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The Fortnightly 100: Which Utility Ranks the Highest?

Fortnightly Magazine - September 1 1998

to use an input-oriented analysis. In this study, we examine each holding company as a productive unit that converts inputs to outputs. We refer to each such entity as a Decision-Making-Unit (DMU).

Traditionally, research on technical efficiency has relied on one of two approaches: 1) a parametric approach using econometric tools or, 2) a non-parametric approach using linear programming techniques, such as DEA. Econometric methods involve estimating a production function based, on average, on how various inputs are used by a group of similar producers. These techniques require that certain statistical assumptions be satisfied (e.g., that there should exist no significant relationship among various independent variables or inputs) and some knowledge of the functional form. On the other hand, DEA, being nonparametric, requires no such assumptions. DEA also optimizes each company individually (by benchmarking it against its closest peers), whereas traditional statistical methods rely on averages.

The DEA Method

Using historical production data, DEA measures how efficiently a producing unit converts inputs to output. DEA uses mathematical optimization to construct a piecewise convex production frontier based on the most efficient companies. Companies that form the production frontier are considered efficient and receive a score of 1; all other companies receive an efficiency score between 0 and 1 based on distance from the production frontier.

Figure 1 is a graphical presentation of a simple one-input, one-output DEA production frontier. DMUs A, B, and C form the efficient production frontier (most efficient). Given their input levels, they are able to produce more output relative to any other DMU. All three receive an efficiency score of 1.0. D, E, and F are less efficient (fall below the efficient frontier). D, E, and F could move closer to the efficient frontier by using less input for the current level of output or increase their output given the existing inputs by using, for example, better technology. These DMUs thus can move from their current positions (D, E, and F) to the closest efficient position (D*, E*, and F*). Based on similarities in the input and output mix, DEA identifies efficient peers for each of the inefficient units. For example, unit D may end up with unit A as the peer against which it is compared and its efficiency score (the horizontal distance to the production frontier, DD*) is computed. Similarly, unit E's peers maybe utilities A and B, and F's may be B and C.

To assess changes in technical efficiency over time, we use the Malmquist productivity index. Overall change in productivity consists of not only the change in efficiency, but also change in technology. The advantage of the Malmquist productivity index is that it is comprised of these two distinct elements. For ease of interpretation, we use the natural log of the Malmquist index, thereby reporting change in productivity as a percent increase or decrease.

For each inefficient company, it is possible to calculate individual target values for labor, capital, operation and maintenance and fuel. The target values represent realistic goals for operating at peak efficiency with respect to identified peers. These are the changes