Partially Conditional Average Treatment Effect on Treated for Difference-in-Differences

Jiale Yang, Zongwu Cai and Qixian Zhong
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Jiale Yang: Department of Statistics and Data Science, Xiamen University, Xiamen, Fujian, China
Zongwu Cai: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA
Qixian Zhong: Department of Statistics and Data Science, Xiamen University, Xiamen, Fujian, China

No 202611, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: Causal inference has been widely applied across various fields, with Difference-in-Differences (DiD) emerging as one of the most popular methods for estimating the causal effect of a treatment or policy change in settings where treatment timing is staggered or occurs at a specific point in time. However, in many scenarios, not all covariates are of primary interest. This paper studies the partially conditional average treatment effect on the treated and extends to the multi-period DiD settings under the assumption of conditional parallel trends. The proposed approach is a two-stage doubly robust estimator, which allows us to both feature the heterogeneity and enhance the interpretability of the treatment effects by focusing on a subset of covariates of interest. The property of double robustness ensures a consistent estimator as long as either the outcome regression model or the propensity score model is correctly specified. Beyond the proposed new methodology, we derive asymptotic theories by establishing the convergence rate and asymptotically normality of the nonparametric estimator and further examine the double robustness and practical applicability through several simulation studies. Finally, the proposed methods are used to study the impact of the Deferred Action for Childhood Arrivals program on educational outcomes for non-citizen immigrants in the US.

Keywords: Double robustness; Heterogeneity; Kernel smoothing; Local linear regression; Multi-period DiD. (search for similar items in EconPapers)
Date: 2026-04, Revised 2026-04
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