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Persistent and transient productive inefficiency: a maximum simulated likelihood approach


  • Massimo Filippini


  • William Greene


The productive efficiency of a firm can be seen as composed of two parts, one persistent and one transient. The received empirical literature on the measurement of productive efficiency has paid relatively little attention to the difference between these two components. Ahn and Sickles (Econ Rev 19(4):461–492, 2000 ) suggested some approaches that pointed in this direction. The possibility was also raised in Greene (Health Econ 13(10):959–980, 2004 . doi: 10.1002/hec.938 ), who expressed some pessimism over the possibility of distinguishing the two empirically. Recently, Colombi (A skew normal stochastic frontier model for panel data, 2010 ) and Kumbhakar and Tsionas (J Appl Econ 29(1):110–132, 2012 ), in a milestone extension of the stochastic frontier methodology have proposed a tractable model based on panel data that promises to provide separate estimates of the two components of efficiency. The approach developed in the original presentation proved very cumbersome actually to implement in practice. Colombi ( 2010 ) notes that FIML estimation of the model is ‘complex and time consuming.’ In the sequence of papers, Colombi ( 2010 ), Colombi et al. (A stochastic frontier model with short-run and long-run inefficiency random effects, 2011 , J Prod Anal, 2014 ), Kumbhakar et al. (J Prod Anal 41(2):321–337, 2012 ) and Kumbhakar and Tsionas ( 2012 ) have suggested other strategies, including a four step least squares method. The main point of this paper is that full maximum likelihood estimation of the model is neither complex nor time consuming. The extreme complexity of the log likelihood noted in Colombi ( 2010 ), Colombi et al. ( 2011 , 2014 ) is reduced by using simulation and exploiting the Butler and Moffitt (Econometrica 50:761–764, 1982 ) formulation. In this paper, we develop a practical full information maximum simulated likelihood estimator for the model. The approach is very effective and strikingly simple to apply, and uses all of the sample distributional information to obtain the estimates. We also implement the panel data counterpart of the Jondrow et al. (J Econ 19(2–3):233–238, 1982 ) estimator for technical or cost inefficiency. The technique is applied in a study of the cost efficiency of Swiss railways. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Massimo Filippini & William Greene, 2016. "Persistent and transient productive inefficiency: a maximum simulated likelihood approach," Journal of Productivity Analysis, Springer, vol. 45(2), pages 187-196, April.
  • Handle: RePEc:kap:jproda:v:45:y:2016:i:2:p:187-196
    DOI: 10.1007/s11123-015-0446-y

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    References listed on IDEAS

    1. Roberto Colombi & Subal Kumbhakar & Gianmaria Martini & Giorgio Vittadini, 2014. "Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency," Journal of Productivity Analysis, Springer, vol. 42(2), pages 123-136, October.
    2. Awudu Abdulai & Hendrik Tietje, 2007. "Estimating technical efficiency under unobserved heterogeneity with stochastic frontier models: application to northern German dairy farms," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 34(3), pages 393-416, September.
    3. Roberto Colombi & Gianmaria Martini & Giorgio Vittadini, 2011. "A Stochastic Frontier Model with short-run and long-run inefficiency random effects," Working Papers 1101, Department of Economics and Technology Management, University of Bergamo.
    4. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    5. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    6. William Greene, 2004. "Distinguishing between heterogeneity and inefficiency: stochastic frontier analysis of the World Health Organization's panel data on national health care systems," Health Economics, John Wiley & Sons, Ltd., vol. 13(10), pages 959-980.
    7. Rafael Cuesta, 2000. "A Production Model With Firm-Specific Temporal Variation in Technical Inefficiency: With Application to Spanish Dairy Farms," Journal of Productivity Analysis, Springer, vol. 13(2), pages 139-158, March.
    8. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
    9. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    10. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    11. Seung Ahn & Robin Sickles, 2000. "Estimation of long-run inefficiency levels: a dynamic frontier approach," Econometric Reviews, Taylor & Francis Journals, vol. 19(4), pages 461-492.
    12. Cornwell, Christopher & Schmidt, Peter & Sickles, Robin C., 1990. "Production frontiers with cross-sectional and time-series variation in efficiency levels," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 185-200.
    13. Battese, G E & Coelli, T J, 1995. "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-332.
    14. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    15. Kumbhakar,Subal C. & Lovell,C. A. Knox, 2003. "Stochastic Frontier Analysis," Cambridge Books, Cambridge University Press, number 9780521666633, July - De.
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    More about this item


    Productive efficiency; Stochastic frontier analysis; Panel data; Transient and persistent efficiency; C1; C23; D2; D24;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D2 - Microeconomics - - Production and Organizations
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity


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