IDEAS home Printed from https://ideas.repec.org/a/psc/journl/v13y2021i4p455-486.html
   My bibliography  Save this article

Bayesian Estimation of Capital Stock and Depreciation in the Production Function Framework

Author

Listed:
  • Jakub Boratyński

    (University of Łódź)

  • Jacek Osiewalski

    (Cracow University of Economics)

Abstract

We propose a Bayesian approach to estimating productive capital stocks and depreciation rates within the production function framework, using annual data on output, employment and investment only. Productive capital stock is a concept related to the input of capital services to production, in contrast to the more common net capital stock estimates, representing market value of fixed assets. We formulate a full Bayesian model and employ it in a series of illustrative empirical examples. We find that parameters of our model, from which the time-path of capital is derived, are weakly identified with the data at hand. Nevertheless, estimation is feasible with the use of prior information on the production function parameters and the characteristics of productivity growth. We show how precision of the estimates can be improved by augmenting the model with an equation for the rate of return.

Suggested Citation

  • Jakub Boratyński & Jacek Osiewalski, 2021. "Bayesian Estimation of Capital Stock and Depreciation in the Production Function Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 13(4), pages 455-486, December.
    • Handle: RePEc:psc:journl:v:13:y:2021:i:4:p:455-486
    as

    Download full text from publisher

    File URL: http://cejeme.org/publishedarticles/2021-09-14-637750913428980508-4489.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Doms, Mark E, 1996. "Estimating Capital Efficiency Schedules within Production Functions," Economic Inquiry, Western Economic Association International, vol. 34(1), pages 78-92, January.
    2. Raouf Boucekkine & Ramón Ruiz-Tamarit, 2003. "Capital Maintenance and Investment: Complements or Substitutes?," Journal of Economics, Springer, vol. 78(1), pages 1-28, January.
    3. Escribá-Pérez, F.J. & Murgui-García, M.J. & Ruiz-Tamarit, J.R., 2018. "Economic and statistical measurement of physical capital: From theory to practice," Economic Modelling, Elsevier, vol. 75(C), pages 246-255.
    4. Barañano, Ilaski & Romero-Ávila, Diego, 2015. "Long-term growth and persistence with obsolescence," Economic Modelling, Elsevier, vol. 51(C), pages 328-339.
    5. George Bitros, 2010. "The theorem of proportionality in contemporary capital theory: An assessment of its conceptual foundations," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(4), pages 367-401, December.
    6. Michał Gradzewicz & Jakub Growiec & Marcin Kolasa & Łukasz Postek & Paweł Strzelecki, 2018. "Poland’s uninterrupted growth performance: new growth accounting evidence," Post-Communist Economies, Taylor & Francis Journals, vol. 30(2), pages 238-272, March.
    7. Nadiri, M Ishaq & Prucha, Ingmar R, 1996. "Estimation of the Depreciation Rate of Physical and R&D Capital in the U.S. Total Manufacturing Sector," Economic Inquiry, Western Economic Association International, vol. 34(1), pages 43-56, January.
    8. Nicholas Oulton & Sylaja Srinivasan, 2003. "Capital stocks, capital services, and depreciation: an integrated framework," Bank of England working papers 192, Bank of England.
    9. Ariél Pakes & Zvi Griliches, 1984. "Estimating Distributed Lags in Short Panels with an Application to the Specification of Depreciation Patterns and Capital Stock Constructs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 243-262.
    10. Coen, Robert M, 1975. "Investment Behavior, the Measurement of Depreciation, and Tax Policy," American Economic Review, American Economic Association, vol. 65(1), pages 59-74, March.
    11. Epstein, L. & Denny, M., 1980. "Endogenous capital utilization in a short-run production model : Theory and an empiral application," Journal of Econometrics, Elsevier, vol. 12(2), pages 189-207, February.
    12. Raouf Boucekkine & Fernando del Río & Blanca Martínez, 2009. "Technological progress, obsolescence, and depreciation," Oxford Economic Papers, Oxford University Press, vol. 61(3), pages 440-466, July.
    13. Prucha, Ingmar R, 1995. "On the Econometric Estimation of a Constant Rate of Depreciation," Empirical Economics, Springer, vol. 20(2), pages 299-302.
    14. de Rassenfosse, Gaétan & Jaffe, Adam B., 2018. "Econometric evidence on the depreciation of innovations," European Economic Review, Elsevier, vol. 101(C), pages 625-642.
    15. Karim Abadir & Gabriel Talmain, 2001. "Depreciation Rates and Capital Stocks," Manchester School, University of Manchester, vol. 69(1), pages 42-51, January.
    16. Linnemann, Ludger, 2016. "Markups, technology, and capital utilization in the Great Recession," Economics Letters, Elsevier, vol. 142(C), pages 59-63.
    17. Chatterjee, Santanu, 2005. "Capital utilization, economic growth and convergence," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2093-2124, December.
    18. Osiewalski, J., 1988. "Posterior and predictive densities for nonlinear regression : A partly linear model case," Other publications TiSEM 2b2ba23e-f33d-495a-81d0-6, Tilburg University, School of Economics and Management.
    19. Dale W. Jorgenson & Paul Schreyer, 2013. "Industry-Level Productivity Measurement And The 2008 System Of National Accounts," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(2), pages 185-211, June.
    20. Charles R. Hulten, 1991. "The Measurement of Capital," NBER Chapters, in: Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in Income and Wealth, pages 119-158, National Bureau of Economic Research, Inc.
    21. J. Beaulieu & Joe Mattey, 1998. "The Workweek of Capital and Capital Utilization in Manufacturing," Journal of Productivity Analysis, Springer, vol. 10(2), pages 199-223, October.
    22. Jacek Osiewalski & Justyna Wróblewska & Kamil Makieła, 2020. "Bayesian comparison of production function-based and time-series GDP models," Empirical Economics, Springer, vol. 58(3), pages 1355-1380, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. N. V. Suvorov & E. A. Rutkovskaya & E. E. Balashova & S. I. Maksimtsova & S. V. Treschina & Yu.V. Beletskii, 2022. "Assessing the Performance of Fixed Assets in the Russian Economy," Studies on Russian Economic Development, Springer, vol. 33(4), pages 367-376, August.

