Regularized Conditional Estimators of Unit Inefficiency in Stochastic Frontier Analysis, with Application to Electricity Distribution Market

Zangin Zeebari (), Kristofer Månsson (), Pär Sjölander () and Magnus Söderberg
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Zangin Zeebari: Jönköping University
Kristofer Månsson: Jönköping University
Pär Sjölander: Jönköping University

No 345, Ratio Working Papers from The Ratio Institute

Abstract: The practical value of Stochastic Frontier Analysis (SFA) is positively related to the level of accuracy at which it estimates unit-specific inefficiencies. Conventional SFA unit inefficiency estimation is based on the mean/mode of the inefficiency, conditioned on the estimated composite error. This approach shrinks the inefficiency towards its mean/mode, which generates a distribution that is different from the distribution of the unconditional inefficiency; thus, the accuracy of the estimated inefficiency is negatively correlated with the distance the inefficiency is located from its mean/mode. We propose a regularized estimator based on Bayesian risk (expected loss) that restricts the unit inefficiency to satisfy the underlying theoretical mean and variation assumptions. We analytically investigate some properties of the maximum a posteriori probability estimator under mild assumptions and derive a regularized conditional mode estimator for three different inefficiency densities commonly used in SFA applications. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimator outperforms the conventional (unregularized) approach when the inefficiency is greater than its mean/mode. With real data from electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators give substantially different results for highly inefficient companies.

Keywords: Electricity Distribution; Productivity; Regularized Posterior Likelihood; Stochastic Frontier Analysis (search for similar items in EconPapers)
JEL-codes: C21 D24 L94 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2021-03-24
New Economics Papers: this item is included in nep-ecm, nep-eff and nep-ene
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Journal Article: Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market (2023)
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