  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.
