The difference between the actual incidence and the predicted incidence is an estimate of the treatment effect. Because the standard error of each prediction is large, we combine estimates across events to obtain an average treatment effect. We also perform the same analysis for the event counties focusing on a “placebo event” occurring 10 weeks before the actual event. This exercise allows us to determine whether our method systematically mispredicts the outcomes for event counties, and to evaluate the possible existence of pre-event trend in “unexplained” cases occurring prior to the event (which, in principle, could produce spurious treatment effects after the event). Although our methods involve prediction models, it is important to understand that the nature of these predictions differ in critical ways from the types of predictions generated by epidemiological models. In the typical epidemiological analysis, predictions for a collection of jurisdictions between a fixed point in time, t (often the present), and some subsequent point in time, t 0 , are based only on data pertaining to period t and earlier periods (e.g., current and past data). In contrast, our approach is to predict outcomes in an event jurisdiction between periods t and t 0 based not only on that jurisdiction’s history up until t, but also on the complete histories of comparable counties through period t 0 . In other words, our predictions employ “future” data for comparable counties, whereas epidemiological models do not. Consequently, in contrast to the epidemiologists, we are not forecasting into an unobserved period of time. Rather, we are observing outcomes within the forecast period for comparable counties, and making inferences about the county of interest based on similarities. For the vast majority of county matching procedures we employ, our estimate of the average treatment effect across the eighteen rallies implies that they increased subsequent confirmed cases of COVID-19 by more than 250 per 100,000 residents. In contrast, the pseudo-treatment effects for the placebo events are small, slightly negative, and statistically insignificant. The striking contrast between the estimated treatment effects for the actual events and the pseudo-treatment effects for the placebo events underscores the reliability of our results. Extrapolating the average treatment effects to the entire sample, we conclude that these eighteen rallies ultimately resulted in more than 30,000 incremental confirmed cases of COVID-19. Applying county-specific post-event death rates, we conclude that the rallies likely led to more than 700 deaths (not necessarily among attendees). We are aware of a small handful of related analyses. Dave et al. (2020) focus on the Tulsa rally. Based on a synthetic control involving comparable counties, they find no elevation in new cases or deaths. A problem with focusing on a single event is that COVID-19 outcomes are highly variable, as indicated by the magnitudes of the standard errors of the forecasts in our analysis. In such settings, measuring the average treatment effect over multiple events, as in our study, produces more reliable results. Like us, Waldrop and Gee (2020) follow the strategy of focusing on a collection of rallies,1 but their analysis simply asks whether cases in the three weeks following the rally were above or below pre-existing trends. Our analysis involves more elaborate forecasts and encompasses up to 10 weeks of post-event data. The latter difference may be particular important, in that the effects of a superspreader event may snowball over time. Even so, the study’s conclusions 1Because they focused on a shorter post-event window, they employed data on 22 rally events, whereas we study 18. 3 corroborate ours: “...the Trump rallies are often followed by increased community spread of the coronavirus...”. Analysis in Nayer (2020) points to a similar conclusion. The paper is organized as follows. Section 2 describes the data used in our analysis, Section 3 details our methods and presents our main results, Section 4 presents additional analyses of highly impacted counties, and Section 5 concludes. 2 Data 2.1 Trump rallies We focus on rallies held between June 20th and September 22nd.
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