Estimating Production Functions with Partially Latent Inputs

55 Pages Posted: 2 Feb 2021 Last revised: 6 Apr 2021

See all articles by Minji Bang

Minji Bang

University of Pennsylvania - Department of Economics

Wayne Yuan Gao

University of Pennsylvania - Department of Economics

Andrew Postlewaite

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: January 14, 2021

Abstract

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.

Keywords: production functions, latent variables, endogeneity, semiparametric estimation, instrumental variables, matching

Suggested Citation

Bang, Minji and Gao, Wayne and Postlewaite, Andrew and Sieg, Holger, Estimating Production Functions with Partially Latent Inputs (January 14, 2021). PIER Working Paper No. 21-003, Available at SSRN: https://ssrn.com/abstract=3777381 or http://dx.doi.org/10.2139/ssrn.3777381

Minji Bang

University of Pennsylvania - Department of Economics ( email )

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

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

Andrew Postlewaite (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
215-898-7350 (Phone)
215-573-2057 (Fax)

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

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
12
Abstract Views
139
PlumX Metrics