Alessandro Bonatti, Gonzalo Cisternas. The Review of Economic Studies, 87(2), 750–791, 2020
[PDF] [External Link] [Slides]
We study the implications of aggregating consumers’ purchase histories into scores that proxy for unobserved willingness to pay. A long-lived consumer interacts with a sequence of firms. Each firm relies on the consumer’s current score–a linear aggregate of noisy purchase signals—to learn about her preferences and to set prices. If the consumer is strategic, she reduces her demand to manipulate her score, which reduces the average equilibrium price. Firms in turn prefer scores that overweigh past signals relative to applying Bayes’ rule with disaggregated data, as this mitigates the ratchet effect and maximizes the firms’ ability to price discriminate. Consumers with high average willingness to pay benefit from data collection, because the gains from low average prices dominate the losses from price discrimination. Finally, hidden scores—those only observed by the firms—reduce demand sensitivity, increase average prices, and reduce consumer surplus, sometimes below the naive-consumer level.