IDEAS home Printed from https://ideas.repec.org/a/aea/aejmac/v9y2017i4p225-53.html
   My bibliography  Save this article

The Substitution Elasticity, Factor Shares, and the Low-Frequency Panel Model

Author

Listed:
  • Robert S. Chirinko
  • Debdulal Mallick

Abstract

The value of the elasticity of substitution between labor and capital (σ) is a crucial assumption in understanding the secular decline in the labor share of income. This paper develops and implements a new strategy for estimating this crucial parameter by combining a low-pass filter with panel data to identify the low-frequency/long-run relations appropriate to production function estimation. Standard estimation methods, which do not filter out transitory variation, generate downwardly biased estimates of 40 percent to 70 percent relative to the benchmark value. Despite correcting for this bias, our preferred estimate of 0.40 is substantially below the Cobb-Douglas assumption of σ = 1.

Suggested Citation

  • Robert S. Chirinko & Debdulal Mallick, 2017. "The Substitution Elasticity, Factor Shares, and the Low-Frequency Panel Model," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(4), pages 225-253, October.
    • Handle: RePEc:aea:aejmac:v:9:y:2017:i:4:p:225-53
    Note: DOI: 10.1257/mac.20140302
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/articles?id=10.1257/mac.20140302
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/attachments?retrieve=TF3gqEKfFjxf3UVyi_hsmjfLmeM3xa4W
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/attachments?retrieve=vEEv4Bqfs8cNJBRNVtPRn-DcwHZCJbQA
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/attachments?retrieve=eQvsz1v6ieRa_0IFMA9v6pCu5rRy8fPD
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    ---><---

