Stochastic frontier analysis by means of maximum likelihood and the method of moments

The stochastic frontier analysis (Aigner et al., 1977, Meeusen and van de Broeck, 1977)is widely used to estimate individual efficiency scores. The basic idea lies in the introductionof an additive error term consisting of a noise and an inefficiency term. Most oftenthe assumption of a half-normal distributed inefficiency term is applied, but other distributionsare also discussed in relevant literature. The natural estimation method seems tobe Maximum Likelihood (ML) estimation because of the parametric assumptions. But simulationresults obtained for the half normal model indicate that a method of momentsapproach (MOM) (Olson et al., 1980) is superior for small and medium sized samples incombination with inefficiency not strongly dominating noise (Coelli, 1995). In this paperwe provide detailed simulation results comparing the two estimation approaches for boththe half-normal and the exponential approach to inefficiency.Based on the simulation results we obtain decision rules for the choice of the superior estimationapproach. Both estimation methods, ML and MOM, are applied to a sample ofGerman commercial banks based on the Bankscope database for estimation of cost efficiencyscores.[...]