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ISOELASTIC ELASTICITY OF SUBSTITUTION PRODUCTION FUNCTIONS

Published online by Cambridge University Press:  28 February 2019

Jakub Growiec Open the ORCID record for Jakub Growiec [Opens in a new window]  and
Jakub Mućk Open the ORCID record for Jakub Mućk [Opens in a new window]
Jakub Growiec*
Affiliation:
SGH Warsaw School of Economics and Narodowy Bank Polski
Jakub Mućk
Affiliation:
SGH Warsaw School of Economics and Narodowy Bank Polski
*
Address correspondence to: Jakub Growiec, Szkoła Główna Handlowa w Warszawie, Katedra Ekonomii Ilościowej, al. Niepodległości 162, 02-554 Warszawa, Poland; e-mail: [email protected]. Phone/Fax: (+48) 225649322.
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Abstract

We generalize the normalized constant elasticity of substitution (CES) production function by allowing the elasticity of substitution to vary isoelastically with (i) the relative factor share, (ii) the marginal rate of substitution, (iii) the capital–labor ratio, (iv) the capital share, (v) the capital’s rate of return, or (vi) the capital–output ratio. Ensuing isoelastic elasticity of substitution (IEES) functions have intuitively and analytically desirable properties, for example, self-duality. Empirically, for the post-war US economy we robustly reject the CES specification in favor of the IEES alternative. Assuming the IEES production structure we find that the capital–labor elasticity of substitution has remained around 0.8–0.9 from 1948 to the 1980s, followed by a period of secular decline.

Keywords

Production FunctionFactor ShareElasticity of SubstitutionFactor-Augmenting Technical Change
Type
Articles
Information
Macroeconomic Dynamics , Volume 24 , Issue 7 , October 2020 , pp. 1597 - 1634
Copyright
© Cambridge University Press 2019

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Footnotes

We are grateful to the Associate Editor, two anonymous Referees, Peter McAdam and Ingmar Schumacher, participants of the 2015 CEF conference (Taipei), 2015 WIEM conference (Warsaw), 2016 MMF conference (Bath), 2016 NBP Summer Workshop, and seminars in Copenhagen (University of Copenhagen, MEHR seminar), Luxembourg and Warsaw (Warsaw Economic Seminars), for their useful comments and discussions. The authors declare that they have no relevant or material financial interests that relate to the research described in this paper. The views expressed herein belong to the authors and have not been endorsed by Narodowy Bank Polski.

