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A Bayesian semiparametric approach to stochastic frontiers and productivity


  • Tsionas, Mike G.
  • Mallick, Sushanta K.


In this paper we take up the analysis of production functions / frontiers removing the assumptions of known functional form for the productivity equation, given the heterogeneity of productivity and the endogeneity of inputs at firm level. The assumption of exogenous regressors is removed through taking account of the first order conditions of profit maximization. We introduce latent dynamic stochastic productivity in our framework and perform Bayesian analysis using a Sequential Monte Carlo Particle-Filtering approach. We investigate the performance of the new approach relative to alternative methods in the literature, in a substantive application to Indian non-financial firms, and find that total factor productivity (TFP) growth has remained stagnant at firm level in India despite rapid growth at the aggregate level, with technical efficiency or catching-up effect driving TFP growth in the recent years rather than technological progress or frontier shift.

Suggested Citation

  • Tsionas, Mike G. & Mallick, Sushanta K., 2019. "A Bayesian semiparametric approach to stochastic frontiers and productivity," European Journal of Operational Research, Elsevier, vol. 274(1), pages 391-402.
  • Handle: RePEc:eee:ejores:v:274:y:2019:i:1:p:391-402
    DOI: 10.1016/j.ejor.2018.10.026

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    References listed on IDEAS

    1. Kim, Kyoo il & Petrin, Amil & Song, Suyong, 2016. "Estimating production functions with control functions when capital is measured with error," Journal of Econometrics, Elsevier, vol. 190(2), pages 267-279.
    2. Sumru Altuğ & Robert A. Miller, 1998. "The Effect of Work Experience on Female Wages and Labour Supply," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 45-85.
    3. Christine Amsler & Artem Prokhorov & Peter Schmidt, 2014. "Using Copulas to Model Time Dependence in Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 497-522, August.
    4. Matousek, Roman & Tzeremes, Nickolaos G., 2016. "CEO compensation and bank efficiency: An application of conditional nonparametric frontiers," European Journal of Operational Research, Elsevier, vol. 251(1), pages 264-273.
    5. Godsill, Simon J. & Doucet, Arnaud & West, Mike, 2004. "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 156-168, January.
    6. Sushanta Mallick & Yong Yang, 2013. "Productivity Performance of Export Market Entry and Exit: Evidence from Indian Firms," Review of International Economics, Wiley Blackwell, vol. 21(4), pages 809-824, September.
    7. Tran, Kien C. & Tsionas, Mike G., 2016. "Zero-inefficiency stochastic frontier models with varying mixing proportion: A semiparametric approach," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1113-1123.
    8. Kevork, Ilias S. & Pange, Jenny & Tzeremes, Panayiotis & Tzeremes, Nickolaos G., 2017. "Estimating Malmquist productivity indexes using probabilistic directional distances: An application to the European banking sector," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1125-1140.
    9. Sun, Kai & Kumbhakar, Subal C. & Tveterås, Ragnar, 2015. "Productivity and efficiency estimation: A semiparametric stochastic cost frontier approach," European Journal of Operational Research, Elsevier, vol. 245(1), pages 194-202.
    10. Haidar, Jamal Ibrahim, 2012. "Trade and productivity: Self-selection or learning-by-exporting in India," Economic Modelling, Elsevier, vol. 29(5), pages 1766-1773.
    11. Tzeremes, Nickolaos G., 2015. "Efficiency dynamics in Indian banking: A conditional directional distance approach," European Journal of Operational Research, Elsevier, vol. 240(3), pages 807-818.
    12. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    13. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    14. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    15. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    16. Sungho Park & Sachin Gupta, 2012. "Handling Endogenous Regressors by Joint Estimation Using Copulas," Marketing Science, INFORMS, vol. 31(4), pages 567-586, July.
    17. Sushanta K. MALLICK & Ricardo M. SOUSA, 2017. "The skill premium effect of technological change: New evidence from United States manufacturing," International Labour Review, International Labour Organization, vol. 156(1), pages 113-131, March.
    18. Bournakis, Ioannis & Mallick, Sushanta, 2018. "TFP estimation at firm level: The fiscal aspect of productivity convergence in the UK," Economic Modelling, Elsevier, vol. 70(C), pages 579-590.
    19. Ulrich Doraszelski & Jordi Jaumandreu, 2013. "R&D and Productivity: Estimating Endogenous Productivity," Review of Economic Studies, Oxford University Press, vol. 80(4), pages 1338-1383.
    20. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
    21. Creal, Drew D. & Tsay, Ruey S., 2015. "High dimensional dynamic stochastic copula models," Journal of Econometrics, Elsevier, vol. 189(2), pages 335-345.
    22. Nicolas Chopin & Sumeetpal S. Singh, 2013. "On the Particle Gibbs Sampler," Working Papers 2013-41, Center for Research in Economics and Statistics.
    23. Fukuyama, Hirofumi & Matousek, Roman, 2017. "Modelling bank performance: A network DEA approach," European Journal of Operational Research, Elsevier, vol. 259(2), pages 721-732.
    24. Fethi, Meryem Duygun & Pasiouras, Fotios, 2010. "Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey," European Journal of Operational Research, Elsevier, vol. 204(2), pages 189-198, July.
    25. Ferrara, Giancarlo & Vidoli, Francesco, 2017. "Semiparametric stochastic frontier models: A generalized additive model approach," European Journal of Operational Research, Elsevier, vol. 258(2), pages 761-777.
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    2. Tsionas, Mike G. & Andrikopoulos, Athanasios, 2020. "On a High-Dimensional Model Representation method based on Copulas," European Journal of Operational Research, Elsevier, vol. 284(3), pages 967-979.
    3. Glass, Anthony J. & Kenjegalieva, Karligash & Douch, Mustapha, 2020. "Uncovering spatial productivity centers using asymmetric bidirectional spillovers," European Journal of Operational Research, Elsevier, vol. 285(2), pages 767-788.
    4. Guangming Rao & Bin Su & Jinlian Li & Yong Wang & Yanhua Zhou & Zhaolin Wang, 2019. "Carbon Sequestration Total Factor Productivity Growth and Decomposition: A Case of the Yangtze River Economic Belt of China," Sustainability, MDPI, Open Access Journal, vol. 11(23), pages 1-28, November.

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