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Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…

Methodology · Statistics 2026-04-06 Jianan Zhu , Jeffrey Zhang , Zijian Guo , Siyu Heng

The difference-in-differences (DID) design is widely used in observational studies to estimate the causal effect of a treatment when repeated observations over time are available. Yet, almost all existing methods assume linearity in the…

Applications · Statistics 2020-09-29 Soichiro Yamauchi

State-level policy evaluations commonly employ a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. Motivated by applied state-level opioid policy…

Difference-in-differences is a popular method for observational health policy evaluation. It relies on a causal assumption that in the absence of intervention, treatment groups' outcomes would have evolved in parallel to those of comparison…

Methodology · Statistics 2026-02-09 Alyssa Bilinski , Laura A. Hatfield

Many policy evaluations involve vectors of category-specific quantities, either categorical outcomes (e.g., employment type, major choice) or compositional measures (e.g., GDP by sector, votes by party, electricity generation by source). In…

Econometrics · Economics 2026-02-19 Onil Boussim

We propose a Bayesian nonparametric (BNP) approach to causal inference using observational data consisting of outcome, treatment, and a set of confounders. The conditional distribution of the outcome given treatment and confounders is…

Methodology · Statistics 2025-12-01 Yongseok Hur , Joonhyuk Jung , Juhee Lee

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…

Econometrics · Economics 2025-12-10 Daisuke Kurisu , Yuta Okamoto , Taisuke Otsu

We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero…

Econometrics · Economics 2026-01-16 Michel F. C. Haddad , Martin Huber , José Eduardo Medina-Reyes , Lucas Z. Zhang

This paper considers identification and estimation of causal effect parameters from participating in a binary treatment in a difference in differences (DID) setup when the parallel trends assumption holds after conditioning on observed…

Econometrics · Economics 2024-06-25 Carolina Caetano , Brantly Callaway , Stroud Payne , Hugo Sant'Anna Rodrigues

In matched observational studies with continuous treatments, individuals with different treatment doses but the same or similar covariate values are paired for causal inference. While inexact covariate matching (i.e., covariate imbalance…

Methodology · Statistics 2025-02-13 Anthony Frazier , Siyu Heng , Wen Zhou

Difference-in-differences (DID) is popular because it can allow for unmeasured confounding when the key assumption of parallel trends holds. However, there exists little guidance on how to decide a priori whether this assumption is…

Methodology · Statistics 2025-05-07 Audrey Renson , Oliver Dukes , Zach Shahn

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…

Econometrics · Economics 2020-12-02 Brantly Callaway , Pedro H. C. Sant'Anna

Fairness studies of algorithmic decision-making systems often simplify complex decision processes, such as bail or loan approvals, into binary classification tasks. However, these approaches overlook that such decisions are not inherently…

Machine Learning · Computer Science 2025-11-13 Ayan Majumdar , Deborah D. Kanubala , Kavya Gupta , Isabel Valera

We provide a simple distribution regression estimator for treatment effects in the difference-in-differences (DiD) design. Our procedure is particularly useful when the treatment effect differs across the distribution of the outcome…

Econometrics · Economics 2026-05-20 Iván Fernández-Val , Jonas Meier , Aico van Vuuren , Francis Vella

Causal inference methods are widely applied in the fields of medicine, policy, and economics. Central to these applications is the estimation of treatment effects to make decisions. Current methods make binary yes-or-no decisions based on…

Machine Learning · Computer Science 2020-04-24 Will Y. Zou , Smitha Shyam , Michael Mui , Mingshi Wang , Jan Pedersen , Zoubin Ghahramani

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…

Econometrics · Economics 2020-05-07 Pedro H. C. Sant'Anna , Jun B. Zhao

A popular method for estimating a causal treatment effect with observational data is the difference-in-differences (DiD) model. In this work, we consider an extension of the classical DiD setting to the hierarchical context in which data…

Methodology · Statistics 2019-10-17 James Normington , Eric F. Lock , Thomas A. Murray , Caroline S. Carlin

We consider the identification of average treatment effects on the treated (ATT) in difference-in-differences (DiD) settings in the presence of endogenous sample selection. We first establish that the conventional DiD estimand generally…

Econometrics · Economics 2026-02-17 Gayani Rathnayake , Akanksha Negi , Otavio Bartalotti , Xueyan Zhao

Bipartite experiments arise in various fields, in which the treatments are randomized over one set of units, while the outcomes are measured over another separate set of units. However, existing methods often rely on strong model…

Methodology · Statistics 2025-04-16 Sizhu Lu , Lei Shi , Yue Fang , Wenxin Zhang , Peng Ding

Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In…

Econometrics · Economics 2023-06-13 Kyle Butts