A unified framework for efficient estimation of general treatment models
A unified framework for efficient estimation of general treatment models
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DOI：
10.1920/wp.cem.2019.6419
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发表时间：
2018-08
影响因子：
1.8
通讯作者：
C. Ai;O. Linton;Kaiji Motegi;Zheng Zhang
中科院分区：
文献类型：
--
作者：
C. Ai;O. Linton;Kaiji Motegi;Zheng Zhang
本文提出了一个加权优化框架，统一了二值，多值和连续处理-以及离散和连续处理的混合物-在无混杂处理分配下。该框架采用一般损失函数，将处理的平均、分位数和非对称最小二乘因果效应作为特殊情况。对于这个一般框架，我们首先推导了处理因果效应的半参数效率界，将现有的界结果扩展到更广泛的模型类别。然后，我们提出了一个通过求解扩展方程集来估计权值的因果效应的广义优化估计量。在某些充分条件下，我们建立了因果效应估计量的相合性和渐近正态性，并证明了该估计量达到了半参数效率界，从而将现有的因果效应有效估计文献推广到更广泛的应用领域。最后，讨论了治疗效果曲线和平均结果等因果函数的估计。为了评估所提出的程序的有限样本性能，我们进行了小规模的模拟研究，发现所提出的估计具有实用价值。在实证应用中，我们在二元处理模型中发现了政治广告对竞选捐款的显著因果效应，而在连续处理模型中则没有。
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.