7. Assessing Bias in the Estimation of Causal Effects: Rosenbaum Bounds on Matching Estimators and Instrumental Variables Estimation with Imperfect Instruments

Propensity score matching provides an estimate of the effect of a “treatment” variable on an outcome variable that is largely free of bias arising from an association between treatment status and observable variables. However, matching methods are not robust against “hidden bias” arising from unobserved variables that simultaneously affect assignment to treatment and the outcome variable. One strategy for addressing this problem is the Rosenbaum bounds approach, which allows the analyst to determine how strongly an unmeasured confounding variable must affect selection into treatment in order to undermine the conclusions about causal effects from a matching analysis. Instrumental variables (IV) estimation…