# Empirical Measurement Of Efficiency And Productivity Of Utilities

### Introduction

Utilities are a vital part of our everyday lives. Everybody uses some form of energy or utility at various stages during the day and every good produced in this country has involved the use of energy and utilities. Demand for energy is set to increase significantly in the near future. Energy comes from burning fuels such as coal, gas and oil. These fuels are non-renewable and finite and so therefore it is important that we make efficient use of them now and for future generations. If there is an improvement in efficiency and productivity in the utility industry, then this could mean lower operating costs for them and these lower costs can be passed onto consumers in the form of lower prices. The measurement of efficiency and productivity of utilities is also important for regulators. It assists them in their determination of price controls. Utilities are usually monopolies by nature and so it is highly important that they are regulated. In the UK, the Office of Gas and Electricity Markets (OFGEM) are responsible for regulating Distribution Network Operators. In facr OFGEM are currently conducting a price control review. I am going to use mathematical econometric methods such as Data Envelopment Analysis, Stochastic Frontier Analysis and Corrected Ordinary Least Squares to test the efficiency and productivity of utilities in the UK.

According to Lovell (1993) Productive efficiency has two elements. The first element is technical efficiency. This refers to the ability of firms to avoid waste by producing as much output as input allows usage, or by using as little input as output production allows. Analysis of technical efficiency can have an output increasing orientation or an input saving orientation.

The second element, allocative efficiency, is the ability to combine inputs and outputs in optimal proportions taking into consideration existing prices.

### Literature Review

Previous academic research has been undertaken into the costs and efficiency of utilities.

Some of these are shown in the table below. Also included in the table is some general literature on efficiency and productivity measurement. The literature I have covered is not limited to the table below. Other literature will be added throughout this paper in my references and in my bibliography.

The measurement of economic efficiency has been closely linked to the use of frontier functions. The present literature in both areas starts with a paper by Michael J. Farrell (1957). The diagram below explains Farrell's analysis of efficiency.

Assuming constant returns to scale (CRS) as Farrell (1957) originally does in his paper, the technological set is explained by the unit isoquant YY'that captures the minimum combination of inputs per unit of output needed to produce a unit of output. As a result, under this framework, every package of inputs along the unit isoquant is considered as technically efficient while any point above and to the right of it, such as point P, defines a technically inefficient producer since the input package that is being used is more than enough to produce a unit of output. Therefore, the distance RP along the ray OP measures

the technical inefficiency of producer located at point P. This distance illustrates the amount by which all inputs can be divided without decreasing the amount of output. Geometrically, the technical inefficiency level associated to package P can be expressed by the ratio RP/OP, and thus; the technical efficiency (TE) of the producer under analysis (1-RP/OP) would be given by the ratio OR/OP. If information on market prices is known and a particular behavioural objective such as cost minimization is assumed in such a way that the input price ratio is reflected by the slope of the isocost-line CC', allocative inefficiency can also be derived from the unit isoquant plotted in the diagram. In this instance, the relevant distance is given by the line segment SR, which in relative terms would be the ratio SR/OR. With regard to the least cost combination of inputs given by point R', the above ratio indicates the cost reduction that a producer would be able to attain if it moved from a technically but not allocatively efficient input package (R) to a both technically and allocatively efficient one (R'). Therefore, the allocative efficiency (AE) that describes the producer at point P is given by the ratio OS/OR. (Murillo-Zamorano, 2004)

Most ideas on efficiency measurement are based on parametric or non-parametric frontier methods. I am going to use an example of both in this project. Another important piece of literature that is useful in the application of efficiency measurement techniques is a book by Timothy J. Coelli et al (2005), An introduction to Efficiency and Productivity Analysis. They provide an in-depth analysis and a guide as to how to apply techniques such as DEA and SFA.

