Estimating efficiency in the presence of extreme outliers: A logistic-half normal stochastic frontier model with application to highway maintenance costs in England

In Stochastic Frontier Analysis the presence of outliers in the data, which can often be safely ignored in other forms of linear modelling, has potentially serious consequences in that it may lead to implausibly large variation in efficiency predictions when based on the conditional mean. This motivates the development of alternative stochastic frontier specifications which are appropriate when the two-sided error has heavy tails. Several existing proposals to this effect have proceeded by specifying thick tailed distributions for both error components in order to arrive at a closed form log-likelihood. In contrast, we use simulation-based methods to pair the canonical inefficiency distributions (in this example half-normal) with a logistically distributed noise term. We apply this model to estimate cost frontiers for highways authorities in England, and compare results obtained from the conventional normal-half normal stochastic frontier model. We show that the conditional mean yields less extreme inefficiency predictions for large residuals relative to the use of the normal distribution for noise.