    References listed on IDEAS

    as
    1. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
    2. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    3. Simon Gilchrist & John C. Williams, 2000. "Putty-Clay and Investment: A Business Cycle Analysis," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 928-960, October.
    4. Chirinko, Robert S, 1993. "Business Fixed Investment Spending: Modeling Strategies, Empirical Results, and Policy Implications," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1875-1911, December.
    5. Berthold Herrendorf & Christopher Herrington & Ákos Valentinyi, 2015. "Sectoral Technology and Structural Transformation," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(4), pages 104-133, October.
    6. Bridgman, Benjamin, 2018. "Is Labor'S Loss Capital'S Gain? Gross Versus Net Labor Shares," Macroeconomic Dynamics, Cambridge University Press, vol. 22(8), pages 2070-2087, December.
    7. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    8. Matthew Rognlie, 2015. "Deciphering the Fall and Rise in the Net Capital Share," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 50(1 (Spring), pages 1-69.
    9. 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.
    10. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    11. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    12. Thomas Piketty & Gabriel Zucman, 2014. "Capital is Back: Wealth-Income Ratios in Rich Countries 1700–2010," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1255-1310.
    13. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    14. 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.
    15. Robert S. Chirinko, 1992. "Business Fixed Investment Spending: A Critical survey of Modeling Strategies, Empirical Results, and Policy Implications," Working Papers 9213, Harris School of Public Policy Studies, University of Chicago.
    16. Dale W. Jorgenson & Kevin J. Stiroh, 2000. "Raising the Speed Limit: U.S. Economic Growth in the Information Age," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 31(1), pages 125-236.
    17. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.
    18. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    19. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    20. Alan J. Auerbach & Kevin Hassett, 2015. "Capital Taxation in the Twenty-First Century," American Economic Review, American Economic Association, vol. 105(5), pages 38-42, May.
    21. Mallick, Debdulal, 2012. "The role of the elasticity of substitution in economic growth: A cross-country investigation," Labour Economics, Elsevier, vol. 19(5), pages 682-694.
    22. L. R. Klein & R. F. Kosobud, 1961. "Some Econometrics of Growth: Great Ratios of Economics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(2), pages 173-198.
    23. Jason G. Cummins & Giovanni L. Violante, 2002. "Investment-Specific Technical Change in the US (1947-2000): Measurement and Macroeconomic Consequences," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(2), pages 243-284, April.
    24. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7, October.
    25. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    26. Chirinko, Robert S. & Mallick, Debdulal, 2011. "Cointegration, factor shares, and production function parameters," Economics Letters, Elsevier, vol. 112(2), pages 205-206, August.
    27. Levy, Daniel & Dezhbakhsh, Hashem, 2003. "International Evidence on Output Fluctuation and Shock Persistence," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 50(7), pages 1499-1530.
    28. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    29. Brent Neiman, 2014. "The Global Decline of the Labor Share," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(1), pages 61-103.
    30. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6, National Bureau of Economic Research, Inc.
    31. Greenwood, Jeremy & Hercowitz, Zvi & Krusell, Per, 1997. "Long-Run Implications of Investment-Specific Technological Change," American Economic Review, American Economic Association, vol. 87(3), pages 342-362, June.
    32. Caballero, Ricardo J, 1994. "Small Sample Bias and Adjustment Costs," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 52-58, February.
    33. Griffin, James M, 1981. "Engineering and Econometric Interpretations of Energy-Capital Complementarity: Comment," American Economic Review, American Economic Association, vol. 71(5), pages 1100-1104, December.
    34. Matthew Rognlie, 2015. "Deciphering the Fall and Rise in the Net Capital Share: Accumulation or Scarcity?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 46(1 (Spring), pages 1-69.
    35. Engle, Robert F & Foley, Duncan K, 1975. "An Asset Price Model of Aggregate Investment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 625-647, October.
    36. 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.
    37. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2015. "Production Technology Estimates and Balanced Growth," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 40-65, February.
    38. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    39. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1.
    40. repec:hal:pseose:halshs-01109372 is not listed on IDEAS
    41. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-1014, December.
    42. Robert S. Chirinko & Steven M. Fazzari & Andrew P. Meyer, 2011. "A New Approach to Estimating Production Function Parameters: The Elusive Capital--Labor Substitution Elasticity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 587-594, October.
    43. Berndt, Ernst R & Wood, David O, 1981. "Engineering and Econometric Interpretations of Energy-Capital Complementarity: Reply and Further Results," American Economic Review, American Economic Association, vol. 71(5), pages 1105-1110, December.
    44. Chirinko, Robert S. & Fazzari, Steven M. & Meyer, Andrew P., 2011. "A New Approach to Estimating Production Function Parameters: The Elusive Capital–Labor Substitution Elasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 587-594.
    45. F. A. Lutz, 1961. "The Theory of Capital," International Economic Association Series, Palgrave Macmillan, number 978-1-349-08452-4 edited by D. C. Hague, December.
    46. Nicholas Kaldor, 1961. "Capital Accumulation and Economic Growth," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 177-222, Palgrave Macmillan.
    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. Robert S. Chirinko & Debdulal Mallick, 2014. "The Substitution Elasticity, Factor Shares, Long-Run Growth, and the Low-Frequency Panel Model," CESifo Working Paper Series 4895, CESifo.
    2. 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.
    3. Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," 2019 Meeting Papers 1458, Society for Economic Dynamics.
    4. Song, Eunbi, 2021. "What drives labor share change? Evidence from Korean industries," Economic Modelling, Elsevier, vol. 94(C), pages 370-385.
    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. Gene M. Grossman & Elhanan Helpman & Ezra Oberfield & Thomas Sampson, 2017. "Balanced Growth Despite Uzawa," American Economic Review, American Economic Association, vol. 107(4), pages 1293-1312, April.
    7. Clemens Struck & Adnan Velic, 2017. "To Augment Or Not To Augment? A Conjecture On Asymmetric Technical Change," Trinity Economics Papers tep0117, Trinity College Dublin, Department of Economics.
    8. Paul, Saumik, 2019. "A Decline in Labor's Share with Capital Accumulation and Complementary Factor Inputs: An Application of the Morishima Elasticity of Substitution," IZA Discussion Papers 12219, Institute of Labor Economics (IZA).
    9. Kenneth G. Stewart & Jiang Li, 2018. "Are factor biases and substitution identifiable? The Canadian evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 51(2), pages 528-548, May.
    10. Gene M. Grossman & Elhanan Helpman & Ezra Oberfield & Thomas Sampson, 2021. "Endogenous Education and Long-Run Factor Shares," American Economic Review: Insights, American Economic Association, vol. 3(2), pages 215-232, June.
    11. 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.
    12. Judzik, Dario & Sala, Hector, 2015. "The determinants of capital intensity in Japan and the US," Journal of the Japanese and International Economies, Elsevier, vol. 35(C), pages 78-98.
    13. Kenneth G. Stewart & Jiang Li, 2018. "Are factor biases and substitution identifiable? The Canadian evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 51(2), pages 528-548, May.
    14. Dongya Koh & Raül Santaeulàlia-Llopis, 2017. "Countercyclical Elasticity of Substitution," Working Papers 946, Barcelona School of Economics.
    15. Trenczek, Jan & Wacker, Konstantin M., 2023. "Human Capital Misallocation and Output per Worker Differences: Beyond Cobb-Douglas," GLO Discussion Paper Series 1331, Global Labor Organization (GLO).
    16. Akaev, Askar & Devezas, Tessaleno & Ichkitidze, Yuri & Sarygulov, Askar, 2021. "Forecasting the labor intensity and labor income share for G7 countries in the digital age," Technological Forecasting and Social Change, Elsevier, vol. 167(C).
    17. Daan Steenkamp, 2018. "Factor Substitution and Productivity in New Zealand," The Economic Record, The Economic Society of Australia, vol. 94(304), pages 64-79, March.
    18. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    19. Maya Eden & Paul Gaggl, 2018. "On the Welfare Implications of Automation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 15-43, July.
    20. Andrew Glover & Jacob Short, 2020. "Can Capital Deepening Explain the Global Decline in Labor's Share?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 35, pages 35-53, January.

    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:aea:aejmac:v:9:y:2017:i:4:p:225-53. 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: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.html .

    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.