IDEAS home Printed from https://ideas.repec.org/a/bpj/bejmac/vcontributions.4y2004i1n4.html
   My bibliography  Save this article

Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution

Author

Listed:
  • Antràs Pol

    (Harvard University)

Abstract

I present new estimates of the elasticity of substitution between capital and labor using data from the private sector of the U.S. economy for the period 1948-1998. I first adopt Berndt's (1976) specification, which assumes that technological change is Hicks neutral. Consistently with his results, I estimate elasticities of substitution that are not significantly different from one. I next show, however, that restricting the analysis to Hicks-neutral technological change necessarily biases the estimates of the elasticity towards one. When I modify the econometric specification to allow for biased technical change, I obtain significantly lower estimates of the elasticity of substitution. I conclude that the U.S. economy is not well described by a Cobb-Douglas aggregate production function. I present estimates based on both classical regression analysis and time series analysis. In the process, I deal with issues related to the nonsphericality of the disturbances, the endogeneity of the regressors, and the nonstationarity of the series involved in the estimation.

Suggested Citation

  • Antràs Pol, 2004. "Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-36, April.
    • Handle: RePEc:bpj:bejmac:v:contributions.4:y:2004:i:1:n:4
    DOI: 10.2202/1534-6005.1161
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1534-6005.1161
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1534-6005.1161?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bentolila Samuel & Saint-Paul Gilles, 2003. "Explaining Movements in the Labor Share," The B.E. Journal of Macroeconomics, De Gruyter, vol. 3(1), pages 1-33, October.
    2. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    3. repec:ucp:bknber:9780226304557 is not listed on IDEAS
    4. Judd, Kenneth L, 1987. "The Welfare Cost of Factor Taxation in a Perfect-Foresight Model," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 675-709, August.
    5. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    6. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995. "Capital Utilization and Returns to Scale," NBER Chapters, in: NBER Macroeconomics Annual 1995, Volume 10, pages 67-124, National Bureau of Economic Research, Inc.
    7. Douglas Gollin, 2002. "Getting Income Shares Right," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 458-474, April.
    8. Diamond, Peter & McFadden, Daniel & Rodriguez, Miguel, 1978. "Measurement of the Elasticity of Factor Substitution and Bias of Technical Change," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 2, chapter 5, McMaster University Archive for the History of Economic Thought.
    9. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    10. Fair, Ray C, 1970. "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors," Econometrica, Econometric Society, vol. 38(3), pages 507-516, May.
    11. Murray Brown, 1967. "The Theory and Empirical Analysis of Production," NBER Books, National Bureau of Economic Research, Inc, number brow67-1.
    12. Chirinko, Robert S., 2002. "Corporate Taxation, Capital Formation,and the Substitution Elasticity Between Labor and Capital," National Tax Journal, National Tax Association;National Tax Journal, vol. 55(2), pages 339-355, June.
    13. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    14. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
    15. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    16. Coen, Robert M, 1969. "Tax Policy and Investment Behavior: Comment," American Economic Review, American Economic Association, vol. 59(3), pages 370-379, June.
    17. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    18. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    19. Berndt, Ernst R, 1976. "Reconciling Alternative Estimates of the Elasticity of Substitution," The Review of Economics and Statistics, MIT Press, vol. 58(1), pages 59-68, February.
    20. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
    21. Susanto Basu, 1996. "Procyclical Productivity: Increasing Returns or Cyclical Utilization?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(3), pages 719-751.
    22. Daron Acemoglu, 2002. "Directed Technical Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 781-809.
    23. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    24. Robert J. Gordon, 1990. "The Measurement of Durable Goods Prices," NBER Books, National Bureau of Economic Research, Inc, number gord90-1.
    25. 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.
    26. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    27. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    28. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    29. Kalt, Joseph P, 1978. "Technological Change and Factor Substitution in the United States: 1929-1967," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 761-775, October.
    30. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
    31. Dhrymes, Phoebus J & Zarembka, Paul, 1970. "Elasticities of Substitution for Two-Digit Manufacturing Industries: A Correction," The Review of Economics and Statistics, MIT Press, vol. 52(1), pages 115-117, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rainer Klump & Peter McAdam & Alpo Willman, 2004. "Factor Substitution and Factor Augmenting Technical Progress in the US: A Normalized Supply-Side System Approach," DEGIT Conference Papers c009_030, DEGIT, Dynamics, Economic Growth, and International Trade.
    2. Bellocchi, Alessandro & Travaglini, Giuseppe, 2023. "Can variable elasticity of substitution explain changes in labor shares?," Journal of Macroeconomics, Elsevier, vol. 76(C).
    3. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.
    4. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    5. Knoblach, Michael & Rößler, Martin & Zwerschke, Patrick, 2016. "The Elasticity of Factor Substitution Between Capital and Labor in the U.S. Economy: A Meta-Regression Analysis," CEPIE Working Papers 03/16, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    6. Michael Knoblach & Martin Roessler & Patrick Zwerschke, 2020. "The Elasticity of Substitution Between Capital and Labour in the US Economy: A Meta‐Regression Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 62-82, February.
    7. PETER McADAM & ALPO WILLMAN, 2013. "Technology, Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(8), pages 1547-1579, December.
    8. Lawrence Robert Z., 2015. "Recent Declines in Labor's Share in U.S. Income: A Preliminary Neoclassical Account," Working Paper Series rwp15-034, Harvard University, John F. Kennedy School of Government.
    9. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    10. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2008. "Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 645-666, June.
    11. Cristiano Cantore & Miguel León-Ledesma & Peter McAdam & Alpo Willman, 2014. "Shocking Stuff: Technology, Hours, And Factor Substitution," Journal of the European Economic Association, European Economic Association, vol. 12(1), pages 108-128, February.
    12. Miguel A. Leon-Ledesma & Mathan Satchi, 2015. "Appropriate Technology and the Labour Share," Studies in Economics 1505, School of Economics, University of Kent, revised Nov 2016.
    13. Dongya Koh & Raül Santaeulàlia‐Llopis & Yu Zheng, 2020. "Labor Share Decline and Intellectual Property Products Capital," Econometrica, Econometric Society, vol. 88(6), pages 2609-2628, November.
    14. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    15. Miguel A León-Ledesma & Mathan Satchi, 2019. "Appropriate Technology and Balanced Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 807-835.
    16. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-1357, September.
    17. Hugo Erken & Piet Donselaar & Roy Thurik, 2018. "Total factor productivity and the role of entrepreneurship," The Journal of Technology Transfer, Springer, vol. 43(6), pages 1493-1521, December.
    18. Gómez, Manuel A., 2008. "Dynamics Of The Saving Rate In The Neoclassical Growth Model With Ces Production," Macroeconomic Dynamics, Cambridge University Press, vol. 12(2), pages 195-210, April.
    19. Gechert, Sebastian & Havranek, Tomas & Irsova, Zuzana & Kolcunova, Dominika, 2019. "Death to the Cobb-Douglas Production Function? A Quantitative Survey of the Capital-Labor Substitution Elasticity," EconStor Preprints 203136, ZBW - Leibniz Information Centre for Economics.
    20. Samuele Ialenti & Guido Pialli, 2024. "The increase in the elasticity of substitution between capital and labour: a repeated cross-country investigation," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 33(3), pages 380-400, April.

    More about this item

    Keywords

    Capital-Labor Substitution; Technological Change;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General
    • O - Economic Development, Innovation, Technological Change, and Growth

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:bejmac:v:contributions.4:y:2004:i:1:n:4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.