The determinants of the cost efficiency of electric generating plants: A stochastic frontier approach.

• Author: Hiebert, L. Dean

1. Introduction

   The purpose of this article is to provide a detailed analysis of the operating cost efficiencies of electricity generating plants over the period 1988-1997. I estimate the operating efficiencies of fossil-fueled steam generating plants and examine factors that influence plant operating performance. I use the estimation procedure of Battese and Coelli (1995) to simultaneously estimate a stochastic frontier cost function and a function relating plant efficiency levels to plant-specific factors and other explanatory variables. A comprehensive data set allows me to investigate the influence of capacity utilization, ownership form, and utility experience on plant efficiency levels. Since significant regulatory change in the electricity industry had begun during this time period, I also investigate the impact of state-level regulatory change on plant operating efficiency.

   A number of authors have analyzed the efficiencies of electricity generating plants relative to a best practice frontier, including Kopp and Smith (1980), Schmidt and Lovell (1979), Stevenson (1980), Cote (1989), Reifschneider and Stevenson (1991), Hammond (1992), Pollitt (1995), and Fare, Grosskopf, and Logan (1983, 1985). These studies find considerable evidence of inefficiency in electricity generation during the 1960s and 1970s. The present study provides more recent information regarding generating plant efficiencies during a period of significant regulatory and structural change. Studies investigating the determinants of power plant departures from the frontier have focused primarily on the effects of ownership mode. Pollitt (1995) provides a comprehensive review of these studies. Reifschneider and Stevenson (1991) examine the impact on cost efficiency of a number of variables, including the capacity utilization of the firm's generating facilities. More recently, Knittel (2001) examines the impact of in centive regulation on plant efficiency levels. Steiner (2000) uses a cross-country data set to assess the impact of privatization and regulatory change on the performance of the electricity generation segment of the industry. This study extends the literature on the determinants of generating plant efficiencies by considering a broader range of factors that may contribute to divergence from the best practice frontier.

   The remainder of the article is organized as follows. Section 2 presents the stochastic frontier cost model. Section 3 specifies the functional form of the frontier and defines the variables included in the empirical analysis. Section 4 describes the data. The empirical results are presented in section 5. The last section concludes the article.

2. The Stochastic Frontier Cost Model

   I estimate a stochastic frontier variable cost function in which plant capacity and other technology characteristics are treated as fixed. The cost frontier represents the minimum attainable cost given output levels, input prices, and the existing production technology. (1) The stochastic frontier variable cost function for panel data is defined by

   ln [VC.sub.it] = C([y.sub.it], [p.sub.it], [k.sub.it], [x.sub.it]) + [U.sub.it] + [V.sub.it], (1)

   where subscripts i and t represent the ith plant in the tth time period, [y.sub.it] denotes output, [p.sub.it] is a vector of variable input prices, [k.sub.it] is plant capacity, and [x.sub.it] is a vector representing technology-related characteristics of the plant. The [V.sub.it] are assumed to be independent and identically distributed as N(0,[[sigma].sup.2.sub.v]. independent of the [U.sub.it], which are unobservable nonnegative random variables assumed to be independent and identically distributed as truncations at zero of N([mu], [[sigma].sup.2]). The symmetric error terms [V.sub.it] capture measurement error and random disturbances resulting from factors beyond the control of the firm. The one-sided error terms [U.sub.it] represent the increase in cost relative to the frontier due to managerial operating inefficiency given output levels, input prices, and the existing production technology.

   Several authors have investigated the determinants of variations in inefficiency among producers using a two-stage procedure (cf., Pitt and Lee 1981). In the first stage, a stochastic frontier function is used to obtain estimates of the inefficiencies. In the second stage, these inefficiencies are regressed on a vector (or matrix) of explanatory variables. This two-stage approach poses significant estimation problems. In the first stage, the inefficiencies are assumed to be independently and identically distributed, while in the second stage, they are assumed to be a function of firm-specific factors, contradicting the assumption of independence. Recently, Kumbhakar, Ghosh, and McGuckin (1991) and Reifschneider and Stevenson (1991) have addressed this inconsistency. They assume that the inefficiency effects are explicit functions of various explanatory variables and estimate the parameters of both the stochastic frontier and the model for the inefficiency effects simultaneously in a single-stage procedure. Ba ttese and Coelli (1995) extend these models to accommodate panel data. This article uses the model specified by Battese and Coelli to estimate the effects of various plant and firm characteristics as well as changes in the regulatory environment on the cost inefficiencies of coal- and gas-fueled generating plants.

   Following Battese and Coelli (1995), the inefficiency effects [U.sub.it] in the stochastic frontier are specified as

   [U.sub.it] = [z.sub.it][delta] + [W.sub.it], (2)

   where [z.sub.it] is a vector of explanatory variables associated with plant inefficiency, [delta] is a vector of parameters to be estimated, and the [W.sub.it] are random variables assumed to be independent and identically distributed as truncations of N(0, [[sigma].sup.2]) such that [U.sub.it] is nonnegative ([W.sub.it] [greater than or equal to] -[z.sub.it][delta]). Thus, the distribution of the inefficiency effects [U.sub.it] is defined by the truncation at zero of N([z.sub.it][delta], [[sigma].sup.2]).

   Given the values of the explanatory variables in the stochastic frontier function, the operating cost efficiency of the ith plant in the tth year is defined by the ratio of expected cost if the producer were fully efficient ([U.sub.it] = 0) to the corresponding expected cost given the value of the inefficiency effect [U.sub.it],

   [CE.sub.it] = E([VC.sub.it]\[y.sub.it], [p.sub.it], [k.sub.it], [x.sub.it], [U.sub.it] = 0)/E([VC.sub.it]\[y.sub.it], [p.sub.it], [k.sub.it], [x.sub.it], [U.sub.it]). (3)

   This measure can assume values between zero and one and indicates the extent to which the plant operator succeeds in minimizing costs given the output level, input prices, and fixed characteristics of the plant. Given the frontier variable cost function (Eqn. 1), operating cost efficiency is equivalent to

   [CE.sub.it] = exp(-[U.sub.it]). (4)

   A prediction of cost efficiency is based on the conditional mean of Equation 4 given the realized values of the composed error terms [U.sub.it] + [V.sub.it] of the stochastic frontier (see Battese and Coelli 1993).

3. Functional Form and Variables

   To implement the model, I assume that C([y.sub.it], [p.sub.it], [k.sub.it], [x.sub.it]) is the translogarithmic function. Since residuals are used to measure efficiency, it is important to choose a flexible functional form for the cost function in order to capture the features of the frontier. The translogarithmic functional form is frequently used in the electricity cost literature. The stochastic frontier cost function can be written as

   ln [VC.sub.it] = [[beta].sub.0] + [[beta].sub.y]ln [y.sub.it] + [[beta].sub.p]ln [p.sub.it] + [[beta].sub.k]ln [k.sub.it] + [[beta].sub.T]T + [summation over (3/j=1)] [[beta].sub.tj]ln [x.sub.jit] + 1/2 [[beta].sub.yy][(ln...