Estimating Production Functions in Differentiated-Product Industries with Quantity Information and External Instruments

94 Pages Posted: 27 Jan 2021

See all articles by Nicolás de Roux

Nicolás de Roux

Universidad de los Andes - Department of Economics

Marcela Eslava

University of the Andes (CEDE)

Santiago Franco

University of Chicago

Eric A. Verhoogen

Columbia University - School of International & Public Affairs (SIPA); IZA Institute of Labor Economics; Centre for Economic Policy Research (CEPR)

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Date Written: January 26, 2021

Abstract

This paper develops a new method for estimating production-function parameters that can be applied in differentiated-product industries with endogenous quality and variety choice. We take advantage of data on physical quantities of outputs and inputs from the Colombian manufacturing survey, focusing on producers of rubber and plastic products. Assuming constant elasticities of substitution of outputs and inputs within firms, we aggregate from the firm-product to the firm level and show how quality and variety choices may bias standard estimators. Using real exchange rates and variation in the "bite" of the national minimum wage, we construct external instruments for materials and labor choices. We implement a simple two-step instrumental-variables method, first estimating a difference equation to recover the materials and labor coefficients and then estimating a levels equation to recover the capital coefficient. Under the assumption that the instruments are uncorrelated with firms' quality and variety choices, this method yields consistent estimates, free of the quality and variety biases we have identified. Our point estimates differ from those of existing methods and changes in our preferred productivity estimator perform relatively well in predicting future export growth.

Keywords: production-function estimation, quality, variety, external instruments

JEL Classification: L1, D24, O14, L65

Suggested Citation

de Roux, Nicolás and Eslava, Marcela and Franco, Santiago and Verhoogen, Eric A., Estimating Production Functions in Differentiated-Product Industries with Quantity Information and External Instruments (January 26, 2021). Documento CEDE No. 2, Available at SSRN: https://ssrn.com/abstract=3774458 or http://dx.doi.org/10.2139/ssrn.3774458

Nicolás De Roux (Contact Author)

Universidad de los Andes - Department of Economics ( email )

Carrera 1a No. 18A-10
Bogota, AA4976
Colombia

Marcela Eslava

University of the Andes (CEDE) ( email )

Carrera 1a No. 18A-10
Santafe de Bogota, AA4976
Colombia

Santiago Franco

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Eric A. Verhoogen

Columbia University - School of International & Public Affairs (SIPA) ( email )

420 West 118th Street
New York, NY 10027
United States

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

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