Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates

58 Pages Posted: 8 Feb 2021 Last revised: 14 Mar 2021

See all articles by Minji Bang

Minji Bang

University of Pennsylvania - Department of Economics

Andrew Postlewaite

University of Pennsylvania - Department of Economics

Wayne Yuan Gao

University of Pennsylvania - Department of Economics

Holger Sieg

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 3 versions of this paper

Date Written: February 2021

Abstract

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 framework that accounts for the endogeneity of the covariates. We illustrate the usefulness 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.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Suggested Citation

Bang, Minji and Postlewaite, Andrew and Gao, Wayne and Sieg, Holger, Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates (February 2021). NBER Working Paper No. w28436, Available at SSRN: https://ssrn.com/abstract=3781323

Minji Bang (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

Andrew Postlewaite

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7350 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://www.econ.upenn.edu/~apostlew

Wayne Gao

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.waynegao.com

Holger Sieg

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
2
Abstract Views
63
PlumX Metrics