Investigating the Relative Efficiency and Productivity Change of Upper Secondary Schools: the Case of Schools in the Region of Central Greece

Abstract

The study investigates the relative efficiency and productivity change of upper secondary schools in the region of Central Greece during the period 2015–2018. It measures the technical and scale efficiencies and productivity change by using input-oriented data envelopment and Malmquist analysis. Empirical analysis reveals that few are efficient and most are inefficient, which causes a significant waste of resources. The efficiency under constant returns to scale varies in interval [0.64–1.000] and under variable returns to scale in interval [0.78–1.000], with average efficiency score being 0.852 (85.2%) and 0.936 (93.6%), respectively. These show that schools could produce on average the same quantity of outputs with 14.8% or 6.4% less quantity of inputs. The scale efficiency varies in the interval [0.64–1.000] and the average is 0.908 (90.8%). This finding suggests that schools on average refrain 9.2% from the optimal scale. The results show that average values of efficiency are moving around the average performance of upper secondary schools of other countries in the world and the European Union. The total factor productivity change, of production factors, has risen by an annual average of 6.8% relative to the base year 2015. To further improve performance, it is proposed to set up an observatory that will measure performance annually and indicate schools with lower performance (e.g. 80%), to be taught by benchmarking schools to improve their performance and reduce the waste of valuable resources. These results can be used by the administration and political institutions to reduce the waste of resources, to improve the achievements of schools.

Appendices

Appendix 1

Table 6 Mean (2015–2018) of technical and scale efficiencies of upper secondary schools

Appendix 2

We investigate the performance of upper secondary schools by size criterion, dividing them into two groups. The first groups (S1) which we characterize as relatively large, since they are larger than the average value of 163 students, and the second groups (S2) which we characterize as relatively small, since they are smaller than the average value of 163 students.

S1: The constant returns to scale TE, five upper secondary schools (7.8%) (U3, U17, U18, U21, U24) of the 64 were efficient. TE scores range from 0.639 to 1.000. The average efficiency score is 0.927. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.073 (or 7.3%) less quantity of inputs. The variable returns to scale TE, ten upper secondary schools (15.6%) (U3, U4, U6, U7, U17, U18, U21, U23, U24, U27) of the 64 were efficient. TE scores range from 0.783 to 1.000. The average efficiency score is 0.947. This finding show that on average upper secondary schools could produce the same quantity of outputs with 0.053 (or 5.3%) less quantity of inputs. The scale efficiency, six upper secondary schools (9.4%) (U9, U10, U37, U38, U41, U56) of the 64 were efficient. TE scores range from 0.639 to 1.000. The average efficiency score is 0.979. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.021 (or 2.1%) less quantity of inputs.

The findings suggest also that on average, total factor productivity, fifteen of upper secondary schools (55.6%) (U1, U2, U4, U7, U12, U14, U17, U18, U19, U20, U22, U23, U24, U26, U27) have an increase in average total factor productivity (i.e., total factor productivity > 1) during the period 2015–2018, ranging between 0.8 and 34.6%. On the other hand, the remaining thirty twelve of upper secondary schools (44.4%) (U3, U5, U6, U8, U9, U10, U11, U13, U15, U16, U21, U25) have registered regression in terms of total factor productivity (i.e., total factor productivity < 1) during the same period, ranging between – 9.6 and – 0.1%. This finding suggests that it was the poor technology, which needed to be updated, or that best-practice technology has not been used in the management. The worst deterioration in the average total factor of productivity occurred in U13 (– 19.6%). This productivity loss was due to the technological regression, despite no alteration in the efficiency change.

S2: On the other hand, the constant returns to scale TE, six upper secondary schools (9.4%) (U9, U10, U37, U38, U41, U56) of the 64 were efficient. TE scores range from 0.639 to 1.000. The average efficiency score is 0.804. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.196 (or 19.6%) less quantity of inputs. On the other hand, the variable returns to scale TE, nineteen upper secondary schools (29.7%) (U6, U9, U10, U20, U21, U24, U34, U35, U37, U38, U41, U43, U44, U47, U56, U60,U61,U62, U64) of the 64 were efficient. TE scores range from 0.806 to 1.000. The average efficiency score is 0.929. This finding shows that on average upper secondary schools could produce the same quantity of outputs with 0.071 (or 7.1%) less quantity of inputs. The SE, five upper secondary schools (7.8%) (U3, U17, U18, U21, U24) of the 64 were efficient. TE scores range from 0.901 to 1.000. The average efficiency score is 0.865. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.135 (or 13.5%) less quantity of inputs. That is, the level of constant returns to scale TE (S1, S2), variable returns to scale TE (S1, S2), SE (S1, S2) of the upper secondary schools on average appears to be satisfactory.

