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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. 

Regional quarantine policies, in which a portion of a population surrounding infections is locked down, are an important tool to contain disease. However, jurisdictional governments—such as cities, counties, states, and countries—act with minimal coordination across borders. We show that a regional quarantine policy’s effectiveness depends on whether 1) the network of interactions satisfies a growth balance condition, 2) infections have a short delay in detection, and 3) the government has control over and knowledge of the necessary parts of the network (no leakage of behaviors). As these conditions generally fail to be satisfied, especially when interactions cross borders, we show that substantial improvements are possible if governments are outward looking and proactive: triggering quarantines in reaction to neighbors’ infection rates, in some cases even before infections are detected internally. We also show that even a few lax governments—those that wait for nontrivial internal infection rates before quarantining—impose substantial costs on the whole system. Our results illustrate the importance of understanding contagion across policy borders and offer a starting point in designing proactive policies for decentralized jurisdictions. 

Abstract During the Coronavirus Disease 2019 (COVID-19) epidemic, many health professionals used social media to promote preventative health behaviors. We conducted a randomized controlled trial of the effect of a Facebook advertising campaign consisting of short videos recorded by doctors and nurses to encourage users to stay at home for the Thanksgiving and Christmas holidays ( NCT04644328 and AEARCTR-0006821 ). We randomly assigned counties to high intensity ( n  = 410 (386) at Thanksgiving (Christmas)) or low intensity ( n  = 410 (381)). The intervention was delivered to a large fraction of Facebook subscribers in 75% and 25% of randomly assigned zip codes in high- and low-intensity counties, respectively. In total, 6,998 (6,716) zip codes were included, and 11,954,109 (23,302,290) users were reached at Thanksgiving (Christmas). The first two primary outcomes were holiday travel and fraction leaving home, both measured using mobile phone location data of Facebook users. Average distance traveled in high-intensity counties decreased by −0.993 percentage points (95% confidence interval (CI): –1.616, −0.371; P = 0.002) for the 3 days before each holiday compared to low-intensity counties. The fraction of people who left home on the holiday was not significantly affected (adjusted difference: 0.030; 95% CI: −0.361, 0.420; P = 0.881). The third primary outcome was COVID-19 infections recorded at the zip code level in the 2-week period starting 5 days after the holiday. Infections declined by 3.5% (adjusted 95% CI: −6.2%, −0.7%; P = 0.013) in intervention compared to control zip codes. Social media messages recorded by health professionals before the winter holidays in the United States led to a significant reduction in holiday travel and subsequent COVID-19 infections.