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

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Author Info
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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Publisher 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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Related research
Keywords: Capital-Labor Substitution; Equilibrium Indeterminacy; Capital Utilization; Real Business Cycles; Labor Income;

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Find related papers by JEL classification:
E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
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  5. 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.
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  6. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Blackwell Publishing, vol. 102(1), pages 41-56, March. [Downloadable!] (restricted)
  7. Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, vol. 8(04), pages 436-465, September. [Downloadable!]
  8. Gomme, Paul & Greenwood, Jeremy, 1995. "On the cyclical allocation of risk," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 91-124. [Downloadable!] (restricted)
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  9. Rainer Klump & Olivier de La Grandville, 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
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  11. Patrick Pintus, 2006. "Indeterminacy with almost constant returns to scale: capital-labor substitution matters," Economic Theory, Springer, vol. 28(3), pages 633-649, 08. [Downloadable!] (restricted)
  12. Wen, Yi, 1998. "Capacity Utilization under Increasing Returns to Scale," Journal of Economic Theory, Elsevier, vol. 81(1), pages 7-36, July. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
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