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Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income

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  • Jang-Ting Guo

    ()
    (Department of Economics, University of California Riverside)

  • Kevin J. Lansing

    (Federal Reserve Bank of San Francisco)

Abstract

This paper examines the quantitative relationship between the elasticity of capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven áuctuations) in a one-sector growth model. Our analysis employs a ìnormalizedîversion 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 laborís share of income becomes pro-cyclical as the elasticity of substitution increases above unity, whereas laborís 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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Bibliographic Info

Paper provided by University of California at Riverside, Department of Economics in its series Working Papers with number 200804.

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Length: 17 pages
Date of creation: Apr 2008
Date of revision: Apr 2008
Handle: RePEc:ucr:wpaper:200804

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Keywords: Capital-Labor Substitution; Equilibrium Indeterminacy; Capital Utilization; Real Business Cycles; Labor Income;

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References

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  1. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  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. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
  4. 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.
  5. Lloyd-Braga, Teresa & Nourry, Carine & Venditti, Alain, 2006. "Indeterminacy with Small Externalities: The Role of Non-Separable Preferences," CEPR Discussion Papers 5541, C.E.P.R. Discussion Papers.
  6. 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.
  7. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
  8. Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," NBER Technical Working Papers 0290, National Bureau of Economic Research, Inc.
  9. Gomme, P. & Greenwood, J., 1993. "On the Cyclical Allocation of Risk," RCER Working Papers 355, University of Rochester - Center for Economic Research (RCER).
  10. Robert S. Chirinko, 2008. "ó: The Long And Short Of It," CESifo Working Paper Series 2234, CESifo Group Munich.
  11. Ellen R. McGrattan & James A. Schmitz, Jr., 1999. "Maintenance and repair: too big to ignore," Quarterly Review, Federal Reserve Bank of Minneapolis, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-13.
  12. Jang-Ting Guo & Kevin J. Lansing, 2007. "Maintenance expenditures and indeterminacy under increasing returns to scale," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(2), pages 147-158.
  13. 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.
  14. Boldrin, Michael & Horvath, Michael, 1995. "Labor Contracts and Business Cycles," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 103(5), pages 972-1004, October.
  15. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, Elsevier, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  16. Wen, Yi, 1998. "Capacity Utilization under Increasing Returns to Scale," Journal of Economic Theory, Elsevier, vol. 81(1), pages 7-36, July.
  17. Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 8(04), pages 436-465, September.
  18. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 105(2), pages 249-83, April.
  19. Jean-Michel Grandmont & P, A, Pintus & R, De Vilder, 1997. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Working Papers 97-28, Centre de Recherche en Economie et Statistique.
  20. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  21. 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.
  22. Patrick Pintus, 2006. "Indeterminacy with almost constant returns to scale: capital-labor substitution matters," Economic Theory, Springer, vol. 28(3), pages 633-649, 08.
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Cited by:
  1. Fabien Tripier, 2009. "Elasticity of factor substitution and the rise in labor's share of income during the Great Depression," Working Papers hal-00419343, HAL.

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