DEA is a nonparametric method in economics used to estimate production frontiers. It involves the use of linear programming methods to construct a non-parametric piece-wise surface (or frontier) over the data. Efficiency measures are then calculated relative to this surface. The term ‘data envelopment analysis' was first used in a paper by Charnes, Cooper and Rhodes (1978). They proposed a model that had input orientation and assumed constant returns to scale.

Coelli et al (2005) discusses the input- and output-oriented Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS). It discusses how the models can be used to measure technical and scale efficiencies and how non-increasing returns to scale DEA can be used to identify the nature of scale economies. Some extensions of the basic DEA models are also discussed. These include the stochastic DEA models proposed by Land, Lovell and Sten (1993) and Olsen and Petersen (1995); the Flexible Disposable Hull (FDH) approach of Deprins, Simar and Tulkens (1984), which relaxes convexity assumptions and the Malmquist index approach of Fare, Grosskopf, Norris and Zhang (1994).

The paper on Norwegian electricity distributors by Forsund and Kittelsen (1998) provides an example of how the DEA technique can be extended. They use a malmquist index approach. Specifying a piecewise linear constant returns to scale frontier technology based on best practice observations, they found that productivity development according to the Malmquist index approach showed an overall positive development of between 1.5 and 2% per year.

Data Envelopment Analysis seems to be a common tool for the measurement of efficiency and productivity. Its popularity has increased in the analysis of productive efficiency. This may because it does not require any functional form in the construction of the frontier, nor does it require any assumptions to be made about the distribution of the efficiency.

However, there are some limitations and shortcomings of DEA. One in particular is that it does not account for statistical noise. One can use the parametric Stochastic Frontier Approach (SFA) to overcome this problem. The SFA model was first developed by Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977). In early applications of SFA models to panel data, there was a common assumption that the productive efficiency is a time-invariant characteristic that can be captured by firm specific effects in a random or fixed effects model. However in more topical papers, the random effects model has been extended to include time-variant inefficiency. (Massimo and Fillipini 2008). Cornwell, Schmidt and Sickles (1990), Kumbhakar (1990), and Battese and Coelli (1992) are the main studies that consider a time function to account for variation efficiency.

SFA has a disadvantage to the non-parametric methods because it requires more structure on the shape of the frontier by giving a functional form for it. However an advantage of parametric methods is that they allow for random errors and so are less likely to misidentify measurement errors, transitory differences in cost, or a specification error as inefficiency.

SFA is easily adaptable to panel data structure. An example of where it has been used in the measurement of efficiency is in a paper by Massimo and Filippini (2008). Their study was on multi-utilities in Switzerland between 1997 and 2005. They found that the benchmarking of multi-output companies was more difficult than utilities with similar output and that appropriate panel data models can be used to identify the inefficient companies and determine to a certain degree, which part of their excess costs has been persistent and which part has varied over time. This shows that the SFA is useful in pointing out the presence of global scale economies.

COLS is also a useful measure of efficiency. It is a method commonly used by governments and regulators. An example of such a regulator is OFGEM. According to Melvyn Weeks, there are two broad approaches to the estimation of an efficiency frontier. A traditional panel estimator model such as COLS is characterized by a set of distributional assumptions and an assumption of a deterministic frontier. In a deterministic frontier model, any deviation from a frontier is due to inefficiency. If the frontier is constructed based on a cost (production) function, then deviations will be positive (negative) as a result of higher costs (less output) than predicted by the frontier.

Frontier methods have usually been estimated using COLS or maximum likelihood (MLE) techniques. In a paper by Olsen, Schmidt and Waldman (1980) a Monte Carlo approach is used to study the advantages of the two estimation techniques. The study shows that MLE is better than COLS in sample sizes larger than 400 and that COLS is a better technique in smaller samples. This finding is relevant here as it shows COLS is the appropriate technique to use in this project.

### Methodology

I am going to use data from recent OFGEM reports on benchmarking and price controls. The data consists of inputs and outputs of 14 DNO's in the UK. The diagram below is an example of the sort of data I will be using. It is a table of operational costs for the 14 DNO's in the UK.

