The Future Strikes Back. Using Future Treatments to Detect and Reduce Hidden Bias

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Conventional advice discourages controlling for post-outcome variables in regression
analysis. By contrast, 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 confounder that affects
treatment also affects the future value 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
involving future treatments, we (1) introduce a simple new approach 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 alternative approaches; (4) analyze true state dependence and
selection as key challenges. (5) Importantly, we also introduce a new non-parametric test that
uses future treatments to detect hidden bias even when future-treatment estimation fails to
reduce bias. We illustrate these results empirically with an analysis of the effect of parental
income on children’s educational attainment.

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