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Beyond Cobb-Douglas: Estimation of a CES Production Function with Factor Augmenting Technology

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  • Devesh Raval
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    Abstract

    Both the recent literature on production function identification and a considerable body of other empirical work on firm expansion assume a Cobb-Douglas production function. Under this assumption, all technical differences are Hicks neutral. I provide evidence from US manufacturing plants against Cobb-Douglas and present an alternative production function that better fits the data. A Cobb Douglas production function has two empirical implications that I show do not hold in the data: a constant cost share of capital and strong comovement in labor productivity and capital productivity (revenue per unit of capital). Within four digit industries, differences in cost shares of capital are persistent over time. Both the capital share and labor productivity increase with revenue, but capital productivity does not. A CES production function with labor augmenting differences and an elasticity of substitution between labor and capital less than one can account for these facts. To identify the labor capital elasticity, I use variation in wages across local labor markets. Since the capital cost to labor cost ratio falls with local area wages, I strongly reject Cobb-Douglas: capital and labor are complements. Now productivity differences are no longer neutral, which has implications on how productivity affects firms’ decisions to expand or contract. Non neutral technical improvements will result in higher stocks of capital but not necessarily more hiring of labor. Specifying the correct form of the production function is more generally important for empirical work, as I demonstrate by applying my methodology to address questions of misallocation of capital.

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    File URL: ftp://ftp2.census.gov/ces/wp/2011/CES-WP-11-05.pdf
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    Bibliographic Info

    Paper provided by Center for Economic Studies, U.S. Census Bureau in its series Working Papers with number 11-05.

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    Length: 60 pages
    Date of creation: Feb 2011
    Date of revision:
    Handle: RePEc:cen:wpaper:11-05

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    1. Lucia Foster & John Haltiwanger & Chad Syverson, 2005. "Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability?," Working Papers 05-11, Center for Economic Studies, U.S. Census Bureau.
    2. León-Ledesma, Miguel A. & McAdam, Peter & Willman, Alpo, 2009. "Identifying the elasticity of substitution with biased technical change," Working Paper Series 1001, European Central Bank.
    3. Richard Rogerson & Diego Restuccia, 2004. "Policy Distortions and Aggregate Productivity with Heterogeneous Plants," 2004 Meeting Papers 69, Society for Economic Dynamics.
    4. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    5. Daniel Yi Xu & Virgiliu Midrigan, 2009. "Accounting for Plant-level Misallocation," 2009 Meeting Papers 223, Society for Economic Dynamics.
    6. Thomas J. Holmes, 1996. "The effects of state policies on the location of industry: evidence from state borders," Staff Report 205, Federal Reserve Bank of Minneapolis.
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      by himaginary in himaginaryの日記 on 2012-08-28 07:00:00
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    Cited by:
    1. Zhang, Hongsong, 2013. "Biased Technology and Contribution of Technological Change to Economic Growth: Firm-Level Evidence," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150225, Agricultural and Applied Economics Association.

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