Background: Interpreting instrumental variable results often requires further assumptions in addition to the core assumptions of relevance, independence, and the exclusion restriction. Methods: We assess whether instrument-exposure additive homogeneity renders the Wald estimand equal to the average derivative effect (ADE) in the case of a binary instrument and a continuous exposure. Results: Instrument-exposure additive homogeneity is insufficient for ADE identification when the instrument is binary, the exposure is continuous and the effect of the exposure on the outcome is non-linear on the additive scale. For a binary exposure, the exposure-outcome effect is necessarily additive linear, so the homogeneity condition is sufficient. Conclusions: For binary instruments, instrument-exposure additive homogeneity identifies the ADE if the exposure is also binary. Otherwise, additional assumptions (such as additive linearity of the exposure-outcome effect) are required.

翻译：背景:解释工具变量结果往往要求除相关、独立和排除限制的核心假设外,进一步假设相关、独立和排除限制。方法:我们评估仪器接触添加同质性是否使Wald估计值与二进制仪器和连续接触情况下的平均衍生效应相等。结果:仪器接触添加同质性不足以在仪器为二进制时识别亚经德,接触是连续的,接触结果对结果的影响在添加尺度上是非线性。对于二进制接触而言,接触结果的效果必然是添加线性线性,因此同质性条件就足够了。结论:对于二进制仪器而言,仪器接触添加同质性添加同质性能在接触也是二进制的情况下确定亚经德。否则,还需要额外的假设(例如接触结果的添加性等)。