A comparative analysis of the efficiency of national education systems

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).

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.