1. Does the increase in competition between schools improve the quality of the service? The role of educational reform in Chile. (2018). McIntosh, Steven ; Farias, Javiera Cartagena.
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2. On the allocation of resources for secondary schools. (2012). De Witte, Kristof ; Blank, Jos ; Blank, Jos L. T., ; Haelermans, Carla.
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3. The Effects of School Competition on Academic Achievement and Grading Standards. (2009). Himmler, Oliver.
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4. Board structure and firm technical efficiency: Evidence from Canadian state-owned enterprises. (2007). Dia, Mohamed ; Bozec, Richard .
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5. Ownership-efficiency relationship and the measurement selection bias. (2006). Breton, Gaetan ; Bozec, Richard ; Dia, Mohamed .
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6. Geography, Resources and Primary School Performance. (2002). Gibbons, Stephen.
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7. Benchmarking and Incentives in the NHS. (2000). Grout, P ; Propper, C ; Jenkins, A.
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8. The Relationship between Resource Allocation and Pupil Attainment: A Review. (2000). Walker, James ; Vignoles, Anna ; Machin, Stephen ; Reynolds, David ; Levacic, Rosalind .
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9. Schools, Education and Social Exclusion. (1999). Sparkes, Jo.
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1. Aigner, D., Lovell, C.A.K. and Schmidt, P. (1977) Formulation and estimation of stochastic frontier production function models, Journal of Econometrics, 6, 2137.

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10. Bradley, S. and Taylor, J. (1998) The effect of school size on exam performance in Secondary schools, Oxford Bulletin of Economics and Statistics, 60, 291-324.

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12. Card, D. and Krueger, A. (1992) School quality and black-white relative earnings: a direct assessment, Quarterly Journal of Economics, 107, 151-200.

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19. de Groot, H., McMahon, W.W. and Fredericks, J. (1991) The cost structure of American research universities, Review of Economics and Statistics, 73, 284-290.

20. DEA measures efficiency relative to the best practice observed within each year. Some researchers have conducted dymanic DEA exercises (Lynde and Richmond, 1998). This involves pooling data across years and assessing the extent to which technical efficiency varies both across decision-making units and over time. We report the results of a similar exercise later in the paper. Schools at the bottom of the league tables may receive, via the formula funding mechanism, extra resources to pay for staff, due to special educational needs of pupils. It is largely for this reason that we instrument for the pupil-teacher ratio.
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21. Excellent introductions to DEA may be found in the books by Silkman (1986) and by Norman and Stoker (1991). Somewhat more advanced treatments are offered by Ganley and Cubbin (1992) and by FÃre et al. (1994). The Warwick DEA package is used to solve the suite of linear programmes.
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26. Ganley, J.A. and Cubbin, J.S. (1992) Public sector efficiency measurement: applications of data envelopment analysis, Amsterdam: Elsevier.
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37. Lovell, C.A.K., Walters, L.C. and Wood, L.L. (1994) Stratified models of education production using modified DEA and regression analysis, in Charnes, A., Cooper, W.W., Lewin, A.Y. and Seiford, L.M. (eds) Data envelopment analysis: theory, methodology and applications, Massachussets: Kluwer.
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38. Lynde, C. and Richmond, J. (1998) Productivity and Efficiency in the UK: A Time Series Application of DEA, Economic Modeling, forthcoming.

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40. Makepeace, G.H. (1994) Lifetime earnings and the training decisions of young men in Britain, Paper presented at the EMRU Labour Economics Conference, Lancaster University.
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43. Millington, J. and Bradley, S. (1998) The effect of spatial competition on secondary school exam performance, CREEd Discussion Paper 4/98, Department of Economics, Lancaster University.

