The stochastic frontier model with heterogeneous technical efficiency_x000D_ explained by exogenous variables is augmented with a sparse spatial autoregressive component for a cross-section data, and a spatial-temporal component for a panel data. An_x000D_ estimation procedure that takes advantage of the additivity of the model is proposed, computational advantages over simultaneous maximum likelihood estimation of all parameters is exhibited. The technical efficiency estimates are comparable to existing_x000D_ models and estimation procedures based on maximum likelihood methods. A spatial or spatial-temporal component can improve estimates of technical efficiency in a production frontier that is usually biased downwards.