IDEAS home Printed from https://ideas.repec.org/p/aiz/louvad/2015018.html
   My bibliography  Save this paper

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

Author

Listed:
  • Daraio, Cinzia
  • Simar, Leopold
  • Wilson, Paul

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2015. "Testing the "Separability" Condition in Two-Stage Nonparametric Models of Production," LIDAM Discussion Papers ISBA 2015018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  • Handle: RePEc:aiz:louvad:2015018
    as

    Download full text from publisher

    File URL: https://dial.uclouvain.be/pr/boreal/fr/object/boreal%3A165161/datastream/PDF_01/view
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    6. 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.
    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.
    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. 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.
    2. 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.
    3. Titl, Vitezslav & De Witte, Kristof, 2022. "How politics influence public good provision," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    4. 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.
    5. Yauheniya Varabyova & Carl Rudolf Blankart & Jonas Schreyögg, 2017. "Using nonparametric conditional approach to integrate quality into efficiency analysis: empirical evidence from cardiology departments," Health Care Management Science, Springer, vol. 20(4), pages 565-576, December.
    6. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    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.
    14. 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.
    15. 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.
    16. Núñez, F. & Arcos-Vargas, A. & Villa, G., 2020. "Efficiency benchmarking and remuneration of Spanish electricity distribution companies," Utilities Policy, Elsevier, vol. 67(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.
    18. Ioannis E. Tsolas, 2020. "Financial Performance Assessment of Construction Firms by Means of RAM-Based Composite Indicators," Mathematics, MDPI, vol. 8(8), pages 1-16, August.

    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. 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.
    4. 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.
    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. Cordero, Jose Manuel & Polo, Cristina & Simancas, Rosa, 2022. "Assessing the efficiency of secondary schools: Evidence from OECD countries participating in PISA 2015," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    7. 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.
    8. Frédérique Fève & Jean-Pierre Florens & Léopold Simar, 2023. "Proportional incremental cost probability functions and their frontiers," Empirical Economics, Springer, vol. 64(6), pages 2721-2756, June.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Caitlin O’Loughlin & Léopold Simar & Paul W. Wilson, 2023. "Methodologies for assessing government efficiency," Chapters, in: António Afonso & João Tovar Jalles & Ana Venâncio (ed.), Handbook on Public Sector Efficiency, chapter 4, pages 72-101, Edward Elgar Publishing.
    16. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2019. "Quality and its impact on efficiency," LIDAM Discussion Papers ISBA 2019004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. 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.
    18. 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.
    19. Jose M. Cordero & Cristina Polo & Daniel Santín, 2020. "Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation," Operational Research, Springer, vol. 20(4), pages 2245-2265, December.
    20. Mastromarco, Camilla & Simar, Léopold & Van Keilegom, Ingrid, 2022. "Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach," LIDAM Discussion Papers ISBA 2022035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    More about this item

    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:aiz:louvad:2015018. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nadja Peiffer (email available below). General contact details of provider: https://edirc.repec.org/data/isuclbe.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.