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Estimating elasticities of substitution with nested CES production functions: Where do we stand?

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  • Lagomarsino, Elena

Abstract

Prompt by an increasing interest by climate change modelers, a rich literature estimating elasticities of substitution in a nested CES production framework has recently developed. This article reviews such literature. We critically describe the nesting structures, estimation approaches, data sources and aggregation, econometric techniques, and types of substitution elasticities used by previous literature, to offer a comprehensive description of the various options available to a researcher attempting this estimation. We also provide suggestions for potential improvements to the estimation process. In particular, we warn researchers to use CES production functions with caution in empirical applications given their restrictive build-in assumptions.

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  • Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
  • Handle: RePEc:eee:eneeco:v:88:y:2020:i:c:s0140988320300918
    DOI: 10.1016/j.eneco.2020.104752
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    as
    1. Kurt Kratena, 2007. "Technical Change, Investment and Energy Intensity," Economic Systems Research, Taylor & Francis Journals, vol. 19(3), pages 295-314.
    2. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," Review of Economic Studies, Oxford University Press, vol. 34(3), pages 249-283.
    3. 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.
    4. Jacoby, Henry D. & Reilly, John M. & McFarland, James R. & Paltsev, Sergey, 2006. "Technology and technical change in the MIT EPPA model," Energy Economics, Elsevier, vol. 28(5-6), pages 610-631, November.
    5. Mahmood Moghimzadeh & Kern O. Kymn, 1986. "Cost Shares, Own, and Cross-Price Elasticities in U.S. Manufacturing with Disaggregated Energy Inputs," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 65-80.
    6. Thompson, Gary D., 1988. "Choice Of Flexible Functional Forms: Review And Appraisal," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 13(2), pages 1-15, December.
    7. Turnovsky, Michelle & Folie, Michael & Ulph, Alistair, 1982. "Factor Substitutability in Australian Manufacturing with Emphasis on Energy Inputs," The Economic Record, The Economic Society of Australia, vol. 58(160), pages 61-72, March.
    8. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    9. Chung, Jae Wan, 1987. "On the Estimation of Factor Substitution in the Translog Model," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 409-417, August.
    10. Alexeeva-Talebi, Victoria & Böhringer, Christoph & Löschel, Andreas & Voigt, Sebastian, 2012. "The value-added of sectoral disaggregation: Implications on competitive consequences of climate change policies," Energy Economics, Elsevier, vol. 34(S2), pages 127-142.
    11. Azusa OKAGAWA & Kanemi BAN, 2008. "Estimation of substitution elasticities for CGE models," Discussion Papers in Economics and Business 08-16, Osaka University, Graduate School of Economics.
    12. Yazid Dissou & Lilia Karnizova & Qian Sun, 2015. "Industry-level Econometric Estimates of Energy-Capital-Labor Substitution with a Nested CES Production Function," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 43(1), pages 107-121, March.
    13. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    14. Henningsen, Arne & Henningsen, Géraldine, 2012. "On estimation of the CES production function—Revisited," Economics Letters, Elsevier, vol. 115(1), pages 67-69.
    15. Griffin, James M & Gregory, Paul R, 1976. "An Intercountry Translog Model of Energy Substitution Responses," American Economic Review, American Economic Association, vol. 66(5), pages 845-857, December.
    16. Turner, Karen, 2009. "Negative rebound and disinvestment effects in response to an improvement in energy efficiency in the UK economy," Energy Economics, Elsevier, vol. 31(5), pages 648-666, September.
    17. Haller, Stefanie A. & Hyland, Marie, 2014. "Capital–energy substitution: Evidence from a panel of Irish manufacturing firms," Energy Economics, Elsevier, vol. 45(C), pages 501-510.
    18. Berndt, Ernst R & Wood, David O, 1979. "Engineering and Econometric Interpretations of Energy-Capital Complementarity," American Economic Review, American Economic Association, vol. 69(3), pages 342-354, June.
    19. van der Werf, Edwin, 2008. "Production functions for climate policy modeling: An empirical analysis," Energy Economics, Elsevier, vol. 30(6), pages 2964-2979, November.
    20. Iqbal, Mahmood, 1986. "Substitution of Labour, Capital and Energy in the Manufacturing Sector of Pakistan," Empirical Economics, Springer, vol. 11(2), pages 81-95.
    21. Medina, J. & Vega-Cervera, J. A., 2001. "Energy and the non-energy inputs substitution: evidence for Italy, Portugal and Spain," Applied Energy, Elsevier, vol. 68(2), pages 203-214, February.
    22. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," Review of Economic Studies, Oxford University Press, vol. 34(2), pages 201-218.
    23. Thursby, Jerry G & Lovell, C A Knox, 1978. "An Investigation of the Kmenta Approximation to the CES Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 363-377, June.
    24. Baccianti, Claudio, 2013. "Estimation of sectoral elasticities of substitution along the international technology frontier," ZEW Discussion Papers 13-092, ZEW - Leibniz Centre for European Economic Research.
    25. Feng, Shenghao & Zhang, Keyu, 2018. "Fuel-factor nesting structures in CGE models of China," Energy Economics, Elsevier, vol. 75(C), pages 274-284.
    26. Kemfert, Claudia, 1998. "Estimated substitution elasticities of a nested CES production function approach for Germany," Energy Economics, Elsevier, vol. 20(3), pages 249-264, June.
    27. 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.
