When there are efficiency spillovers, we can use a spatial autoregressive stochastic frontier model to estimate total (spillover-corrected) efficiencies. Glass et al. (2016) 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.
Kutlu, Levent. "Calculating efficiency for spatial autoregressive stochastic frontier model." Economics Letters 225 (2023): 111043. https://doi.org/10.1016/j.econlet.2023.111043