A spatial autoregressive stochastic frontier model for panel data incorporating a model of technical inefficiency

By integrating Battese and Coelli’s (1995) model and the spatial autoregressive model (SAR), a spatial autoregressive stochastic frontier model for panel data is developed. The main feature of this frontier model is a spatial lag term of explained variables and the joint structure of a production possibility frontier with a model of technical inefficiency. The model addresses both spatial dependence and heteroskedastic technical inefficiency. This study applies maximum likelihood methods considering the endogenous spatial lag term. The proposed model nests several existing models. Further, an empirical analysis using data on the Japanese manufacturing industry is conducted and the existing models are tested against the proposed model, which is found to be statistically supported. The findings suggest that estimates in the existing spatial and non-spatial models may exhibit bias because of lack of determinants of technical inefficiency, as well as a spatial lag. This bias also affects the technical efficiency score and its ranking.