On the Distributional Assumptions in the StoNED Model

Abstract

In a recent paper Johnson and Kuosmanen (2011) propose a new, semi-parametric, general cost-frontier model, the stochastic nonparametric envelopment of data (StoNED). The model is semi-parametric in the sense that the cost function is estimated nonparametrically, while the functional form of the distribution for the error term is parametrically specified. A common assumption for this distribution is that it is a convolution of a truncated normal distribution, representing inefficiency, and a normal distribution, representing noise. This parametric form has the drawback that a negative skewness implies a negative expected inefficiency. It can thus never capture a negatively skewed distribution with a positive expectation. In this paper we investigate this assumption and its consequences for an analysis of inefficiency. Furthermore, we propose a solution to the problem and investigate its performance by means of a Monte Carlo simulation.