Data is nonrival: a person's location history, medical records, and driving data can be used by many firms simultaneously. Nonrivalry leads to increasing returns. As a result, there may be social gains to data being used broadly across firms, even in the presence of privacy considerations. Fearing creative destruction, firms may choose to hoard their data, leading to the inefficient use of nonrival data. Giving data property rights to consumers can generate allocations that are close to optimal. Consumers balance their concerns for privacy against the economic gains that come from selling data broadly.