This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep tail characteristics: the extreme quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then we define the extreme quantile treatment effect (EQTE) and the extreme average treatment effect (EATE), which can be identified through the commonly adopted unconfoundedness condition and estimated with the aid of extreme value theory. Our limiting theory is for the EQTE and EATE processes indexed by a set of quantile levels and hence facilitates uniform inference. Simulations suggest that our method works well in finite samples and an empirical application illustrates its practical merit.
翻译:本文涉及与持续估价的处理相对应的无法观察的潜在结果的反事实分布对深海尾部的治疗效应的估计和推断。我们考虑对深尾特性采取两种措施:极端微量函数和尾尾端中值函数,其定义为四分位水平以外的有条件平均值。然后我们界定极端微量处理效应(EQTE)和极端平均治疗效应(EATE),这些效应可以通过通常采用的无根据状态加以确定,并在极端价值理论的帮助下加以估计。我们的限制理论是EQTE和EATE工艺以一组量级水平指数化,从而有利于统一推断。模拟表明,我们的方法在有限的样本中运作良好,经验应用显示了其实际价值。