The use of panel data, repeated observations on each production unit, considerably enrich the econometric analysis of stochastic production frontier models and have several potential advantages over simple cross-section data. First, it offers a more efficient econometric estimation of the production frontier model. Second, it provides consistent estimators of firm inefficiency, as long as the time dimension of the data set is sufficiently large. Third, it removes the necessity to make specific distributional assumptions regarding the one-sided error term associated with technical inefficiencies in the sample. Fourth, it does not require inefficiency to be independent of the regressors included in the production frontier.[iv] Fifth, it permits the simultaneous identification of both technical change and time-varying technical inefficiency, establishing thus a clear link between technical change, technical efficiency and productivity.
Since the very first detailed discussion of efficiency measurement within the context of panel data (i.e., Pitt and Lee, 1981; Schmidt and Sickles, 1984), several alternative models have been progressively developed extending the existing methodological framework to account for different theoretical issues in empirical frontier modeling. These can broadly be divided into three groups. Within the first group, models may be classified according to the method of estimation. In this case, we may distinguish between those making use of specific distributional assumptions regarding the one-sided error term, such as maximum likelihood (ML) estimators, and those that do not such as the traditional panel data model techniques (i.e. fixed or random effects and instrumental variables estimator). Within both groups, models may be classified according to type of panel data used, i.e., balanced, unbalanced, rotating. Lastly, within the third group, production frontier models may be classified according to the temporal pattern of technical inefficiency, which can be time-invariant or time-variant.
In empirical applications there has been no clear preference for one of the several alternative model specifications since no one has an absolute advantage over the others. Moreover, the choice among them is further complicated by the fact that, in general, they are not nested to each other which implies that there are no statistical criteria to discriminate among them. Hence, the choice for the appropriate model of pooling is based on a priori grounds related with the particular objectives of each empirical application or with data availability as well as the underlying hypotheses for each production frontier model. However, empirical evidence suggests that the economic optima, including efficiency, are sensitive to the choice of the estimation technique. It is evident, therefore, that all these necessitate considering the comparative performance of these models in real world applications.
In the empirical literature on frontier modeling with panel data, the issues of model specification and selection of estimation technique have not been explored in detail. The objective of this paper is to contribute in the existing literature providing a more comprehensive comparison of the most widely applied model specifications used to measure output-oriented time-varying technical inefficiency with panel data. The paper explores the sensitivity of obtained technical inefficiency estimates to the choice of the model of pooling, while maintaining an identical data set and retaining the same assumptions about the underlying production technology. In particular ten of the most widely applied frontier models are estimated and compared using a balanced panel data set from the Greek agricultural sector consisting of 100 olive-growing farms observed over the 1987-93 period.