In measuring the efficiency of the utilities, I am going to consider technical efficiency and allocative efficiency. Technical efficiency measures the ability of the firm to obtain the maximum output from the given inputs. Allocative efficiency measures the ability of the firm to use inputs in optimal proportions given their prices. Computing these efficiency measures involves estimating the unknown production frontier. In studies of costs and efficiency, two main approaches have been used; a parametric and a non-parametric approach. They both require the specification of a cost or production function. The parametric approach requires the specification and econometric estimation of a statistical or parametric function, while the non-parametric approach provides a piecewise linear frontier by enveloping the observed data points. So, the non-parametric technique has come to be known as DEA. Unlike the parametric approach, DEA does not require the specification of a particular functional form for the cost or production function. Therefore, the resulting efficiency estimates are not functional form dependant. The accuracy of the efficiency estimates are conditional on the accuracy of the chosen functional forms' approximation to the cost or production function.

Unlike the stochastic frontier approach (SFA), DEA does not allow for the presence of a random error term. Therefore, DEA attributes any deviation from the efficient frontier as being purely because of inefficiency and so DEA may overstate the true levels of relative inefficiency.

### Image

The diagram above plots the ratio of output y1 to x against the ratio of output y2 to x, and the piecewise linear boundary which joins up firms A, B, C and D is the production frontier. All distribution-making units (DMUs) on the frontier are efficient since none can produce more of both outputs (for a given input level) than any other unit on the frontier. In contrast, firm E, which lies inside the frontier, is inefficient, and the ratio OE/OE' measures firm E's efficiency relative to the other DMUs in the data set.

I am also going to look at the stochastic frontier approach (SFA). A parametric method such as SFA has a disadvantage to the non-parametric methods because it requires more structure on the shape of the frontier by giving a functional form for it. However an advantage of parametric methods is that they allow for random errors and so are less likely to misidentify measurement errors, transitory differences in cost, or a specification error as inefficiency. Also, SFA is easily adaptable to panel data structure and so it is appropriate for this project. The main challenge in implementing the parametric methods is determining the best way to separate random error from inefficiency, as neither of them are observed. SFA employs a composed error model in which inefficiencies are assumed to follow an asymmetric distribution, usually the half normal, while random errors are assumed to follow a symmetric distribution, usually the standard normal. The reason for this is because inefficiencies cannot subtract from costs, and so can be drawn from a truncated distribution, while a random error can add and subtract costs and so can be drawn from a symmetric distribution. There is an assumption that both the inefficiencies and random errors are orthogonal to the input prices, output quantities, and any other cost function regressors specified. The efficiency of each firm is based on the conditional mean of the inefficiency term given the residual which is an estimate of the composed error.

A positive feature of the SFA approach is that it will always rank the efficiencies of the firms in the same order as their cost function residuals despite which distributional assumptions are imposed. That means that firms with lower cost for a given set of input prices, output quantities, and any other cost function regressors will always be ranked as more efficient, because the conditional mean or mode of the inefficiencies is always increasing in the size of the residual. This aspect of SFA has intuitive appeal for a measure of performance for regulatory purposes because a firm is measured as high in the efficiency rankings if it keeps costs relatively low for its given exogenous conditions.

It is difficult to say which technique is preferred between DEA and SFA as the true level of efficiency is unknown.

I am also going to apply corrected ordinary least squares (COLS). COLS is commonly used by governments and regulators. It is simply a shifted average function. It entails choosing the firm with the minimum residual and shifting the OLS regression line down towards this best performing company as illustrated in the diagram below.

