### A Monte Carlo Analysis for Stochastic Distance Function Frontier

#### Abstract

Being different from a Data Envelopment Analysis (DEA) whose results can be decomposed, the parametric stochastic frontier method can not deal with multiple outputs and multiple inputs easily and directly. Although stochastic cost frontier and stochastic revenue frontier can potentially be used to describe a multi-output, multi-input production, these functions only allow the possibility of specifying a multi-product technology when price information is available and some required behavioral assumptions are satisfied. An alternative for cost or revenue function called distance functions was developed by Shephard (1953). Fare et al. (1993) first used parametric linear programming (PLP) approach to estimate a translog distance function. In 1996, Tim Coelli and Sergio Perelman (1996) applied this approach (called stochastic distance function frontier) to adjust the function form of stochastic frontier and make it suitable for multi-product analysis. Since then, the stochastic distance function frontier has begun to be widely used in particular applications. But, in all these studies, the stochastic distance function frontier approach required changing the function form and thus it made the influence of function assumption on results stronger. Some econometricians proposed that the distance function approach in handling multi-product stochastic frontier might introduce regressor endogeneity and induce estimator inconsistency in estimation. It is also proposed that Multi-output stochastic distance functions suffer from input-output separability and linear homogeneity in outputs. However, we can not observe any studies on Monte Carlo test of stochastic distance function frontier. The principle purpose of this study is to contribute to the methodology discussion of stochastic distance function frontier using Monte Carlo analysis for multi-product efficiency measurement. Thus, a Monte Carlo analysis for stochastic distance function frontier model was developed to test the asymptotic properties. The technology for the framework of stochastic distance function, used to overcome the criticisms related to the stochastic frontier approach, is specified as a translog function. Then, the basic method to estimate the stochastic frontier is provided and the maximum likelihood function is also given. In the Monte Carlo experiment, 1000 replications are set for analysis. The results show that, except for the scenario with equal outputs, stochastic distance function frontier will yield biased estimators even with large sample size. The 2-output model will give better estimators than 3-output model. An increasing sample size will improve the relative performance of ML estimations for stochastic distance function frontier. Therefore, the Monte Carlo analysis indicates the result that the stochastic distance function frontier is probably biased for multi-output production.

#### Keywords

Stochastic distance function frontier; Monte Carlo analysis; Bias; Estimator

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Online ISSN: 2029-5839