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Frontier estimation in the presence of measurement error with unknown variance

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  • Kneip, Alois
  • Simar, Leopold
  • 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.
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Suggested Citation

  • Kneip, Alois & Simar, Leopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," LIDAM Reprints ISBA 2015004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2015004
    Note: In : Journal of Econometrics, vol. 184, no.2, p. 379-393 (2015)
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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).
    20. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    21. 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.

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    More about this item

    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

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