Journal of Quantitative Economics

, Volume 17, Issue 3, pp 513–524 | Cite as

A Hierarchical Stochastic Frontier Model for Efficiency Measurement Under Technology Heterogeneity

  • Ioannis SkevasEmail author
Original Article


This article proposes an extension to the typical random-coefficients frontier model that allows the incorporation of firm management indicator(s) in the distribution of firms’ technology parameters. Such a modelling approach does not only relax the homogeneous technology assumption but also empirically tests for the factors that may be responsible for variation in firms’ technology parameters. The proposed approach is used to measure the technical efficiency of German dairy farms for the period 2001–2009. Estimation is performed using Bayesian techniques. The empirical findings suggest that German dairy farms achieve high levels of technical efficiency, while farms’ degree of intensification indeed drives several technology parameters. Furthermore, model comparison based on Bayes factors reveals that the employed model outperforms a simple stochastic frontier model and a random-coefficients stochastic frontier model.


Technology heterogeneity Dairy farms Bayesian techniques Technical efficiency Intensification 

JEL Classification

C11 C23 D22 Q12 


  1. Abid, I., and M. Goaied. 2017. Benchmarking banking efficiency using a meta-profit function. Journal of Quantitative Economics 15 (1): 45–74.CrossRefGoogle Scholar
  2. Aigner, D., C.A.K. Lovel, and P. Schmidt. 1977. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6 (1): 21–37.CrossRefGoogle Scholar
  3. Alvarez, A., and J. del Corral. 2010. Identifying different technologies using a latent class model: extensive versus intensive dairy farms. European Review of Agricultural Economics 37 (2): 231–250.CrossRefGoogle Scholar
  4. Alvarez, A., J. del Corral, D. Solís, and J.A. Pérez. 2008. Does intensification improve the economic efficiency of dairy farms? Journal of Dairy Science 91 (9): 3693–3698.CrossRefGoogle Scholar
  5. Emvalomatis, G. 2012. Productivity growth in German dairy farming using a flexible modelling approach. Journal of Agricultural Economics 63 (1): 83–101.CrossRefGoogle Scholar
  6. Greene, W. 2005. Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics 126 (2): 269–303.CrossRefGoogle Scholar
  7. Hynes, S., and E. Garvey. 2009. Modelling Farmers’ participation in an agri-environmental scheme using panel data: an application to the rural environment protection scheme in Ireland. Journal of Agricultural Economics 60 (3): 546–562.CrossRefGoogle Scholar
  8. Kalirajan, K.P., and M.B. Obwona. 1994. Frontier production function: The stochastic coefficients approach. Oxford Bulletin of Economics and Statistics 56 (1): 87–96.CrossRefGoogle Scholar
  9. Kass, R.E., and A.E. Raftery. 1995. Bayes factors. Journal of the American Statistical Association 90 (430): 773–795.CrossRefGoogle Scholar
  10. Koop, G., M.F.J. Steel, and J. Osiewalski. 1995. Posterior analysis of stochastic frontier models using Gibbs sampling. Computational Statistics 10: 353–373.Google Scholar
  11. Kumbhakar, S. C. and C. A. K. Lovell. 2003. Stochastic frontier analysis. Cambridge: Cambridge University Press.Google Scholar
  12. Lewis, S.M., and A.E. Raftery. 1997. Estimating bayes factors via posterior simulation with the Laplace-metropolis estimator. Journal of the American Statistical Association 92 (438): 648–655.Google Scholar
  13. Meeusen, W., and J. van den Broeck. 1977. Efficiency estimation from Cobb–Douglas production functions with composed error. International Economic Review 18 (2): 435–444.CrossRefGoogle Scholar
  14. Orea, L., and S.C. Kumbhakar. 2004. Efficiency measurement using a latent class stochastic frontier model. Empirical Economics 29 (1): 169–183.CrossRefGoogle Scholar
  15. Reinhard, S., C.A.K. Lovell, and G. Thijssen. 2002. Analysis of environmental efficiency variation. American Journal of Agricultural Economics 84 (4): 1054–1065.CrossRefGoogle Scholar
  16. Sauer, J., and C.J.M. Paul. 2013. The empirical identification of heterogeneous technologies and technical change. Applied Economics 45 (11): 1461–1479.CrossRefGoogle Scholar
  17. Tanner, M.A., and W.H. Wong. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82 (398): 528–540.CrossRefGoogle Scholar
  18. Tsionas, E.G. 2002. Stochastic frontier models with random coefficients. Journal of Applied Econometrics 17 (2): 127–147.CrossRefGoogle Scholar
  19. van den Broeck, J., G. Koop, J. Osiewalski, and M.F.J. Steel. 1994. Stochastic frontier models: A Bayesian perspective. Journal of Econometrics 61 (2): 273–303.CrossRefGoogle Scholar

Copyright information

© The Indian Econometric Society 2018

Authors and Affiliations

  1. 1.Department of Food Business and Development, Cork University Business SchoolUniversity College CorkCorkIreland

Personalised recommendations