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Capital-labor substitution, equilibrium indeterminacy, and the cyclical behavior of labor income

  • Jang-Ting Guo
  • Kevin J. Lansing

This paper examines the quantitative relationship between the elasticity of capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector neoclassical growth model. Our analysis employs a “normalized” version of the CES production function so that all steady-state allocations and factor income shares are held constant as the elasticity of substitution is varied. We demonstrate numerically that higher elasticities cause the threshold degree of increasing returns for indeterminacy to decline monotonically, albeit very gradually. When the elasticity of substitution is unity (the Cobb-Douglas case), our model requires increasing returns to scale of around 1.08 for indeterminacy. When the elasticity of substitution is raised to 5, which far exceeds any empirical estimate, the threshold degree of increasing returns reduces to around 1.05. We also demonstrate analytically that labor’s share of income becomes procyclical as the elasticity of substitution increases above unity, whereas labor’s share in postwar U.S. data is countercyclical. This observation, together with other empirical evidence, indicates that the elasticity of capital-labor substitution in the U.S. economy is actually below unity.

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Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2008-06.

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Date of creation: 2008
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Handle: RePEc:fip:fedfwp:2008-06
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  1. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  2. 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.
  3. Paul Gomme & Jeremy Greenwood, 1992. "On the cyclical allocation of risk," Discussion Paper / Institute for Empirical Macroeconomics 71, Federal Reserve Bank of Minneapolis.
  4. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
  5. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  6. Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(3), pages 697-707, July.
  7. Boldrin, Michael & Horvath, Michael, 1995. "Labor Contracts and Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 103(5), pages 972-1004, October.
  8. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  9. Wen, Yi, 1998. "Capacity Utilization under Increasing Returns to Scale," Journal of Economic Theory, Elsevier, vol. 81(1), pages 7-36, July.
  10. Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, vol. 8(04), pages 436-465, September.
  11. Klump, Rainer & Saam, Marianne, 2006. "Calibration of normalised CES production functions in dynamic models," ZEW Discussion Papers 06-78, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  12. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-83, April.
  13. Ellen R. McGrattan & James A. Schmitz, Jr., 1999. "Maintenance and repair: too big to ignore," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-13.
  14. 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.
  15. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
  16. Turnovsky, Stephen J., 2002. "Intertemporal and intratemporal substitution, and the speed of convergence in the neoclassical growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1765-1785, August.
  17. Robert S. Chirinko & Steven M. Fazzari & Andrew P. Meyer, 2004. "That Elusive Elasticity: A Long-Panel Approach to Estimating the Capital-Labor Substitution Elasticity," CESifo Working Paper Series 1240, CESifo Group Munich.
  18. Patrick Pintus, 2006. "Indeterminacy with almost constant returns to scale: capital-labor substitution matters," Economic Theory, Springer, vol. 28(3), pages 633-649, 08.
  19. Robert S. Chirinko, 2008. "ó: The Long And Short Of It," CESifo Working Paper Series 2234, CESifo Group Munich.
  20. Teresa Lloyd-Braga & Carine Nourry & Alain Venditti, 2006. "Indeterminacy with small externalities: The role of non-separable preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(3-4), pages 217-239.
  21. Jang-Ting Guo & Kevin J. Lansing, 2005. "Maintenance expenditures and indeterminacy under increasing returns to scale," Working Paper Series 2005-10, Federal Reserve Bank of San Francisco.
  22. 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.
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