Abstract
In this paper, we propose a method for cost efficiency measurement that is based on local estimation in several stages. The method is based on weighted least squares where weights depend on the distance of an observation to all other observations and on the distance to the cost frontier. The new element in the method is that it also includes the information from the cost share equations and includes cost efficiency in the weighting matrix. The latter is derived from a first stage and implemented in a second stage analysis. An application to a data set of Dutch school boards in secondary education shows that it works well in practice. It produces a number of reliable estimates. It also shows a variation in outcomes that would be hard to cover with, for instance, traditional procedures such as SFA on a translog cost function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21–37. https://doi.org/10.1016/0304-4076(77)90052-5.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.
Blank, J. L. T. (2000). Public provision and performance: Contributions from efficiency and productivity measurement. Amsterdam: Elsevier.
Blank, J. L. T., & Eggink, E. (2004). The decomposition of cost efficiency: An empirical application of the shadow cost function model to Dutch general hospitals. Health Care Management Science, 7, 79–88.
Blank, J. L. T., & Heezik van, A. A. S. (2017). Productiviteit van overheidsbeleid, deel III: de Nederlandse veiligheid en justitie, 1980–2014. forthcoming.
Blank, J. L. T., & Meesters, A. (2012). Iteratively weighted least squares on stochastic frontier estimation. Applied to the Dutch hospital industry. In R. Banker, A. Emrouznejad, A. L. Miranda Lopez, & M. R. de Almeida (Eds.), Data envelopment analysis: Theory and applications. Proceedings of the 10th international conference on DEA (pp. 167–185). Natal.
Blank, J. L. T., & van Heezik, A. A. S. (2015). Productiviteit van overheidsbeleid, deel I: het Nederlandse onderwijs, 1980–2012. Den Haag/Delft: Eburon.
Blank, J. L. T., van Heezik, A. A. S., & Niaounakis, T. K. (2016). Productiviteit van overheidsbeleid, deel II: de Nederlandse zorg, 1980–2013. Den Haag/Delft: Eburon.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444. https://doi.org/10.1016/0377-2217(78)90138-8.
Christensen, L. R., Jorgenson, D. W., & Lau, L. J. (1973). Transcendental logarithmic production Frontiers. The Review of Economics and Statistics, 55(1), 28–45. Retrieved from http://www.jstor.org/stable/1927992.
Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis (2nd ed.). New York: Springer.
Debreu, G. (1951). The coefficient of resource utilization. Econometrica, 19(3), 273–292. Retrieved from http://www.jstor.org/stable/1906814.
Fan, Y., Li, Q., & Weersink, A. (1996). Semiparametric estimation of stochastic production frontier models. Journal of Business & Economic Statistics, 14(4), 460–468
Färe, R., Grosskopf, S., & Lovell, C. A. K. (1986). Scale economies and duality. Journal of Economics-Zeitschrift Fur Nationalokonomie, 46(2), 175–182. https://doi.org/10.1007/bf01229228.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253–290. Retrieved from http://www.jstor.org/stable/2343100.
Fried, H. O., Lovell, C. A. K., & Schmidt, S. S. (2008). The measurement of productive efficiency and productivity growth. New York: Oxford University Press.
Johnson, A., & Kuosmanen, T. (2015). An introduction to CNLS and StoNED methods for efficiency analysis: Economic insights and computational aspects. Benchmarking for Performance Evaluation., 1–80, Retrieved from http://link.springer.com/chapter/10.1007/978-81-322-2253-8_3.
Kumbhakar, S. C. (1997). Modelling allocative inefficiency in a Translog cost function and cost share equations. Journal of Econometrics, 76, 351–356.
Kumbhakar, S. C., & Lovell, C. (2000). Stochastic frontier analysis. New York: Cambridge University Press.
Kumbhakar, S. C., & Tsionas, E. G. (2005). The joint measurement of technical and allocative inefficiencies: An application of Bayesian inference in nonlinear random-effects models. Journal of the American Statistical Association, 100(471), 736–747.
Kuosmanen, T. (2008). Representation theorem for convex nonparametric least squares. The Econometrics Journal, 8(2), 308–325. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1368-423X.2008.00239.x/full.
Maietta, O. W. (2002). The effect of the normalisation of the shadow price vector on the cost function estimation. Economics Letters, 77, 381–385.
Materov, I. S. (1981). On full identification of the stochastic production frontier model. Ekonomika I Matematicheskie Metody, 17, 784–788.
Meeusen, W., & Van den Broeck, J. (1977). Efficiency estimation from cobb-Douglas production functions with composed error. International Economic Review, 8, 435–444.
Parmeter, C., & Kumbhakar, S. (2014). Efficiency analysis: A primer on recent advances. New York: Miami.
Ray, S. C., Kumbhakar, S. C., & Dua, P. (2015). Benchmarking for performance evaluation: A production frontier approach. Benchmarking for performance evaluation: A production frontier approach. New Delhi: Springer India. https://doi.org/10.1007/978-81-322-2253-8.
Shephard, R. W. (1953). Theory of cost and production functions. (P. U. Press, Ed.). Princeton: Princeton University Press.
Urlings, T., & Blank, J. L. T. (2012). Benchmark bedrijfsvoering voortgezet onderwijs. IPSE Studies Research Reeks. Delft: TU Delft, IPSE Studies.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Blank, J.L.T. (2018). Frontier Estimation of a Cost Function System Model with Local Least Squares: An Application to Dutch Secondary Education. In: Greene, W., Khalaf, L., Makdissi, P., Sickles, R., Veall, M., Voia, MC. (eds) Productivity and Inequality. NAPW 2016. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-68678-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-68678-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68677-6
Online ISBN: 978-3-319-68678-3
eBook Packages: Business and ManagementBusiness and Management (R0)