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Testing the "Separability" Condition in Two-Stage Nonparametric Models of Production

Author

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  • Cinzia Daraio

    (Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome La Sapienza, Rome, Italy)

  • Leopold Simar

    (Institut de Statistique, Biostatistique et Sciences Actuarielles, Universite' Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • Paul W. Wilson

    (Department of Economics and School of Computing, Clemson University, Clemson, SC 29634)

Abstract

Simar and Wilson (J. Econometrics, 2007) provided a statistical model that can rationalize two-stage estimation of technical efficiency in nonparametric settings. Two-stage estimation has been widely used, but requires a strong assumption: the second-stage environmental variables cannot affect the support of the input and output variables in the first stage. In this paper, we provide a fully nonparametric test of this assumption. The test relies on new central limit theorem (CLT) results for unconditional efficiency estimators developed by Kneip et al. (Econometric Theory, 2015a) and new CLTs for conditional efficiency estimators developed in this paper. The test can be implemented relying on either asymptotic normality of the test statistics or using bootstrap methods to obtain critical values. Our simulation results indicate that our tests perform well both in terms of size and power. We present a real-world empirical example by updating the analysis performed by Aly et al. (R. E. Stat., 1990) on U.S. commercial banks; our tests easily reject the assumption required for two-stage estimation, calling into question results that appear in hundreds of papers that have been published in recent years.

Suggested Citation

  • Cinzia Daraio & Leopold Simar & Paul W. Wilson, 2015. "Testing the "Separability" Condition in Two-Stage Nonparametric Models of Production," DIAG Technical Reports 2015-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  • Handle: RePEc:aeg:report:2015-08
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    References listed on IDEAS

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    1. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    2. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    3. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    4. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    5. Seok-Oh Jeong & Byeong Park & Léopold Simar, 2010. "Nonparametric conditional efficiency measures: asymptotic properties," Annals of Operations Research, Springer, vol. 173(1), pages 105-122, January.
    6. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
    7. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    8. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1663-1697, December.
    9. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    10. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
    11. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    12. Wheelock, David C. & Wilson, Paul W., 2001. "New evidence on returns to scale and product mix among U.S. commercial banks," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 653-674, June.
    13. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    14. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    15. Aly, Hassan Y, et al, 1990. "Technical, Scale, and Allocative Efficiencies in U.S. Banking: An Empirical Investigation," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 211-218, May.
    16. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
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    4. Nicola Galluzzo, 2021. "Estimation of the impact of CAP subsidies as environmental variables on Romanian farms," Economia agro-alimentare, FrancoAngeli Editore, vol. 23(3), pages 1-24.
    5. Cordero, José Manuel & Salinas-Jiménez, Javier & Salinas-Jiménez, M Mar, 2017. "Exploring factors affecting the level of happiness across countries: A conditional robust nonparametric frontier analysis," European Journal of Operational Research, Elsevier, vol. 256(2), pages 663-672.
    6. José Manuel Cordero & Cristina Polo & Daniel Santín & Gabriela Sicilia, 2016. "Monte-Carlo Comparison of Conditional Nonparametric Methods and Traditional Approaches to Include Exogenous Variables," Pacific Economic Review, Wiley Blackwell, vol. 21(4), pages 483-497, October.
    7. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    8. Devicienti, Francesco & Manello, Alessandro & Vannoni, Davide, 2017. "Technical efficiency, unions and decentralized labor contracts," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1129-1141.
    9. Ricardo Sellers-Rubio & Aurora Calderón-Martínez, 2021. "Brand strategy scope and advertising spending: The more the better?," Tourism Economics, , vol. 27(1), pages 70-85, February.
    10. Núñez, F. & Arcos-Vargas, A. & Villa, G., 2020. "Efficiency benchmarking and remuneration of Spanish electricity distribution companies," Utilities Policy, Elsevier, vol. 67(C).
    11. Yauheniya Varabyova & Jonas Schreyögg, 2018. "Integrating quality into the nonparametric analysis of efficiency: a simulation comparison of popular methods," Annals of Operations Research, Springer, vol. 261(1), pages 365-392, February.
    12. Manh D. Pham & Valentin Zelenyuk, 2018. "Slack-based directional distance function in the presence of bad outputs: theory and application to Vietnamese banking," Empirical Economics, Springer, vol. 54(1), pages 153-187, February.
    13. Cordero, Jose M. & Polo, Cristina & Santín, Daniel & Simancas, Rosa, 2018. "Efficiency measurement and cross-country differences among schools: A robust conditional nonparametric analysis," Economic Modelling, Elsevier, vol. 74(C), pages 45-60.
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    15. Maria Giovanna BRANDANO & Claudio DETOTTO & Marco VANNINI, 2019. "Comparative Efficiency Of Agricultural Cooperatives And Conventional Firms In A Sample Of Quasi‐Twin Companies," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 90(1), pages 53-76, March.
    16. Veronese da Silva, Aline & Costa, Marcelo Azevedo & Lopes-Ahn, Ana Lúcia, 2022. "Accounting multiple environmental variables in DEA energy transmission benchmarking modelling: The 2019 Brazilian case," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    17. Manello, Alessandro, 2017. "Productivity growth, environmental regulation and win–win opportunities: The case of chemical industry in Italy and Germany," European Journal of Operational Research, Elsevier, vol. 262(2), pages 733-743.

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    Keywords

    technical efficiency ; conditional efficiency ; two-stage estimation ; bootstrap ; separability ; data envelopment analysis (DEA) ; free-disposal hull (FDH).;
    All these keywords.

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