44. More recent advances in DEA have involved adaptations of the basic method which allow the analysis of situations in which returns to scale are variable (Banker, 1984), and in which the analysis may specify priorities thus in some way constraining the input or output weights vectors (Thanassoulis and Dyson, 1992).
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45. Norman, M. and Stoker, B. (1991) Data envelopment analysis: the assessment of performance, Chichester: Wiley.
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46. Of the schools deemed technically efficient in 1993, two have a 100 per cent attendance rate. This raises an issue concerning bias due to measurement errorin the attendance variable. The jackknife results reported later provide us with some reassurance that such bias should not be a cause for concern. 1997 was chosen as the endpoint because we do not have School Census data for 1998.
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47. Prais, S.J. (1995) Productivity, education and training: an international perspective, Cambridge University Press, Cambridge.

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52. Silkman, R.H. (ed.)(1986) Measuring efficiency: an assessment of data envelopment analysis, San Francisco: Jossey Bass.
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53. Smith, P. and Mayston, D. (1987) Measuring efficiency in the public sector, Omega, 15, 181-189.

54. Social Exclusion Unit (1998) Truancy and school exclusion, cm3957, May.
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55. Some studies have identified a negative relationship between class size and studentsâ subsequent labour market outcomes (Card and Krueger, 1992). In any event it begs the question of OLS estimated production (or cost) functions as to how positive (or negative) residuals should be interpreted. The recent use of the appropriate frontier models in the context of cost functions has not hitherto been mirrored in the context of educational production functions, though this is something that we attempt in the present paper.
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56. Thanassoulis, E. and Dunstan, P. (1994) Guiding schools to improved performance using data envelopment analysis, Journal of the Operational Research Society, 45, 1247-1262.
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57. Thanassoulis, E. and Dyson, R.G. (1992) Estimating preferred input and output levels using data envelopment analysis, European Journal of Operational Research, 56, 8097.

