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Uniform Inference for Nonlinear Endogenous Treatment Effects with High-Dimensional Covariates

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  • Qingliang Fan
  • Zijian Guo
  • Ziwei Mei
  • Cun-Hui Zhang

Abstract

Nonlinearity and endogeneity are common in causal effect studies with observational data. In this paper, we propose new estimation and inference procedures for nonparametric treatment effect functions with endogeneity and potentially high-dimensional covariates. The main innovation of this paper is the double bias correction procedure for the nonparametric instrumental variable (NPIV) model under high dimensions. We provide a useful uniform confidence band of the marginal effect function, defined as the derivative of the nonparametric treatment function. The asymptotic honesty of the confidence band is verified in theory. Simulations and an empirical study of air pollution and migration demonstrate the validity of our procedures.

Suggested Citation

  • Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Uniform Inference for Nonlinear Endogenous Treatment Effects with High-Dimensional Covariates," Papers 2310.08063, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2310.08063
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