Estimation of cost efficiency with heteroscedasticity: An application to electricity utilities

This paper deals with the estimation of efficiency. Efficiency is measured relative to the cost frontier which is defined as C*(W,Y) = min(X){W'X\f(X) greater than or equal to Y, X greater than or equal to 0} where W is the vector of input prices, X is the vector of inputs, Y is the actual output produced and f( ) is a function of the production technology. The condition f(X) greater than or equal to Y, X greater than or equal to 0 implies that the maximum possible output, given X greater than or equal to 0, can never be less than the actual output. A firm is defined as cost inefficient if its actual cost exceeds the minimum cost given by the cost frontier, which is to be estimated by using data on actual costs, output and input prices. We first consider a panel data model where cost inefficiency is decomposed into a permanent component and a residual component. The model can be viewed as a one-way error component model (ECM) with an additional error term introduced to capture the residual component of cost inefficiency. Second, the ECM is generalized to accommodate firm-specific variances for the permanent inefficiency component. Finally, we propose a multistep procedure to estimate the cost Function parameters and to predict cost inefficiency. The model is applied to examine efficiency in the production of electricity by 10 major investor-owned electricity utilities in Texas during 1966-85. The production technology is represented by a cost function that is assumed to be the same for every utility (except For heterogeneous intercepts), but it is allowed to shift over time owing to changes in technology. Empirically we find evidence for permanent and residual cost inefficiencies. Furthermore, the data support the ECM with firm-specific variances and rejects the homoscedastic ECM. Cost inefficiency is found to vary widely across utilities, ranging from 8% to 36% with a mean of 27%. Technical change, defined as the rate of cost diminution over rime with everything else unchanged is found to be quite small (less than +/- 1%), especially during 1971-85.