58. The proportion of pupils ineligible for free school meals reflects the socio-economic composition of the student body. Many studies have shown that a pupils socio-economic background affects their attainment at primary and secondary school (Feinstein, 1998; Feinstein and Symons, 1997), and so in the absence of a measure of prior attainment, the proportion of pupils ineligible for free school meals will act as a proxy (Thomas and Mortimore, 1994). Note that we also included the proportion of pupils with special educational needs in an earlier specification but this had little effect on the calculated efficiencies. We computed eastings and northings for each school based on postcode, using the Postzon package. Hence different values for the radii were assumed and a count made of the number of schools falling in the relevant area.
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59. This proportion is unusually low. To check the accuracy of the data for this school we obtained an OFSTED Inspection Report (1995) which suggests that âRecruitment difficulties in the past have resulted in some posts being filled by non-qualified staff and a small number of lessons are taught by non-specialists.â Newly qualified staff have subsequently been recruited (see Table 2). This implies that the proportion of qualified teaching staff for school 4 is accurate.
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60. Thomas, S. and Mortimore, P. (1994) A multi-level analysis of the 1993 GCSE Examination results in Lancashire, Institute of Education, University of London.
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61. We instrument the pupil-teacher ratio variable since it is endogenous. Good schools attract more pupils and so the pupil-teacher ratio will rise in the short-term if schools are reluctant to hire new teachers (Bradley et al, 1999). The instruments for the pupil-teacher ratio include the lagged exam performance of the school, school type and other school level variables. To check the plausibility of the technical efficiencies obtained from DEA we consulted the OFSTED inspectors reports for the top 8 schools. In each case a high proportion of lessons are deemed to be satisfactory or better, the management of the school is good and the ethos of these schools is one of support and care for the pupils. The implication is that the educational process is efficient in these schools.
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1. Technical efficiency of small-scale honey producer in Ethiopia: A Stochastic Frontier Analysis. (2015). Shiferaw, Kaleb ; Gebremedhin, Berhanu Berhanu .
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2. Costos Ambientales y Eficiencia Productiva en la Producción Agraria del Partido de Pergamino. (2013). Lema, Daniel ; Calcaterra, Carlos P. ; Cabrini, Silvina M..
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3. Constraints to increasing agricultural productivity in Nigeria: A review. (2009). Pender, John ; Phillip, Dayo ; Oni, Omobowale Ayoola ; Nkonya, Ephraim.
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4. Modelling Exogenous Variables in Human Capital Formation through a Heteroscedastic Stochastic Frontier. (2008). Laureti, Tiziana.
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5. Efficiency analysis of the Portuguese beam trawl fleet that targets the common prawn Palaemon serratus (Pennant). (2008). Rosa, Agostinho ; Coelho, Luís ; Oliveira, Manuela ; Lopes, Rui J. ; Gaspar, Manuel B..
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6. Land Titles and Rice Production in Vietnam. (2007). Van den Broeck, Katleen ; Tarp, Finn ; Newman, Carol.
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7. Identifying Technically Efficient Fishing Vessels: A Non-Empty, Minimal Subset Approach. (2006). Schnier, Kurt ; Horrace, William ; Flores-Lagunes, Alfonso.
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8. Relative Efficiency, Scale Effect, and Scope Effect of Public Hospitals: Evidence from Australia. (2006). Zhao, Zhong ; Mahmood, Amir ; Wang, Jian.
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9. CAN FISCAL POLICY EXPLAIN TECHNICAL INEFFICIENCY OF PRIVATISED FIRMS? A PARAMETRIC AND NONPARAMETRIC APPROACH. (2005). ALFANO, Maria Rosaria ; D'Orio, Giovanni.
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10. Efficiency of public spending in developing countries : an efficiency frontier approach. (2005). Pang, Gaobo ; Herrera, Santiago.
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11. Entry, Cost Reduction and Competition in The Portuguese Mobile Telephone Industry. (2005). Pereira, Pedro ; Gagnepain, Philippe.
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12. EFECTOS DE LAS FUSIONES SOBRE EL MERCADO FINANCIERO COLOMBIANO. (2005). Estrada, Dairo.
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13. THE IMPACT OF DE-REGULAMENTATION ON THE BRAZILIAN BANKING INDUSTRY: A PRODUCTION METAFRONTIER APPROACH. (2005). Benegas, Mauricio ; Marinho, Emerson ; Paulo de M. Jorge Neto, ; Chabalgoity, Luiz.
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14. Distinguishing between heterogeneity and inefficiency: stochastic frontier analysis of the World Health Organizations panel data on national health care systems. (2004). Greene, William.
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15. ‘Comparing Brazil and USA electricity performance; what was the impact of privatisation?’. (2004). Mota, Raffaella L..
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16. The Politics of Tax Administration: Evidence from Spain. (2003). Esteller-Moré, Alejandro.
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17. Efficiency Analysis of UAE Banks. (2003). Rao, Ananth.
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18. An efficiency analysis of banking systems: a comparison of European and United States large commercial banks using different functional forms.. (2003). Maggi, Bernardo ; Stefania P. S. Rossi, .
