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Efficiency and Technological Heterogeneity in Spanish Universities: A Stochastic Metafrontier Approach

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  • Orosco Gavilán, Juan Carlos
  • Orea Sánchez, Luis
  • Veiga, Helena
  • Wiper, Michael Peter

Abstract

This study analyses the technical efficiency of 72 Spanish universities (48 public and 24 private) over the 2011--2018 period using a stochastic frontier and metafrontier approach, distinguishing between public and private institutions. In a first stage, the estimation of group-specific frontiers reveals substantial differences in their production technologies: while public universities operate under a more balanced and stable structure, private universities rely more heavily on enrolment expansion and exhibit a more flexible technology. The inclusion of temporal dynamics shows that technological change is biased in the public sector, reflecting adjustments in the input mix, whereas in the private sector it is largely neutral but non-linear, associated with changes in the level of performance. In a second stage, the metafrontier estimation identifies a common technology shaped by human resources, institutional structure, and the scale of demand, while confirming the existence of trade-offs between teaching and research activities. The inefficiency equation indicates that scientific impact and regional R\&D intensity reduce the technology gap, whereas greater academic diversification and higher regional university density tend to widen it. The decomposition of efficiency reveals a clear segmentation of the system: public universities exhibit higher efficiency levels and lower dispersion, while private universities display greater heterogeneity. Quantitatively, public universities exhibit an average meta-technical efficiency of 0.836 and a technology gap ratio of 0.950, whereas private universities reach only 0.547 and 0.815, respectively. Overall, the results show that the differences between both groups are not limited to efficiency levels, but also reflect distinct production technologies, dynamic adjustment processes, and institutional environments. These findings have important implications for the design of higher education policies.

Suggested Citation

  • Orosco Gavilán, Juan Carlos & Orea Sánchez, Luis & Veiga, Helena & Wiper, Michael Peter, 2026. "Efficiency and Technological Heterogeneity in Spanish Universities: A Stochastic Metafrontier Approach," DES - Working Papers. Statistics and Econometrics. WS 50251, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:50251
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    References listed on IDEAS

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    1. Barnabe Walheer, 2024. "Meta-frontier: literature review and toolkit," Operational Research, Springer, vol. 24(2), pages 1-28, June.
    2. Tommaso Agasisti & Geraint Johnes, 2010. "Heterogeneity and the evaluation of efficiency: the case of Italian universities," Applied Economics, Taylor & Francis Journals, vol. 42(11), pages 1365-1375.
    3. Laureti, Tiziana & Secondi, Luca & Biggeri, Luigi, 2014. "Measuring the efficiency of teaching activities in Italian universities: An information theoretic approach," Economics of Education Review, Elsevier, vol. 42(C), pages 147-164.
    4. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    5. Daraio, Cinzia & Bonaccorsi, Andrea & Simar, Léopold, 2015. "Efficiency and economies of scale and specialization in European universities: A directional distance approach," Journal of Informetrics, Elsevier, vol. 9(3), pages 430-448.
    6. Dong-hyun Oh & Jeong-dong Lee, 2010. "A metafrontier approach for measuring Malmquist productivity index," Empirical Economics, Springer, vol. 38(1), pages 47-64, February.
    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. Tommaso Agasisti & Guo-liang Yang & Yao-yao Song & Carolyn-Thi Thanh Dung Tran, 2021. "Evaluating the higher education productivity of Chinese and European “elite” universities using a meta-frontier approach," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 5819-5853, July.
    9. Timothy J. Coelli & D.S. Prasada Rao & Christopher J. O’Donnell & George E. Battese, 2005. "An Introduction to Efficiency and Productivity Analysis," Springer Books, Springer, edition 0, number 978-0-387-25895-9, January.
    10. George E. Battese & D. S. Prasada Rao, 2002. "Technology Gap, Efficiency, and a Stochastic Metafrontier Function," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 1(2), pages 87-93, August.
    11. Cliff Huang & Tai-Hsin Huang & Nan-Hung Liu, 2014. "A new approach to estimating the metafrontier production function based on a stochastic frontier framework," Journal of Productivity Analysis, Springer, vol. 42(3), pages 241-254, December.
    12. Zoghbi, Ana Carolina & Rocha, Fabiana & Mattos, Enlinson, 2013. "Education production efficiency: Evidence from Brazilian universities," Economic Modelling, Elsevier, vol. 31(C), pages 94-103.
    13. Berbegal-Mirabent, Jasmina & Lafuente, Esteban & Solé, Francesc, 2013. "The pursuit of knowledge transfer activities: An efficiency analysis of Spanish universities," Journal of Business Research, Elsevier, vol. 66(10), pages 2051-2059.
    14. 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.
    15. 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.
    16. Gralka, Sabine, 2018. "Stochastic frontier analysis in higher education: A systematic review," CEPIE Working Papers 05/18, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    17. Bo Cheng, 2025. "Efficiency analysis of 67 Chinese research universities considering inter-university heterogeneity: Evidence from a meta-frontier network SBM DEA model," PLOS ONE, Public Library of Science, vol. 20(9), pages 1-18, September.
    18. Arbona, Alexei & Giménez, Víctor & López-Estrada, Sebastián & Prior, Diego, 2022. "Efficiency and quality in Colombian education: An application of the metafrontier Malmquist-Luenberger productivity index," Socio-Economic Planning Sciences, Elsevier, vol. 79(C).
    19. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
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