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A Unified Framework for Efficient Estimation of General Treatment Models

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  • Ai, C.
  • Linton, O.
  • Motegi, K.
  • Zhang, Z.

Abstract

This paper presents a weighted optimization framework that unifies the binary, multivalued, continuous, as well as mixture of discrete and continuous treatment, under the 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 estimation for the causal effect with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we establish consistency and asymptotic normality of the proposed estimator of the causal effect and show that the estimator attains our 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. To illustrate the applicability of the procedure, we revisit the literature on campaign advertise and campaign contributions. Unlike the existing procedures which produce mixed results, we find no evidence of campaign advertise on campaign contribution.

Suggested Citation

  • Ai, C. & Linton, O. & Motegi, K. & Zhang, Z., 2019. "A Unified Framework for Efficient Estimation of General Treatment Models," Cambridge Working Papers in Economics 1934, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1934
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    3. Jiang, Qingshan & Xu, Li & Huang, Can, 2022. "Covariates distributions balancing for continuous treatment," Economics Letters, Elsevier, vol. 217(C).
    4. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for a Continuous Treatment," Papers 2402.02535, arXiv.org.
    5. 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).
    6. Wei Huang & Oliver Linton & Zheng Zhang, 2021. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Papers 2102.08063, arXiv.org, revised Sep 2021.
    7. 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.

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