Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates

TL;DR

This paper introduces a novel method leveraging monotonicity restrictions to identify models with partially latent covariates, enabling semiparametric estimation in econometric models with complex data structures.

Contribution

It provides a nonparametric identification approach for latent covariates using monotonicity assumptions, applicable in industrial and labor economics contexts.

Findings

Latent covariates can be nonparametrically identified under monotonicity.

The method allows semiparametric estimation within an IV framework.

Application to pharmacy production functions reveals industry technology differences.

Abstract

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.