We propose an instrumental variable framework for identifying and estimating average and quantile effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution of the potential outcomes and unobservables determining treatment assignment. This representation allows us to introduce an identifying assumption, so-called copula invariance, that restricts the local dependence of the copula with respect to the treatment propensity. We show that copula invariance identifies treatment effects for the entire population and other subpopulations such as the treated. The identification results are constructive and lead to straightforward semiparametric estimation procedures based on distribution regression. An application to the effect of sleep on well-being uncovers interesting patterns of heterogeneity.

翻译：摘要：本文提出一个工具变量框架，用于识别和估计二元工具变量下离散与连续治疗的平均效应与分位数效应。该方法的基础是构建潜在结果与决定治疗分配不可观测因素联合分布的局部Copula表示。该表示使我们能够引入一个称为Copula不变性的识别假设，该假设限制了Copula相对于治疗倾向的局部依赖性。我们证明Copula不变性能识别整个人群及接受治疗等子人群的治疗效应。识别结果具有建设性，并导致基于分布回归的简易半参数估计程序。通过对睡眠对幸福感影响的实证分析，揭示了有趣的异质性模式。