to alternative DID estimators, the proposed estimators are consistent if either (but not necessarily both) a propensity score or outcome regression working models are correctly specified. We also derive the semiparametric efficiency bound for the ATT in DID designs when either panel or repeated cross-section…

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Covariate Distribution Balance via Propensity Scores

通过倾向得分实现协变量分布平衡

This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by making the underlying covariate distribution of different treatment groups as close to each other as possible. Our estimators are data-driven, do not rely on tuning parameters such as bandwidths, admit an asymptotic linear representation, and…

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Nonparametric Tests for Treatment Effect Heterogeneity with Duration Outcomes

持续时间结果下处理效应异质性的非参数检验

This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional…

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Specification Tests for the Propensity Score

倾向得分的设定检验

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the "curse of dimensionality" when the vector of covariates is high-dimensional, are…

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Program Evaluation with Right-Censored Data

右删失数据下的政策评估

In a unified framework, we provide estimators and confidence bands for a variety of treatment effects when the outcome of interest, typically a duration, is subjected to right censoring. Our methodology accommodates average, distributional, and quantile treatment effects under different identifying assumptions including unconfoundedness, local treatment effects, and nonlinear differences-in-differences. The proposed estimators are easy to implement, have close-form…

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