The technical efficiency performance of the higher education systems based on data envelopment analysis with an illustration for the Spanish case


It is important for policymakers and managers of higher education institutions knowing how well their universities are operating. This article aimed to show that data envelopment analysis (DEA) can be an excellent benchmarking instrument in higher education. First, by using several inputs and outputs at the institutional level, DEA can identify technically efficient institutions that may work as a benchmark in the sector becoming a reliable tool for ranking universities. Second, a bootstrapped–truncated regression allows us to understand the factors affecting technical efficiency of the institutions under evaluation. The case of Spanish public universities is taken as an example to verify the usefulness of the proposed methods. Our empirical strategy was based on a two-stage procedure to evaluate their internal efficiency in the provision of teaching and research. In the first stage, we estimated a technical efficiency score for each university. The average efficiency among Spanish universities was about 92%. In the second stage, we regressed the efficiency scores against a set of covariates to investigate their association with the level of university (in)efficiency. We found that universities with a higher percentage of grantees tend to be less inefficient, and a higher percentage of academics with tenure enhances the productive efficiency of the Spanish higher education sector. Finally, we computed Spearman’s rank correlations between DEA efficiency scores and the classification of Spanish institutions in university rankings such as the SCImago and Shanghai rankings. The results revealed that the ranking positions given by DEA scores to Spanish universities matched their positions in recognized rankings.

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Fig. 1


  1. 1.

    The Shanghai Jiao Tong University Institute of Higher Education Academic Ranking of World Universities (ARWU), also known as the Shanghai Ranking.

  2. 2.

    Docampo’s findings (2011) support the use of the Shanghai ranking at the aggregate level to monitor the research performance of the different university systems around the world.

  3. 3.

    Position #85 in ARWU 2018.

  4. 4.

    The DEA results are sensitive to the choice of inputs and outputs that are chosen in the efficiency analysis.

  5. 5.

    Technology, in the sense of the economic theory, refers to the known ways of transforming inputs into outputs.

  6. 6.

    Efficiency requires knowledge of the outputs of universities, inputs going into those outputs, and the production relationship between them (Johnes and Taylor 1990).

  7. 7.

    Closely related to the analysis of educational production is the study of education costs. However, the study of the production process from an economic point of view is outside the scope of this paper.

  8. 8.

    For example, it would be useless to produce many theoretical physicists efficiently if society does not need them.

  9. 9.

    On the other hand, allocative efficiency exhibits the ability of the firm to choose an optimal set of resources given the input prices.

  10. 10.

    DEA is a nonparametric technique that, through linear programming, approximates the true but unknown production function without imposing any restriction on the sample distribution.

  11. 11.

    We would like to avoid the exposition of the technical details involved since DEA is well established in the literature. See, among others, Emrouznejad et al. (2008), Liu et al. (2013), Seiford (1997) and Zhu (2016).

  12. 12.

    See Thanassoulis et al. (2016) for a comprehensive review of applications of DEA in secondary and tertiary education.

  13. 13.

    Named after Charnes et al. (1978).

  14. 14.

    Charnes et al. (1978) gave the model in two orientations: input and output orientations.

  15. 15.

    Named after Banker et al. (1984).

  16. 16.

    In most countries, HEIs are mainly funded by public funds. It seems reasonable to assume that the objective of the universities is oriented toward making the best use of available resources.

  17. 17.

    [(ϕ − 1) 100] is the percentage increase in outputs that could be achieved by the DMU under study with input quantities held constant.

  18. 18.

    It is likely that the production technology is different for the latter.

  19. 19.

    Before the university reform of 2010, university degrees in Spain were simultaneously made up of short-cycle university studies (3 years, equivalent to undergraduate studies) and long-cycle university studies (4 or 5 years, equivalent to graduate studies).

  20. 20.

    Using the number of university graduates as an output has two problems. On the one hand, the temporal dimension, since it is not known how long the students have been at the university until they obtain the diploma (many students need more years than those programmed to achieve their university degree). On the other hand, it does not take into account dropouts.

  21. 21.

    In this paper, we considered the contribution of a variable to the total efficiency as determined by its level (of input or output) times the weight. See Angulo-Meza and Lins (2002) for further details.

  22. 22.

    We had no information to measure the so-called third mission of universities.

  23. 23.

    We already discussed in footnote 21 the limitations of using the number of (under)graduates as output.

  24. 24.

    The Spanish university grading system is based on decimal grades from 0 to 10 (the highest score), passing with a 5.

  25. 25.

    Grants from the Spanish Ministry of Education, 2008/2009 academic year (AY).

  26. 26.

    Quotient between current operating expenses in 2008 (€) and total number of students enrolled in the 2008/2009 AY.

  27. 27.

    In Spain, to get tenure, academics must show high scientific productivity.

  28. 28.

    When a CRS technology applies, the input-oriented DEA gives the same technical efficiency scores—in this case, between 0 and 1, but they are the inverse of those scores shown in the second column in Table 2. Therefore, this is an advantage in our study by having assumed an output-oriented DEA.

  29. 29.

    DEA produces a measure of efficiency relative to that achieved by the other producers or DMUs in the sample.

  30. 30.

    We have chosen the classification of 2012.

  31. 31.

    Pérez, F. (Dir.) (2013). Rankings ISSUE 2013. Indicadores sintéticos de las universidades españolas. Valencia, Spain: IVIE-Fundación BBVA. Available at:

  32. 32.

    The ISSUE-V ranking of the Spanish public universities also takes into account the size of each university.

  33. 33.

    Adaptation made by D. Docampo of the 2012 Shanghai ranking and published by the IVIE in the source cited in footnote number 32.

  34. 34.

    There was a strong (positive) correlation mainly with the SCImago and Shanghai rankings.

  35. 35.

    As long as the inputs and outputs of the educational production process are properly chosen. In our case, hypothesis testing shown in Table 5 reveals that the choice of inputs and outputs was adequate.

  36. 36.

    Through using DEA, each DMU can select the best input and output weights through solving a linear programming problem in order to get a higher efficiency (Davoodi and Rezai 2012).


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Salas-Velasco, M. The technical efficiency performance of the higher education systems based on data envelopment analysis with an illustration for the Spanish case. Educ Res Policy Prac 19, 159–180 (2020).

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  • Higher education policy
  • Data envelopment analysis
  • Benchmarking
  • Bootstrapped–truncated regression
  • University rankings

JEL Classification

  • D22
  • I23
  • C50