Estimating Production Functions with Partially Latent Inputs

This paper develops a new method for identifying and estimating production functions with partially latent inputs. Such data structures arise naturally when 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 inputs can be nonparametrically identified, if they are strictly monotone functions of a scalar shock a la Olley and Pakes (1996). With the latent inputs identified, semiparametric estimation of the production function proceeds within an IV framework that accounts for the imputation of inputs. 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 skill production functions and illustrates important differences in child investments between married and divorced couples.