| The notion of efficiency in the production process has concerned economists and firms’ managers through years. In microeconomic theory, producers were treated as successful optimizers but several works showed that, despite their attempts, they did not always achieve this objective. If one considers the production possibility curve as a “frontier” of each producer's maximum effectiveness, it is easy to understand the need for further research on this frontier. Any production process below this curve, that is, a deviation from the optimum, could be considered as the standard against which a producer's efficiency (or better “inefficiency”) is measured.
The possibility of obtaining producer-specific estimates of efficiency has greatly enhanced the appeal of Stochastic Frontier (SF) models. Since the appearance of Stochastic Frontier models it has been widely accepted that these models provide a number of advantages over non-frontier and parametric models. These models allow for technical inefficiency, but they also acknowledge the fact that random shocks outside the control of producers can affect output.
We consider the SF production model introduced by Aigner, Lovell, and Schmidt (ALS) (1977) and Meeusen and van den Broeck (MB) (1977) Yi=Xi*β+εi, where εi=vi-ui is the stochastic error of the model. The symmetric term of the composed error vi represents random disturbances, while the non-negative asymmetric term ui represents disturbances due to technical efficiency (or better inefficiency). Because of this composed error term, εi, the stochastic frontier models are also referred to as “composed error” models.
Technical efficiency is defined as TEi = exp(ui), and the point of the model is to estimate ui or TEi. Thus it is necessary for distribution assumptions to be made regarding the composed error term εi. Because in most of the cases the distribution assumption of symmetric error term vi coincides with the Normal distribution, the identification of the model relies heavily on the distribution of ui. Concerning the distributional assumptions of one sided error term ui, MB (1977) assigned an exponential distribution to ui, Battese and Corra (1977) assigned a half normal distribution, and ALS (1977) considered both distributions for ui.
To this extent several tests regarding the model's error distribution have been proposed in the literature, such as LM tests, the information matrix test of White, Pearson's chi-squared test and the Kolmogorov-Smirnov (KS) test.
In this research we will test the aforementioned parametric assumptions which constitute an integral part of modelling in the context of SF models. Specifically, we will develop testing procedures for the distribution of ui. |
