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A unified framework for efficient estimation of general treatment models

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  • Chunrong Ai
  • Oliver Linton
  • Kaiji Motegi
  • Zheng Zhang

Abstract

This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment—as well as mixture of discrete and continuous treatment—under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile, and asymmetric least squares causal effect of treatment as special cases. For this general framework, we first derive the semiparametric efficiency bound for the causal effect of treatment, extending the existing bound results to a wider class of models. We then propose a generalized optimization estimator for the causal effect with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we establish the consistency and asymptotic normality of the proposed estimator of the causal effect and show that the estimator attains the semiparametric efficiency bound, thereby extending the existing literature on efficient estimation of causal effect to a wider class of applications. Finally, we discuss estimation of some causal effect functionals such as the treatment effect curve and the average outcome. To evaluate the finite sample performance of the proposed procedure, we conduct a small‐scale simulation study and find that the proposed estimation has practical value. In an empirical application, we detect a significant causal effect of political advertisements on campaign contributions in the binary treatment model, but not in the continuous treatment model.

Suggested Citation

  • Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
  • Handle: RePEc:wly:quante:v:12:y:2021:i:3:p:779-816
    DOI: 10.3982/QE1494
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    Cited by:

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    2. 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).
    3. Huang, W. & Linton, O. & Zhang, Z., 2021. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Cambridge Working Papers in Economics 2113, Faculty of Economics, University of Cambridge.
    4. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for a Continuous Treatment," Papers 2402.02535, arXiv.org.
    5. Yukitoshi Matsushita & Taisuke Otsu & Keisuke Takahata, 2022. "Estimating density ratio of marginals to joint: Applications to causal inference," STICERD - Econometrics Paper Series 619, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    7. Lin Liu & Chang Li, 2023. "New $\sqrt{n}$-consistent, numerically stable higher-order influence function estimators," Papers 2302.08097, arXiv.org.

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