Modeling dependence between error components of the stochastic frontier model using copula: Application to intercrop coffee production in Northern Thailand

In the standard stochastic frontier model, the two-sided error term V and the one-sided technical inefficiency error term W are assumed to be independent. In this paper, we relax this assumption by modeling the dependence between V and W using copulas. Nine copula families are considered and their parameters are estimated using maximum simulated likelihood. The best model is then selected using the AIC or BIC criteria. This methodology was applied to coffee production data from Northern Thailand. For these data, the best model was the one based on the Clayton copula. The main finding of this study is that the dependence between V and W is significant and cannot be ignored. In particular, the standard stochastic frontier model with independence assumption grossly overestimated the technical efficiency of coffee production. These results call for a reappraisal of previous production efficiency studies using the SFM with independence assumption, which may occasionally lead to overoptimistic conclusions.