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This paper extends difference-in-differences to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends…

Econometrics · Economics 2026-01-05 Lucas Z. Zhang

Applied analysts often use the differences-in-differences (DID) method to estimate the causal effect of policy interventions with observational data. The method is widely used, as the required before and after comparison of a treated and…

Applications · Statistics 2019-02-04 Luke J. Keele , Dylan S. Small , Jesse Y. Hsu , Colin B. Fogarty

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

Consider a general setting in which data on an outcome is collected in two `groups' at two time periods, with certain group-periods deemed `treated' and others `untreated'. A special case is the canonical Difference-in-Differences (DiD)…

Methodology · Statistics 2025-09-15 Zach Shahn , Laura Hatfield

Most of the widely used estimators of the average treatment effect (ATE) in causal inference rely on the assumptions of unconfoundedness and overlap. Unconfoundedness requires that the observed covariates account for all correlations…

Statistics Theory · Mathematics 2025-07-01 Yang Cai , Alkis Kalavasis , Katerina Mamali , Anay Mehrotra , Manolis Zampetakis

Difference-in-differences (DID) is one of the most widely used causal inference frameworks in observational studies. However, most existing DID methods are designed for binary treatments and cannot be readily applied to non-binary treatment…

Methodology · Statistics 2025-12-01 Siyu Heng , Yuan Huang , Hyunseung Kang

Difference-in-differences (DID) is commonly used to estimate treatment effects but is infeasible in settings where data are unpoolable due to privacy concerns or legal restrictions on data sharing, particularly across jurisdictions. In this…

Econometrics · Economics 2025-07-28 Sunny Karim , Matthew D. Webb , Nichole Austin , Erin Strumpf

This paper addresses one of the most prevalent problems encountered by political scientists working with difference-in-differences (DID) design: missingness in panel data. A common practice for handling missing data, known as complete case…

Methodology · Statistics 2024-12-02 Sooahn Shin

This paper develops doubly robust estimators for direct (DATT) and spillover (SATT) average treatment effects on the treated in network-based difference-in-differences (DiD) designs. Unlike standard DiD methods, the proposed approach…

Methodology · Statistics 2025-09-30 Kuan Sun , Zhiguo Xiao

While a difference-in-differences (DID) design was originally developed with one pre- and one post-treatment period, data from additional pre-treatment periods are often available. How can researchers improve the DID design with such…

Applications · Statistics 2022-02-14 Naoki Egami , Soichiro Yamauchi

We develop a new identification strategy for average treatment effects on the treated (ATT) in panel data with discrete outcomes. Standard difference-in-differences (DiD) relies on parallel trends, which is frequently violated in…

Econometrics · Economics 2026-03-10 Young Ahn , Hiroyuki Kasahara

Triple difference designs have become increasingly popular in empirical economics. The advantage of a triple difference design is that, within a treatment group, it allows for another subgroup of the population -- potentially less impacted…

Econometrics · Economics 2025-06-04 Laura Caron

In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships are often restricted to those meeting specific income or…

We study estimation of the local average treatment effect on the treated ($LATT$) in instrumented difference-in-differences (IDiD) designs with covariates and staggered instrument exposure. We derive the efficient influence function (EIF)…

Econometrics · Economics 2026-05-06 Jonas Skjold Raaschou-Pedersen

We study identification and estimation in the Regression Discontinuity Design (RDD) with a multivalued treatment variable. We also allow for the inclusion of covariates. We show that without additional information, treatment effects are not…

Econometrics · Economics 2020-07-02 Carolina Caetano , Gregorio Caetano , Juan Carlos Escanciano

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

This paper proposes a novel approach for estimating treatment effects in panel data settings, addressing key limitations of the standard difference-in-differences (DID) approach. The standard approach relies on the parallel trends…

Econometrics · Economics 2026-01-14 Shoya Ishimaru

We propose a new method for estimating causal effects in longitudinal/panel data settings that we call generalized difference-in-differences. Our approach unifies two alternative approaches in these settings: ignorability estimators (e.g.,…

Methodology · Statistics 2023-12-12 Denis Agniel , Max Rubinstein , Jessie Coe , Maria DeYoreo

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

Researchers commonly use difference-in-differences (DiD) designs to evaluate public policy interventions. While methods exist for estimating effects in the context of binary interventions, policies often result in varied exposures across…

Methodology · Statistics 2025-02-07 Gary Hettinger , Youjin Lee , Nandita Mitra