Ceris-Cnr, W.P. N° 2/2002 technology (e.g., Greene, 1980b; Kumbhakar, Ghosh and McGuckin, 1991)18; extending the analysis to the dual cost function (e.g., Schmidt and Lovell, 1979; Ferrier and Lovell, 1990; Kumbhakar, 1991)19; accommodating panel data (e.g., Battese and Coelli, 1988; Cornwell, Schmidt and Sickles, 1990; Kumbhakar, 1990; Battese and Coelli, 1992; Lee and Schmidt, 1993)20. More importantly for the purpose of this work, a number of later empirical studies (e.g., Pitt and lee, 1981; Kalirajan, 1981; Kalirajan and Shand, 1989; Mester, 1997) have investigated the determinants of productive inefficiencies among firms in an industry by regressing the predicted inefficiency effects, obtained from an estimated stochastic frontier, upon a vector of firm-specific factors, such as the degree of competitive pressure, input and output quality indicators, various managerial characteristics, etc., in a second-stage analysis. There is, however, a significant problem with this two-stage approach. In the first stage, the inefficiency effects are assumed to be independently and identically distributed in order to use the approach of Jondrow et al. (1982) to predict the values of the technical inefficiency effects. However, in the second stage, the predicted inefficiency effects are assumed to be a function of a number of firm-specific factors, which implies that they are not identically distributed, unless all the coefficients of the factors are simultaneously equal to zero. Kumbhakar, Ghosh and McGuckin (1991) and Reifschneider and Stevenson (1991) noted the above inconsistency and specified stochastic frontier models in which the inefficiency effects were defined as explicit functions of some firm-specific factors, and all parameters were estimated in a single-stage maximum likelihood (ML) procedure. Huang and Liu (1994) also presented a model for a stochastic frontier 18 19 20 The Cobb-Douglas functional form has been commonly used in the empirical estimation of frontier models. Its simplicity is a very attractive feature. This simplicity, however, is associated with a number of restrictive properties. The Cobb-Douglas technology exhibit the same value of returns to scale for all firms in the sample. Further, the elasticities of substitution between productive factors are equal to one. The cost frontier approach appears to be a significant improvement to the efficiency analysis. It accounts for the possibility of exogenous output and endogenous inputs, permits the measurement of technical and allocative inefficiency, and can be easily extended to account for multiple outputs. Further, the objective of (total or variable) cost minimisation may often be a proper assumption. It is particularly suitable in environments where output is demand driven, and so also can be considered to be exogenous. Many regulated industries, such as electricity generation, gas distribution, or public transit service, satisfy these exogeneity criteria. Moreover, in many industries output is not storable, and so the output maximization objective that underlies the estimation of output-oriented technical efficiency would be inappropriate. Panel data have some advantages over cross-sectional data in the estimation of stochastic frontier models. First, when panel data are available there is no need to specify a particular distribution for the inefficiency effects, because the parameters of the model can be estimated using the traditional panel data techniques of fixed-effects (dummy variables) or random-effects. Second, also by proceeding with the more commonly used maximum likelihood (ML) methods, the availability of panel data generally implies that there are a larger number of degrees of freedom for the estimation of parameters. Third, panel data permit the investigation of efficiency change over time. 14