We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change in measure between the observed distribution and a hypothetical target distribution that would identify the causal parameter of interest. The framework yields a sensitivity analysis that generalizes existing bounds for Average Potential Outcome (APO), Regression Discontinuity (RD), and instrumental variables (IV) exclusion failure designs. Our partial identification results extend results from the APO context to allow even unbounded likelihood ratios. Our proposed sensitivity analysis consistently estimates sharp bounds under plausible conditions and estimates valid bounds under mild conditions. We find that our method performs well in simulations even when targeting a discontinuous and nearly infinite bound.

翻译：我们提出了一种针对线性估计量的新型敏感性分析框架，该框架可处理因识别失败（可视为观测到错误的结果分布）导致的问题。该方法通过观测分布与能够识别目标因果参数的假设目标分布之间的测度变化来衡量识别失败程度。该框架衍生出的敏感性分析可推广现有针对平均潜在结果（APO）、断点回归（RD）及工具变量（IV）排除性失效设计的界限。我们的部分识别结果将APO场景下的结论扩展至允许无界似然比的情形。所提出的敏感性分析在合理条件下可一致估计sharp界，并在温和条件下估计有效界。即使针对不连续且接近无穷大的边界，该方法在模拟实验中仍表现良好。