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A comparative analysis of the efficiency of national education systems

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Abstract

The present study assesses the performance of 54 participating countries in PISA 2006. It employs efficiency indicators that relate result variables with resource variables used in the production of educational services. Desirable outputs of educational achievement and undesirable outputs of educational inequality are considered jointly as result variables. A construct that captures the quality and quantity of educational resources consumed is used as resource variables. Similarly, environmental variables of each educational system are included in the efficiency evaluation model; while these resources are not controllable by the managers of the education systems, they do affect outcomes. We find that European countries are characterized by weak management, the Americans (mainly Latin Americans) by a weak endowment of resources, and the Asians by a high level of heterogeneity. In particular, Asia combines countries with optimal systems (South Korea and Macao-China); countries with managerial problems (Hong Kong, China-Taipei, Japan and Israel); others where the main challenge is the weak endowment of resources (Jordan and Kyrgyzstan), and, finally, others where the main problem is in the long run since it concerns structural conditions of a socioeconomic and cultural nature (Turkey, Thailand, and Indonesia).

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Notes

  1. A production function corresponds to the technology that transforms inputs in output.

  2. Non-parametric frontier models are characterized by not using a given functional form to construct the production function, but instead construct an empirical production function based on the data of the inputs employed and the outputs obtained.

  3. As examples of this kind of study we can mention Bessent and Bessent (1980), Färe et al. (1989), Smith and Mayston (1987), Bessent et al. (1982), Thanassoulis and Dunstan (1994), Pedraja and Salinas (1996), Mancebón and Muñiz (2008) or on university education, Flegg et al.(2004), Joumady and Ris (2005) and Chang et al. (2009).

  4. It is simplified since the figure only captures the existence of one output, one input and two possible endowment levels of environmental variables and includes a traditional model that seeks to expand the desired results.

  5. This maximum output considers not only increasing the desired outputs but also decreasing the undesired outputs.

  6. The list of countries is displayed in the Table 1.

  7. The Program for International Student Assessment (PISA) index of economic, social and cultural status was created on the basis of the following variables: the International Socio-Economic Index of Occupational Status (ISEI); the highest level of education of the student’s parents, converted into years of schooling; the PISA index of family wealth; the PISA index of home educational resources; and the PISA index of possessions related to “classical” culture in the family home.

  8. This indicator is similar to (1 + ϕ2), except that the restriction of the environmental variables has been eliminated and is therefore compared with an optimal socioeconomic situation. This contribution of this coefficient is obtained by relating both maximum output coefficients (λ2 = (1 + ϕ3)/(1 + ϕ2)) corresponding to the negative impact of the environmental factors on the maximum results that a system can obtain.

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Acknowledgments

C. Thieme acknowledges the financial support of Fondecyt, grant 11085061.

Author information

Authors and Affiliations

  1. Facultad de Economía y Empresa, Universidad Diego Portales, Av. Manuel Rodríguez Sur 253, Santiago de Chile, Chile

    Claudio Thieme

  2. Departamento de Economía de la Empresa, Universitat Autònoma de Barcelona, Cerdanyola, Catalonia, Spain

    Víctor Giménez & Diego Prior

Authors
  1. Claudio Thieme
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  2. Víctor Giménez
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  3. Diego Prior
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Corresponding author

Correspondence to Claudio Thieme.

Appendix

Appendix

We present here below the range of equations and linear programs used to measure the managerial technical efficiency (ϕ1), the medium and long-term maximum potential output (ϕ2), and the very long-term maximum potential output (ϕ3):

$$ \phi_{1} = \phi $$
(1)
$$ \phi_{2} = \phi $$
(2)
$$ \phi_{3} = \phi $$
(3)
$$ \sum\limits_{j = 1}^{I} {z_{j} } y_{rj}^{d} \ge (1 + \phi )y_{r0}^{d} \quad r = 1, \ldots ,M^{d} $$
(4)
$$ \sum\limits_{j = 1}^{I} {z_{j} } y_{kj}^{nd} \le (1 - \phi )y_{k0}^{nd} \quad k = 1, \ldots ,M^{nd} $$
(5)
$$ \sum\limits_{j = 1}^{I} {z_{j} } x_{ij} \le x_{i0} \quad i = 1, \ldots ,N $$
(6)
$$ \sum\limits_{j = 1}^{I} {z_{j} e_{pj} \le e_{p0} } \quad p = 1, \ldots ,P $$
(7)
$$ \sum\limits_{j = 1}^{I} {z_{j} x_{ij} = x_{i} } \quad i = 1, \ldots ,N $$
(8)
$$ \sum\limits_{j = 1}^{I} {z_{j} e_{pj} = e_{p} } \quad p = 1, \ldots ,P $$
(9)
$$ \sum\limits_{j = 1}^{I} {z_{j} } x_{ij} \le x_{ij}^{\max } \quad i = 1, \ldots ,N $$
(10)

The managerial technical efficiency evaluation of the unit under observation (DMU “o”) with an orientation to output is carried out resolving the linear program consisting of maximizing the expression (1) subject to restrictions (4), (5), (6), and (7) where \( y_{rj}^{d} \) represents the desired output “r” of the DMU “j”; \( y_{kj}^{nd} \) represents the undesired output “k” of the DMU “j”; x ij the controllable inputs of the productive process; and e pj the environmental variables (social, economic, and cultural factors of the population). z j are variables of the model upon which the benchmark group is constructed.

To determine the maximum improvement of results possible for a country and the optimal amount of resources that a country should allocate, the linear program [2] in a first stage determines the maximum percentage increase of all desired outputs (and the decrease of the undesired) considering the observed level of the environmental variables and leaving the endowment of resources free. In a second stage, once the maximum output has been calculated, the linear program determines the lowest level of inputs associated to the maximum output. In this way, we can determine the efficient endowment of existing resources. This is operationalized maximizing the expression (2) subject to restrictions (4), (5), (7), and (8). Variable ϕ2 represents the maximum potential increase attainable in all outputs, given the environmental conditions observed (e pO ). Observe how x i defines the optimal endowment of controllable inputs associated to the attainment of the maximum output of the educational system.

Lastly, the very long-term maximum potential output is calculated maximizing the expression (3), subject to the restrictions (4), (5), (8), (9), and (10). In this last evaluation, all the educational systems are compared considering only their educational achievement and inequality results. In other words, the distance is calculated that separates the results of a country from the frontier of best practices, without considering that they may be operating under negative environmental conditions or with a resource endowment below the optimum.

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Thieme, C., Giménez, V. & Prior, D. A comparative analysis of the efficiency of national education systems. Asia Pacific Educ. Rev. 13, 1–15 (2012). https://doi.org/10.1007/s12564-011-9177-6

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