IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2604.26088.html

Stochastic Frontier meets Breakdown Frontier

Author

Listed:
  • Santiago Acerenza
  • Francisco Rosas

Abstract

This paper studies sensitivity analysis in stochastic frontier models by developing relaxations of the baseline assumptions imposed on the latent inefficiency and noise components, and characterize bounds for a benchmark technical-efficiency object under such relaxations. We then derive the associated breakdown frontier for conclusions about conditional technical efficiency and illustrate the procedure using a well-known dataset. We show the estimation and inference of the breakdown frontier. We also extend the analysis for widely used alternative specifications of the stochastic frontier error structure, that is, the Normal-Truncated Normal, Normal-Exponential, and Normal-Half Normal cases. Finally, we suggest avenues for extending this analysis under heteroskedasticity, the relaxation of input exogeneity, and applications using panel data. Code for empirical implementation is also provided.

Suggested Citation

  • Santiago Acerenza & Francisco Rosas, 2026. "Stochastic Frontier meets Breakdown Frontier," Papers 2604.26088, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2604.26088
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2604.26088
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chen, Yi-Yi & Schmidt, Peter & Wang, Hung-Jen, 2014. "Consistent estimation of the fixed effects stochastic frontier model," Journal of Econometrics, Elsevier, vol. 181(2), pages 65-76.
    2. Qushim, Berdikul & Gillespie, Jeffrey M. & Bhandari, Basu Deb & Scaglia, Guillermo, 2018. "Technical And Scale Efficiencies Of U.S. Grass-Fed Beef Production: Whole-Farm And Enterprise Analyses," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 50(3), pages 408-428, August.
    3. Maria Martinez Cillero & Fiona Thorne & Michael Wallace & James Breen, 2019. "Technology heterogeneity and policy change in farm-level efficiency analysis: an application to the Irish beef sector," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 46(2), pages 193-214.
    4. Ryan Mutter & William Greene & William Spector & Michael Rosko & Dana Mukamel, 2013. "Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes," Journal of Productivity Analysis, Springer, vol. 39(2), pages 101-110, April.
    5. Léopold Simar & Ingrid Keilegom & Valentin Zelenyuk, 2017. "Nonparametric least squares methods for stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 47(3), pages 189-204, June.
    6. Taining Wang & Feng Yao & Subal C. Kumbhakar, 2024. "A flexible stochastic production frontier model with panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(4), pages 564-588, June.
    7. Roberto Colombi & Subal Kumbhakar & Gianmaria Martini & Giorgio Vittadini, 2014. "Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency," Journal of Productivity Analysis, Springer, vol. 42(2), pages 123-136, October.
    8. Oliver Hines & Oliver Dukes & Karla Diaz-Ordaz & Stijn Vansteelandt, 2022. "Demystifying Statistical Learning Based on Efficient Influence Functions," The American Statistician, Taylor & Francis Journals, vol. 76(3), pages 292-304, July.
    9. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-111, January.
    10. Adams, Robert M & Berger, Allen N & Sickles, Robin C, 1999. "Semiparametric Approaches to Stochastic Panel Frontiers with Applications in the Banking Industry," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 349-358, July.
    11. Zuckerman, Stephen & Hadley, Jack & Iezzoni, Lisa, 1994. "Measuring hospital efficiency with frontier cost functions," Journal of Health Economics, Elsevier, vol. 13(3), pages 255-280, October.
    12. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    13. Subal Kumbhakar & Gudbrand Lien & J. Hardaker, 2014. "Technical efficiency in competing panel data models: a study of Norwegian grain farming," Journal of Productivity Analysis, Springer, vol. 41(2), pages 321-337, April.
    14. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    15. 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.
    16. Willam Greene, 2005. "Fixed and Random Effects in Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 23(1), pages 7-32, January.
    17. Mucong Xin & Shuhao Tan & Huanguang Qiu & Jianjun Tang, 2025. "Environmental Regulations and Smallholder Farmers' Technical Efficiency: Empirical Evidence From Pastoral China," Journal of Agricultural Economics, Wiley Blackwell, vol. 76(3), pages 555-569, September.
    18. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    19. Aaron Fisher & Edward H. Kennedy, 2021. "Visually Communicating and Teaching Intuition for Influence Functions," The American Statistician, Taylor & Francis Journals, vol. 75(2), pages 162-172, May.
    20. Ferrier, Gary D. & Lovell, C. A. Knox, 1990. "Measuring cost efficiency in banking : Econometric and linear programming evidence," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 229-245.
