Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency
In this paper, we analyze the productivity of farms across n = 370 municipalities located in the Center-West region of Brazil. We propose a stochastic frontier model with a latent spatial structure to account for possible unknown geographical variation of the outputs. This spatial component is included in the one-sided disturbance term. We explore two different distributions for this term, the exponential and the truncated normal. We use the Bayesian paradigm to fit the proposed models. We also compare between an independent normal prior and a conditional autoregressive prior for these spatial effects. The inference procedure takes explicit account of the uncertainty when considering these spatial effects. As the resultant posterior distribution does not have a closed form, we make use of stochastic simulation techniques to obtain samples from it. Two different model comparison criteria provide support for the importance of including these latent spatial effects, even after considering covariates at the municipal level. Neste texto, analisamos a produtividade de estabelecimentos agrícolas localizados em 370 municípios da região Centro-Oeste do Brasil. Propomos um modelo de fronteira estocástica de produção com estrutura espacial latente que representa os determinantes não-observados da ineficiência da produtividade da agropecuária. Esse componente espacial condiciona a distribuição da ineficiência. Usamos o paradigma bayesiano para estimar os modelos propostos. Foram exploradas duas distribuições diferentes para este termo, a normal truncada e a exponencial, e utilizamos duas especificações para a variável latente, suposta independente entre os municípios, ou dependente dos municípios vizinhos segundo um modelo auto-regressivo espacial. O procedimento de inferência considera explicitamente todas as incertezas quando incluímos o termo espacial. Como a distribuição a posteriori não tem uma expressão analítica, utilizamos técnicas estocásticas da simulação para obter a
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