Ceris-Cnr, W.P. N° 2/2002

managerial effort8. If it is so, then we may conclude that incentive theory and modern
regulatory economics are necessary components in the production analysis of regulated
utilities. On the policy side, this investigation allows to assess if the subsidization
schemes recently introduced in Italy are suitable in order to recover efficiency, which is
one of the goals pursued by the legislative reform.

3.

The econometric model

The frontier concept arises in the econometric practice when one considers that
theoretical production and cost functions represent the maximum and minimum values,
respectively, of an optimization problem. In this sense the notion of cost function may
be interpreted as a frontier relationship, i.e., a benchmark behavior, because it is
impossible for a firm to achieve costs lower than the minimum requirement, whereas
higher levels are often observed in the real world, which reveal the presence of xinefficiency in the production process.
In the case of unbalanced panel data the general stochastic frontier specification
for a variable cost function can be written as:
VC ft = VC (Y ft , Pft , Z ft , τ ft ; β ) exp{ψ ft },

[1]

with ψ ft = v ft + u ft ,

[2]

where VC denotes variable cost, Y represents a vector of output, P is an m × 1 vector of
prices of variable factors, Z is an n × 1 vector of variables including quasi-fixed inputs
and network characteristics, τ indicates the year of the observation involved, and β is a
k × 1 vector of technology parameters to be estimated. For all variables the subscript f
indexes firm ( f = 1, …, F), and t indexes observation (t = 1, …, Tf ). The f subscript on T
is used to indicate the unbalanced nature of the panel. For all f 1 ≤ Tf ≤ T, with T
denoting the maximum number of observations available for a firm9.
As usually in the frontier literature, the error term ψft is decomposed into two
components: (i) the white noise component, vft, which capture the effects of all
exogenous shocks to the production process and (ii) the inefficiency term, uft,
representing firm- and time-specific cost inefficiency. The statistical noise term, vft,
makes the frontier cost function VC(.) stochastic and can take both positive and negative
8

9

A preliminary analysis in this direction, based on average cost and productivity indicators, is provided
in Fraquelli et al. (2001a).
Although it is assumed that there are T time periods for which observations are available for at least
one of the F firms involved, it is not necessary that all the firms are observed for all T periods in an
unbalanced panel data specification of the econometric model.

10