Abstract

To make the conventional synthetic control method more flexible to es

timate the average treatment effect (ATE), this article proposes a quasi synthetic

control method for nonlinear models under the index model framework with possible

high-dimensional covariates, together with a suggestion of using the minimum average variance estimation (MAVE) method to estimate parameters and the LASSO-

type procedure to choose high-dimensional covariates. We derive the asymptotic

distribution of the proposed ATE estimators for both finite and diverging dimensions of covariates. A properly designed Bootstrap method is proposed to obtain

confidence intervals and its theoretical justification is provided. When the dimension of covariates is greater than the sample size, we suggest using the robust version

of sure independence screening procedure based on the distance correlation to first

reduce the dimensionality and then apply the MAVE approach to estimate parameters. Finally, Monte Carlo simulation studies are conducted to examine the finite

sample performance of our proposed estimators and Bootstrap procedure. In addition, an empirical application to reanalyzing data from the National Supported

Work Demonstration demonstrates the practical usefulness of our proposed method.

Information

Preprint No.SS-2023-0271
Manuscript IDSS-2023-0271
Complete AuthorsZongwu Cai, Ying Fang, Ming Lin, Zixuan Wu
Corresponding AuthorsMing Lin
Emailslinming50@xmu.edu.cn

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Acknowledgments

We thank the Co-Editor (Professor Huixia Judy Wang), the Associate Editor, and three anonymous referees for their constructive and helpful comments

and suggestions that improved significantly the quality of the paper. Also,

the authors gratefully acknowledge the financial supports, in part, from the

National Science Fund of China (NSFC) key project grants #72033008 and

72133002, Basic Science Center Program of NSFC with grant #71988101.

Disclosure Statement

The authors claim that there are no relevant financial or non-financial

competing interests to report for this article. Also, the authors declare that

they do not use any generative AI and AI-assisted technologies in the writing

process.

Supplementary Materials

The online Supplementary Material contains proofs of Theorems 1-3, the

algorithm for the MAVE method, and summary statistics of the empirical

data.

Supplementary materials are available for download.