We propose an instrumental variable framework for identifying and estimating causal 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 practical estimation and inference procedures based on distribution regression. An application to estimating the effect of sleep on well-being uncovers interesting patterns of heterogeneity.

翻译：本文提出一种工具变量框架，用于识别和估计二元工具变量下离散与连续处理的因果效应。该方法的基础是潜在结果与决定处理分配不可观测变量的联合分布的局部联结函数表示。该表示使我们能够引入一种识别假设，即所谓的联结函数不变性，该假设限制了联结函数在处理倾向方面的局部依赖性。我们证明，联结函数不变性能够识别整个总体及其他子总体（如已处理群体）的处理效应。识别结果具有构造性，并导出了基于分布回归的实用估计与推断方法。在睡眠对幸福感影响估计的应用中，我们发现了有趣的异质性模式。