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A New Approach to Estimating Production Function Parameters: The Elusive Capital--Labor Substitution Elasticity


  • Robert S. Chirinko
  • Steven M. Fazzari
  • Andrew P. Meyer


Parameters of taste and technology are central to a wide variety of economic models and issues. This article proposes a simple method for estimating production function parameters from panel data, with a particular focus on the elasticity of substitution between capital and labor. Elasticity estimates have varied widely, and a consensus estimate remains elusive. Our estimation strategy exploits long-run variation and thus avoids several pitfalls, including difficult-to-specify dynamics, transitory time-series variation, and positively sloped supply schedules, that can bias the estimated elasticity. Our results are based on an extensive panel comprising 1860 firms. Our approach generates a precisely estimated elasticity of 0.40. Although existing estimates range widely, we document a remarkable convergence of results from two related approaches applied to a common dataset. The method developed here may prove useful in estimating other structural parameters from panel datasets.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:4:p:587-594 DOI: 10.1198/jbes.2011.08119

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    References listed on IDEAS

    1. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    2. Jianqing Fan & Mingjin Wang & Qiwei Yao, 2008. "Modelling multivariate volatilities via conditionally uncorrelated components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 679-702.
    3. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    4. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, March.
    6. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    7. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    8. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    11. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    12. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    13. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    14. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Blog mentions

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    1. Long-run Estimates of Interfuel and Interfactor Elasticities
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    1. Koh, Dongya; Santaeulàlia-Llopis, Raül; Zheng, Yu, 2015. "Labor share decline and intellectual property products capital," Economics Working Papers ECO2015/05, European University Institute.
    2. 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 Group Munich.
    3. Robert A. Blecker, 2016. "Wage-led versus profit-led demand regimes: the long and the short of it," Review of Keynesian Economics, Edward Elgar Publishing, vol. 4(4), pages 373-390, October.
    4. Ma, Chunbo & Stern, David I., 2016. "Long-run estimates of interfuel and interfactor elasticities," Resource and Energy Economics, Elsevier, vol. 46(C), pages 114-130.
    5. Stern, David I. & Gerlagh, Reyer & Burke, Paul J., 2017. "Modeling the emissions–income relationship using long-run growth rates," Environment and Development Economics, Cambridge University Press, vol. 22(06), pages 699-724, December.
    6. Stern, David, 2014. "Rethinking the Emissions-Income Relationship in Terms of Growth Rates," 2014 Conference (58th), February 4-7, 2014, Port Maquarie, Australia 165877, Australian Agricultural and Resource Economics Society.
    7. 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.
    8. McAdam, Peter & Christopoulos, Dimitris, 2015. "Efficiency, Inefficiency and the MENA Frontier," Working Paper Series 1757, European Central Bank.
    9. Judzik, Dario, 2014. "Heterogeneous labor demand: sectoral elasticity and trade effects in the U.S., Germany and Sweden," MPRA Paper 62768, University Library of Munich, Germany.
    10. 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.
    11. Daniel Berkowitz, 2016. "Recasting the Iron Rice Bowl: The Reform of China's State Owned Enterprises," Working Paper 5858, Department of Economics, University of Pittsburgh.
    12. Csereklyei, Zsuzsanna & Stern, David I., 2015. "Global energy use: Decoupling or convergence?," Energy Economics, Elsevier, vol. 51(C), pages 633-641.
    13. Robert A. Blecker, 2015. "Wage-led Versus Profit-led Demand Regimes: The Long and Short of It," Working Papers 2015-05, American University, Department of Economics.
    14. George Sorg-Langhans & Clemens Struck & Adnan Velic, 2017. "On the Factor Content of Trade," Trinity Economics Papers tep0817, Trinity College Dublin, Department of Economics, revised Jan 2018.
    15. repec:aea:aejmac:v:9:y:2017:i:4:p:225-53 is not listed on IDEAS
    16. André Cieplinski, 2017. "Employee Control, Work Content and Wages," Department of Economics University of Siena 775, Department of Economics, University of Siena.
    17. Daniel Berkowitz, 2016. "Capital-Labor Substitution, Institutions and Labor Shares," Working Paper 5981, Department of Economics, University of Pittsburgh.
    18. 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.
    19. Dongya Koh & Raül Santaeulàlia-Llopis, 2017. "Countercyclical Elasticity of Substitution," Working Papers 946, Barcelona Graduate School of Economics.
    20. 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).
    21. Jan Hanousek & Anastasiya Shamshur & Jiri Tresl, 2017. "Firm Efficiency, Foreign Ownership and CEO Gender in Corrupt Environments," CERGE-EI Working Papers wp595, The Center for Economic Research and Graduate Education - Economics Institute, Prague.

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