This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise naturally in industrial organization and labor economics settings where data are collected using an "input-based sampling" strategy, e.g., if the sampling unit is one...

Different markets are cleared by different types of prices—seller-specific prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market....