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Average Treatment Effect Localization: Projection Methods in Synthetic Control

Ruei-Chi Lee

arXiv 8 Sep 2026 · Econometrics

arXiv:2609.10617 · PDF · Extracted main text

Abstract

Many real-world policies and business interventions require assessing short-term effects to inform timely decisions, even though most causal inference methods focus on long-term average treatment effects. In this paper, we introduce average treatment effect localization (ATEL), which captures localized, short-term policy impacts in panel data settings with a single treated unit and provides early indicators of policy impact. To accommodate both time-varying and nonlinear effects of observed and unobserved covariates, we propose a nonparametric model for untreated outcome, interpreted as a time-varying factor model via sieve approximation. Estimating the time-varying factor model is challenging due to the boundary bias and identification. Our estimation method based on diversified projection can effectively address these issues. We develop an asymptotic distribution theory to facilitate inference for the ATEL estimator. In an empirical application, we apply our proposed methodology to assess the impact of right-to-carry laws on violent crime rate.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Liangjun Su and Xia Wang (2017) On time-varying factor models: Estimation and testing1.00095100%
2Alberto Abadie and Alexis Diamond and Jens Hainmueller (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program1.00053100%
3Jianqing Fan and Yuan Liao (2022) Learning Latent Factors From Diversified Projections and Its Applications to Over-Estimated and Weak Factors0.87452100%
4Kathleen T. Li and Garrett P. Sonnier (2023) Statistical Inference for the Factor Model Approach to Estimate Causal Effects in Quasi-Experimental Settings0.84333100%
5Gobillon, Laurent and Magnac, Thierry (2016) Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls0.73732100%
6Jushan Bai and Serena Ng (2021) Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data0.73732100%
7Fernández-Val, Iván and Freeman, Hugo and Weidner, Martin (2021) Low-rank approximations of nonseparable panel models0.64422100%
8Abadie, Alberto and Gardeazabal, Javier (2003) The Economic Costs of Conflict: A Case Study of the Basque Country0.64422100%
9Jushan Bai (2009) Panel Data Models with Interactive Fixed Effects0.64422100%
10Aneja, Abhay and Donohue, John and Zhang, Alexandria (2011) The Impact of Right-to-Carry Laws and the NRC Report: Lessons for the Empirical Evaluation of Law and Policy0.64422100%

Showing the top 10 of 53 scored citations.