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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,multi-valued, 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 etimation 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.

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  • Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2018. "A Unified Framework for Efficient Estimation of General Treatment Models," Papers 1808.04936, arXiv.org, revised Aug 2018.
  • Handle: RePEc:arx:papers:1808.04936
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    References listed on IDEAS

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    1. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
    2. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    3. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
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