Advances in data collection have made it increasingly easy to collect information on advertising exposures. However, translating this seemingly rich data into measures of advertising response has proven difficult, largely because of concerns that advertisers target customers with a higher propensity to buy or increase advertising during periods of peak demand. We show how this problem can be addressed by studying a setting where a firm randomly held out customers from each campaign, creating a sequence of randomized field experiments that mitigates (many) potential endogeneity problems. Exploratory analysis of individual holdout experiments shows positive effects for both email and catalog; however, the estimated effect for any individual campaign is imprecise, because of the small size of the holdout. To pool data across campaigns, we develop a hierarchical Bayesian model for advertising response that allows us to account for individual differences in purchase propensity and marketing response. Building on the traditional ad-stock framework, we are able to estimate separate decay rates for each advertising medium, allowing us to predict channel-specific short- and long-term effects of advertising and use these predictions to inform marketing strategy. We find that catalogs have substantially longer-lasting impact on customer purchase than emails. We show how the model can be used to score and target individual customers based on their advertising responsiveness, and we find that targeting the most responsive customers increases the predicted returns on advertising by approximately 70% versus traditional recency, frequency, and monetary value-based targeting.