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

Author

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  • Nicolás de Roux
  • Marcela Eslava
  • Santiago Franco
  • Eric Verhoogen

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.

Suggested Citation

  • Nicolás de Roux & Marcela Eslava & Santiago Franco & Eric Verhoogen, 2021. "Estimating Production Functions in Differentiated-Product Industries with Quantity Information and External Instruments," NBER Working Papers 28323, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:28323
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    References listed on IDEAS

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    1. Sanderson, Eleanor & Windmeijer, Frank, 2016. "A weak instrument F-test in linear IV models with multiple endogenous variables," Journal of Econometrics, Elsevier, vol. 190(2), pages 212-221.
    2. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    3. Gabriele Rovigatti & Vincenzo Mollisi, 2018. "Theory and practice of total-factor productivity estimation: The control function approach using Stata," Stata Journal, StataCorp LP, vol. 18(3), pages 618-662, September.
    4. Sebastian Kripfganz & Claudia Schwarz, 2019. "Estimation of linear dynamic panel data models with time‐invariant regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(4), pages 526-546, June.
    5. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    6. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    7. Amit Gandhi & Salvador Navarro & David A. Rivers, 2020. "On the Identification of Gross Output Production Functions," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 2973-3016.
    8. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
    9. Isaiah Andrews, 2018. "Valid Two-Step Identification-Robust Confidence Sets for GMM," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 337-348, May.
    10. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
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    Cited by:

    1. Francesco Amodio & Nicolás de Roux, 2021. "Labor Market Power in Developing Countries: Evidence from Colombian Plants," Documentos CEDE 019267, Universidad de los Andes – Facultad de Economía – CEDE.
    2. Andrés Álvarez & Juan Camilo Chaparro & Carolina González & Santiago Levy & Darío Maldonado & Marcela Meléndez & Natalia Ramírez & Marta Juanita Villaveces, 2022. "Reporte ejecutivo de la Misión de Empleo de Colombia," Documentos de trabajo 020156, Escuela de Gobierno - Universidad de los Andes.
    3. Jamil, Nida & Chaudhry, Theresa Thompson & Chaudhry, Azam, 2022. "Trading textiles along the new silk route: The impact on Pakistani firms of gaining market access to China," Journal of Development Economics, Elsevier, vol. 158(C).
    4. Austan Goolsbee & Chad Syverson, 2022. "The Strange and Awful Path of Productivity in the US Construction Sector," NBER Chapters, in: Technology, Productivity, and Economic Growth, National Bureau of Economic Research, Inc.

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    More about this item

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology; Plastics
    • O14 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Industrialization; Manufacturing and Service Industries; Choice of Technology

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