    28. Berndt, Ernst R & Wood, David O, 1975. "Technology, Prices, and the Derived Demand for Energy," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 259-268, August.
    29. Pindyck, Robert S, 1979. "Interfuel Substitution and the Industrial Demand for Energy: An International Comparison," The Review of Economics and Statistics, MIT Press, vol. 61(2), pages 169-179, May.
    30. Chang, Kuo-Ping, 1994. "Capital-energy substitution and the multi-level CES production function," Energy Economics, Elsevier, vol. 16(1), pages 22-26, January.
    31. Koetse, Mark J. & de Groot, Henri L.F. & Florax, Raymond J.G.M., 2008. "Capital-energy substitution and shifts in factor demand: A meta-analysis," Energy Economics, Elsevier, vol. 30(5), pages 2236-2251, September.
    32. Dargay, Joyce M, 1983. " The Demand for Energy in Swedish Manufacturing Industries," Scandinavian Journal of Economics, Wiley Blackwell, vol. 85(1), pages 37-51.
    33. Apostolakis, Bobby E., 1990. "Energy--capital substitutability/ complementarity : The dichotomy," Energy Economics, Elsevier, vol. 12(1), pages 48-58, January.
    34. Simon Koesler & Michael Schymura, 2015. "Substitution Elasticities In A Constant Elasticity Of Substitution Framework - Empirical Estimates Using Nonlinear Least Squares," Economic Systems Research, Taylor & Francis Journals, vol. 27(1), pages 101-121, March.
    35. Gasper A. Garofalo & Devinder M. Malhotra, 1988. "Aggregation of Capital and Its Substitution with Energy," Eastern Economic Journal, Eastern Economic Association, vol. 14(3), pages 251-262, Jul-Sep.
    36. Su, Xuanming & Zhou, Weisheng & Nakagami, Ken'Ichi & Ren, Hongbo & Mu, Hailin, 2012. "Capital stock-labor-energy substitution and production efficiency study for China," Energy Economics, Elsevier, vol. 34(4), pages 1208-1213.
    37. Despotakis, Kostas A. & Fisher, Anthony C., 1988. "Energy in a regional economy: A computable general equilibrium model for california," Journal of Environmental Economics and Management, Elsevier, vol. 15(3), pages 313-330, September.
    38. Antoszewski, Michał, 2019. "Wide-range estimation of various substitution elasticities for CES production functions at the sectoral level," Energy Economics, Elsevier, vol. 83(C), pages 272-289.
    39. Zha, Donglan & Zhou, Dequn, 2014. "The elasticity of substitution and the way of nesting CES production function with emphasis on energy input," Applied Energy, Elsevier, vol. 130(C), pages 793-798.
    40. Thomas W. Hertel & Timothy D. Mount, 1985. "The Pricing of Natural Resources in a Regional Economy," Land Economics, University of Wisconsin Press, vol. 64(3), pages 229-243.
    41. 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.
    42. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," Review of Economic Studies, Oxford University Press, vol. 29(4), pages 291-299.
    43. Michael Denny & J. Douglas May & Cheryl Pinto, 1978. "The Demand for Energy in Canadian Manufacturing: Prologue to an Energy Policy," Canadian Journal of Economics, Canadian Economics Association, vol. 11(2), pages 300-313, May.
    44. Frondel, Manuel, 2011. "Modelling energy and non-energy substitution: A brief survey of elasticities," Energy Policy, Elsevier, vol. 39(8), pages 4601-4604, August.
    45. 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.
    46. Lecca, Patrizio & Swales, Kim & Turner, Karen, 2011. "An investigation of issues relating to where energy should enter the production function," Economic Modelling, Elsevier, vol. 28(6), pages 2832-2841.
    47. Hisnanick, John J. & Kyer, Ben L., 1995. "Assessing a disaggregated energy input : Using confidence intervals around translog elasticity estimates," Energy Economics, Elsevier, vol. 17(2), pages 125-132, April.
    48. Manuel Frondel & Christoph M. Schmidt, 2002. "The Capital-Energy Controversy: An Artifact of Cost Shares?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 53-79.
    49. Roy, Joyashree & Sanstad, Alan H. & Sathaye, Jayant A. & Khaddaria, Raman, 2006. "Substitution and price elasticity estimates using inter-country pooled data in a translog cost model," Energy Economics, Elsevier, vol. 28(5-6), pages 706-719, November.
    50. Berndt, Ernst R. & Christensen, Laurits R., 1973. "The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929-68," Journal of Econometrics, Elsevier, vol. 1(1), pages 81-113, March.
    51. Ernst Berndt & Charles Kolstad & Jong-Kun Lee, 1993. "Measuring the Energy Efficiency and Productivity Impacts of Embodied Technical Change," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 33-56.
    52. Prywes, Menahem, 1986. "A nested CES approach to capital-energy substitution," Energy Economics, Elsevier, vol. 8(1), pages 22-28, January.
    53. Hazilla, Michael & Kopp, Raymond J., 1986. "Testing for separable functional structure using temporary equilibrium models," Journal of Econometrics, Elsevier, vol. 33(1-2), pages 119-141.
    54. Ha, Soo Jung & Lange, Ian & Lecca, Patrizio & Turner, Karen, 2012. "Econometric estimation of nested production functions and testing in a computable general equilibrium analysis of economy-wide rebound effec ts," Stirling Economics Discussion Papers 2012-08, University of Stirling, Division of Economics.
    55. Khiabani, Nasser & Hasani, Karim, 2010. "Technical and allocative inefficiencies and factor elasticities of substitution: An analysis of energy waste in Iran's manufacturing," Energy Economics, Elsevier, vol. 32(5), pages 1182-1190, September.
    56. Field, Barry C & Grebenstein, Charles, 1980. "Capital-Energy Substitution in U.S. Manufacturing," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 207-212, May.
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    More about this item

    Keywords

    KLEM production functions; Substitution elasticities; Energy and capital substitution estimation; Nested CES;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General
    • Q48 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Government Policy
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General

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