    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. F. J. Escribá-Pérez & M. J. Murgui-García & J. R. Ruiz-Tamarit, 2019. "Capital Stock and Depreciation: Theory and an Empirical Application," LIDAM Discussion Papers IRES 2019004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Diego Romero-Avila & DIEGO ROMERO-ÁVILA & ILASKI BARAÑANO, 2012. "Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence," EcoMod2012 3757, EcoMod.
    3. Chatterjee, Santanu, 2005. "Capital utilization, economic growth and convergence," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2093-2124, December.
    4. Barañano Mentxaka, Ilaski & Romero-Avila, Diego, 2013. "Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence," IKERLANAK http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    5. F. J. Escribá‐Pérez & M. J. Murgui‐García & J. R. Ruiz‐Tamarit, 2023. "Endogenous capital stock and depreciation in the United States," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(1), pages 139-167, February.
    6. Belousova, Irina, 2017. "The role of endogenous capital depreciation rate in Dynamic Stochastic General Equilibrium models: Evidence from Canada," MPRA Paper 102036, University Library of Munich, Germany.
    7. José A. Hernández & Ignacio Mauleón, 2002. "Estimating the Capital Stock," Documentos de trabajo conjunto ULL-ULPGC 2002-03, Facultad de Ciencias Económicas de la ULPGC.
    8. Albonico, Alice & Kalyvitis, Sarantis & Pappa, Evi, 2014. "Capital maintenance and depreciation over the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 273-286.
    9. Chinloy, Peter & Jiang, Cheng & John, Kose, 2020. "Investment, depreciation and obsolescence of R&D," Journal of Financial Stability, Elsevier, vol. 49(C).
    10. M. Ishaq Nadiri & Ingmar Prucha, 2001. "Dynamic Factor Demand Models and Productivity Analysis," NBER Chapters, in: New Developments in Productivity Analysis, pages 103-172, National Bureau of Economic Research, Inc.
    11. Alice Albonico & Sarantis Kalyvitis & Evi Pappa, 2011. "Real Business Cycles with Capital Maintenance," Quaderni di Dipartimento 147, University of Pavia, Department of Economics and Quantitative Methods.
    12. George Bitros, 2010. "The theorem of proportionality in contemporary capital theory: An assessment of its conceptual foundations," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(4), pages 367-401, December.
    13. Prucha, Ingmar, 1997. "Estimation of a variable rate of depreciation: a dummy variable approach," Structural Change and Economic Dynamics, Elsevier, vol. 8(3), pages 319-325, August.
    14. Barañano, Ilaski & Romero-Ávila, Diego, 2015. "Long-term growth and persistence with obsolescence," Economic Modelling, Elsevier, vol. 51(C), pages 328-339.
    15. Boikos, Spyridon, 2020. "Capital utilization, obsolescence and technological progress," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    16. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    17. Georg Duernecker, 2014. "Technology Adoption, Turbulence, And The Dynamics Of Unemployment," Journal of the European Economic Association, European Economic Association, vol. 12(3), pages 724-754, June.
    18. Raouf Boucekkine & Fernando del Río & Blanca Martínez, 2009. "Technological progress, obsolescence, and depreciation," Oxford Economic Papers, Oxford University Press, vol. 61(3), pages 440-466, July.
    19. Dalgaard, Carl-Johan & Winther Hansen, Jes, 2005. "Capital utilization and the foundations of club convergence," Economics Letters, Elsevier, vol. 87(2), pages 145-152, May.
    20. Pedro Andres Garzon Delvaux & Heinrich Hockmann & Peter Voigt & Pavel Ciaian & Sergio Gomez y Paloma, 2018. "The impact of private R&D on the performance of food-processing firms: Evidence from Europe, Japan and North America," JRC Research Reports JRC104144, Joint Research Centre.

    More about this item

    Keywords

    productive capital stock; depreciation rate; aggregate production function; Bayesian analysis;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

    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:psc:journl:v:13:y:2021:i:4:p:455-486. 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: Damian Jelito (email available below). General contact details of provider: http://cejeme.org/ .

    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.