Semiparametric estimation of spatial autoregressive smooth-coefficient panel stochastic frontier models

This paper considers the estimation of a spatial autoregressive stochastic frontier model, where the production frontier coefficients, as well as the spatial parameter, are allowed to depend on a set of observed environmental factors. The inefficiency term is multiplicatively separable into a scaling function of either the same or totally different set of environmental factors and a standard half-normal random variable. A two-step semiparametric procedure is developed using a combination of local GMM and maximum likelihood approaches. We also derive the estimators of direct and indirect average partial effects and predictors of technical efficiency. We work out the asymptotic theory for the proposed second step estimator and propose a test of the relevance of the environmental factors. A special case of the model where the spatial parameter is a non-zero constant is also considered. The finite sample behavior of the proposed estimator and test are examined using Monte Carlo simulations. An empirical application to the Chinese chemical industry is included to illustrate the usefulness of our proposed models and methods.