When a user shares her data with an online platform, she typically reveals relevant information about other users. We model a data market in the presence of this type of externality in a setup where one or multiple platforms estimate a user’s type with data they acquire from all users and (some) users value their privacy. We demonstrate that the data externalities depress the price of data because once a user’s information is leaked by others, she has less reason to protect her data and privacy. These depressed prices lead to excessive data sharing. We characterize conditions under which shutting down data markets improves (utilitarian) welfare. Competition between platforms does not redress the problem of excessively low price for data and too much data sharing, and may further reduce welfare. We propose a scheme based on mediated data-sharing that improves efficiency.