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


  • Devesh Raval


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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  • Devesh Raval, 2011. "Beyond Cobb-Douglas: Estimation of a CES Production Function with Factor Augmenting Technology," Working Papers 11-05, Center for Economic Studies, U.S. Census Bureau.
  • Handle: RePEc:cen:wpaper:11-05

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    References listed on IDEAS

    1. Diego Restuccia & Richard Rogerson, 2008. "Policy Distortions and Aggregate Productivity with Heterogeneous Plants," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 707-720, October.
    2. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-1357, September.
    3. Chad Syverson, 2011. "What Determines Productivity?," Journal of Economic Literature, American Economic Association, vol. 49(2), pages 326-365, June.
    4. 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.
    5. Benjamin Moll, 2014. "Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation?," American Economic Review, American Economic Association, vol. 104(10), pages 3186-3221, October.
    6. Lucia Foster & John Haltiwanger & Chad Syverson, 2008. "Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability?," American Economic Review, American Economic Association, vol. 98(1), pages 394-425, March.
    7. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
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    1. [経済]竹馬に乗ったナンセンス・再訪
      by himaginary in himaginaryの日記 on 2012-08-28 12:00:00


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    Cited by:

    1. Nguyen, Huy, 2014. "The effect of land fragmentation on labor allocation and the economic diversity of farm households: The case of Vietnam," MPRA Paper 57521, University Library of Munich, Germany.
    2. Knoblach, Michael & Rößler, Martin & Zwerschke, Patrick, 2016. "The Elasticity of Factor Substitution Between Capital and Labor in the U.S. Economy: A Meta-Regression Analysis," CEPIE Working Papers 03/16, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    3. 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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