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Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market

Author

Listed:
  • Zangin Zeebari

    (Jönköping University
    Karolinska Institutet)

  • Kristofer Månsson

    (Jönköping University)

  • Pär Sjölander

    (Jönköping University)

  • Magnus Söderberg

    (Halmstad University
    Ratio Institute
    Griffith University)

Abstract

In stochastic frontier analysis, the conventional estimation of unit inefficiency is based on the mean/mode of the inefficiency, conditioned on the composite error. It is known that the conditional mean of inefficiency shrinks towards the mean rather than towards the unit inefficiency. In this paper, we analytically prove that the conditional mode cannot accurately estimate unit inefficiency, either. We propose regularized estimators of unit inefficiency that restrict the unit inefficiency estimators to satisfy some a priori assumptions, and derive the closed form regularized conditional mode estimators for the three most commonly used inefficiency densities. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimators outperform the conventional (unregularized) estimators when the inefficiency is greater than its mean/mode. Based on real data from the electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators provide substantially different results for highly inefficient companies.

Suggested Citation

  • Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.
    • Handle: RePEc:kap:jproda:v:59:y:2023:i:1:d:10.1007_s11123-022-00651-2
    DOI: 10.1007/s11123-022-00651-2
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    More about this item

    Keywords

    Uncertainty modelling; Productivity; Regularized Estimators; Constrained Estimators; Conditional Estimators;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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