Rows and Columns: A Theory of Returns to Data

A firm learns how covariates affect an outcome, then predicts it. Some covariates, like a user's next search, arrive too late to use but help the firm learn. With enough of them, each observation adds more than the last in small samples; without them, each adds less. Each covariate helps the firm learn the others' effects; how fast prediction error falls with sample size measures these spillovers. This reconciles conflicting evidence on returns to data. Suppliers of covariates with rights over data claim more than the data are worth; rights for individuals avoid this unless enough covariates arrive late.