Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation: The Case of Norwegian Electricity Distribution Firms.

AuthorKumbhakar, Subal C.

    Applications of stochastic frontier analysis (SFA) to study efficiency of firms that generate and/or distribute electricity have overwhelmingly focused on technical inefficiency. The implicit assumption is that all firms are either fully allocatively efficient (i.e., there is no input misallocation (under or overutilization) that results from failure to minimize costs exactly because of some institutional, structural, and managerial problems) or their level of allocative inefficiency is negligible and can be ignored. There are only a handful of papers that deal with allocative inefficiency and the cost therefrom. Most studies that use the cost function tend to ignore allocative inefficiency and focus on technical inefficiency. Of these studies, only a handful have decomposed transient (short-term/time-varying) and persistent (long-term/time-invariant) cost inefficiencies. However, none has estimated both technical and allocative inefficiency and costs therefrom, as well as decompose technical inefficiency and its cost into persistent and transient components. The purpose of this paper is to do this using panel data for Norwegian electricity distribution firms.

    Electricity distribution firms in Norway have the characteristics of natural monopolies within their service territories. As part of a move towards greater market orientation introduced to the industry during the 1990s, the firms are regulated. The Norwegian regulator, Norwegian Water Resources and Energy Directorate (NVE), uses a benchmarking model to estimate each firm's technical efficiency score, while ignoring input misallocation. The efficiency scores, which the regulator calculates for each firm, determine sixty per cent of the firms' revenue cap. From a regulator's point of view, the focus is to motivate the firms to increase productivity and efficiency without intruding into micro management. However, by ignoring input misallocation in the regulation model, a firm can be found to be fully efficient in the benchmarking model of the regulator, yet in practice, the firm could reduce costs of production by changing its input allocation. This unidentified scope for cost saving could be important to society, consumers of electricity, and the owners of the electricity distribution firms. NVE's regulation model also does not distinguish between transient and persistent technical efficiency. Again, this might not be a direct problem within the task given to the regulator, but if the goal is to minimize overall (economic) costs, one should distinguish between different sources of inefficiency. The reason is that it is likely that the sources of inefficiency might differ between firms, and disentangling these sources might influence the overall technical inefficiency score. Also ignoring persistent inefficiency, for example, might affect the estimates of the technology.

    In this study, we apply panel data that make it possible to disentangle persistent and transient inefficiency. We also investigate input misallocation, which is potentially more serious than technical inefficiency (see Kumbhakar and Wang, 2006a), because the estimated technology parameters may be inconsistent. (1)

    Previous studies that estimate both technical inefficiency and input misallocation have commonly adopted the dual approach that utilizes the duality between the cost and production functions. However, estimation of a cost function with both technical inefficiency and input misallocation is quite complex (Kumbhakar and Tsionas, 2005; Kumbhakar and Wang, 2006b). Estimation of the production function alone cannot accommodate input misallocation. The alternative is to use a primal system that uses the production function and the first-order conditions for cost minimization. Schmidt and Lovell (1979) used this approach, which is flexible enough to incorporate both technical inefficiency and input misallocation, and costs therefrom. However, they used a Cobb-Douglas (CD) production function. Subsequently, Kumbhakar and Tsionas (2005) and Kumbhakar and Wang (2006b) extended their modeling approach and used a translog production function. Although the latter studies used panel data, their model is essentially cross-sectional. Because the computation of the cost of technical and allocative inefficiency is nontrivial under a translog specification, Kumbhakar and Wang (2006b) concluded that there is no easy solution to the estimation of both components of inefficiency. Some studies have used the production function and the first-order conditions for profit maximization or a profit function and the implied demand system using Hotelling's lemma to estimate the profit loss from each component (see Kumbhakar et al., 2015a and references therein). An advantage of this approach is that it accounts for endogeneity of both inputs and outputs. Another approach is to study the observed demands to determine whether these are the cost-minimizing demands consistent with observed prices. Alternatively, one can seek to find the set of prices that would make observed demand cost minimizing. In relation to the approaches described above, several variations have been presented over the years (for more details, see Kumbhakar et al., 2015a, Ch. 8, and Greene, 1993).

