SFA, TFA and a new thick frontier: graphical and analytical comparisons

This article compares OLS, the normal-half normal stochastic frontier approach (SFA) and the thick frontier approach (TFA) to an alternative thick frontier approach based on a mixture approach. Unlike the TFA approach, the new approach developed here uses all of the data, does not require grouping of the data into an arbitary number of size categories, does not require an arbitrarily chosen fraction (usually the lowest quartile) of lowest average cost firms upon which to base the frontier. The new thick frontier requires the estimation of only one more parameter than the SFA model, and is flexible enough to describe skewness in the data of almost any type. This article presents comparisons of the empirical relationships between these methods using a multiproduct cost function and data on US savings and loans in 1988. The new thick frontier method produces a much thinner 'thick' frontier characterizing a much greater fraction of the data than the old TFA approach.