Applied work under interference typically models outcomes as functions of own treatment and a low-dimensional exposure mapping of others' treatments, even when that mapping may be misspecified. We ask what policy object such exposure-based procedures target. Taking the marginal policy effect as primitive, we show that any researcher-chosen exposure mapping induces a unique pseudo-true outcome model: the best approximation to the underlying potential outcomes within the class of functions that depend only on that mapping. This yields a decomposition of the marginal policy effect into exposure-based direct and spillover effects, and each component optimally approximates its oracle counterpart, with a sign-preserving interpretation under monotonicity. We then study a structured misspecification setting in which outcomes depend on both network spillovers and a global equilibrium channel, while the analyst may model only one. In this setting, we obtain a sharper asymptotic decomposition into direct, local, and global components, implying that existing estimators recover their respective oracle channel-specific effects even when the other channel is present but omitted from the maintained model.The analysis also yields phase transitions in convergence rates and higher-order expansions for Z-estimators. A semi-synthetic experiment calibrated to a large cash-transfer study illustrates the empirical relevance of the framework.
翻译:在干涉效应存在的情况下,应用研究通常将结果建模为自身处理变量和他人处理的低维暴露映射的函数,即使该映射可能存在误设定。本文探究此类基于暴露的程序所针对的政策对象。以边际政策效应为基本量,我们证明研究者选择的任何暴露映射都会诱导一个唯一的伪真实结果模型:即在仅依赖于该映射的函数类中对潜在结果的最优近似。这实现了将边际政策效应分解为基于暴露的直接效应和溢出效应,且每个分量都能最优地近似其对应基准版本,并在单调性条件下保持符号解释。随后,我们研究了一种结构化的误设定场景,其中结果同时取决于网络溢出效应和全局均衡渠道,而分析者可能仅建模其中一个渠道。在此设定下,我们得到向直接、局部和全局分量的更尖锐渐近分解,这表明即使另一渠道存在但被维护模型省略,现有估计量仍能恢复其对应的基准渠道特定效应。该分析还揭示了Z估计量的收敛速率相变及高阶展开。基于大型现金转移研究校准的半合成实验验证了该框架的实证相关性。