IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v197y2009i2p792-798.html
   My bibliography  Save this article

Using least squares and tobit in second stage DEA efficiency analyses

Author

Listed:
  • McDonald, John

Abstract

The paper examines second stage DEA efficiency analyses, within the context of a censoring data generating process (DGP) and a fractional data DGP, when efficiency scores are treated as descriptive measures of the relative performance of units in the sample. It is argued that the efficiency scores are not generated by a censoring process but are fractional data. Tobit estimation in this situation is inappropriate. In contrast, ordinary least squares is a consistent estimator, and, if White's [White, H., 1980. A heteroskedastic-consistent covariance matrix and a direct test for heteroskedasticity. Econometrica 48, 817-838] heteroskedastic-consistent standard errors are calculated, large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances. For a more refined analysis Papke and Wooldridge's [Papke, L.E., Wooldridge, J.M., 1996. Econometric methods for fractional response variables with an application to 401(k) plan participation rates. Journal of Applied Econometrics 11 (6), 619-632] method has some advantages, but is more complex and requires special programming.

Suggested Citation

  • McDonald, John, 2009. "Using least squares and tobit in second stage DEA efficiency analyses," European Journal of Operational Research, Elsevier, vol. 197(2), pages 792-798, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:792-798
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00669-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Boris Bravo-Ureta & Daniel Solís & Víctor Moreira López & José Maripani & Abdourahmane Thiam & Teodoro Rivas, 2007. "Technical efficiency in farming: a meta-regression analysis," Journal of Productivity Analysis, Springer, vol. 27(1), pages 57-72, February.
    3. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    4. Boland, Lawrence A, 1979. "A Critique of Friedman's Critics," Journal of Economic Literature, American Economic Association, vol. 17(2), pages 503-522, June.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Chilingerian, Jon A., 1995. "Evaluating physician efficiency in hospitals: A multivariate analysis of best practices," European Journal of Operational Research, Elsevier, vol. 80(3), pages 548-574, February.
    8. Hoff, Ayoe, 2007. "Second stage DEA: Comparison of approaches for modelling the DEA score," European Journal of Operational Research, Elsevier, vol. 181(1), pages 425-435, August.
    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. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    11. Harold Fried & Shelton Schmidt & Suthathip Yaisawarng, 1999. "Incorporating the Operating Environment Into a Nonparametric Measure of Technical Efficiency," Journal of Productivity Analysis, Springer, vol. 12(3), pages 249-267, November.
    12. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    13. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-321, May.
    14. 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.
    15. Laure Latruffe & Kelvin Balcombe & Sophia Davidova & Katarzyna Zawalinska, 2004. "Determinants of technical efficiency of crop and livestock farms in Poland," Applied Economics, Taylor & Francis Journals, vol. 36(12), pages 1255-1263.
    16. John McDonald, 1974. "Errors in Economic Time Series: Some Implications for Estimation in Econometric Models," The Economic Record, The Economic Society of Australia, vol. 50(2), pages 278-286, June.
    17. repec:bla:scandj:v:94:y:1992:i:0:p:s173-87 is not listed on IDEAS
    18. repec:bla:ecorec:v:50:y:1974:i:130:p:278-86 is not listed on IDEAS
    19. Korostelev, A. P. & Simar, L. & Tsybakov, A. B., 1995. "Estimation of monotone boundaries," LIDAM Reprints CORE 1178, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    21. Rajiv D. Banker & Ram Natarajan, 2008. "Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis," Operations Research, INFORMS, vol. 56(1), pages 48-58, February.
    22. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    23. John McDonald, 1997. "Manorial Efficiency in Domesday England," Journal of Productivity Analysis, Springer, vol. 8(2), pages 199-213, May.
    24. John Ruggiero & Donald F. Vitaliano, 1999. "Assessing The Efficiency Of Public Schools Using Data Envelopment Analysis And Frontier Regression," Contemporary Economic Policy, Western Economic Association International, vol. 17(3), pages 321-331, July.
    25. Frazer, William J, Jr & Boland, Lawrence A, 1983. "An Essay on the Foundations of Friedman's Methodology," American Economic Review, American Economic Association, vol. 73(1), pages 129-144, March.
    26. Korostelev, A.P. & Simar , L. & Tsybakov, A.B., 1995. "On estimation of monotone and convex boundaries," LIDAM Reprints CORE 1139, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    27. McDonald, John, 1976. "On the Insensitivity of the Autoregressive Moving Average Representations of Some Australian Qtrly Time Series," Econometrica, Econometric Society, vol. 44(6), pages 1277-1287, November.
    28. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    29. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 29-59, Supplemen.
    Full references (including those not matched with items on IDEAS)

