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Causal inference of general treatment effects using neural networks with a diverging number of confounders

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  • Chen, Xiaohong
  • Liu, Ying
  • Ma, Shujie
  • Zhang, Zheng

Abstract

Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome or treatment to confounders nonparametrically. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using artificial neural networks (ANNs) to approximate the unknown nuisance function of growing-dimensional confounders. We establish a new approximation error bound for the ANNs to the nuisance function belonging to a mixed smoothness class without a known sparsity structure. We show that the ANNs can alleviate the “curse of dimensionality” under this circumstance. We establish the root-n consistency and asymptotic normality of the proposed general treatment effects estimators, and apply a weighted bootstrap procedure for conducting inference. The proposed methods are illustrated via simulation studies and a real data application.

Suggested Citation

  • Chen, Xiaohong & Liu, Ying & Ma, Shujie & Zhang, Zheng, 2024. "Causal inference of general treatment effects using neural networks with a diverging number of confounders," Journal of Econometrics, Elsevier, vol. 238(1).
  • Handle: RePEc:eee:econom:v:238:y:2024:i:1:s0304407623002713
    DOI: 10.1016/j.jeconom.2023.105555
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    Cited by:

    1. Sihui Zhao & Xinbo Wang & Lin Liu & Xin Zhang, 2024. "Covariate Adjustment in Randomized Experiments Motivated by Higher-Order Influence Functions," Papers 2411.08491, arXiv.org, revised Dec 2024.

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    More about this item

    Keywords

    Artificial neural networks; Barron space; Mixed smoothness class; ReLU; Diverging confounders; Propensity score; Quantile treatment effects; Weighted bootstrap;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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