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The normalized CES production function: theory and empirics

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  • Klump, Rainer
  • McAdam, Peter
  • Willman, Alpo

Abstract

The elasticity of substitution between capital and labor and, in turn, the direction of technical change are critical parameters in many fields of economics. Until recently, though, the application of production functions with non-unitary substitution elasticities (i.e., non Cobb Douglas) was hampered by empirical and theoretical uncertainties. As has recently been revealed, JEL Classification: C22, E23, E25, O30, O51

Suggested Citation

  • Klump, Rainer & McAdam, Peter & Willman, Alpo, 2011. "The normalized CES production function: theory and empirics," Working Paper Series 1294, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20111294
    Note: 50336
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    1. Bentolila Samuel & Saint-Paul Gilles, 2003. "Explaining Movements in the Labor Share," The B.E. Journal of Macroeconomics, De Gruyter, vol. 3(1), pages 1-33, October.
    2. repec:ucp:bknber:9780226304557 is not listed on IDEAS
    3. Cristiano Cantore & Miguel León-Ledesma & Peter McAdam & Alpo Willman, 2014. "Shocking Stuff: Technology, Hours, And Factor Substitution," Journal of the European Economic Association, European Economic Association, vol. 12(1), pages 108-128, February.
    4. Antràs Pol, 2004. "Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-36, April.
    5. Lawrence F. Katz & Kevin M. Murphy, 1992. "Changes in Relative Wages, 1963–1987: Supply and Demand Factors," The Quarterly Journal of Economics, Oxford University Press, vol. 107(1), pages 35-78.
    6. Gene M. Grossman (ed.), 1996. "Economic Growth," Books, Edward Elgar Publishing, volume 0, number 553, June.
    7. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2008. "Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 645-666, June.
    8. 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.
    9. Xue, Jianpo & Yip, Chong K., 2012. "Factor Substitution And Economic Growth: A Unified Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 16(4), pages 625-656, September.
    10. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
    11. 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.
    12. Leo Kaas & Leopold Von Thadden, 2003. "Unemployment, Factor Substitution and Capital Formation," German Economic Review, Verein für Socialpolitik, vol. 4(4), pages 475-495, November.
    13. 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.
    14. Robert S. Chirinko, 2008. "ó: The Long And Short Of It," CESifo Working Paper Series 2234, CESifo.
    15. Guo, Jang-Ting & Lansing, Kevin J., 2009. "Capital-labor substitution and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1991-2000, December.
    16. Leo Kaas & Leopold von Thadden, 2003. "Unemployment, Factor Substitution and Capital Formation," German Economic Review, Verein für Socialpolitik, vol. 4, pages 475-495, November.
    17. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
    18. Chirinko, Robert S. & Fazzari, Steven M. & Meyer, Andrew P., 1999. "How responsive is business capital formation to its user cost?: An exploration with micro data," Journal of Public Economics, Elsevier, vol. 74(1), pages 53-80, October.
    19. 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.
    20. Irmen Andreas & Klump Rainer, 2009. "Factor Substitution, Income Distribution and Growth in a Generalized Neoclassical Model," German Economic Review, De Gruyter, vol. 10(4), pages 464-479, December.
    21. H. S. Houthakker, 1955. "The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis," Review of Economic Studies, Oxford University Press, vol. 23(1), pages 27-31.
    22. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    23. Griliches, Zvi, 1969. "Capital-Skill Complementarity," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 465-468, November.
    24. Robert W. Dimand & Barbara J. Spencer, 2009. "Trevor Swan and the Neoclassical Growth Model," History of Political Economy, Duke University Press, vol. 41(5), pages 107-126, Supplemen.
    25. Chirinko, Robert S., 2002. "Corporate Taxation, Capital Formation,and the Substitution Elasticity Between Labor and Capital," National Tax Journal, National Tax Association;National Tax Journal, vol. 55(2), pages 339-355, June.
    26. J. K. Whitaker, 1964. "A Note on the CES Production Function," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 166-167.
    27. 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.
    28. Duffy, John & Papageorgiou, Chris, 2000. "A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
    29. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
    30. Kennedy, Charles & Thirlwall, A P, 1973. "Technological Change and the Distribution of Income: A Belated Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 780-784, October.
    31. Jaume Ventura, 1997. "Growth and Interdependence," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 57-84.
    32. Miguel A. Leon-Ledesma & Mathan Satchi, 2010. "A Note on Balanced Growth with a less than unitary Elasticity of Substitution," Studies in Economics 1007, School of Economics, University of Kent.
    33. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-296, November.
