  This paper develops a new method for identifying econometric models with
partially latent covariates. Such data structures arise 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 of multiple
labor input factors. We show that the latent covariates can be
nonparametrically identified, if they are functions of a common shock
satisfying some plausible monotonicity assumptions. With the latent covariates
identified, semiparametric estimation of the outcome equation proceeds within a
standard IV framework that accounts for the endogeneity of the covariates. We
illustrate the usefulness of our method using a new application that focuses on
the production functions of pharmacies. We find that differences in technology
between chains and independent pharmacies may partially explain the observed
transformation of the industry structure.
