Sensitivity Analysis for Linear Estimators

TL;DR

This paper introduces a new sensitivity analysis framework for linear estimators that accounts for identification failures, providing generalized bounds and robust estimates even in complex scenarios.

Contribution

It presents a novel, generalized sensitivity analysis method for linear estimators that handles identification failures and extends partial identification results.

Findings

Method performs well in simulations with nearly infinite bounds

Provides sharp bounds under plausible conditions

Estimates valid bounds under mild assumptions

Abstract

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.