Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency

This paper analyzes the productivity of farms across 370 municipalities in the Center-West region of Brazil. A stochastic frontier model with a latent spatial structure is proposed to account for possible unknown geographical variation of the outputs. The paper compares versions of the model that include the latent spatial effect in the mean of output or as a variable that conditions the distribution of inefficiency, include or not observed municipal variables, and specify independent normal or conditional autoregressive priors for the spatial effects. The Bayesian paradigm is used to estimate the proposed models. As the resultant posterior distributions do not have a closed form, stochastic simulation techniques are used to obtain samples from them. Two model comparison criteria provide support for including the latent spatial effects, even after considering covariates at the municipal level. Models that ignore the latent spatial effects produce significantly different rankings of inefficiencies across agents.