    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. Huguenin, Jean-Marc, 2015. "Adjusting for the environment in DEA: A comparison of alternative models based on empirical data," Socio-Economic Planning Sciences, Elsevier, vol. 52(C), pages 41-54.
    2. Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. Fabio Carlucci & Andrea Cirà & Paolo Coccorese, 2018. "Measuring and Explaining Airport Efficiency and Sustainability: Evidence from Italy," Sustainability, MDPI, vol. 10(2), pages 1-17, February.
    6. Roxani Karagiannis, 2015. "A system-of-equations two-stage DEA approach for explaining capacity utilization and technical efficiency," Annals of Operations Research, Springer, vol. 227(1), pages 25-43, April.
    7. Esmeralda Ramalho & Joaquim Ramalho & Pedro Henriques, 2010. "Fractional regression models for second stage DEA efficiency analyses," Journal of Productivity Analysis, Springer, vol. 34(3), pages 239-255, December.
    8. Banker, Rajiv & Natarajan, Ram & Zhang, Daqun, 2019. "Two-stage estimation of the impact of contextual variables in stochastic frontier production function models using Data Envelopment Analysis: Second stage OLS versus bootstrap approaches," European Journal of Operational Research, Elsevier, vol. 278(2), pages 368-384.
    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. Chaouk, Mohammed & Pagliari, Dr Romano & Moxon, Richard, 2020. "The impact of national macro-environment exogenous variables on airport efficiency," Journal of Air Transport Management, Elsevier, vol. 82(C).
    11. Kourtesi, Sofia & De Witte, Kristof & Polymeros, Apostolos, 2016. "Technical Efficiency in the Agricultural Sector - Evidence from a Conditional Quantile-Based Approach," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 17(2), June.
    12. Cordero, José Manuel & Alonso-Morán, Edurne & Nuño-Solinis, Roberto & Orueta, Juan F. & Arce, Regina Sauto, 2015. "Efficiency assessment of primary care providers: A conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 240(1), pages 235-244.
    13. Ester Gutiérrez & Sebastián Lozano, 2022. "Cross-country comparison of the efficiency of the European forest sector and second stage DEA approach," Annals of Operations Research, Springer, vol. 314(2), pages 471-496, July.
    14. 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.
    15. Nolwenn Roudaut & Anne Vanhems, 2012. "Explaining firms efficiency in the Ivorian manufacturing sector: a robust nonparametric approach," Journal of Productivity Analysis, Springer, vol. 37(2), pages 155-169, April.
    16. Fadzlan Sufian & Muzafar Shah Habibullah, 2010. "Bank-specific, Industry-specific and Macroeconomic Determinants of Bank Efficiency," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 4(4), pages 427-461, November.
    17. Juan Carlos Matallín-Sáez & Amparo Soler-Domínguez & Emili Tortosa-Ausina, 2019. "Does active management add value? New evidence from a quantile regression approach," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1734-1751, October.
    18. Lee, Chi-Chuan & Huang, Tai-Hsin, 2017. "Cost efficiency and technological gap in Western European banks: A stochastic metafrontier analysis," International Review of Economics & Finance, Elsevier, vol. 48(C), pages 161-178.
    19. J. Carlos Matallín-Sáez & Amparo Soler-Domínguez & Emili Tortosa-Ausina, 2013. "Does active management add value? New evidence from a quantile regression," Working Papers 2013/01, Economics Department, Universitat Jaume I, Castellón (Spain).
    20. De Witte, Kristof & Geys, Benny, 2013. "Citizen coproduction and efficient public good provision: Theory and evidence from local public libraries," European Journal of Operational Research, Elsevier, vol. 224(3), pages 592-602.

    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:eee:ejores:v:197:y:2009:i:2:p:792-798. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.