×

Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools. (English) Zbl 1339.91045

Summary: Our paper reports on the use of data envelopment analysis (DEA) for the assessment of performance of secondary schools in Malaysia during the implementation of the policy of teaching and learning mathematics and science subjects in the English language (PPSMI). The novelty of our application is that it makes use of the hybrid returns-to-scale (HRS) DEA model. This combines the assumption of constant returns to scale with respect to quantity inputs and outputs (teaching provision and students) and variable returns to scale (VRS) with respect to quality factors (attainment levels on entry and exit) and socio-economic status of student families. We argue that the HRS model is a better-informed model than the conventional VRS model in the described application. Because the HRS technology is larger than the VRS technology, the new model provides a tangibly better discrimination on efficiency than could be obtained by the VRS model. To assess the productivity change of secondary schools over the years surrounding the introduction of the PPSMI policy, we adapt the Malmquist productivity index and its decomposition to the case of HRS model.

MSC:

91B06 Decision theory
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)

References:

[1] Avkiran, N. K., Investigating technical and scale efficiencies of Australian universities through data envelopment analysis, Socio-Economic Planning Sciences, 35, 57-80 (2001)
[2] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[3] Bradley, S.; Johnes, G.; Millington, J., The effect of competition on the efficiency of secondary schools in England, European Journal of Operational Research, 135, 545-568 (2001) · Zbl 0988.90519
[4] Briec, W.; Kerstens, K., Infeasibilities and directional distance functions: With application to the determinateness of the Luenberger productivity indicator, Journal of Optimization Theory and Applications, 141, 55-73 (2009) · Zbl 1165.90008
[5] Cooper, W. W.; Seiford, L. M.; Tone, K., Introduction to data envelopment analysis and its uses (2006), Springer: Springer New York
[6] Färe, R.; Grosskopf, S.; Førsund, F. R.; Hayes, K.; Heshmati, A., Measurement of productivity and quality in non-marketable services: With application to schools, Quality Assurance in Education, 14, 21-36 (2006)
[7] Färe, R.; Grosskopf, S.; Lindgren, B.; Roos, P., Productivity developments in Swedish hospitals: A Malmquist output index approach, (Charnes, A.; Cooper, W. W.; Lewin, A. Y.; Seiford, L. M., Data envelopment analysis: Theory, methods and applications (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, MA), 253-272 · Zbl 0862.90094
[8] Färe, R.; Grosskopf, S.; Norris, M.; Zhang, Z., Productivity growth, technical progress, and efficiency change in industrialized countries, American Economic Review, 84, 66-83 (1994)
[9] Fried, H. O.; Lovell, C. A.K.; Schmidt, S. S., Efficiency and productivity, (Fried, H. O.; Lovell, C. A.K.; Schmidt, S. S., The measurement of productive efficiency and productivity growth (2008), Oxford University Press: Oxford University Press New York), 3-91
[10] Grifell-Tatjé, E.; Lovell, C. A.K., Deregulation and productivity decline: The case of Spanish savings banks, European Economic Review, 40, 1281-1303 (1996)
[11] Grosskopf, S., Some remarks on productivity and its decompositions, Journal of Productivity Analysis, 20, 459-474 (2003)
[12] Grosskopf, S.; Hayes, K. J.; Taylor, L. L.; Weber, W. L., Anticipating the consequences of school reform: A new use of DEA, Management Science, 45, 608-620 (1999)
[13] Grosskopf, S.; Moutray, C., Evaluating performance in Chicago public high schools in the wake of decentralization, Economics and Education Review, 20, 1-14 (2001)
[14] Johnes, J., Efficiency and productivity change in the English higher education sector from 1996/97 to 2004/5, The Manchester School, 76, 653-674 (2008)
[15] Johnes, J.; Bradley, S.; Little, A., Efficiency in the further education sector in England, Open Journal of Statistics, 2, 131-140 (2012)
[16] Lovell, C. A.K., The decomposition of Malmquist productivity indexes, Journal of Productivity Analysis, 20, 437-458 (2003)
[17] Ouellette, P.; Vierstraete, V., Malmquist indexes with quasi-fixed inputs: An application to school districts in Québec, Annals of Operations Research, 173, 57-76 (2010) · Zbl 1187.91156
[18] Podinovski, V. V., Bridging the gap between the constant and variable returns-to-scale models: Selective proportionality in data envelopment analysis, Journal of the Operational Research Society, 55, 265-276 (2004) · Zbl 1097.91026
[19] Podinovski, V. V., Efficiency and returns to scale on the “no free lunch” assumption only, Journal of Productivity Analysis, 22, 227-257 (2004)
[20] Podinovski, V. V., Production technologies based on combined proportionality assumptions, Journal of Productivity Analysis, 32, 21-26 (2009)
[21] Portela, M. C.S.; Camanho, A. S.; Borges, D., Performance assessment of secondary schools: The snapshot of a country taken by DEA, Journal of the Operational Research Society, 63, 1098-1115 (2012)
[22] Portela, M. C.A. S.; Thanassoulis, E., Decomposing school and school-type efficiency, European Journal of Operational Research, 132, 357-373 (2001) · Zbl 0985.90055
[23] Rockafellar, R. T., Convex analysis (1970), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0229.90020
[24] Thanassoulis, E.; Kortelainen, M.; Johnes, G.; Johnes, J., Costs and efficiency of higher education institutions in England: A DEA analysis, Journal of the Operational Research Society, 62, 1282-1297 (2011)
[25] Thanassoulis, E.; Portela, M. C.S.; Despić, O., Data envelopment analysis: The mathematical programming approach to efficiency analysis, (Fried, H. O.; Lovell, C. A.K.; Schmidt, S. S., The measurement of productive efficiency and productivity growth (2008), Oxford University Press: Oxford University Press New York), 251-420
[26] Ting, S. H., Impact of language planning on language choice in friendship and transaction domains in Sarawak, Malaysia, Current Issues in Language Planning, 11, 397-412 (2010)
[27] Yahaya, M. F.B.; Noor, M. A.B. M.; Mokhtar, A. A.B.; Rawian, R. B.M.; Othman, M. B.; Jusoff, K., Teaching of mathematics and science in English: The teachers’ voices, English Language Teaching, 2, 141-147 (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.