References

Acemoglu, D. (2003) Labor-and capital-augmenting technical change. Journal of the European Economic Association 1, 1–37.CrossRefGoogle Scholar
Acemoglu, D. and Restrepo, P. (2018) The race between machine and man: Implications of technology for growth, factor shares and employment. American Economic Review 108, 1488–1542.Google Scholar
Antony, J. (2010) A class of changing elasticity of substitution production functions. Journal of Economics 100, 165–183.CrossRefGoogle Scholar
Antràs, P. (2004), Is the U.S. aggregate production function Cobb-Douglas? New estimates of the elasticity of substitution. Contributions to Macroeconomics 4, 1-36, Article 4.Google Scholar
Arrow, K. J., Chenery, H. B., Minhas, B. S. and Solow, R. M. (1961), Capital-labor substitution and economic efficiency. Review of Economics and Statistics 43, 225–250.CrossRefGoogle Scholar
Blackorby, C. and Russell, R. R. (1989) Will the real elasticity of substitution please stand up? (a comparison of the Allen/Uzawa and Morishima elasticities). American Economic Review 79, 882–888.Google Scholar
Bretschger, L. and Smulders, S. (2012) Sustainability and substitution of exhaustible natural resources: How structural change affects long-term R&D investments. Journal of Economic Dynamics and Control 36, 536–549.CrossRefGoogle Scholar
Cantore, C., Levine, P., Pearlman, J. and Yang, B. (2015) CES technology and business cycle fluctuations. Journal of Economic Dynamics and Control 61, 133–151.CrossRefGoogle Scholar
Cantore, C., Ferroni, F. and Leon-Ledesma, M. (2017) The dynamics of hours worked and technology. Journal of Economic Dynamics and Control 82(C), 67–82.CrossRefGoogle Scholar
Caselli, F. and Coleman, W. J. (2006) The world technology frontier. American Economic Review 96, 499–522.CrossRefGoogle Scholar
Chambers, R. G. (1988) Applied Production Analysis: A Dual Approach. Cambridge, UK: Cambridge University Press.Google Scholar
Chirinko, R. S. (2008) σ: The long and short of it. Journal of Macroeconomics 30, 671–686.CrossRefGoogle Scholar
Chirinko, R. S. and Mallick, D. (2017) The substitution elasticity, factor shares, and the low-frequency panel model. American Economic Journal: Macroeconomics 9(4), 225–253.Google Scholar
Christensen, L. R., Jorgenson, D. W. and Lau, L. J. (1973) Transcendental logarithmic production frontiers. Review of Economics and Statistics 55, 29–45.Google Scholar
Dasgupta, P. S. and Heal, G. M. (1979) Economic Theory and Exhaustible Resources. Cambridge, UK: Cambridge University Press.Google Scholar
de La Grandville, O. (1989) In quest of the slutsky diamond. American Economic Review 79, 468–481.Google Scholar
Duffy, J. and Papageorgiou, C. (2000) The specification of the aggregate production function: A cross-country empirical investigation. Journal of Economic Growth 5, 83–116.CrossRefGoogle Scholar
Duffy, J., Papageorgiou, C. and Perez-Sebastian, F. (2004) Capital-skill complementarity? Evidence from a panel of countries. The Review of Economics and Statistics 86(1), 327–344.CrossRefGoogle Scholar
Elsby, M., Hobijn, B. and Sahin, A. (2013) The decline of the U.S. labor share. Brookings Papers on Economic Activity 47(2), 1–63.CrossRefGoogle Scholar
Fernald, J. (2012) A Quarterly, Utilization-Adjusted Series on Total Factor Productivity. Federal Reserve Bank of San Francisco, Working Paper Series 2012–19.Google Scholar
Geary, R. C. (1950) A note on ‘A constant utility index of the cost of living’. Review of Economic Studies 18, 65–66.CrossRefGoogle Scholar
Gorman, W. M. (1965), Production functions in which the elasticities of substitution stand in fixed proportions to each other. Review of Economic Studies 32, 217–224.CrossRefGoogle Scholar
Growiec, J. (2008a) Production functions and distributions of unit factor productivities: Uncovering the link. Economics Letters 101, 87–90.CrossRefGoogle Scholar
Growiec, J. (2008b) A new class of production functions and an argument against purely labor-augmenting technical change. International Journal of Economic Theory 4, 483–502.CrossRefGoogle Scholar
Growiec, J. (2013) A microfoundation for normalized CES production functions with factor-augmenting technical change. Journal of Economic Dynamics and Control 37, 2336–2350.CrossRefGoogle Scholar
Growiec, J., McAdam, P. and Mućk, J. (2018) Endogenous labor share cycles: Theory and evidence. Journal of Economic Dynamics and Control 87, 74–93.Google Scholar
Hanoch, G. (1971) CRESH production functions. Econometrica 39, 695–712.CrossRefGoogle Scholar
Herrendorf, B., Herrington, C. and Valentinyi, A. (2015) Sectoral technology and structural transformation. American Economic Journal: Macroeconomics 7, 104–133.Google Scholar
Irmen, A. (2011) Steady-state growth and the elasticity of substitution. Journal of Economic Dynamics and Control 35, 1215–1228.CrossRefGoogle Scholar
Jones, C. I. (2005) The shape of production functions and the direction of technical change. Quarterly Journal of Economics 120, 517–549.Google Scholar
Jones, L. E. and Manuelli, R. E. (1990) A convex model of equilibrium growth: Theory and policy implications. Journal of Political Economy 98, 1008–1038.CrossRefGoogle Scholar
Kadiyala, K. R. (1972) Production functions and elasticity of substitution. Southern Economic Journal 38, 281–284.CrossRefGoogle Scholar
Karabarbounis, L. and Neiman, B. (2014) The global decline of the labor share. The Quarterly Journal of Economics 129(1), 61–103.CrossRefGoogle Scholar
Karagiannis, G., Palivos, T. and Papageorgiou, C. (2005) A variable elasticity of substitution (VES) aggregate production function: Theory and evidence. In: Diebolt, C. and Kyrtsou, C. (eds.) New Trends in Macroeconomics. New York, NY: Springer Verlag.Google Scholar
