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Isoelastic Elasticity of Substitution Production Functions


  • Jakub Growiec
  • Jakub Muck


We generalize the normalized Constant Elasticity of Substitution (CES) production function by allowing the elasticity of substitution to vary isoelastically with (i) relative factor shares, (ii) marginal rates of substitution, (iii) capital–labor ratios, or (iv) capital–output ratios. Ensuing four variants of Isoelastic Elasticity of Substitution (IEES) production functions have a range of intuitively desirable properties and yield empirically testable predictions for the functional relationship between relative factor shares and (raw or technology-adjusted) capital–labor ratios. As an empirical application, the parameters of IEES functions are estimated in a three-equation supply-side system with factor-augmenting technical change, based on data on aggregate production in the post-war US economy. Our estimates consistently imply that the elasticity of substitution between capital and labor has remained relatively stable, at about 0.8–0.9, from 1948 to the 1980s, followed by a period of secular decline.

Suggested Citation

  • Jakub Growiec & Jakub Muck, 2016. "Isoelastic Elasticity of Substitution Production Functions," Working Papers 2016-001, Warsaw School of Economics, Collegium of Economic Analysis.
  • Handle: RePEc:sgh:kaewps:2016001

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    References listed on IDEAS

    1. McAdam, Peter & Muck, Jakub & Growiec, Jakub, 2015. "Will the true labor share stand up?," Working Paper Series 1806, European Central Bank.
    2. Smulders, Sjak & de Nooij, Michiel, 2003. "The impact of energy conservation on technology and economic growth," Resource and Energy Economics, Elsevier, vol. 25(1), pages 59-79, February.
    3. repec:eee:dyncon:v:87:y:2018:i:c:p:74-93 is not listed on IDEAS
    4. Thomas Piketty & Gabriel Zucman, 2014. "Capital is Back: Wealth-Income Ratios in Rich Countries 1700–2010," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1255-1310.
    5. repec:lsu:lsuwpp:2003-12 is not listed on IDEAS
    6. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    7. 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.
    8. Jürgen Antony, 2010. "A class of changing elasticity of substitution production functions," Journal of Economics, Springer, vol. 100(2), pages 165-183, June.
    9. John Duffy & Chris Papageorgiou & Fidel Perez-Sebastian, 2004. "Capital-Skill Complementarity? Evidence from a Panel of Countries," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 327-344, February.
    10. PETER McADAM & ALPO WILLMAN, 2013. "Technology, Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(8), pages 1547-1579, December.
    11. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.
    12. Saam, Marianne, 2008. "Openness to trade as a determinant of the macroeconomic elasticity of substitution," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 691-702, June.
    13. Robert S. Chirinko, 2008. "ó: The Long And Short Of It," CESifo Working Paper Series 2234, CESifo Group Munich.
    14. Irmen, Andreas, 2011. "Steady-state growth and the elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1215-1228, August.
    15. Ezra Oberfield & Devesh Raval, 2012. "Micro data and macro technology," Working Paper Series WP-2012-11, Federal Reserve Bank of Chicago.
    16. Chris Papageorgiou & Marianne Saam, 2008. "Two-level CES Production Technology in the Solow and Diamond Growth Models," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(1), pages 119-143, March.
    17. Xue, Jianpo & Yip, Chong K., 2013. "Aggregate elasticity of substitution and economic growth: A synthesis," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 60-75.
    18. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    19. Miguel A. Leon-Ledesma & Mathan Satchi, 2015. "Appropriate Technology and the Labour Share," Studies in Economics 1505, School of Economics, University of Kent, revised Nov 2016.
    20. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2004. "Factor substitution and factor augmenting technical progress in the US: a normalized supply-side system approach," Working Paper Series 367, European Central Bank.
    21. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    22. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor-augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502.
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    More about this item


    production function; factor share; elasticity of substitution; marginal rate of substitution; normalization;

    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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