Inference on Treatment Effects after Selection among High-Dimensional ControlsaEuro
Inference on Treatment Effects after Selection among High-Dimensional ControlsaEuro
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DOI：
10.1093/restud/rdt044
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发表时间：
2014-04-01
影响因子：
5.8
通讯作者：
Hansen, Christian
中科院分区：
文献类型：
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作者：
Belloni, Alexandre;Chernozhukov, Victor;Hansen, Christian
我们提出了稳健的方法来推断治疗变量对标量结果的影响，在一个可能存在非高斯和异方差扰动的模型中，存在非常多的回归变量。我们允许回归变量的数量大于样本大小。为了使信息推理可行，我们要求模型是近似稀疏的；也就是说，我们要求混杂因素的影响可以通过包括相对较少的身份未知的变量来控制到最小的近似误差。后一种情况使得通过选择大致正确的一组回归变量来估计治疗效果成为可能。我们发展了一种新的估计和一致有效的推断方法，称为“后双选”方法。我们方法的主要吸引人的特点是，它允许不完美的控制选择，并提供在一大类模型上一致有效的置信度区间。相比之下，标准的模型后选择估计器无法提供统一的推断，即使在具有少量固定控制数量的简单情况下也是如此。因此，我们的方法解决了对一大类有趣的模型进行模型选择后的统一推理问题。我们还将我们的方法推广到具有二元处理变量的完全异质模型。我们用数值模拟和一个考虑堕胎对犯罪率影响的应用程序来说明所开发的方法的使用。
We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of very many regressors in a model with possibly non-Gaussian and heteroscedastic disturbances. We allow for the number of regressors to be larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by including a relatively small number of variables whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of regressors. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus, our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We also present a generalization of our method to a fully heterogeneous model with a binary treatment variable. We illustrate the use of the developed methods with numerical simulations and an application that considers the effect of abortion on crime rates.