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:实际应用中,在干扰存在条件下的研究通常将结果建模为个体自身处理水平的函数,以及他人处理的低维暴露映射,即便该映射可能存在误设定。本文探究此类基于暴露过程的经验方法所针对的政策对象。以边际政策效应为基础,我们证明任何由研究者选择的暴露映射均能诱导出唯一的伪真实结果模型:即在该映射所依赖的函数类中,对潜在结果的最优逼近。由此可将边际政策效应分解为基于暴露的直接效应和溢出效应,且各分量均能最优逼近其基准对应项,在单调性条件下具备符号保持性。随后我们研究一类结构化误设定场景:结果同时依赖于网络溢出效应和全局均衡渠道,而分析者可能仅对其中一种渠道建模。在此场景中,我们得到更精细的渐近分解为直接、局部和全局分量,表明即使存在未纳入维持模型的其他渠道,现有估计量仍能恢复其各自基准的渠道特异性效应。该分析还揭示了Z估计量的收敛速率相变及高阶展开式。基于大规模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。