    34. Yuhn, Ky-hyang, 1991. "Economic Growth, Technical Change Biases, and the Elasticity of Substitution: A Test of the De La Grandville Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 73(2), pages 340-346, May.
    35. McAdam, Peter & Willman, Alpo & León-Ledesma, Miguel A., 2010. "In dubio pro CES - Supply estimation with mis-specified technical change," Working Paper Series 1175, European Central Bank.
    36. 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.
    37. Per Krusell & Lee E. Ohanian & JosÈ-Victor RÌos-Rull & Giovanni L. Violante, 2000. "Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis," Econometrica, Econometric Society, vol. 68(5), pages 1029-1054, September.
    38. Azariadis, Costas, 1996. "The Economics of Poverty Traps: Part One: Complete Markets," Journal of Economic Growth, Springer, vol. 1(4), pages 449-496, December.
    39. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    40. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(4), pages 695-727, June.
    41. Thursby, Jerry, 1980. "Alternative CES Estimation Techniques," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 295-299, May.
    42. 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.
    43. McAdam, Peter & Willman, Alpo & León-Ledesma, Miguel A., 2011. "Aggregation, the skill premium, and the two-level production function," Working Paper Series 1400, European Central Bank.
    44. Norbert Berthold & Rainer Fehn & Eric Thode, 2002. "Falling Labor Share and Rising Unemployment: Long–Run Consequences of Institutional Shocks?," German Economic Review, Verein für Socialpolitik, vol. 3(4), pages 431-459, November.
    45. Berndt, Ernst R, 1976. "Reconciling Alternative Estimates of the Elasticity of Substitution," The Review of Economics and Statistics, MIT Press, vol. 58(1), pages 59-68, February.
    46. Daron Acemoglu, 2002. "Directed Technical Change," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 781-809.
    47. David H. Autor & Lawrence F. Katz & Melissa S. Kearney, 2008. "Trends in U.S. Wage Inequality: Revising the Revisionists," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 300-323, May.
    48. H. D. Dickinson, 1954. "A Note on Dynamic Economics," Review of Economic Studies, Oxford University Press, vol. 22(3), pages 169-179.
    49. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    50. Caballero, Ricardo J, 1994. "Small Sample Bias and Adjustment Costs," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 52-58, February.
    51. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 171-201.
    52. Rainer Klump & Harald Preissler, 2000. "CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
    53. Robert J. Gordon, 1990. "The Measurement of Durable Goods Prices," NBER Books, National Bureau of Economic Research, Inc, number gord90-1, June.
    54. Olivier de La Grandville & Rainer Klump, 2000. "Economic Growth and the Elasticity of Substitution: Two Theorems and Some Suggestions," American Economic Review, American Economic Association, vol. 90(1), pages 282-291, March.
    55. Ramanathan, R, 1975. "The Elasticity of Substitution and the Speed of Convergence in Growth Models," Economic Journal, Royal Economic Society, vol. 85(339), pages 612-613, September.
    56. 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.
    57. F. A. Lutz, 1961. "The Theory of Capital," International Economic Association Series, Palgrave Macmillan, number 978-1-349-08452-4 edited by D. C. Hague, April.
    58. Wong, Tsz-Nga & Yip, Chong K., 2010. "Indeterminacy and the elasticity of substitution in one-sector models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 623-635, April.
    59. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    60. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 517-549.
    61. 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.
    62. Rowthorn, Robert, 1999. "Unemployment, Wage Bargaining and Capital-Labour Substitution," Cambridge Journal of Economics, Oxford University Press, vol. 23(4), pages 413-425, July.
    63. Rainer Klump, 2001. "Trade, money and employment in intertemporal optimizing models of growth," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 10(4), pages 411-428.
    64. de La Grandville Olivier, 2012. "How Much Should a Nation Save? A New Answer," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-36, April.
    65. Mallick, Debdulal, 2010. "Capital-labor substitution and balanced growth," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1131-1142, December.
    66. Kumar, T Krishna & Gapinski, James H, 1974. "Nonlinear Estimation of the CES Production Parameters: A Monte Carlo Study," The Review of Economics and Statistics, MIT Press, vol. 56(4), pages 563-567, November.
    67. Nakamura, Hideki & Nakamura, Masakatsu, 2008. "Constant-Elasticity-Of-Substitution Production Function," Macroeconomic Dynamics, Cambridge University Press, vol. 12(5), pages 694-701, November.
    68. Nicholas Kaldor, 1961. "Capital Accumulation and Economic Growth," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 177-222, Palgrave Macmillan.
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    More about this item

    Keywords

    constant elasticity of substitution production function; estimation; factor-augmenting technical change; growth theory; identification; normalization;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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