Maximum entropy: a stochastic frontier approach for electricity distribution regulation

Isabel Soares,Pedro Macedo,Elvira Silva

doi:10.1007/s11149-019-09383-y

Isabel Soares, Pedro Macedo + Show 1 more

Open Access

https://doi.org/10.1007/s11149-019-09383-y

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Abstract

The literature on incentive-based regulation in the electricity sector indicates that the size of this sector in a country constrains the choice of frontier methods as well as the model specification itself to measure economic efficiency of regulated firms. The aim of this study is to propose a stochastic frontier approach with maximum entropy estimation, which is designed to extract information from limited and noisy data with minimal statements on the data generation process. Stochastic frontier analysis with generalized maximum entropy and data envelopment analysis—the latter one has been widely used by national regulators—are applied to a cross-section data on thirteen European electricity distribution companies. Technical efficiency scores and rankings of the distribution companies generated by both approaches are sensitive to model specification. Nevertheless, the stochastic frontier analysis with generalized maximum entropy results indicate that technical efficiency scores have similar distributional properties and these scores as well as the rankings of the companies are not very sensitive to the prior information. In general, the same electricity distribution companies are found to be in the highest and lowest efficient groups, reflecting weak sensitivity to the prior information considered in the estimation procedure.

Highlights

Incentive-based regulation in the electricity sector has been introduced in many countries during the last three decades
Some national regulators have been facing a problem of ill-posed frontier models
In the case of regulation of the electricity sector, an ill-posed model arises mainly from (i) limited information available - small sample sizes, incomplete data, and when the number of unknown parameters exceeds the number of observations; (ii) models affected by collinearity and/or outliers; and (iii) missing data

Summary

Introduction

Incentive-based regulation in the electricity sector has been introduced in many countries during the last three decades. Data problems (or lack of data) and the size of a country’s electricity sector are among the reasons pointed out by some national regulators for not employing frontier approaches (Haney and Pollitt 2009). In the case of regulation of the electricity sector, an ill-posed model arises mainly from (i) limited information available - small sample sizes, incomplete data, and when the number of unknown parameters exceeds the number of observations; (ii) models affected by collinearity and/or outliers; and (iii) missing data (e.g., unobserved heterogeneity). This study proposes a frontier approach, based on stochastic frontier analysis (SFA) with the generalized maximum entropy (GME) estimator to measure productive (technical) efficiency of a sample of thirteen European electricity distribution companies.

A Brief literature review

Distance function and GME estimation

1: The radial input distance function is a function

Data and empirical results

Conclusions