The distance between another comparator and this efficiency frontier is considered to be a measure of that firm's inefficiency. In other words, comparative efficiency measurements using COLS regression take the view that this residual is an indicator of the corresponding firm's inefficiency. The diagram above shows how the frontier adjustment is performed and how inefficiency is determined for each comparator. The efficiency frontier passes through the observation: xf, yf as that matches up to the firm with the largest absolute value among the negative residuals. The representative inefficient firm with the observation: xi, yi has a target frontier cost of yi*. Its relative percentage inefficiency can be measured as: 100 * (1-yi*/yi). COLS results in the most extreme description of the efficiency frontier, and presumes that inefficiency is the only omitted variable. It also maximizes the measured efficiency. (Weyman-Jones, 2008, page 10)

The technique of regression analysis is described by the following steps: 1) selecting both the cost (or output) measure and exogenous variables, 2) estimating a cost (or production) function for the industry, and 3) calculating the efficiency coefficient for each firm within the industry. Predicted versus actual output provides a measure of relative performance. The quality of these results can then be statistically evaluated to provide the policy-maker with a framework for evaluating firms. The linear vs. non-linear issue can be looked at by including parameters that capture scale economies or diseconomies.

An advantage of COLS is that it reveals information about cost structures and distinguishes between different variables' roles in affecting output. Coefficients can be understood in terms of cost drivers or how inputs contribute to output.

A disadvantage is that a large data set is needed in order to get reliable results. The regression results are sensitive to functional form if the error term is not properly interpreted, which can lead to extensively varying conclusions, depending on how the regression is initially set up.(IBNET, 2009)

### Bibliography

### Boo.ks

- Coelli, Timothy J. Prasada Rao, D.S. O'Donnell, Christopher J. Battese, George E. (2005), An Introduction to Efficiency and Productivity Analysis, Second Edition
- Dogramaci, A., Fre, R., Shephard, R.W. (1988), Applications of modern production theory: efficiency and productivity, Springer, 1988

### Journal Articles

- Aigner, D., Lovell, C. A. K. and P. Schmidt (1977). Formulation and estimation of stochastic frontier production function models, Journal of Econometrics, 6, pp. 21-37.
- Farrell, M.J. (1957), The measurement of productive efficiency, Journal of the Royal Statistical Society. Series A (General), Vol. 120, No.3, pp. 235-290.
- Farsi, M., Filippini, M. (2008), An Analysis of Cost-Efficiency in Swiss Multi-utilities, Energy Economics 31 (2009) 306-315.
- Forsund, F.R., Kittelsen, S.A.C. (1997), Productivity development of Norwegian electricity distribution utilities, Resource and Energy Economics 20 (1998) 207-224.
- Helm, D. (1994), British Utility Regulation: Theory Practice and Reform, Oxford Review of Economic Policy, Vol. 10, No. 3.
- Hjalmarsson, L., Kumbhakar Subal C. and Heshmati, A. (1996), DEA, DFA and SFA: A comparison, The Journal of Productivity Analysis, 7, 303-327.
- Kuosmanen, T., Johnson, A. (2008) Data Envelopment Analysis as Nonparametric Least Squares Regression.
- Lovell, C.A.K. (1993), Production Frontiers and Productive efficiency.
- Murillo-Zamorano, L.R. (2004), Economic efficiency and frontier techniques. Journal of Economic Surveys, Vol. 18, no. 1, 33-77.
- Olsen, J.A., Schmidt, P., Waldman, D.M. (1980), A Monte Carlo study of estimators of stochastic frontier production functions, Journal of Econometrics 13 (1980), pp. 67-82

### Papers

- Weyman-Jones, T. (2008), Econometric Models for Performance Measurement
- Weyman-Jones, T. (2007), Performance Measurement with Data Envelopment Analysis, DEA, UKEPAN International Training Workshop on Performance Measurement

### Websites

- The International Benchmarking Network for Water and Sanitation Utilities (IBNET) (2009), Benchmarking Methodologies, Performance re
- Office of Gas and Electricity Markets (OFGEM) (2009), Electricity Distribution Price Control Review Final Proposals - Allowed revenue cost assessment, available at: ofgem.gov.uk