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Normalizing VES production functions: extending the supply-side system approach

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  • Del Río, Fernando
  • Rebelo, Francisco

Abstract

This paper extends the Klump et al. (2007) normalization procedure to Variable Elasticity of Substitution (VES) production functions. Normalization addresses identification issues in VES model estimation, allowing joint estimation of substitution elasticities and factor-augmenting technical change, while offering a tractable extension of the normalized supply-side system that bridges the gap between CES and more flexible VES specifications.

Suggested Citation

  • Del Río, Fernando & Rebelo, Francisco, 2026. "Normalizing VES production functions: extending the supply-side system approach," Economics Letters, Elsevier, vol. 259(C).
    • Handle: RePEc:eee:ecolet:v:259:y:2026:i:c:s0165176525006317
    DOI: 10.1016/j.econlet.2025.112794
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    References listed on IDEAS

    as
    1. Kazi, Umar A, 1980. "The Variable Elasticity of Substitution Production Function: A Case Study for Indian Manufacturing Industries," Oxford Economic Papers, Oxford University Press, vol. 32(1), pages 163-175, March.
    2. del Río, Fernando & Lores, Francisco-Xavier, 2023. "Accounting for spanish economic development 1850–2019," Economic Modelling, Elsevier, vol. 121(C).
    3. Fernando del Río & Francisco‐Xavier Lores, 2023. "Accounting for the role of investment frictions in recessions," Economica, London School of Economics and Political Science, vol. 90(360), pages 1089-1118, October.
    4. Gómez, Manuel A., 2023. "Factor substitution, long-run equilibrium, and convergence speed in the Lucas model," Economics Letters, Elsevier, vol. 232(C).
    5. Antony, Jürgen, 2009. "A dual elasticity of substitution production function with an application to cross-country inequality," Economics Letters, Elsevier, vol. 102(1), pages 10-12, January.
    6. Serrano-Quintero, Rafael, 2023. "The aggregate productivity slowdown: A system approach," Economics Letters, Elsevier, vol. 223(C).
    7. Fernando del Río & Francisco‐Xavier Lores, 2019. "The Decline in Capital Efficiency and Labour Share," Economica, London School of Economics and Political Science, vol. 86(344), pages 635-662, October.
    8. Marc Nerlove, 1967. "Recent Empirical Studies of the CES and Related Production Functions," NBER Chapters, in: The Theory and Empirical Analysis of Production, pages 55-136, National Bureau of Economic Research, Inc.
    9. 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.
    10. Andreas Irmen & Rainer Klump, 2009. "Factor Substitution, Income Distribution and Growth in a Generalized Neoclassical Model," German Economic Review, Verein für Socialpolitik, vol. 10(4), pages 464-479, November.
    11. Revankar, Nagesh S, 1971. "A Class of Variable Elasticity of Substitution Production Functions," Econometrica, Econometric Society, vol. 39(1), pages 61-71, January.
    12. repec:bla:germec:v:10:y:2009:i::p:464-479 is not listed on IDEAS
    13. Del Río, Fernando & Rebelo, Francisco, 2025. "OECD labour share trends: Factor efficiency vs. market distortions in a neoclassical framework," Economic Analysis and Policy, Elsevier, vol. 87(C), pages 2554-2591.
    14. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    15. Gómez, Manuel A., 2018. "Factor substitution and convergence speed in the neoclassical model with elastic labor supply," Economics Letters, Elsevier, vol. 172(C), pages 89-92.
    16. Rainer Klump & Peter McAdam & Alpo Willman, 2007. "Factor Substitution and Factor-Augmenting Technical Progress in the United States: A Normalized Supply-Side System Approach," The Review of Economics and Statistics, MIT Press, vol. 89(1), pages 183-192, February.
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    Keywords

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    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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