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20. Assessing the efficient cost of sustaining Britain’s rail network: perspectives based on Zonal comparisons. (2003). Smith, Andrew ; Kennedy, John.
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21. Semiparametric Bayesian Inference for Stochastic Frontier Models. (2002). Steel, Mark ; Griffin, Jim.
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22. Confidence Statements for Efficiency Estimates from Stochastic Frontier Models. (2002). Schmidt, Peter ; Horrace, William.
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23. New evidence on the Feds productivity in providing payments services. (2002). Wilson, Paul ; Wheelock, David ; Gilbert, R..
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24. Property Rights in a Fishery: Regulatory Change and Firm Performance. (2002). Grafton, R. Quentin ; Fox, Kevin ; Squires, Dale ; Kirkley, James .
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25. The Matching Efficiency of Regional Labour Markets: A Stochastic Production Frontier Estimation, France 1990-1995. (2001). Sneessens, Henri ; Perelman, Sergio ; Ibourk, Aomar ; Maillard, Benedicte .
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26. Selling Picasso paintings: the efficiency of auction houses.. (2001). Zanola, Roberto ; Førsund, Finn ; Forsund, Finn R..
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27. Banks inefficiency and economic growth: a micro-macro approach. (2000). Zazzaro, Alberto ; Papi, Luca ; Lucchetti, Riccardo (Jack).
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28. X-Inefficiencies in the Residential Real Estate Market: A Stochastic Frontier Approach. (2000). Lewis, Danielle ; Anderson, Randy I. ; Randy I . Anderson, ; Zumpano, Leonard V..
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29. On the origins of data envelopment analysis. (2000). Sarafoglou, Nikias ; Førsund, Finn ; Forsund, F. R..
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30. Measuring the Performance of Chiles Tax Administration. (2000). Serra, Pablo.
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31. An Analysis of Paddy Productivity Growth in West Bengal and Orissa. (2000). Pillai, Renuka .
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32. Mergers Among German Cooperative Banks. A Panel-based Stochastic Frontier Analysis. (1999). Welzel, Peter ; Lang, Günter.
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33. Monte Carlo simulations of DEA efficiency measures and hypothesis tests. (1999). Kittelsen, Sverre.
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34. Stochastic Frontier Production Function With Errors-In-Variables. (1999). Dhawan, Rajeev ; Jochumzen, Peter.
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35. Organizational Form and Expense Preference: Spanish Experience. (1999). Lozano-Vivas, Ana ; HASAN, IFTEKHAR.
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36. Deregulation and efficiency: the case of private Korean banks. (1999). Hao, Jonathan ; Yang, Won Keun ; Hunter, William C..
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37. The informativeness of stochastic frontier and programming frontier efficiency scores: Cost efficiency and other measures of bank holding company performance. (1999). Kwan, Simon ; Ferrier, Gary ; Eisenbeis, Robert.
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38. Local Electricity Distribution in Italy: Comparative Efficiency Analysis and Methodological Cross-Checking. (1999). Scarsi, Gian.
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39. Measuring the efficiency in spanish municipal refuse collection services. (1999). Suarez Pandiello, Javier ; Bosch, Núria ; Pedraja, Francisco ; Suarez-Pandiello, Javier .
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40. Learning Efficiency of Economics Students. (1998). Zimmermann, Klaus ; Bauer, Thomas.
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41. A Monte Carlo Analysis of Technical Inefficiency Predictors. (1998). Kumbhakar, Subal ; Lothgren, Mickael .
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42. Comparison of Frontier Efficiency Methods: An Application to the U.S. Life Insurance Industry. (1997). Cummins, John ; Zi, Hongmin .
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43. Costs in UK Higher Education: A System-Wide Perspective. (1997). Johnes, Geraint.
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44. Consistency conditions for regulatory analysis of financial institutions: a comparison of frontier efficiency methods. (1997). Ferrier, Gary ; Berger, Allen ; Bauer, Paul ; Humphrey, David B..
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45. A new approach to stochastic frontier estimation: DEA+. (1996). Gstach, Dieter .
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46. An analysis of inefficiencies in banking: a stochastic cost frontier approach. (1996). Kwan, Simon ; Eisenbeis, Robert.
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47. A Frontier Model for Landscape Ecology: The Tapir in Honduras. (1995). Ley, Eduardo ; Flesher, Kevin.
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48. The effect of financial liberalization on allocation of credit : panel data evidence for Ecuador. (1993). Weiss, Andrew ; Schiantarelli, Fabio ; Jaramillo, Fidel .
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49. Catch Efficiency in the Chilean Pelagic Fishery: Does size matter ?. (). Vergara Marezco, Sebastián ; Pea-Torres, Julio ; Basch, Michael .
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50. Actual and potential returns to schooling in Spain. (). Martín-Román, Ángel ; Angel Martín Román, ; Carmen García Prieto, ; Carlos Pérez Domínguez, .
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