Abstract
Average efficiency is popular in the empirical education literature for comparing the aggregate performance of regions or countries using the efficiency results of their disaggregated decision-making units (DMUs) microdata. The most common approach for calculating average efficiency is to use a set of inputs and outputs from a representative sample of DMUs, typically schools or high schools, in order to characterize the performance of the population in the analyzed education system. Regardless of the sampling method, the use of sample weights is standard in statistics and econometrics for approximating population parameters. However, weight information has been disregarded in the literature on production frontier estimation using nonparametric methodologies in education. The aim of this chapter is to propose a preliminary methodological strategy to incorporate sample weight information into the estimation of production frontiers using robust nonparametric models. Our Monte Carlo results suggest that current sample designs are not intended for estimating either population production frontiers or average technical efficiency. Consequently, the use of sample weights does not significantly improve the efficiency estimation of a population with respect to an unweighted sample. In order to enhance future efficiency and productivity estimations of a population using samples, we should define an independent sampling design procedure for the set of DMUs based on the population’s production frontier.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For a detailed explanation of this sampling design, see chapter “Testing Positive Endogeneity in Inputs in Data Envelopment Analysis” of the PISA 2015 Technical Report.
- 2.
References
Afonso, A., & Aubyn, M. S. (2005). Non-parametric approaches to education and health efficiency in OECD countries. Journal of Applied Economics, 8(2), 227–246.
Afonso, A., & Aubyn, M. S. (2006). Cross-country efficiency of secondary education provision: A semi-parametric analysis with non-discretionary inputs. Economic Modelling, 23(3), 476–491.
Agasisti, T., & Zoido, P. (2018). Comparing the efficiency of schools through international benchmarking: Results from an empirical analysis of OECD PISA 2012 data. Educational Researcher, 47(6), 352–362.
Aigner, D. J., & Chu, S. F. (1968). On estimating the industry production function. American Economic Review, 58, 826–839.
Aigner, D. J., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production functions. Journal of Econometrics, 6, 21–37.
Allen, R., Athanassopoulos, A., Dyson, R. G., & Thanassoulis, E. (1997). Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions. Annals of Operations Research, 73, 13–34.
Aparicio, J., & Santin, D. (2018). A note on measuring group performance over time with pseudo-panels. European Journal of Operational Research, 267(1), 227–235.
Aparicio, J., Cordero, J. M., & Pastor, J. T. (2017a). The determination of the least distance to the strongly efficient frontier in data envelopment analysis oriented models: Modelling and computational aspects. Omega, 71, 1–10.
Aparicio, J., Crespo-Cebada, E., Pedraja-Chaparro, F., & Santín, D. (2017b). Comparing school ownership performance using a pseudo-panel database: A Malmquist-type index approach. European Journal of Operational Research, 256(2), 533–542.
Aparicio, J., Cordero, J. M., Gonzalez, M., & Lopez-Espin, J. J. (2018). Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries. Omega, 79, 9–20.
Aragon, Y., Daouia, A., & Thomas-Agnan, C. (2005). Nonparametric frontier estimation: A conditional quantile-based approach. Econometric Theory, 21(2), 358–389.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.
Cazals, C., Florens, J. P., & Simar, L. (2002). Nonparametric frontier estimation: A robust approach. Journal of Econometrics, 106(1), 1–25.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.
Cordero, J. M., Cristobal, V., & Santín, D. (2018). Causal inference on education policies: A survey of empirical studies using PISA, TIMSS and PIRLS. Journal of Economic Surveys, 32(3), 878–915.
Daouia, A., & Simar, L. (2007). Nonparametric efficiency analysis: A multivariate conditional quantile. Journal of Econometrics, 140, 375–400.
Daraio, C., & Simar, L. (2007). Conditional nonparametric frontier models for convex and nonconvex technologies: A unifying approach. Journal of Productivity Analysis, 28, 13–32.
De Jorge, J., & Santín. (2010). Determinantes de la eficiencia educativa en la Unión Europea. Hacienda Pública Española, 193, 131–155.
