MEASURING THE TECHNICAL EFFICIENCIES OF SECONDARY SCHOOLS IN NEW SOUTH WALES USING A STOCHASTIC FRONTIER PRODUCTION MODEL WITH PANEL DATA

This study examines the effects of school and non-school inputs such as, financial resources, teacher characteristics, family socio-economic status, and student composition on student outcomes in their final year in the context of Australian secondary schools. The need for school efficiency and performance studies as measured by the academic performance of student’s vis-à-vis the money spent, while considering socio-demographic variables outside the control of the schools is important. This paper uses the stochastic frontier model to estimate the technical efficiencies for each school using a balanced panel dataset of six years from 2005 to 2010.

Technical efficiency involves the schools making decisions to maximize output given a certain level of inputs. Schools have no jurisdiction over how the resources are allocated to the school. Therefore, this paper considers technical efficiency to be the most relevant measure for schools in New South Wales. Using technical efficiency, it is possible to determine whether increasing outputs can be achieved by raising efficiency but not inputs.
Three models are considered – Pitt/Lee, Pitt/Lee with heteroskedasticity (PLH) and Battese/Coelli (BC). The BC model is a time variant model whereas the PLH model is time invariant. We assume that the two variables most likely to be the cause of heteroskedasticity are the school expenditure and teachers’ salaries. The PLH model has one efficiency value for each school for all the six years combined whereas the BC model has an efficiency value for each school for each of the six years. When the average of the efficiencies for each school is calculated, the correlation coefficient between the PLH efficiencies and the BC averaged efficiencies is 0.965. Therefore, the PLH efficiencies are used in the paper.

The dependent variable is ln(ATAR) where ATAR is the Australian Tertiary Admission Rank which is the median ATAR for students in their final year for each school. The results for SCMED are a good predictor for the current Year 12 ATAR scores. The Attend variable is positive and significant indicating how important attendance at school is. There are only three variables that have a significant, negative impact – average teachers’ salaries per student, average salaries of other staff per student and the proportion of indigenous students per student. It was expected that the greater the proportion of indigenous students in the school the lower the ATAR is likely to be.

The efficiencies are subdivided into the three regions - Metropolitan, Hunter and Illawarra and Country. The differences in the average ATAR and efficiencies for the three regions were not significantly different but the maximums and minimums were very different. The efficiency matrix alerts us to the large number of schools in Quadrant III where the schools are inefficient and also below average in the educational outcomes. Overall 37.5% of schools are in Quadrant I (efficient and effective schools) and 30% in Quadrant III (neither efficient nor effective). The Hunter & Illawarra region has a few schools with a very high median ATAR but with marginal inefficiency. The Metropolitan schools have the widest variation with a large number of schools in Quadrant III with low ATARs and low efficiency. The pattern for the Country schools is interesting as they are clustered around the average ATAR score and the average efficiency.