Maximum likelihood estimation of a stochastic frontier model with residual covariance

In theoretical literature on productivity, the disturbance terms of the stochastic frontier model are assumed to be independent random variables. In this paper, we consider a stochastic production frontier model with residuals that are both spatially and time-wise correlated. We introduce generalizations of the Maximum Likelihood Estimation procedure suggested in Cliff and Ord (1973) and Kapoor (2003). We assume the usual error component specification, but allow for possible correlation between individual specific errors components. The model combines specifications usually considered in the spatial literature with those in the error components literature. Our specifications are such that the model’s disturbances are potentially spatially correlated due to geographical or economic activity. For instance, for agricultural farmers, spatial correlations can represent productivity shock spillovers, based on geographical proximity and weather. These spillovers effect estimation of efficiency.