Asymptotic properties of a spatial autoregressive stochastic frontier model

This paper considers asymptotic properties of a spatial autoregressive stochastic frontier model. Relying on the asymptotic theory for nonlinear spatial NED processes, we prove the consistency and asymptotic distribution of the maximum likelihood estimator under regularity conditions. When inefficiency exists, all parameter estimators have the $$\sqrt{n}$$ n -rate of convergence and are asymptotically normal. However, when there is no inefficiency, only some parameter estimators have the $$\sqrt{n}$$ n -rate of convergence, and the rest have slower convergence rates. We also investigate a corrected two stage least squares estimator that is computationally simple, and derive the asymptotic distributions of the score and likelihood ratio test statistics that test for the existence of inefficiency.