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Government secondary school finances in New South Wales: accounting for students’ prior achievements in a two-stage DEA at the school level

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Abstract

This study measures the efficiency of government secondary schools in New South Wales, Australia, using a two-stage semi-parametric production frontier approach to schooling. In contrast to previous research comparing school performance with two-stage data envelopment analysis (DEA), we control for prior academic achievement of students by using a rich data set from 2008 to 2010. We employ detailed financial data for deriving the envelope for the efficient production frontier of the schools. Using Simar and Wilson’s (J Econ 136:31-64, 2007, J Prod Anal 36:205-218, 2011a) double bootstrap procedure for two-stage DEA, the study finds that schools with lower total student numbers, a higher average of years of service of teachers, a higher ratio of special education students that attracts extra government funding, and girls only do better than other schools. On the other hand, a negative influence comes from a school’s location in provincial and outer metropolitan areas. An important result is that the socio-economic background of students attending a school has no significant effect on their academic performance, whereas higher prior academic achievements have a positive and statistically significant impact on student achievement. These results are relevant to decision makers for the school sector, in particular for funding criteria contained in the Gonski (Review of funding for schooling - Final report (December). Canberra: Commonwealth Government of Australia, 2011) review report.

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Notes

  1. For example, Perry and McConney (2010) did not include financial school data in their analysis of students’ academic achievements in Australian schools in relation to socio economic status data. Mante and O’Brien (2002) calculated measures of technical efficiency of Australian schools in Victoria but again without including financial data on schools. On the other hand, Lamb et al. (2004) included funding from various sources for Victorian schools in regressions explaining student achievement scores.

  2. For an introduction to DEA analysis with numerous applications, along with computer codes, to Australian school data, see Blackburn et al. (2014a).

  3. For a longitudinal study on non-government (private) Australian schools in the state of Victoria, see Marks (2015a). Also, analysing school-level data instead of student-level data can lead to misleading results if relevant student factors are omitted, as discussed for example by Marks (2010, p. 269) for socio-economic status when prior student academic achievements are not controlled for.

  4. A related paper by one of the authors (Chakraborty and Blackburn, 2013) used only a subset of the data that we use in this paper and it also applied DEA that is subject to the critique of Simar and Wilson (2007, 2011a), whereas our DEA here is not.

  5. Worthington (2001) provided a general explanation of DEA and a review of empirical studies applying it to schools. Cook and Seiford (2009) surveyed DEA advancements over a thirty-year period.

  6. This ignores the possibility of having different production functions across some types of schools. However, Australian Government Schools follow a similar “production process” as they operate in similar regulatory environments. We did not include in our analysis non-government schools because they likely follow a different production process in this sense. Also, the number of observations for boys-only and girls-only schools (18 and 22 respectively) in our sample is too small for reliable inference with separate production functions.

  7. They (p. 19) pointed out that their value-added index avoids endogeneity problems due to student performance test scores reflecting student and family characteristics beyond the control of schools, when these are not controlled for.

  8. Grosskopf et al. (2014b) clarified that using expenditures as a proxy for input quantities is valid only when all observations face the same input prices.

  9. Changes were introduced in NSW in 2012.

  10. See, for example, Grosskopf et al. (2014a, b).

  11. Grosskopf et al. (2014a) employed instead cost functions and estimated for this purpose a hedonic wage function model, for which we have insufficient data.

  12. We use an input orientation because our outputs are not under the direct control of the decision makers, whereas the inputs are.

  13. See also Simar and Wilson (2011b).

  14. Using instead 200 observations did not affect the results in any meaningful way. This is consistent with Simar and Wilson (2007, p. 14), who found that 100 replications are “typically sufficient.”

  15. At Year 10, the last year of compulsory schooling, the school’s median test result is reported for the examination average over five subjects.

  16. Table 1 provides detailed statistics for all test scores that we use in our analysis.

  17. We considered variable returns to scale in the DEA, however, the algorithm did not lead to convergence.

  18. We include a dummy variable for selective schools to control for schools that pick students based on academic quality.

  19. Lamb et al. (2004, p. 29) pointed out, in the context of schools in Victoria, that the cohort two years earlier contains many of the same students. Miller and Voon (2011) also discussed the importance of this issue but could not follow our approach due to data unavailability. They included instead in their study Year 3 achievements in 2009 as a proxy for 2009 Year 5 students’ prior academic achievement and stated (p. 377) that “… our measure should be viewed as only a crude proxy for prior academic achievement.”

  20. In principle, DEA could identify just one efficient school, which would suggest an extreme outlier.

  21. We do not report the results in order to conserve space.

  22. Recently, Daraio et al. (2016) developed a formal empirical testing procedure for the separability condition in Simar and Wilson (2007) based on new central limit theorem results that they derived. In addition, they also proposed conditional efficiency estimators for the case when separability is rejected. We leave the test application for future research. Our approach here is instead an explorative and descriptive analysis for checking the separability condition.

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Acknowledgements

This article replaces an earlier unpublished version titled “Efficiency Aspects of Government Secondary School Finances in New South Wales: Results from a Two-Stage Double-Bootstrap DEA at the School Level” that did not control for prior academic achievements. The authors thank, without implicating, colleagues and anonymous referees for very helpful comments that improved the paper considerably.

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Authors and Affiliations

  1. Department of Economics, University of Otago, P.O. Box 56, Dunedin, 9054, New Zealand

    Alfred A. Haug

  2. Foundation Director, Essential Education Economics (E3), Ground Unit 5/199 Pyrmont Street, Pyrmont, Sydney 2009, Australia

    Vincent C. Blackburn

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  1. Alfred A. Haug
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  2. Vincent C. Blackburn
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Correspondence to Alfred A. Haug.

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Haug, A.A., Blackburn, V.C. Government secondary school finances in New South Wales: accounting for students’ prior achievements in a two-stage DEA at the school level. J Prod Anal 48, 69–83 (2017). https://doi.org/10.1007/s11123-017-0502-x

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