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We develop new changes-in-changes (CIC) and distributional synthetic controls (DSC) types of methods when there exists group-level heterogeneity. For CIC, we allow individuals to belong to heterogeneous groups, extending Athey and Imbens…

Econometrics · Economics 2026-02-20 Songnian Chen , Junlong Feng

We consider a general difference-in-differences model in which the treatment variable of interest may be non-binary and its value may change in each period. It is generally difficult to estimate treatment parameters defined with the…

Econometrics · Economics 2023-05-30 Takahide Yanagi

We present a novel extension of the influential changes-in-changes (CiC) framework of Athey and Imbens (2006) for estimating the average treatment effect on the treated (ATT) and distributional causal effects in panel data with unmeasured…

Methodology · Statistics 2025-08-20 Jinghao Sun , Eric J. Tchetgen Tchetgen

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,…

Econometrics · Economics 2026-01-05 Brantly Callaway , Andrew Goodman-Bacon , Pedro H. C. Sant'Anna

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

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

Inferring causal relationships from observational data is often challenging due to endogeneity. This paper provides new identification results for causal effects of discrete, ordered and continuous treatments using multiple binary…

Econometrics · Economics 2024-10-21 Nadja van 't Hoff

The renowned difference-in-differences (DiD) estimator relies on the assumption of 'parallel trends,' which does not hold in many practical applications. To address this issue, the econometrics literature has turned to the triple difference…

Methodology · Statistics 2024-02-21 Sina Akbari , Negar Kiyavash

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an…

Econometrics · Economics 2023-04-18 Xavier D'Haultfoeuille , Stefan Hoderlein , Yuya Sasaki

In observational studies, weighting methods that directly optimize the balance between treatment and covariates have received much attention lately; however these have mainly focused on binary treatments. Inspired by domain adaptation, we…

Statistics Theory · Mathematics 2020-02-27 Guillaume Martinet

Attrition is a common and potentially important threat to internal validity in treatment effect studies. We extend the changes-in-changes approach to identify the average treatment effect for respondents and the entire study population in…

Econometrics · Economics 2024-03-29 Dalia Ghanem , Sarojini Hirshleifer , Désiré Kédagni , Karen Ortiz-Becerra

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…

Methodology · Statistics 2024-07-22 Yingrong Wang , Haoxuan Li , Minqin Zhu , Anpeng Wu , Ruoxuan Xiong , Fei Wu , Kun Kuang

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

Difference-in-differences (DiD) is one of the most popular approaches for empirical research in economics, political science, and beyond. Identification in these models is based on the conditional parallel trends assumption: In the absence…

Econometrics · Economics 2025-10-13 Philipp Bach , Sven Klaassen , Jannis Kueck , Mara Mattes , Martin Spindler

This paper proposes a framework that incorporates the two-way fixed effects model as a special case to conduct causal inference with a continuous treatment. Treatments are allowed to change over time and potential outcomes are dependent on…

Methodology · Statistics 2025-07-01 Zhiguo Xiao , Peikai Wu

Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has…

Machine Learning · Computer Science 2026-05-15 Christopher Stith , Medha Barath , Vahid Balazadeh , Jesse C. Cresswell , Rahul G. Krishnan

CIMTx provides efficient and unified functions to implement modern methods for causal inferences with multiple treatments using observational data with a focus on binary outcomes. The methods include regression adjustment, inverse…

Methodology · Statistics 2022-09-15 Liangyuan Hu , Jiayi Ji

While a randomized control trial is considered the gold standard for estimating causal treatment effects, there are many research settings in which randomization is infeasible or unethical. In such cases, researchers rely on analytical…

Methodology · Statistics 2024-02-21 Julia C. Thome , Peter F. Rebeiro , Andrew J. Spieker , Bryan E. Shepherd

We develop a marginal treatment effect based method to learn about causal effects in multiple treatment models with discrete instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that…

Econometrics · Economics 2026-01-21 Vishal Kamat , Samuel Norris , Matthew Pecenco

We study causal inference in sample selection models where a continuous or multivalued treatment affects both outcome and their observability (eg., employment or survey response). We generalized the widely used Lee (2009)'s bounds for…

Econometrics · Economics 2025-10-29 Ying-Ying Lee , Chu-An Liu
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