Combining information from Heckman and matching estimators: testing and controlling for hidden bias

We demonstrate how the Heckman methodology can be applied to the Rosenbaum sensitivity model and the Rubin matched difference estimator. We develop a statistical test of the conditional independence assumption (CIA), based on Heckit for matched pairs. If the CIA is rejected, the method facilitates the estimation of matched treatment effects adjusted for hidden bias. We illustrate this methodology empirically for the full-time/part-time pay gap for British women. The proposed method has clear utility in establishing whether propensity score matched treatment estimates are prone to unobserved selection bias and for controlling for such bias