Chapter two is structured to give an extensive background to the electricity industry of West Africa in the first part. This is important for the purposes of giving the necessary foundation to the investigations done in chapters four and five. This chapter examined the state of electricity along the power supply chain of various West African countries and illuminated on their marker structure, regulatory regimes or models and challenges. It revealed that the persistent problems that necessitated reforms hinge on the inefficiency of the power sector. It was revealed that the region continues to have a supply and demand gap with high prices of electricity making a significant section of the population unable to access electricity. Also, that if the system could not add to the generation capacity or reduce the cost of electricity,
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the least it could do was to reduce the level of inefficiency. That task continues to be looked at by national policy reformers as well as regional policy reformers giving it a significant level of attention. However, properly estimating the level of inefficiency is probably the first step to minimising it but unfortunately, the literature also revealed the lack of a holistic model for measuring efficiency of the operations of utilities in the value chain and that simplistic ratios that are less representative of the overall efficiency are used instead.
Understanding the concept of efficiency, theoretical underpinnings of frontier economics and the various techniques for measuring efficiency is the general motive of part two of the chapter. Specifically, the main aim was to narrow down on the Stochastic Frontier Approach (SFA) or technique for modelling efficiency. Different sub-models have been discussed in this section with the future benefit of being applied in our empirical study of estimating the efficiency of electricity distribution companies in West Africa. In the end, the moot issue of which distribution underlying the inefficiency term in the SFA technique is resurrected with much credence to Burr Distribution as a likely contender. In order to lay a good foundation for further analysis in chapter five, it was also prudent to explain the political economy analysis framework while reviewing the underlying theories and applications accordingly. Having successfully executed the objectives of the chapter, this research proceeds to chapter three to investigate the potentials of Burr type x as an assumed distribution of Stochastic frontier approach.
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Chapter 3
Formulation and Analyses of the Normal-Burr X Stochastic Production
Frontier Model
3.1 Introduction
As discussed in chapter two, the Stochastic Frontier Model, primarily was developed to measure technical efficiency of production units. In the model, these production units (firms, regions, countries, etc.) are assumed to produce according to a common technology and are considered efficient when they lie on the frontier as they produce the maximum possible output for a given set of inputs. Otherwise, the firms are relatively inefficient which could be due to structural problems or market imperfections and other factors which cause firms to produce below their maximum attainable output. Aigner, Lovell, and Schmidt’s (1977) and Meeusen and van den Broeck (1977), who independently proposed the stochastic frontier model simultaneously accounts for statistical noise and technical inefficiency.
The stochastic frontier model is usually estimated by a maximum likelihood estimation, which requires distributional assumptions of the error terms. Most often, it is assumed that the noise term follows a normal distribution with zero mean and constant variance. For the estimation of the technical inefficiency term, other distributional assumptions have been proposed in the literature and they include a one parameter half normal introduced by Aigner et al. (1977) and exponential by Meeusen and Van den Broeck (1977). For the two parameter distributions, Stevenson (1980) constructed the stochastic frontier model based on truncated normal while Greene (1980, 1990) introduced the gamma distributions. There is no theoretical justification for the selection of any particular distributional form over the other (Coelli, Rao and Battese, 1998).
All the inefficiency distributions in the literature have different strengths and weaknesses. For instance, the exponential and half-normal distributions have a mode at zero, suggesting that a high percentage of the firms under study are perfectly efficient. The distributions like truncated normal and gamma distribution could have non-zero modes. Thus they are more flexible than exponential and half-normal. However, according to Ritter and Simar (1997) it may be difficulty and if not inept to identify the best estimate of the values of the two gamma parameters. The choices of models used in the stochastic frontier in the literature seem to be somewhat arbitrary.
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In this work, Burr X distribution is proposed to be the assumed distribution of technical inefficiency term in the SFA model. The potential of Burr X distributions has been discussed in the chapter 2 and it is expected to be more flexible with the ability to encapsulate the already known and assumed distributions for the inefficiency term (i.e. half normal, truncated, exponential, gamma and Rayleigh). Burr X is known to have some interesting relations with the Rayleigh, Gamma and Weibull distributions. It is also related to the recently proposed Exponentiated exponential and Exponentiated Weibull distributions.
The rest of the chapter is outlined as follows: Section 3.2 introduces the stochastic frontier model for cross-section; Section 3.3 discusses the specification of the Burr X distribution in detail; section 3.4 illustrates the maximum likelihood estimation of Burr parameters; section 3.5 presents the designing stage of the Normal-Burr X SFA followed by log likelihood estimation of the proposed model in section 3.6. Sections 3.7, 3 8 and 3.9 respectively present efficiency estimation of the proposed model, results of the Monte Carlo simulations and conclusion of the chapter.