Capital-labor substitution, equilibrium indeterminacy, and the cyclical behavior of labor income
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.
|Date of creation:||2008|
|Date of revision:|
|Contact details of provider:|| Postal: P.O. Box 7702, San Francisco, CA 94120-7702|
Phone: (415) 974-2000
Fax: (415) 974-3333
Web page: http://www.frbsf.org/
More information through EDIRC
|Order Information:|| Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wen, Yi, 1998. "Capacity Utilization under Increasing Returns to Scale," Journal of Economic Theory, Elsevier, vol. 81(1), pages 7-36, July.
- 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.
- Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, vol. 8(04), pages 436-465, September.
- Gomme, P. & Greenwood, J., 1993.
"On the Cyclical Allocation of Risk,"
RCER Working Papers
355, University of Rochester - Center for Economic Research (RCER).
- Paul Gomme & Jeremy Greenwood, 1992. "On the cyclical allocation of risk," Discussion Paper / Institute for Empirical Macroeconomics 71, Federal Reserve Bank of Minneapolis.
- Gomme, P. & Greenwood, J., 1992. "On the Cyclical Allocation of Risk," UWO Department of Economics Working Papers 9205, University of Western Ontario, Department of Economics.
- 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.
- 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.
- 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.
- 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.
- Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
- GRANDMONT, Jean-Michel & PINTUS, Patrick & de VILDER, Robin, 1997.
"Capital-labor substitution and competitive nonlinear endogenous business cycles,"
CORE Discussion Papers
1997087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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.
- Jess Benhabib & Roger E.A. Farmer, 1992.
"Indeterminacy and Increasing Returns,"
UCLA Economics Working Papers
646, UCLA Department of Economics.
- Benhabib, J. & Farmer, R.E.A, 1991. "Indeterminacy and Increasing Returns," Papers 165, Cambridge - Risk, Information & Quantity Signals.
- Benhabib, Jess & Farmer, Roger E.A., 1991. "Indeterminacy and Increasing Returns," Working Papers 91-59, C.V. Starr Center for Applied Economics, New York University.
- Robert S. Chirinko, 2008. "ó: The Long And Short Of It," CESifo Working Paper Series 2234, CESifo Group Munich.
- Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
- 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.
- Horvath, Michael & Boldrin, Michele, 1995. "Labor contracts and business cycles," UC3M Working papers. Economics 3905, Universidad Carlos III de Madrid. Departamento de Economía.
- Michele Boldrin & Michael Horvath, 1994. "Labor Contracts and Business Cycles," Discussion Papers 1068, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- 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.
- 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.
- Susanto Basu & John G. Fernald, 1996. "Returns to scale in U.S. production: estimates and implications," International Finance Discussion Papers 546, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
- 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.
- 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.
- 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.
- Ellen R. McGrattan & James A. Schmitz, 1999. "Maintenance and repair: too big to ignore," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-13.
- 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.
- Patrick Pintus, 2006. "Indeterminacy with almost constant returns to scale: capital-labor substitution matters," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 633-649, 08.
When requesting a correction, please mention this item's handle: RePEc:fip:fedfwp:2008-06. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Noah Pollaczek)
If references are entirely missing, you can add them using this form.