Acta Univ. Agric. Silvic. Mendelianae Brun. 2019, 67(5), 1347-1356 | DOI: 10.11118/actaun201967051347

The Time Augmented Cobb-Douglas Production Function

Lenka Roubalová, Lenka Viskotová
Department of Statistics and Operation Analysis, Faculty of Business and Economics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic

The main objective of this paper is to propose and verify a time augmentation of the Cobb-Douglas production function parameters which should be able to capture changing conditions over time. The parameters are estimated via the nonlinear least squares method. As data a time series including production and its sources, labour and capital, in the construction industries of six Central European countries for the period 1995-2015 is used. Our results, based on calculation of R2 and Theil's U, prove that the models containing the time augmented parameters are better than the basic one. Also a verification of evaluated models using the economic reality for each country is given. In addition to the superiority of the time augmented models, these are applicable to distinguish the specifics of the development of productivity in individual countries.

Keywords: central European countries, Cobb-Douglas production function, construction industry, nonlinear least squares, parameters constancy, production function

Received: August 27, 2019; Accepted: October 7, 2019; Published: October 31, 2019  Show citation

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Roubalová, L., & Viskotová, L. (2019). The Time Augmented Cobb-Douglas Production Function. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 67(5), 1347-1356. doi: 10.11118/actaun201967051347
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    References

