We propose a novel sensitivity analysis framework for linear estimands when identification failure can be viewed as seeing the wrong distribution of outcomes. Our family of assumptions bounds the density ratio between the observed and true conditional outcome distribution. This framework links naturally to selection models, generalizes existing assumptions for the Regression Discontinuity (RD) and Inverse Propensity Weighting (IPW) estimand, and provides a novel nonparametric perspective on violations of identification assumptions for ordinary least squares (OLS). Our sharp partial identification results extend existing results for IPW to cover other estimands and assumptions that allow even unbounded likelihood ratios, yielding a simple and unified characterization of bounds under assumptions like the c-dependence assumption of Masten and Poirier (2018). The sharp bounds can be written as a simple closed form moment of the data, the nuisance functions estimated in the primary analysis, and the conditional outcome quantile function. We find our method does well in simulations even when targeting a discontinuous and nearly infinite bound.

翻译：我们提出了一种新颖的敏感性分析框架，用于处理线性估计量在识别失效可被视为观察到错误结果分布的情况。我们的假设族限制了观测到的条件结果分布与真实条件结果分布之间的密度比。该框架与选择模型自然关联，推广了回归间断设计（RD）和逆概率加权（IPW）估计量的现有假设，并为普通最小二乘法（OLS）识别假设违反提供了全新的非参数视角。我们的尖锐部分识别结果将现有IPW结果扩展到其他估计量及允许无界似然比的假设，从而在诸如Masten和Poirier（2018）的c依赖假设等条件下，得到简洁统一的界刻画。这些尖锐界可表示为数据的简单闭合矩形式、主分析中估计的干扰函数以及条件结果分位数函数。即使在目标界不连续且近乎无限的情况下，我们的方法在模拟中仍表现良好。