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Quantity, Quality, and Efficiency for a Partially Super-Additive Cost Function: Connecticut Public Schools Revisited

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  • Subhash Ray
  • Kankana Mukherjee

Abstract

The dual cost function is partially super-additive when an output quantity bundle of a given quality can be produced at a lower cost by breaking up the output into a number of smaller bundles of the same quality to be produced by several firms instead of the entire bundle being produced by a single firm. In this paper, we build on Maindiratta's concept of size efficiency and propose a nonparametric method using mixed integer programming to measure cost efficiency allowing for partial super-additivity of the cost function. The proposed method is applied to data from Connecticut public school districts for the years 1980–81 through 1983–84. Copyright Kluwer Academic Publishers 1998

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  • Subhash Ray & Kankana Mukherjee, 1998. "Quantity, Quality, and Efficiency for a Partially Super-Additive Cost Function: Connecticut Public Schools Revisited," Journal of Productivity Analysis, Springer, vol. 10(1), pages 47-62, July.
    • Handle: RePEc:kap:jproda:v:10:y:1998:i:1:p:47-62
    DOI: 10.1023/A:1018322023051
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    References listed on IDEAS

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    1. Subhash C. Ray, 1991. "Resource-Use Efficiency in Public Schools: A Study of Connecticut Data," Management Science, INFORMS, vol. 37(12), pages 1620-1628, December.
    2. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    3. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    4. Maindiratta, Ajay, 1990. "Largest size-efficient scale and size efficiencies of decision-making units in data envelopment analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 57-72.
    5. 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.
    6. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
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    2. Shimshak, Daniel G. & Lenard, Melanie L. & Klimberg, Ronald K., 2009. "Incorporating quality into data envelopment analysis of nursing home performance: A case study," Omega, Elsevier, vol. 37(3), pages 672-685, June.
    3. Shawna Grosskopf & Kathy J. Hayes & Lori L. Taylor, 2009. "The Relative Efficiency Of Charter Schools," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 80(1), pages 67-87, March.
    4. Valentin Zelenyuk, 2018. "Some Mathematical and Historical Clarifications on Aggregation in Efficiency and Productivity Analysis and Connection to Economic Theory," CEPA Working Papers Series WP032018, School of Economics, University of Queensland, Australia.
    5. Pyra Mariusz, 2020. "The Operational Efficiency of Public Higher Vocational Schools in the Lubelskie Voivodeship," Economic and Regional Studies / Studia Ekonomiczne i Regionalne, Sciendo, vol. 13(1), pages 115-125, March.
    6. Ana María Iregui & Ligia Melo & Jorge Ramos, 2007. "Análisis de eficiencia de la educación en Colombia," Revista de Economía del Rosario, Universidad del Rosario, May.
    7. Richter, Magnus, 2017. "Time and quality efficiency of Scotch single malt whisky production: An empirical two-model DEA approach," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 2, number 22017.
    8. Hien Thu Pham & Antonio Peyrache, 2015. "Industry Inefficiency Measures: A Unifying Approximation Proposition," CEPA Working Papers Series WP102015, School of Economics, University of Queensland, Australia.
    9. Yauheniya Varabyova & Jonas Schreyögg, 2018. "Integrating quality into the nonparametric analysis of efficiency: a simulation comparison of popular methods," Annals of Operations Research, Springer, vol. 261(1), pages 365-392, February.
    10. Peyrache, Antonio, 2013. "Industry structural inefficiency and potential gains from mergers and break-ups: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 230(2), pages 422-430.
    11. Grosskopf, Shawna & Hayes, Kathy J. & Taylor, Lori L. & Weber, William L., 2001. "On the Determinants of School District Efficiency: Competition and Monitoring," Journal of Urban Economics, Elsevier, vol. 49(3), pages 453-478, May.
    12. A. Peyrache, 2012. "Industry structural inefficiency and potential gains from mergers and break-ups: an empirical approach," CEPA Working Papers Series WP032012, School of Economics, University of Queensland, Australia.
    13. Antonio Peyrache, 2014. "Cost Constrained Industry Inefficiency," CEPA Working Papers Series WP042014, School of Economics, University of Queensland, Australia.

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