    To the best of our knowledge, there exists only one recent study on technical inefficiency and input misallocation within the electricity distribution industry. Nemeto and Goto (2006) used a CES cost frontier to study technical inefficiency and input misallocation in the Japanese electricity transmission and distribution industry. Using panel data of Japanese utilities for the period 19811998, they reported that technical inefficiency raises costs by 1-28%, while input misallocation raises costs by 8-30%.

    Our approach is an extension of that of Kumbhakar (1988). It involves estimating a production function frontier together with the first-order conditions of cost minimization. Kumbhakar (1988) introduced a production function that is more general than the Cobb-Douglas technology, which permits elasticity of output to vary across firms, and introduced input misallocation separate from random errors in optimization. In our paper, we consider some extensions of the Kumbhakar (1988) model where we disentangle persistent and transient technical inefficiency and at the same time estimate input misallocation for each pair of variable inputs. (2) We also estimate the costs of each of these inefficiency components. Furthermore, our model allows for multiple inputs and outputs, handles endogeneity of inputs and includes the determinants of persistent and transient technical inefficiency. We add panel data features to both the production function and the first-order conditions of cost minimization, which has not been done previously.

    Our study has two main contributions. First, we extend the sparse literature on modeling both technical inefficiency and input misallocation in electricity distribution industries. Second, we extend the modeling and estimation approach by including additional inefficiency components decomposed into persistent and time-varying elements, including inefficiency determinants for both components, and incorporating panel data features to the modeling framework. The data set used contains information on Norwegian electricity distribution firms, observed over the years 2000 to 2016.

    The remainder of the paper is organized as follows. The model specification and estimation method are described in Section 2. Section 3 describes the data, and Section 4 presents the results. Eventually, Section 5 presents a summary of the main results and offers some concluding remarks.


    2.1 The model

    We consider the production function used in Kumbhakar (1988) extended to accommodate a generalized error specification (3)

    [mathematical expression not reproducible]

    where [Y.sub.it] is output vector for firm i and time t(i = 1,..., N; t = 1,...,T), [X.sub.j] are inputs (j = 1,...,J), and [[alpha].sub.0] and [[alpha].sub.j] are the parameters to be estimated. (4) [v.sub.it] is the noise term that captures exogenous shocks unknown to the producer, [u.sub.i0] is persistent inefficiency and [u.sub.it] is transient inefficiency. (5) We extend the model to incorporate a multiple-output separable production technology. Assuming a flexible functional form of F([Y.sub.it]), viz.,

    InF ([Y.sub.it],) = ln[Y.sub.1it] + [[beta].sub.2]ln[Y.sub.2it] + 1/2 [[beta].sub.3], ln[Y.sub.1it][Y.sub.2it] (2)

    and substituting (2) into the log form of (1), we can rewrite (1) as

    [mathematical expression not reproducible] (3)

    If inputs are exogenous, direct estimation of the production function parameters is possible by the maximum likelihood method using distributional assumptions on the inefficiency and noise components when there is a single output. However, for regulated industries such as the electricity distribution firms that we consider, outputs are treated as exogenous, and inputs are endogenous. (6) In this case, estimating (3) will result in inconsistent parameter estimates, even if there is a single output. If outputs are exogenous (i.e., not choice variables), maximization of profit is the same as minimization of cost. Since the electricity distribution industry is a service industry and consequently outputs are exogenously determined, it is standard practice to estimate the technology using the dual cost function. One can then use the duality results to derive the underlying features of the production function. For the production function in (1), one can derive the cost function analytically. That is, from the parameters of the cost function, we can derive the parameters of the production function, and vice versa.

    From microeconomic theory, the firm is said to be allocatively efficient (no input misallo-cation) if it equates the marginal rate of technical substitution between each pair of inputs with...

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