IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v184y2015i2p379-393.html
   My bibliography  Save this article

Frontier estimation in the presence of measurement error with unknown variance

Author

Listed:
  • Kneip, Alois
  • Simar, Léopold
  • Van Keilegom, Ingrid

Abstract

Frontier estimation appears in productivity analysis. Firm’s performance is measured by the distance between its output and an optimal production frontier. Frontier estimation becomes difficult if outputs are measured with noise and most approaches rely on restrictive parametric assumptions. This paper contributes to nonparametric approaches, with unknown frontier and unknown variance of a normally distributed error. We propose a nonparametric method identifying and estimating both quantities simultaneously. Consistency and rate of convergence of our estimators are established, and simulations verify the performance of the estimators for small samples. We illustrate our method with data on American electricity companies.

Suggested Citation

  • Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
  • Handle: RePEc:eee:econom:v:184:y:2015:i:2:p:379-393
    DOI: 10.1016/j.jeconom.2014.09.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407614002279
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2014.09.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    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. Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
    3. 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.
    4. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    5. Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
    6. Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
    7. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    8. Delaigle, A. & Gijbels, I., 2006. "Data-driven boundary estimation in deconvolution problems," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1965-1994, April.
    9. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    10. Lucie Aarts & Piet Groeneboom & Geurt Jongbloed, 2007. "Estimating the Upper Support Point in Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 552-568, September.
    11. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    12. 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).
    13. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    14. Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Consistent density deconvolution under partially known error distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 236-241, February.
    15. Fan, Yanqin & Li, Qi & Weersink, Alfons, 1996. "Semiparametric Estimation of Stochastic Production Frontier Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 460-468, October.
    16. Schwarz, M. & Van Bellegem, S., 2010. "Consistent density deconvolution under partially known error distribution," LIDAM Reprints ISBA 2010013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
    18. 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).
    19. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    20. 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.
    21. S.‐O. Jeong & B. U. Park, 2006. "Large Sample Approximation of the Distribution for Convex‐Hull Estimators of Boundaries," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 139-151, March.
    22. Park, B.U. & Jeong, S.-O. & Simar, L., 2010. "Asymptotic distribution of conical-hull estimators of directional edges," LIDAM Reprints ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    23. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    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. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    3. Christopher F. Parmeter & Léopold Simar & Ingrid Van Keilegom & Valentin Zelenyuk, 2024. "Inference in the nonparametric stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 43(7), pages 518-539, August.
    4. 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.
    5. Tsionas, Mike G., 2020. "Bounded rationality and thick frontiers in stochastic frontier analysis," European Journal of Operational Research, Elsevier, vol. 284(2), pages 762-768.
    6. Christopher F. Parmeter & Alan T. K. Wan & Xinyu Zhang, 2019. "Model averaging estimators for the stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 51(2), pages 91-103, June.
    7. 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.
    8. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2021. "Density deconvolution with Laplace errors and unknown variance," Journal of Productivity Analysis, Springer, vol. 56(2), pages 103-113, December.
    9. Zhou, Jianhua & Parmeter, Christopher F. & Kumbhakar, Subal C., 2020. "Nonparametric estimation of the determinants of inefficiency in the presence of firm heterogeneity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1142-1152.
    10. William C. Horrace & Yulong Wang, 2022. "Nonparametric tests of tail behavior in stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 537-562, April.
    11. Eric Weese & Masayoshi Hayashi & Masashi Nishikawa, 2015. "Inefficiency and Self-Determination: Simulation-based Evidence from Meiji Japan," Discussion Paper Series DP2015-35, Research Institute for Economics & Business Administration, Kobe University.
    12. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    14. Song, Junmo & Oh, Dong-hyun & Kang, Jiwon, 2017. "Robust estimation in stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 243-267.
    15. Léopold Simar & Paul W. Wilson, 2023. "Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1391-1403, October.
    16. Preciado Arreola, José Luis & Johnson, Andrew L. & Chen, Xun C. & Morita, Hiroshi, 2020. "Estimating stochastic production frontiers: A one-stage multivariate semiparametric Bayesian concave regression method," European Journal of Operational Research, Elsevier, vol. 287(2), pages 699-711.
    17. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2021. "Robustified Expected Maximum Production Frontiers," Econometric Theory, Cambridge University Press, vol. 37(2), pages 346-387, April.
    18. 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.
    19. 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.
    20. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2024. "Penalized sieve estimation of zero‐inefficiency stochastic frontiers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 41-65, January.
    21. Papadopoulos, Alecos & Parmeter, Christopher F., 2023. "A specification test for the composed error term in the stochastic frontier model," Economics Letters, Elsevier, vol. 233(C).

    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. Kneip, A. & Simar, L. & Van Keilegom I., 2010. "Boundary estimation in the presence of measurement error with unknown variance," LIDAM Discussion Papers ISBA 2010046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    3. 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.
    4. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    5. Mike Tsionas & Valentin Zelenyuk, 2021. "Goodness-of-fit in Optimizing Models of Production: A Generalization with a Bayesian Perspective," CEPA Working Papers Series WP182021, School of Economics, University of Queensland, Australia.
    6. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    7. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    8. Zelenyuk, Valentin, 2020. "Aggregation of inputs and outputs prior to Data Envelopment Analysis under big data," European Journal of Operational Research, Elsevier, vol. 282(1), pages 172-187.
    9. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    10. Olesen, Ole B. & Petersen, Niels Christian, 2016. "Stochastic Data Envelopment Analysis—A review," European Journal of Operational Research, Elsevier, vol. 251(1), pages 2-21.
    11. 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.
    12. Keshvari, Abolfazl & Kuosmanen, Timo, 2013. "Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation," European Journal of Operational Research, Elsevier, vol. 231(2), pages 481-491.
    13. Davtalab-Olyaie, Mostafa & Asgharian, Masoud & Nia, Vahid Partovi, 2019. "Stochastic ranking and dominance in DEA," International Journal of Production Economics, Elsevier, vol. 214(C), pages 125-138.
    14. Dongwei Su & Xingxing He, 2012. "Ownership structure, corporate governance and productive efficiency in China," Journal of Productivity Analysis, Springer, vol. 38(3), pages 303-318, December.
    15. Martins-Filho, Carlos & Ziegelmann, Flávio Augusto & Torrent, Hudson da Silva, 2013. "Local Exponential Frontier Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    16. Gilbert, R. Alton & Wheelock, David C. & Wilson, Paul W., 2004. "New evidence on the Fed's productivity in providing payments services," Journal of Banking & Finance, Elsevier, vol. 28(9), pages 2175-2190, September.
    17. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2021. "Density deconvolution with Laplace errors and unknown variance," Journal of Productivity Analysis, Springer, vol. 56(2), pages 103-113, December.
    18. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," IDEI Working Papers 625, Institut d'Économie Industrielle (IDEI), Toulouse.
    19. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    20. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.

    More about this item

    Keywords

    Deconvolution; Stochastic frontier estimation; Nonparametric estimation; Penalized likelihood;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    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:eee:econom:v:184:y:2015:i:2:p:379-393. 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/jeconom .

    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.