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Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation

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Abstract

The treatment of the contextual variables (Z) has been one of the most controversial topics in the literature on efficiency measurement. Over the last three decades of research, different methods have been developed to incorporate the effect of such variables in the estimation of efficiency measures. However, it is unclear which alternative provides more accurate estimations. The aim of this work is to assess the performance of two recently developed estimators, namely the nonparametric conditional DEA method (Daraio and Simar in J Prod Anal 24(1):93–121, 2005; J Prod Anal 28:13–32, 2007a) and the StoNEZD (Stochastic Non-Smooth Envelopment of Z-variables Data) approach (Johnson and Kuosmanen in J Prod Anal 36(2):219–230, 2011). To do this, we conduct a Monte Carlo experiment using three different data generation processes to test how each model performs under different circumstances. Our results show that the StoNEZD approach outperforms conditional DEA in all the evaluated scenarios.

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Notes

  1. Kumbhakar et al. (1991) developed this model for cross-sectional data and, subsequently, Battese and Coelli (1995) adapt the model to the existence of panel data.

  2. A similar strategy was also adopted by Andor and Hesse (2014) to evaluate the performance of several methods for measuring efficiency (DEA, SFA and StoNED), although these authors did not consider the potential influence of contextual variables on efficiency.

  3. We describe the model for the single-output multiple input case since introducing the multi-output context would involve the use of directional distance functions for the case of StoNEZD method (Kuosmanen and Johnson 2017), so the comparison with the conditional DEA model would be more complex.

  4. Kuosmanen and Johnson (2010) show that this problem is equivalent to the standard (output-oriented, variable returns to scale) DEA model when a sign constraint on residuals is incorporated to the formulation (\(\varepsilon_{i}^{CNLS - } \le 0 \forall i\)) and considering the problem subject to shape constraints (monotonicity and convexity).

  5. Several other papers propose using multiplicative error structures when CRS or heteroscedasticity are assumed (Kuosmanen et al. 2015). In the present work we use the additive model because those conditions are not assumed.

  6. Kuosmanen et al. (2015) propose a pseudo-likelihood approach (Fan et al. 1996) or nonparametric kernel deconvolution (Hall and Simar 2002) as alternatives to the method of moments. In this study we use the method of moments due to its easier computation and interpretation. Nevertheless, Andor and Hesse (2014) found similar results for the former, while the latter has not been used in any Monte Carlo simulation to evaluate StoNEZD as far as we know.

  7. Kuosmanen et al. (2015) propose to use the point estimator developed by Jondrow et al. (1982), but it is well-known that it is not a consistent estimator of \(u_{i}\) (Andor and Hesse 2014).

  8. See Greene (1980) for details.

  9. The mean results are similar and are available from the authors upon request.

  10. Cordero et al. 2016 show that the percentage of accuracy of conditional DEA identifying efficient units is around 68–72%.

  11. This additional analysis was included in order to address the suggestion made by an anonymous reviewer.

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Acknowledgements

We are deeply indebted to the participants of the VII International Congress on Efficiency and Productivity (EFIUCO) and the 2016 Asia–Pacific Productivity Conference (APPC) in Tianjin for providing valuable comments that have led to a considerable improvement of earlier versions of this paper. Furthermore, the authors would like to express their gratitude to the Spanish Ministry for Economy and Competitiveness for supporting this research through grant ECO2014-53702-P. Cristina Polo and Jose M. Cordero would also like to acknowledge the support and funds provided by the Extremadura Government (Grants GR15_SEJ015 and IB16171).

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Authors and Affiliations

  1. Department of Economics, University of Extremadura, Av. Elvas s/n, 06006, Badajoz, Spain

    Jose M. Cordero & Cristina Polo

  2. Department of Applied, Political and Public Economics, Complutense University of Madrid, Campus de Somosaguas, 28223, Pozuelo de Alarcón, Madrid, Spain

    Daniel Santín

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  1. Jose M. Cordero
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Correspondence to Jose M. Cordero.

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Cordero, J.M., Polo, C. & Santín, D. Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation. Oper Res Int J 20, 2245–2265 (2020). https://doi.org/10.1007/s12351-018-0413-2

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