The instrumental variable method is a prominent approach to recover under certain conditions, valid inference about a treatment causal effect even when unmeasured confounding might be present. In a groundbreaking paper, Imbens and Angrist (1994) established that a valid instrument nonparametrically identifies the average causal effect among compliers, also known as the local average treatment effect under a certain monotonicity assumption which rules out the existence of so-called defiers. An often-cited attractive property of monotonicity is that it facilitates a causal interpretation of the instrumental variable estimand without restricting the degree of heterogeneity of the treatment causal effect. In this paper, we introduce an alternative equally straightforward and interpretable condition for identification, which accommodates both the presence of defiers and heterogenous treatment effects. Mainly, we show that under our new conditions, the instrumental variable estimand recovers the average causal effect for the subgroup of units for whom the treatment is manipulable by the instrument, a subgroup which may consist of both defiers and compliers, therefore recovering an effect estimand we aptly call the Nudge Average Treatment Effect.

翻译：工具变量法是在存在未观测混杂因素的情况下，在特定条件下恢复处理因果效应有效推断的重要方法。在一篇开创性论文中，Imbens和Angrist（1994）证明，在某种单调性假设（该假设排除了所谓“违抗者”的存在）下，有效的工具变量能够非参数地识别“遵从者”群体的平均因果效应，即局部平均处理效应。单调性常被提及的一个吸引人特性在于，它能在不限制处理因果效应异质性程度的前提下，为工具变量估计量提供因果解释。本文提出了一种同样直观且可解释的替代识别条件，该条件同时允许违抗者的存在和处理效应的异质性。我们主要证明，在新条件下，工具变量估计量恢复的是处理可被工具变量操纵的那部分个体（该子群可能同时包含违抗者与遵从者）的平均因果效应，因此我们恰当地将这一恢复的效应估计量称为“推挤平均处理效应”。