9 May 2012 | A. BELLONI, V. CHERNOZHUKOV, AND C. HANSEN
The paper proposes robust methods for inference on treatment effects in high-dimensional settings. It introduces the "post-double-selection" method, which allows for imperfect control selection and provides uniformly valid confidence intervals. The method is applicable to Lasso-type and other sparse model selection techniques. The key idea is that the treatment effect can be estimated by selecting a small subset of controls that approximate the true model. The method ensures robustness by using two selection steps: first, selecting controls relevant to the treatment, and second, selecting controls relevant to the outcome. This approach leads to a consistent and asymptotically normal estimator of the treatment effect, which is uniformly valid across a wide range of models. The paper also demonstrates the method's effectiveness through numerical simulations and an application to the effect of abortion on crime rates. The results show that the method provides more reliable inference than traditional post-model selection approaches, especially in high-dimensional settings. The paper contributes to the literature on partially linear models, treatment effects, and high-dimensional inference, offering a robust and valid method for estimating treatment effects in the presence of many controls.The paper proposes robust methods for inference on treatment effects in high-dimensional settings. It introduces the "post-double-selection" method, which allows for imperfect control selection and provides uniformly valid confidence intervals. The method is applicable to Lasso-type and other sparse model selection techniques. The key idea is that the treatment effect can be estimated by selecting a small subset of controls that approximate the true model. The method ensures robustness by using two selection steps: first, selecting controls relevant to the treatment, and second, selecting controls relevant to the outcome. This approach leads to a consistent and asymptotically normal estimator of the treatment effect, which is uniformly valid across a wide range of models. The paper also demonstrates the method's effectiveness through numerical simulations and an application to the effect of abortion on crime rates. The results show that the method provides more reliable inference than traditional post-model selection approaches, especially in high-dimensional settings. The paper contributes to the literature on partially linear models, treatment effects, and high-dimensional inference, offering a robust and valid method for estimating treatment effects in the presence of many controls.