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Semiparametric smooth-coefficient stochastic frontier model


  • Sun, Kai
  • Kumbhakar, Subal C.


This paper proposes a semiparametric smooth-coefficient (SPSC) stochastic production frontier model where regression coefficients are unknown smooth functions of environmental factors (Z). Technical inefficiency is specified in the form of a parametric scaling function which also depends on the Z variables. Thus, in our SPSC model the Z variables affect productivity directly via the technology parameters as well as through inefficiency. A residual-based bootstrap test of the relevance of the environmental factors in the SPSC model is suggested. An empirical application is also used to illustrate the technique.

Suggested Citation

  • Sun, Kai & Kumbhakar, Subal C., 2013. "Semiparametric smooth-coefficient stochastic frontier model," Economics Letters, Elsevier, vol. 120(2), pages 305-309.
  • Handle: RePEc:eee:ecolet:v:120:y:2013:i:2:p:305-309 DOI: 10.1016/j.econlet.2013.05.001

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    References listed on IDEAS

    1. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    2. Hung-jen Wang & Peter Schmidt, 2002. "One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels," Journal of Productivity Analysis, Springer, vol. 18(2), pages 129-144, September.
    3. Christopher O’Donnell & D. Rao & George Battese, 2008. "Metafrontier frameworks for the study of firm-level efficiencies and technology ratios," Empirical Economics, Springer, vol. 34(2), pages 231-255, March.
    4. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    5. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    6. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1607-1637, December.
    7. George Battese & D. Rao & Christopher O'Donnell, 2004. "A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies," Journal of Productivity Analysis, Springer, vol. 21(1), pages 91-103, January.
    8. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
    9. Kumbhakar, Subal C & Ghosh, Soumendra & McGuckin, J Thomas, 1991. "A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 279-286, July.
    10. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    11. Hung-Jen Wang, 2002. "Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model," Journal of Productivity Analysis, Springer, vol. 18(3), pages 241-253, November.
    12. 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.
    13. 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.
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    Cited by:

    1. Llorca, Manuel & Orea, Luis & Pollitt, Michael G., 2016. "Efficiency and environmental factors in the US electricity transmission industry," Energy Economics, Elsevier, vol. 55(C), pages 234-246.
    2. Tomasz Gerard Czekaj, 2013. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Parametric and Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," IFRO Working Paper 2013/21, University of Copenhagen, Department of Food and Resource Economics.
    3. Im, Hyun Joong & Park, Young Joon & Shon, Janghoon, 2015. "Product market competition and the value of innovation: Evidence from US patent data," Economics Letters, Elsevier, vol. 137(C), pages 78-82.
    4. 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.
    5. repec:eee:ejores:v:263:y:2017:i:3:p:1078-1094 is not listed on IDEAS
    6. Czekaj, Tomasz G., 2015. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," 2015 Conference, August 9-14, 2015, Milan, Italy 211555, International Association of Agricultural Economists.

    More about this item


    Semiparametric smooth-coefficient model; Stochastic frontier; Environmental factors;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • Q12 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets


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