    21. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    22. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    23. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    24. Michael D. Rosko, 2001. "Cost efficiency of US hospitals: a stochastic frontier approach," Health Economics, John Wiley & Sons, Ltd., vol. 10(6), pages 539-551, September.
    25. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    26. Cornwell, Christopher & Schmidt, Peter & Sickles, Robin C., 1990. "Production frontiers with cross-sectional and time-series variation in efficiency levels," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 185-200.
    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. Valentin Zelenyuk & Zhichao Wang, 2023. "Random vs. Explained Inefficiency in Stochastic Frontier Analysis: The Case of Queensland Hospitals," CEPA Working Papers Series WP052023, School of Economics, University of Queensland, Australia.
    2. Roberto Colombi & Gianmaria Martini & Giorgio Vittadini, 2017. "Determinants of transient and persistent hospital efficiency: The case of Italy," Health Economics, John Wiley & Sons, Ltd., vol. 26(S2), pages 5-22, September.
    3. Kok Fong See & Shawna Grosskopf & Vivian Valdmanis & Valentin Zelenyuk, 2021. "What do we know from the vast literature on efficiency and productivity in healthcare? A Systematic Review and Bibliometric Analysis," CEPA Working Papers Series WP072021, School of Economics, University of Queensland, Australia.
    4. Bao Hoang Nguyen & Robin C. Sickles & Valentin Zelenyuk, 2022. "Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 129-171, Springer.
    5. Sickles, Robin C. & Song, Wonho & Zelenyuk, Valentin, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," Working Papers 18-008, Rice University, Department of Economics.
    6. Kutlu, Levent & Tran, Kien C. & Tsionas, Mike G., 2019. "A time-varying true individual effects model with endogenous regressors," Journal of Econometrics, Elsevier, vol. 211(2), pages 539-559.
    7. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    8. Ali M. Oumer & Amin Mugera & Michael Burton & Atakelty Hailu, 2022. "Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia," Journal of Productivity Analysis, Springer, vol. 57(2), pages 213-241, April.
    9. Levent Kutlu & Shasha Liu & Robin C. Sickles, 2022. "Cost, Revenue, and Profit Function Estimates," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 16, pages 641-679, Springer.
    10. Christopher F. Parmeter & Subal C. Kumbhakar, 2025. "The generalized panel data stochastic frontier model: A review and nonparametric estimation," Journal of Productivity Analysis, Springer, vol. 64(3), pages 321-339, December.
    11. Magambo, Isaiah & Dikgang, Johane & Gelo, Dambala & Tregenna, Fiona, 2021. "Environmental and Technical Efficiency in Large Gold Mines in Developing Countries," MPRA Paper 108068, University Library of Munich, Germany.
    12. Marvin A. Titus & Adriana Vamosiu & Shannon Hayes Buenaflor & Casey Maliszewski Lukszo, 2021. "Persistent Cost Efficiency at Public Community Colleges in the US: A Stochastic Frontier Analysis," Research in Higher Education, Springer;Association for Institutional Research, vol. 62(8), pages 1168-1197, December.
    13. Gralka, Sabine, 2018. "Stochastic frontier analysis in higher education: A systematic review," CEPIE Working Papers 05/18, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    14. Martini, Gianmaria & Scotti, Davide & Viola, Domenico & Vittadini, Giorgio, 2020. "Persistent and temporary inefficiency in airport cost function: An application to Italy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 999-1019.
    15. Bao Hoang Nguyen & Zhichao Wang & Valentin Zelenyuk, 2025. "Efficiency of Queensland public hospitals via spatial panel stochastic frontier models," Empirical Economics, Springer, vol. 69(5), pages 2865-2900, November.
    16. Badunenko, Oleg & D’Inverno, Giovanna & De Witte, Kristof, 2023. "On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects," European Journal of Operational Research, Elsevier, vol. 310(1), pages 432-447.
    17. Zhao Wang & Yuanlu Suo & Taining Wang & Subal C. Kumbhakar, 2025. "Are operationally efficient firms greener?," Empirical Economics, Springer, vol. 69(5), pages 2627-2669, November.
    18. Lv, Yulan & Chen, Wei & Cheng, Jianquan, 2020. "Effects of urbanization on energy efficiency in China: New evidence from short run and long run efficiency models," Energy Policy, Elsevier, vol. 147(C).
    19. repec:aen:journl:ej38-5-lien is not listed on IDEAS
    20. Bernstein, David H., 2020. "An updated assessment of technical efficiency and returns to scale for U.S. electric power plants," Energy Policy, Elsevier, vol. 147(C).
    21. Massimo Filippini & William Greene, 2016. "Persistent and transient productive inefficiency: a maximum simulated likelihood approach," Journal of Productivity Analysis, Springer, vol. 45(2), pages 187-196, April.

    More about this item

    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:arx:papers:2604.26088. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.