Parametric versus Non-Parametric Models in Stochastic Frontier Analysis: A Theoretical Review

Abstract

The stochastic frontier analysis has focused on parametric models in which, the parametric functional form of the frontier function is specified, and the method involved estimating the parametric of the frontier function as well as the technical inefficiency component. This approach imposed specific distributional assumptions on the error component and applied the method of Maximum Likelihood Estimation (MLE). The content of this paper is mainly a theoretical review of the literature to extend the frontier of knowledge, particularly on parametric and non-parametric models. In this paper, we first examined the contents of the parametric model followed by the distributional-free approach which does not depend on any specific assumptions. Following the parametric half-normal model, it is observed that, the inefficiency effect, which is treated as a non-negative truncated zero-mean normal distribution and folded zero-mean normal distribution provided similar results and can be used in applied production economics with no theoretical problem. In what follows with the free approach, the Corrected Ordinary Least Squares (OLS), which used residuals provided straightforward inefficiency effect estimates from a one-sided error term compared with the traditional parametric model, and hence its flexibility did not require any underlying distribution of the dataset to be defined in advance. Given the OLS estimates, the non-parametric model can adapt to the distribution of data (data-driven) of the 196 daily farmers, making it particularly useful, when there is little or no prior information about the distribution of data which may not fit well with the parametric models. Given the sample moment-based statistic for the skewness test (skewness test on OLS residuals), if the estimated result follows the expected sign, then the rejection of the null hypothesis provided evidence for the existence of the one-sided error. To help shift the stochastic frontier analysis to more robustness owing to outliers and non-normal error distribution, researchers are encouraged to adopt the non-parametric model, as it is not constrained by a specific functional form of the error term, but determined by the data itself, thus allowing for a more data-driven modelling approach, compared with the parametric model which may not offer the best fit to the data.