Back to the Future: Using Future Treatments to Detect and Reduce Hidden Bias
Conventional advice discourages controlling for post-outcome variables in regression analysis. Here, we show that controlling for commonly available post-outcome (i.e. future) values of the treatment variable can help detect, reduce, and even remove omitted variable bias (unobserved confounding). The premise is that the same unobserved confounders that affect treatment also affect future values of the treatment. Future treatments thus proxy for the unmeasured confounder, and researchers can exploit these proxy measures productively. We establish several new results: Regarding a commonly assumed data-generating process, we (1) introduce a new approach to reduce bias and show that it strictly reduces bias; (2) elaborate on existing approaches and show that they can increase bias; (3) assess the relative merits of approaches; (4) analyze true state dependence and selection as key challenges; and (5) demonstrate that future treatments can test for hidden bias, even when they fail to reduce bias. We illustrate these results empirically with an analysis of the effect of parental wealth on children's educational achievement.