Inference considerations
We apply one-tailed hypothesis tests in most specifications for two reasons. First, low signal-to-noise ratios make measuring the effects of advertising notoriously difficult. One recent contribution concluded that “informative advertising experiments can easily require more than 10 million person-weeks, making experiments costly and potentially infeasible” (We adopt two main approaches to conducting inference throughout: randomization inference and county-level clustering. In randomization inference (It bears emphasis that the assumptions underlying randomization inference differ from those of asymptotic approaches (our clustering approaches): Where the asymptotic approaches test the null hypothesis that the average treatment effect across units is zero, randomization inference tests the more restrictive hypothesis that the effect is zero for every unit, which recent work of Wu and Ding (For our second approach—clustered standard errors—our pre-registration plan stated an intention to estimate uncertainty with state-level clustering (43 clusters) to allow for the possibility that county-level residuals may be correlated within a state. The choice of the level at which to cluster standard errors is the subject of ongoing research in econometrics. It is known that bias can result from having too few clusters on one hand or from not clustering at an aggregate enough level on the other. However, the question of what constitutes “too few” is unresolved; some researchers point to 50 as a reasonable threshold, others to 20 (Our pre-registered preference for state-level clustering was driven by this conventional wisdom. More aggregate clustering typically results in larger standard errors, but, as highlighted by Cameron and Miller (We find this to be the case in our setting, where the standard errors on our effects of interest are smaller under state-level clustering or stratum-level clustering than under county-level clustering. Table S10 demonstrates these results. There, we find that our results from 