The GMM estimation of semiparametric spatial stochastic frontier models

In this paper, we consider the estimation of semiparametric spatial stochastic frontier (SF) models, in which the spatial dependence is modeled by adding the spatially lagged dependent variable as an additional independent variable (following the convention of spatial autoregressive models) and specifying various spatial structures on the inefficiency and/or idiosyncratic error. Thus, the proposed models are inclusive compared with most previous studies. Efficiency modeling in the SF literature has not given enough attention to the spatial interaction of inefficiency, primarily because the estimation of inefficiency in spatial models is challenging using the conventional maximum likelihood method. Therefore, we propose a two-step estimation procedure for our spatial frontier models under the framework of the generalized method of moments (GMM). The proposed method is easy to implement. Further, Monte Carlo Simulations show that our GMM estimators have good finite-sample performance. We apply our GMM estimators to examine the technical efficiency of 41 European countries and the effects of spatial dependence on production (GDP).