We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show these regressions generally fail to estimate convex averages of heterogeneous treatment effects—instead, estimates of each treatment’s effect are contaminated by nonconvex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A reanalysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.

Can information from a credible messenger shift behavior in an information-saturated environment? In a randomized controlled trial involving twenty-eight million individuals in West Bengal, we find that SMS-delivered video messages containing information about COVID-19 symptoms and health-preserving behaviors recorded by a credible messenger increased adherence to targeted and non-targeted preventive behaviors, measured by two objective measures (symptoms reported to a health worker, and phone usage at home), as well as self-reported behaviors. We find large spillovers onto non-targeted recipients. Credible light-touch messaging can play an important role in crisis response, even when similar information is widely available.