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 provides an alternative strategy for the estimation of causal effects, but the method typically reduces the precision of the estimate and has an additional source of uncertainty that derives from the untestable nature of the assumptions of the IV approach. A method of assessing this additional uncertainty is proposed so that the total uncertainty of the IV approach can be compared with the Rosenbaum bounds approach to uncertainty using matching methods. Because the approaches rely on different information and different assumptions, they provide complementary information about causal relationships. The approach is illustrated via an analysis of the impact of unemployment insurance on the timing of reemployment, the postunemployment wage, and the probability of relocation, using data from several panels of the Survey of Income and Program Participation (SIPP).