**3. Methodology**

The stochastic frontier (SF) approach for estimating technical efficiency is based on the idea that an economic unit may operate below its production potential or frontier due to low performance, errors, and some uncontrollable factors. A study of the frontier approach started with Farrell [23] who suggested that efficiency could be measured by comparing realized or actual output with the maximum or potential attainable output. Other than comparing output, we can also compare the actual input use with the minimum required input use. The two methods are called output oriented and input oriented approaches. Their aim is maximizing output with available inputs and technology or minimizing costs for given outputs and technology. The former is more adaptable for industry/firm data and the latter for services data. The empirical part of this study is based on three different models— [8], the true fixed-effects model [9,10], and four error components of the SF model with determinants of inefficiency (following [24] and [25]).

Most theoretical stochastic frontier production functions have not explicitly formulated a model for technical inefficiency effects in terms of appropriate determinants. By using panel data, one can remove the limitations of depending on the distributional assumption of noise and inefficiency components and observing each unit at several different points of time. However, the extended dimension in time adds to the complexity, as it requires the modeler to take into account some heterogeneity effects that may exist beyond what is possible to control using a cross-sectional approach, which lumps individual effects with random errors. This can be achieved by introducing an 'individual (unobservable) effect,' say, α, that is time-invariant but individual-specific. The limitation of such a model is eliminated when using panel data methods.

We can examine whether inefficiency has been persistent over time or whether a unit's inefficiency is time-varying since we have information about units over time. One component of inefficiency may have been persistent over time while another may have varied over time. Regarding time-invariant individual effects, we also need to consider whether an individual effect represents persistent inefficiency or persistent unobserved heterogeneity, as well as whether individual effects are fixed parameters or are they realizations of a random variable [26]. Thus, it is important that policies promote an efficient use of resources that are scarce, and it can serve as an effective policy tool by separating unobserved heterogeneity and inefficiency components.

This study outlines three panel data models which differ in terms of the underlying assumptions made for the temporal behavior of the inefficiency components. All the models treat inefficiency as being individual-specific. This is consistent with the notion of measuring the efficiency of decision-making units. Model 1 allows for inefficiency to be both individual-specific and time-varying and explains the determinants of inefficiency. Model 2 separates inefficiency effects from unobserved individual non-inefficiency heterogeneity effects. Model 3 separates persistent inefficiency and time-varying inefficiency from unobservable individual heterogeneity effects. Thus, the three models are complementary and jointly provide information on province heterogeneity, province inefficiency, the random error term, and the variations in inefficiency in energy use. The three models are now outlined.