De La Fuente, A. (2011). Human capital and productivity. Nordic Economic Policy Review, 2(2), 103–132.
Debreu, G. (1951). The coefficient of resource utilization. Econometrica, 19(3), 273–292.
Deprins, D., Simar, L., & Tulkens, H. (1984). Measuring labor inefficiency in post offices. In M. Marchand, P. Pestieau, & H. Tulkens (Eds.), The performance of public enterprises: Concepts and measurements (pp. 243–267). Amsterdam: North-Holland.
Färe, R., & Zelenyuk, V. (2003). On aggregate Farrell efficiencies. European Journal of Operational Research, 146, 615–620.
Färe, R., Grosskopf, S., & Lovell, C. A. K. (1985). The measurement of efficiency of production. Boston: Kluwer Nijhof Publishers.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society Series A (General), 120(3), 253–290.
Hanushek, E. A., & Kimko, D. D. (2000). Schooling, labor-force quality, and the growth of nations. American Economic Review, 90(5), 1184–1208.
Hanushek, E. A., & Woessmann, L. (2012). Do better schools lead to more growth? Cognitive skills, economic outcomes, and causation. Journal of Economic Growth, 17(4), 267–321.
Hedayat, A. S., & Sinha, B. K. (1991). Design and inference in finite population sampling. New York: Wiley.
Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47(260), 663–685.
Jerrim, J., Lopez-Agudo, L. A., Marcenaro-Gutierrez, O. D., & Shure, N. (2017). What happens when econometrics and psychometrics collide? An example using the PISA data. Economics of Education Review, 61, 51–58.
Koopmans, T. C. (1951). Analysis of production as an efficient combination of activities. In T. C. Koopmans (Ed.), Activity analysis of production and allocation (pp. 33–97). New York: Wiley.
Lavy, V. (2015). Do differences in schools’ instruction time explain international achievement gaps? Evidence from developed and developing countries. The Economic Journal, 125, 397–424.
Levin, H. M. (1974). Measuring efficiency in educational production. Public Finance Quarterly, 2(1), 3–24.
Meeusen, W., & van den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 18, 435–444.
OECD. (2017). PISA 2015 technical report, OECD, Paris.
Pastor, J. T., Lovell, C. K., & Aparicio, J. (2012). Families of linear efficiency programs based on Debreu’s loss function. Journal of Productivity Analysis, 38(2), 109–120.
Särndal, C. E., Swensson, B., & Wretman, J. (1992). Model assisted survey sampling. Springer Science and Business Media, New York.
Shephard, R. W. (1953). Cost and production functions. Princeton University Press, Princeton.
Simar, L., & Wilson, P. W. (1998). Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models. Management Science, 44(1), 49–61.
Strietholt, R., Gustafsson, J. E., Rosen, M., & Bos, W. (2014). Outcomes and causal inference in international comparative assessments. In R. Stietholt, W. Bos, J. E. Gustafsson, & M. Rosen (Eds.), Educational policy evaluation through international comparative assessments. New York: Waxman, Münster.
Woodruff, R. S. (1952). Condence intervals for medians and other position measures. J. Amer. Statist. Assoc. 47, 635–646.
Acknowledgments
The authors are greatly indebted to Fundación Ramon Areces for supporting and encouraging mutual collaboration on productivity analysis in education as part of projects La medición de la eficiencia de la educacion primaria y de sus determinantes en España y en la Union Europea: un análisis con TIMSS-PIRLS 2011 (D. Santín) and Evaluación de la eficiencia en la producción educativa a partir de diseños muestrales (J. Aparicio, M. González and G. Sicilia).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Aparicio, J., González, M., Santín, D., Sicilia, G. (2020). On the Estimation of Educational Technical Efficiency from Sample Designs: A New Methodology Using Robust Nonparametric Models. In: Aparicio, J., Lovell, C., Pastor, J., Zhu, J. (eds) Advances in Efficiency and Productivity II. International Series in Operations Research & Management Science, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-41618-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-41618-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41617-1
Online ISBN: 978-3-030-41618-8
eBook Packages: Economics and FinanceEconomics and Finance (R0)