Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates
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 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 frame-work that accounts for the endogeneity of the covariates. We illustrate the use-fulness of our method using two applications. The ﬁrst focuses on pharmacies: we ﬁnd that production function diﬀerences between chains and independent pharmacies may partially explain the observed transformation of the industry structure. Our second application investigates education achievement functions and illustrates important diﬀerences in child investments between married and divorced couples.