    1. ALKHAREIF, R. M., BARNETT, W. A. and ALSADOUN, N. A. 2017. Estimating the Output Gap for Saudi Arabia. International Journal of Economics and Finance, 9(3): 81-90. DOI: 10.5539/ijef.v9n3p81 Go to original source...
    2. BIEA, N. 2016. Economic growth in Slovakia: Past successes and future challenges. Economic brief 008. Luxembourg: Publications Office of the European Union.
    3. BESANKO, D. and BRAEUTIGAM, R. 2007. Microeconomics. 3rd Edition. Canada: John Willey & Sons.
    4. COBB, C. W. and DOUGLAS, P. H. 1928. A Theory of Production. American Economic Review, 18: 139-165.
    5. COTIS, J. P., ELMESKOV, J. and MOUROUGANE, A. 2005. Estimates of potential output: benefits and pitfalls from a policy perspective. In: Rechling, L. (Ed.). Euro Area Business Cycles: Stylized Facts and Measurement Issues. London: CEPR.
    6. ČERNÝ, J. 2011. Comparison of Cobb-Douglas Production Functions of the Chosen Countries by Using Econometric Model. In: Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011 - part I. University of Economics, 6-9 September. Prague: Professional Publishing, pp. 107-112.
    7. D'AURIA, F. 2010. The production function methodology for calculating potential growth rates and output gaps. Brussels: European Commission, Directorate-General for Economic and Financial Affairs.
    8. EUROPEAN COMMISSION. 2016. EU's top trading partners in 2015: the UnitedStates for exports, China for imports. Pressrelase. Eurostat Press Office. Available at: http://ec.europa.eu/eurostat/documents/2995521/7224419/6-31032016-BPEN.pdf/b82ea736-1c73-487f-8fb5-4954774bb63a [Accessed: 2019, August 11].
    9. EUROPEAN COMISSION. 2018a. European Construction Sector Observatory, Country Profile Austria. [Online]. Available at: https://ec.europa.eu/docsroom/documents/30286/attachments/1/translations/en/renditions/pdf [Accessed: 2019, July 22].
    10. EUROPEAN COMISSION. 2018b. European Construction Sector Observatory, Country Profile Czech Republic. [Online]. Available at: https://ec.europa.eu/docsroom/documents/30287/attachments/1/translations/en/renditions/pdf. [Accessed: 2019, July 22].
    11. EUROPEAN COMISSION. 2018c. European Construction Sector Observatory, Country Profile Germany. [Online]. Available at: https://ec.europa.eu/docsroom/documents/23744/attachments/1/translations/en/renditions/pdf. [Accessed: 2019, July 22].
    12. EUROPEAN COMISSION. 2018d. European Construction Sector Observatory, Country Profile Hungary. [Online]. Available at: https://ec.europa.eu/docsroom/documents/30348/attachments/1/translations/en/renditions/pdf. [Accessed: 2019, July 22].
    13. EUROPEAN COMISSION. 2018e. European Construction Sector Observatory, Country Profile Poland. [Online]. Available at: https://ec.europa.eu/docsroom/documents/30668/attachments/1/translations/en/renditions/pdf. [Accessed: 2019, July 22].
    14. GREENE, W. H. 2012. Econometric analysis. 7th Edition. Boston: Pearson.
    15. HÁJKOVÁ, D. and HURNÍK J. 2007. Cobb-Douglas Production Function: The Case of a Converging Economy. Finance a úvěr, 57(9-10): 465-476.
    16. HECZKOVÁ, M. 2014. Fakta o obchodě se zahraničím. Statistika & My, 9: 19-20.
    17. KMENTA, J. 1967. On Estimation of the CES Production Function. International Economic Review, 8(2): 180-189. DOI: 10.2307/2525600 Go to original source...
    18. KMENTA, J. 1990. Elements of Econometrics. 2nd Edition. New York: Macmillan.
    19. KOTULIC, R., KRAVČÁKOVÁ VOZÁROVÁ, I., NAGY, J., HUTTMANOVÁ, E. and VAVREČKA, R. 2015. Performance of The Slovak Economy in Relation to Labor Productivity and Employment. Economics and Finance, 23: 970-975. Go to original source...
    20. LEVENBERG, K. 1944. A Method for the Solution of Certain Non-Linear Problems in Least Squares. Quarterly of Applied Mathematics, 2: 164-168. DOI: 10.1090/qam/10666 Go to original source...
    21. MAKIN, J. A. and STRONG, S. 2013. New Measures of Factor Productivity in Australia: a Sato approach. Applied Economics Australia, 45(17): 2413-2422. DOI: 10.1080/00036846.2012.665603 Go to original source...
    22. MARQUARDT, D. 1963. An Algorithm for Least-Squares Estimation of Nonlinear Parameter. Journal of the Society for Industrial and Applied Mathematics, 11(2): 431-441. DOI: 10.1137/0111030 Go to original source...
    23. MISHRA, S. K. 2007. A Brief History of Production Functions. The IUP Journal of Managerial Economics, 8(4): 6-34. Go to original source...
    24. NAUDÉ, W. and NAGLER, P. 2017. Technological Innovation and Inclusive Growth in Germany. IZA Discussion Paper Series, 11194. IZA Institute of Labor Economics. Go to original source...
    25. RÕÕM, M. 2001. Potential Output Estimates for Central and East European Countries Using Production Function Method. Working Papers of Eesti Pank, 2: 1-23. Eesti Pank.
    26. ROUBALOVÁ, L., HAMPEL, D. and VISKOTOVÁ, L. 2018. Technological Progress at the Sectoral Level: the Sato Production Function Approach. In: Proceedings of the 36th International Conference on Mathematical Methods in Economics. University of Economics, 12-14 September. Prague: Professional Publishing, pp. 470-475.
    27. ROUBALOVÁ, L. and VISKOTOVÁ, L. 2018. Productivity Development in Selected Central European Countries Measured by the Sato Production Function. Review of economic perspectives, 18(4): 353-370. DOI: 10.2478/revecp-2018-0018 Go to original source...
    28. SATO, R. 1964. Diminishing returns and linear homogeneity: comment. The American Economic Review, 54(5): 744-745.
    29. SATO, R. 1970. The Estimation of Biased Technical Progress and the Production Function. International Economic Review, 11(2): 179-208. DOI: 10.2307/2525662 Go to original source...
    30. THEIL, H. 1966. Applied Economic Forecasting. Amsterdam: North-Holland.
    31. VISKOTOVÁ, L., ROUBALOVÁ, L. and HAMPEL, D. 2019. Starting Parameters For The Estimation Of The Production Functions. In: Proceedings of the 16th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018). Rhodes, Greece 13-18 September. Melville: American Institute of Physics (AIP). Go to original source...
    32. ZIMKOVÁ, E. and BAROCHOVSKÝ, J. 2007. Odhad potenciálneho produktu a produkčnej medzery v slovenských podmienkach. Politická ekonomie, 4: 473-489. DOI: 10.18267/j.polek.609 Go to original source...

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