Measuring efficiency in education: an analysis of different approaches for incorporating non-discretionary inputs

Abstract

Measuring efficiency in the education sector is a highly complex task. One of the reasons is that the main resource of schools (the type of students they have) lie outside of their control, which means that it must be treated differently to other factors in analysis. This study examines the different options available in the literature for incorporating non-controllable inputs in a data envelopment analysis in order to determine the most appropriate model for evaluating schools. Our empirical study presents the results obtained using the model proposed by Fried et al . (1999), though we use bootstrap techniques to avoid problems of bias in the estimations.

Acknowledgement

We acknowledge financial support from the Ministerio de Educación y Ciencia, project MEC/SEJ 2004-080J1/ECON.

Notes

¹Some examples are the studies by Bessent et al . (1982) or Thanassoulis and Dunstan (1994), which approximate the economic situation of families by using the percentage of pupils entitled to discounted meals.

²See Lovell (1993) or Coelli et al . (1998) for a detailed discussion on the methods for analysing technical efficiency.

³Charnes et al. (1981), Bessent et al . (1982), Smith and Mayston (1987), Thanassouliss and Dunstan (1994), Chalos (1997) and Thanassouliss and Silva-Portela (2002) are some examples.

⁴Seiford and Thrall (1990) consider that using DEA is preferable to any other type of analysis when the objective is to measure the efficiency of a group of organisations producing various outputs.

⁵The model defined corresponds with the original version of DEA proposed by Charnes et al . (1978), which assumes a productive technology characterized by an assumption of constant scale returns. This highly restrictive assumption was later relaxed in the study by Banker et al . (1984) with the introduction of a new restriction in the programme to allow variable scale returns: Σλ_j=1.

⁶This analysis sets aside other methods which try to explain possible producer inefficiencies by the influence of ambiental or environmental variables such as the models of Charnes et al . (1981), Pastor (1994) or Daraio and Simar (2005).

⁷Most of computer programmes specifically developed for DEA allow non-controllable inputs to be included automatically using this option. For a review of DEA computer programmes in the market, see Barr (2004).

⁸While some studies use Ordinary Least Square (OLS) (Ray, 1991), others use a Tobit (Kirjavainen and Loikkanen, 1998) because the efficiency scores are censored.

⁹This mechanism consist of adding the largest positive residual from all the residuals to the predicted value to get the adjusted efficiency.

¹⁰The idea of applying bootstrapping techniques in measuring efficiency was already suggested by Simar and Wilson (1998) and also applied by González and Miles (2002) for two Spanish public services.

¹¹The analytical expression of these algorithms are set out in Simar and Wilson (2003).

¹²Oliveira and Santos (2005) use the first algorithm while Afonso and St. Aubyn (2005) applies the second one to correct the scores obtained in first stage.

¹³This suspect is verified in the evaluation of the study educational results of a group of countries carried out by Afonso and St. Aubyn (2005).

¹⁴This is a decisive factor in the decision of its promoters to abandon it, as described in Fried et al . (2002).

¹⁵The slacks can also be calculated using the information of the units making up the sample, with the requirement for independence of errors not being fulfilled.

¹⁶The choice between the algorithm one and two depends on the sample size.

¹⁷Bessent et al . (1982), Smith and Mayston (1987), McCarty and Yaisawarng (1993) or Muñiz (2002) amongst others.

¹⁸We should point out that, taking into account the type of variables used, the concept of efficiency to be measured is not strictly technical efficiency as one input (costs other than personnel) is expressed in monetary terms, but they are very close to it. However, this cannot be considered as allocative efficiency as we do not include the price of inputs which are clearly unknown in this field.

¹⁹In the analysis only variables with a clear influence on two measures of output have been included. Ten nonsignificant variables in the explanation of any one of the output variables have been discarded. Tables A2 and A3 show that only 12 variables account for the percentage of students accepted, while 16 are significantly related to the variable MARKS. The variable ‘GRANT’ (percentage of students with a public grant) has been removed because it is significantly correlated to all variables, as can be seen in Table A4 (this table shows the Pearson coefficient amongst the 12 significant variables).

²⁰Smith and Mayston (1987) were the first to recommend the use of this technique in order to reduce the number of nondiscretional factors in the evaluation of the efficiency of schools.

²¹We have used the single bootstrapping (Algorithm 1) proposed by those authors because it perfoms better than Algorithm 2 when the sample is small (80units).