Kim, H. Y. (1992) The translog production function and variable returns to scale. Review of Economics and Statistics 74, 546–552.CrossRefGoogle Scholar
Kimball, M. S. (1995) The quantitative analytics of the basic neomonetarist model. Journal of Money, Credit and Banking 27, 1241–1277.CrossRefGoogle Scholar
Klenow, P. J. and Rodriguez-Clare, A. (1997) The neoclassical revival in growth economics: Has it gone too far? In: Bernanke, B. S. and Rotemberg, J. J. (eds.), NBER Macroeconomics Annual 1997. Cambridge, MA: MIT Press.Google Scholar
Klump, R. and de La Grandville, O. (2000) Economic growth and the elasticity of substitution: Two theorems and some suggestions. American Economic Review 90, 282–291.CrossRefGoogle Scholar
Klump, R., McAdam, P. and Willman, A. (2007) Factor substitution and factor augmenting technical progress in the US: A normalized supply-side system approach. Review of Economics and Statistics 89, 183–192.CrossRefGoogle Scholar
Klump, R., McAdam, P. and Willman, A. (2012) Normalization in CES production functions: Theory and empirics. Journal of Economic Surveys 26, 769–799.CrossRefGoogle Scholar
Krusell, P., Ohanian, L. E., Rios-Rull, J.-V. and Violante, G. L. (2000) Capital-skill complementarity and inequality: A macroeconomic analysis. Econometrica 68, 1029–1054.CrossRefGoogle Scholar
Leon-Ledesma, M. A. and Satchi, M. (2018) Appropriate technology and balanced growth. Review of Economic Studies, forthcoming.Google Scholar
Leon-Ledesma, M. A., McAdam, P. and Willman, A. (2010) Identifying the elasticity of substitution with biased technical change. American Economic Review 100, 1330–1357.CrossRefGoogle Scholar
Lu, Y.-C. (1967) Variable Elasticity of Substitution Production Functions, Technical Change and Factor Shares. Iowa State University, Ph.D. Thesis. http://books.google.pl/books?id=Y_ytnQEACAAJ.Google Scholar
Madsen, J. B. (2010) The anatomy of growth in the OECD since 1870. Journal of Monetary Economics 57(6), 753–767.CrossRefGoogle Scholar
Mallick, D. (2012) The role of the elasticity of substitution in economic growth: A cross-country investigation. Labour Economics 19, 682–694.CrossRefGoogle Scholar
Matveenko, A. and Matveenko, V. (2015) Technological Choice Generating Normalized CES Production Functions. CERGE-EI, Prague, Working Paper.Google Scholar
McAdam, P. and Willman, A. (2013) Medium run redux. Macroeconomic Dynamics 17(4), 695–727.CrossRefGoogle Scholar
Mishra, S. K. (2010) A brief history of production functions. IUP Journal of Managerial Economics 4, 6–34.Google Scholar
Miyagiwa, K. and Papageorgiou, C. (2007) Endogenous aggregate elasticity of substitution. Journal of Economic Dynamics and Control 31, 2899–2919.CrossRefGoogle Scholar
Mućk, J., McAdam, P. and Growiec, J. (2018) Will the ‘True’ labor share stand up? An applied survey on labor share measures. Journal of Economic Surveys 32, 961–984.CrossRefGoogle Scholar
Oberfield, E. and Raval, D. (2014) Micro Data and Macro Technology. Working Paper No. 20452, National Bureau of Economic Research.CrossRefGoogle Scholar
Palivos, T. and Karagiannis, G. (2010) The elasticity of substitution as an engine of growth. Macroeconomic Dynamics 14(5), 617–628.CrossRefGoogle Scholar
Papageorgiou, C. and Saam, M. (2008) Two-level CES production technology in the solow and diamond growth models. Scandinavian Journal of Economics 110, 119–143.CrossRefGoogle Scholar
Piketty, T. (2014) Capital in the Twenty-First Century. Harvard University Press. Translated from French by A. Goldhammer.CrossRefGoogle Scholar
Piketty, T. and Zucman, G. (2014) Capital is back: Wealth-income ratios in rich countries 1700-2010. Quarterly Journal of Economics 129(3), 1255–1310.CrossRefGoogle Scholar
Revankar, N. S. (1971) A class of variable elasticity of substitution production functions. Econometrica 39, 61–71.CrossRefGoogle Scholar
Rognlie, M. (2015) Deciphering the fall and rise in the net capital share. Brookings Papers on Economic Activity 46, 1–69.Google Scholar
Saam, M. (2008) Openness to trade as a determinant of the macroeconomic elasticity of substitution. Journal of Macroeconomics 30, 691–702.CrossRefGoogle Scholar
Sato, R. (1981) Theory of Technical Change and Economic Invariance: Application of Lie Groups. New York: Academic Press.Google Scholar
Sato, R. and Hoffman, R. F. (1968) Production functions with variable elasticity of factor substitution: Some analysis and testing. Review of Economics and Statistics 50, 453–460.CrossRefGoogle Scholar
Shephard, R. W. (1953) Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.Google Scholar
Smulders, S. and de Nooij, M. (2003) The impact of energy conservation on technology and economic growth. Resource and Energy Economics 25, 59–79.CrossRefGoogle Scholar
Solow, R. M. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics 70, 65–94.CrossRefGoogle Scholar
Stone, R. (1954) Linear expenditure systems and demand analysis: An application to the pattern of British demand. Economic Journal 64, 511–527.CrossRefGoogle Scholar
Villacorta, L. (2016) Estimating Country Heterogeneity in Capital-Labor Substitution Using Panel Data. Banco Central de Chile, Working Paper No. 788.Google Scholar
Xue, J. and Yip, C. K. (2013) Aggregate elasticity of substitution and economic growth: A synthesis. Journal of Macroeconomics 38, 60-75.CrossRefGoogle Scholar
Young, A. T. (2013) U.S. elasticities of substitution and factor augmentation at the industry level. Macroeconomic Dynamics 17(4), 861–897.CrossRefGoogle Scholar
Zhelobodko, E., Kokovin, S., Parenti, M. and Thisse, J.-F. (2012) Monopolistic competition: Beyond the constant elasticity of substitution. Econometrica 80, 2765–2784.Google Scholar
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