IDEAS home Printed from https://ideas.repec.org/p/aeg/report/2015-08.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2015-08.pdf
    File Function: First version, 2015
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Jose M. Cordero & Francisco Pedraja-Chaparro & Elsa C. Pisaflores & Cristina Polo, 2017. "Efficiency assessment of Portuguese municipalities using a conditional nonparametric approach," Journal of Productivity Analysis, Springer, vol. 48(1), pages 1-24, August.
    5. 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.
    6. 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.
    7. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cinzia Daraio & Leopold Simar & Paul W. Wilson, 2016. "Nonparametric Estimation of Efficiency in the Presence of Environmental Variables," DIAG Technical Reports 2016-02, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    3. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2019. "A bootstrap approach for bandwidth selection in estimating conditional efficiency measures," European Journal of Operational Research, Elsevier, vol. 277(2), pages 784-797.
    4. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2020. "Fast and efficient computation of directional distance estimators," Annals of Operations Research, Springer, vol. 288(2), pages 805-835, May.
    5. Nieswand, Maria & Seifert, Stefan, 2018. "Environmental factors in frontier estimation – A Monte Carlo analysis," European Journal of Operational Research, Elsevier, vol. 265(1), pages 133-148.
    6. Bjørndal, Endre & Bjørndal, Mette & Cullmann, Astrid & Nieswand, Maria, 2018. "Finding the right yardstick: Regulation of electricity networks under heterogeneous environments," European Journal of Operational Research, Elsevier, vol. 265(2), pages 710-722.
    7. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    8. Luiza Bădin & Cinzia Daraio & Léopold Simar, 2014. "Explaining inefficiency in nonparametric production models: the state of the art," Annals of Operations Research, Springer, vol. 214(1), pages 5-30, March.
    9. Endre Bjoerndal & Mette Bjoerndal & Astrid Cullmann & Maria Nieswand, 2016. "Finding the Right Yardstick: Regulation under Heterogeneous Environments," Discussion Papers of DIW Berlin 1555, DIW Berlin, German Institute for Economic Research.
    10. Maria Nieswand & Stefan Seifert, 2016. "Operational Conditions in Regulatory Benchmarking Models: A Monte Carlo Analysis," Discussion Papers of DIW Berlin 1585, DIW Berlin, German Institute for Economic Research.
    11. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    12. Halkos, George E. & Tzeremes, Nickolaos G., 2014. "Public sector transparency and countries’ environmental performance: A nonparametric analysis," Resource and Energy Economics, Elsevier, vol. 38(C), pages 19-37.
    13. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, vol. 227(1), pages 182-189.
    14. Camilla Mastromarco & Léopold Simar, 2015. "Effect of FDI and Time on Catching Up: New Insights from a Conditional Nonparametric Frontier Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 826-847, August.
    15. George Halkos & Aksel Sundström & Nickolaos Tzeremes, 2015. "Regional environmental performance and governance quality: a nonparametric analysis," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 17(4), pages 621-644, October.
    16. Tzeremes, Nickolaos G., 2015. "Efficiency dynamics in Indian banking: A conditional directional distance approach," European Journal of Operational Research, Elsevier, vol. 240(3), pages 807-818.
    17. 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.
    18. Halkos, George & Tzeremes, Nickolaos, 2011. "A conditional full frontier modelling for analyzing environmental efficiency and economic growth," MPRA Paper 32839, University Library of Munich, Germany.
    19. 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.
    20. Broadstock, David C. & Matousek, Roman & Meyer, Martin & Tzeremes, Nickolaos G., 2020. "Does corporate social responsibility impact firms' innovation capacity? The indirect link between environmental & social governance implementation and innovation performance," Journal of Business Research, Elsevier, vol. 119(C), pages 99-110.

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aeg:report:2015-08. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antonietta Angelica Zucconi). General contact details of provider: http://edirc.repec.org/data/dirosit.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.