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Capital-Labor-Energy Substitution in Nested CES Production Functions for China

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  • Keting Shen
  • John Whalley

Abstract

In the CGE based policy modeling literature, especially recent literature on policy modeling for global climate change, nested CES production functions over multiple inputs have been widely used. Although lack of reliable estimates of substitution elasticities for nested structures has been acknowledged for a long time, the problem has not yet been solved satisfactorily. This is especially the situation for the Chinese case for which modeling work has global implications. This paper reports estimates of substitution elasticities for normalized nested CES aggregate production functions for China with different nested structures of input factors: capital, labor with or without human capital adjustment, and energy using data for the period 1979-2006. We adopt grid search based non-linear optimization techniques for estimation. The results show that all the substitution elasticities we estimate are positive. For the widely used (K,L)E structure, we find that the substitution elasticity between capital and labor for China is below unity. When human capital adjusted labor is used as input instead of unadjusted raw labor, estimates of substitution elasticity between capital and labor become lower. By considering the significance of estimates, our results suggest that the (E,L)K structure seems more appropriate for the Chinese economy.

Suggested Citation

  • Keting Shen & John Whalley, 2013. "Capital-Labor-Energy Substitution in Nested CES Production Functions for China," NBER Working Papers 19104, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:19104
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Stephen K. Layson, 2015. "The increasing returns to scale CES production function and the law of diminishing marginal returns," Southern Economic Journal, Southern Economic Association, vol. 82(2), pages 408-415, October.
    2. Craxton, Melanie & Merrick, James & Makridis, Christos & Taggart, John, 2017. "On the climate policy implications of substitutability and flexibility in the economy: An in-depth integrated assessment model diagnostic," Technological Forecasting and Social Change, Elsevier, vol. 125(C), pages 289-298.
    3. Mr. Edward F Buffie & Mr. Christopher S Adam, 2020. "The Minimum Wage Puzzle in Less Developed Countries: Reconciling Theory and Evidence," IMF Working Papers 2020/023, International Monetary Fund.
    4. Valeria Costantini & Francesco Crespi & Elena Paglialunga, 2019. "Capital–energy substitutability in manufacturing sectors: methodological and policy implications," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 9(2), pages 157-182, June.
    5. Layson, Stephen K., 2013. "The Law of Diminishing Returns and the Generalized CES Production Function," UNCG Economics Working Papers 13-13, University of North Carolina at Greensboro, Department of Economics.
    6. repec:wly:soecon:v:82:2:y:2015:p:408-415 is not listed on IDEAS
    7. He, Yongda & Lin, Boqiang, 2019. "Heterogeneity and asymmetric effects in energy resources allocation of the manufacturing sectors in China," Energy, Elsevier, vol. 170(C), pages 1019-1035.
    8. Henningsen, Arne & Henningsen, Geraldine & van der Werf, Edwin, 2019. "Capital-labour-energy substitution in a nested CES framework: A replication and update of Kemfert (1998)," Energy Economics, Elsevier, vol. 82(C), pages 16-25.
    9. Valeria Costantini & Elena Paglialunga, 2014. "Elasticity of substitution in capital-energy relationships: how central is a sector-based panel estimation approach?," SEEDS Working Papers 1314, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised May 2014.
    10. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    11. Skelton, Alexandra C.H. & Paroussos, Leonidas & Allwood, Julian M., 2020. "Comparing energy and material efficiency rebound effects: an exploration of scenarios in the GEM-E3 macroeconomic model," Ecological Economics, Elsevier, vol. 173(C).
    12. Haishu Qiao & Ying Li & Julien Chevallier & Bangzhu Zhu, 2016. "Capital–energy substitution in China: regional differences and dynamic evolution," Post-Communist Economies, Taylor & Francis Journals, vol. 28(4), pages 421-435, October.
    13. Xiaofeng Li & Tingjie Lu, 2020. "Capital, labor, and derived demand for information: Evidence from China," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(3), pages 339-353, April.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • Q43 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy and the Macroeconomy
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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