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Constructive Identification of Heterogeneous Elasticities in the Cobb-Douglas Production Function

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  • Tong Li
  • Yuya Sasaki

Abstract

This paper presents the identification of heterogeneous elasticities in the Cobb-Douglas production function. The identification is constructive with closed-form formulas for the elasticity with respect to each input for each firm. We propose that the flexible input cost ratio plays the role of a control function under "non-collinear heterogeneity" between elasticities with respect to two flexible inputs. The ex ante flexible input cost share can be used to identify the elasticities with respect to flexible inputs for each firm. The elasticities with respect to labor and capital can be subsequently identified for each firm under the timing assumption admitting the functional independence.

Suggested Citation

  • Tong Li & Yuya Sasaki, 2017. "Constructive Identification of Heterogeneous Elasticities in the Cobb-Douglas Production Function," Papers 1711.10031, arXiv.org.
    • Handle: RePEc:arx:papers:1711.10031
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    File URL: http://arxiv.org/pdf/1711.10031
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    References listed on IDEAS

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    5. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    6. Paul L. E. Grieco & Shengyu Li & Hongsong Zhang, 2016. "Production Function Estimation With Unobserved Input Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 665-690, May.
    7. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    8. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    9. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63, Elsevier.
    10. Amit Gandhi & Salvador Navarro & David Rivers, 2017. "How Heterogeneous is Productivity? A Comparison of Gross Output and Value Added," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 201727, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    11. Ulrich Doraszelski & Jordi Jaumandreu, 2013. "R&D and Productivity: Estimating Endogenous Productivity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1338-1383.
    12. Hu, Yingyao & Huang, Guofang & Sasaki, Yuya, 2020. "Estimating production functions with robustness against errors in the proxy variables," Journal of Econometrics, Elsevier, vol. 215(2), pages 375-398.
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    Cited by:

    1. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    2. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    3. Ming Li, 2021. "A Time-Varying Endogenous Random Coefficient Model with an Application to Production Functions," Papers 2110.00982, arXiv.org.
    4. Yu Hao & Hiroyuki Kasahara, 2022. "Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data," Papers 2210.02824, arXiv.org, revised Jun 2023.

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