Calculating Efficiency for Spatial Autoregressive Stochastic Frontier Model

When there are efficiency spillovers, we can use a spatial autoregressive stochastic frontier model to estimate total (spillover-corrected) efficiencies. Glass et al. (2016) ( Journal of Econometrics ) provide a formula for total efficiency in this context, which is an approximation. We provide the exact formula for the spillover-corrected efficiency. Moreover, we derive total, direct, and indirect marginal effects of environmental variables on spillover-corrected efficiency