Is the choice of (t−T) in Battese and Coelli (1992) type stochastic frontier models innocuous? Observations and generalisations

In this paper we consider the sensitivity of functional form in the popular panel data stochastic frontier model proposed by Battese and Battese and Coelli (BC, 1992). We demonstrate that adopting the (t−T) efficiency functional form used by BC can, in a model which allows for firm specific patterns of temporal inefficiency variation (as developed by Cuesta, 2000), results in counter intuitive ‘falling-off’ of efficient firms in the final sample year. This motivates us to look at a more general parameterisation. First we show that the choice of a function within the first order exponential class is only an issue for the Cuesta model; in the BC model, parameter estimates and inefficiency estimates are invariant to the form. Second we apply the more general model to a railways dataset and find that this model does not seem to suffer from the most efficient firms falling off the frontier. We discuss how to test restrictions in order to make the model more parsimonious, thus preserving the attractive property of the Cuesta model, namely the ability to test for firm specific patterns of inefficiency variation.