The results indicate, on average total factor productivity, increases at the rate of 8.0% annually during the investigated period. On examining the components of this productivity change, it becomes evident that this is due to the combination of both positive annual average EC (7.7%) and TC (0.4%), respectively. The findings suggest also that twenty four of upper secondary schools (64.9%) (U2, U3, U5, U6, U8, U9, U10, U11, U12, U13, U15, U16, U17, U19, U20, U23, U24, U25, U26, U29, U30, U32, U33, U35) have an increase in average total factor productivity (i.e., total factor productivity > 1) during the period 2015–2018, ranging between 2.7 and 47.1%. On the other hand, the remaining thirteen of upper secondary schools (35.1%) (U1, U4, U7, U14, U18, U21, U22, U27, U28, U31, U34, U36, U37) have registered regression in terms of total factor productivity (i.e., total factor productivity < 1) during the same period, ranging between – 15.9 and – 1.2%. This finding suggests that it was the poor technology, which needed to be updated, or that best-practice technology has not been used in the management. The worst deterioration in the average total factor of productivity occurred in U14 (– 13.2%). This productivity loss was due to the technological regression, despite no alteration in the efficiency change.

We investigate the performance of upper secondary schools by the year of operation criterion, dividing them into two groups as well. The first group of schools (O1), which are characterized as relatively old, meaning they set up prior to the year 2000, while the second group of schools (O2) are the relatively new ones, schools setup after the year 2000.

O1: The constant returns to scale TE, six upper secondary schools (9.4%) (U4, U11, U30, U31, U45, U56) of the 64 were efficient. TE scores range from 0.639 to 1.000. The average efficiency score is 0.854. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.146 (or 14.6%) less quantity of inputs. The variable returns to scale TE, nineteen upper secondary schools (29.7%) (U4, U5, U10, U13, U14, U20, U21, U36, U37, U38, U41, U43, U44, U47, U56, U60,U61,U62, U64) of the 64 were efficient. TE scores range from 0.797 to 1.000. The average efficiency score is 0.939. This finding shows that on average upper secondary schools could produce the same quantity of outputs with 0.061 (or 6.1%) less quantity of inputs. The SE, five upper secondary school (7.8%) (U4, U11, U30, U31, U45) of the 64 were efficient. TE scores range from 0.639 to 1.000. The average efficiency score is 0.910. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.090 (or 9%) less quantity of inputs.

The results indicate that, on average total factor productivity, increases at the rate of 5.1% annually during the investigated period. On examining the components of this productivity change, it becomes evident that this is due to the combination of both positive annual average EC (2.9%) and TC (2.2%), respectively. The findings suggest also that forty six, of upper secondary schools ((71.9% )U2, U3, U4, U5, U6, U7, U9, U10, U12, U15, U16, U21, U22, U23, U27, U28, U30, U31, U32, U33, U34, U36, U37, U38, U39, U40, U41, U42, U43,U44, U45, U46, U47, U48, U49, U50, U51, U52, U53, U54, U55, U56, U57, U59, U60, U63) have an increase in average total factor productivity (i.e., total factor productivity > 1) during the period 2015–2018, ranging between 0.1 and 27.2%. In the remaining eighteen of upper secondary schools (28.1%) (U1, U8, U11, U13, U14, U17, U18, U19, U20, U24, U25, U26, U29, U35, U61, U62, U64) have registered regression in terms of total factor productivity (i.e., total factor productivity < 1) during the same period, ranging between – 10.7 and – 0.4%. This finding suggests that it was the poor technology, which needed to be updated, or that best-practice technology has not been used in the management. The worst deterioration in the average total factor of productivity occurred in U19 (– 10.7%). This productivity loss was due to the technological regression, despite the no alteration in the efficiency change.

O2: On the other hand, the constant returns to scale TE, two upper secondary schools (3.1%) (U3, U9) of the 64 were efficient. TE scores range from 0.687 to 1.000. The average efficiency score is 0.861. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.139 (or 13.9%) less quantity of inputs. The variable returns to scale TE, two upper secondary schools (3.1%) (U3, U9) of the 64 were efficient. TE scores range from 0.783 to 1.000. The average efficiency score is 0.927. This finding shows that on average upper secondary schools could produce the same quantity of outputs with 0.073 (or 7.3%) less quantity of inputs. On the other hand, under the SE, two upper secondary schools (3.1%) (U3, U9) of the 64 were efficient. TE scores range from 0.765 to 1.000. The average efficiency score is 0.926. The results reveal that on average upper secondary schools could produce the same quantity of outputs with 0.074 (or 7.4%) less quantity of inputs. That is, the level of constant returns to scale TE (O1, O2), variable returns to scale TE (O1, O2), scale efficiency (O1, O2) of the upper secondary schools on average appears to be satisfactory.

The positive change in total factor productivity, in nine upper secondary schools (64.3%) (U1, U2, U6, U8, U9, U10, U11, U12, U14) suggests that there is an improvement in technology. In the remaining five upper secondary schools (35.7%) (U3, U4, U5, U7, U13) that change is due to TE change and show that there could be a diffusion of best-practice technology in the management.

Fig. 1

Constant returns to scale efficiency average (2015–2018) and total factor productivity change (2015–2018)