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AVERAGING ESTIMATORS OF HETEROGENEOUS TREATMENT EFFECTS UNDER ADDITIVE MODELS

Published online by Cambridge University Press:  22 October 2025

Na Li ,
Yu Fei ,
Yuhong Yang Open the ORCID record for Yuhong Yang [Opens in a new window]  and
Xinyu Zhang
Na Li
Affiliation:
Kunming University of Science and Technology
Yu Fei
Affiliation:
Yunnan University of Finance and Economics
Yuhong Yang*
Affiliation:
Tsinghua University and Beijing Institute of Mathematical Sciences and Applications
Xinyu Zhang
Affiliation:
Chinese Academy of Sciences and University of Science and Technology of China
*
Address correspondence to Yuhong Yang, Yau Mathematical Sciences Center, Tsinghua University, Beijing, China and Beijing Institute of Mathematical Sciences and Applications, Beijing, China, e-mail: yyangsc@tsinghua.edu.cn.
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Abstract

We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a J-fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some settings and assigning all weight to the correctly specified models if such models exist in the candidate set. Moreover, consistency properties of the optimal weights and model averaging estimators are established. A simulation study and an empirical example demonstrate the superiority of the proposed estimator over other methods.

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Type
ARTICLES
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Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

The authors are very grateful to the editor, associate editor, and two anonymous referees for their constructive comments and suggestions. X.Z.’s work is supported by the National Key Research and Development Program of China (Grant No. 2023YFA1008704) and the National Natural Science Foundation of China (Grant Nos. 72525001 and 72495124). Y.F.’s work is supported by the National Natural Science Foundation of China (Grant No. 12561051) and Yunnan Province XingDian Talent Support Program (Grant No. YNWR-YLXZ-2018-020).

References

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