Abstract
Data envelopment analysis (DEA) has been widely applied to empirically measure the technical efficiency of a set of schools for benchmarking their performance. However, the endogeneity issue in the production of education, which plays a central role in education economics, has received minor attention in the DEA literature. Under a DEA framework, endogeneity arises when at least one input is correlated with the efficiency term. Cordero et al. (European Journal of Operational Research 244:511–518, 2015) highlighted that DEA performs well under negative and moderate positive endogeneity. However, when an input is highly and positively correlated with the efficiency term, DEA estimates are misleading. The aim of this work is to propose a new test, based on defining a grid of input flexible transformations, for detecting the presence of positive endogeneity in inputs. To show the potential ability of this test, we run a Monte Carlo analysis evaluating the performance of the new approach in finite samples. The results show that this test outperforms alternative statistical procedures for detecting positive high correlations between inputs and the efficiency term. Finally, to illustrate our theoretical findings, we perform an empirical application on the education sector.
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Notes
- 1.
For a review of the DEA impact in theoretical and empirical applications, see, for example, Emrouznejad and Yang (2018). It is worth noting that the fifth application field of DEA in 2015 and 2016 was “public policies” where endogeneity issues tend to appear.
- 2.
Endogeneity is receiving a growing interest in the parametric world of production frontiers as well. See, for example, Solis et al. (2007), Kumbhakar et al. (2009), Greene (2010), Mayen et al. (2010), Perelman and Santin (2011), Bravo-Ureta et al. (2012), and Crespo-Cebada et al. (2014) for studying different solutions for dealing with endogeneity when comparing different groups of DMUs in applications related with agriculture, health, or education. Different directions for researching about the endogeneity issues on parametric and nonparametric production frontiers estimations can be found in the Journal of Econometrics (2016) volume 190, where issue 2 is fully devoted to discussing and analyzing problems related with endogeneity.
- 3.
Other possibilities of flexible functions to be used in order to represent \( g\left({x}_{k{i}^{\prime }}\right) \) could be the Taylor polynomials or trigonometric functions based on sine and cosine. Nevertheless, checking these other alternatives falls outside the scope of this paper.
- 4.
Bootstrapping is a kind of resampling where big numbers of samples of the same size as the original one are repeatedly drawn, “with replacement,” from the observed sample (see, e.g., Simar and Wilson 1998).
- 5.
See Cordero et al. (2015) for the detailed procedure to generate the specific correlation coefficient between u and x 3.
- 6.
For an extensive discussion about the challenges and problem that Uruguay faces regarding its education system, see Santín and Sicilia (2015).
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Acknowledgments
J. Aparicio and L. Ortiz thank the financial support from the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía, Industria y Competitividad), the State Research Agency (Agencia Estatal de Investigacion), and the European Regional Development Fund (Fondo Europeo de DEsarrollo Regional) under grant MTM2016-79765-P (AEI/FEDER, UE). D. Santín and G. Sicilia acknowledge the funding received from the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía, Industria y Competitividad) project referenced ECO2017-83759-P.
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Aparicio, J., Ortiz, L., Santin, D., Sicilia, G. (2020). Testing Positive Endogeneity in Inputs in Data Envelopment Analysis. 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_4
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