Skewness-based test diagnosis of technical inefficiency in spatial autoregressive stochastic frontier models

In the Spatial Autoregressive (SAR) Stochastic Frontier (SF) model, the inefficiency term, which distinguishes it from the SAR model, can capture the effects of technical inefficiency. To determine whether inefficiency significantly exists in the cross-sectional SARSF model, this paper proposes a skewness-based test. This test does not rely on the normality assumption for the disturbances and allows inefficiency to follow an unknown one-sided distribution. We establish the asymptotic theory of the test statistic under spatial near-epoch dependent properties. Furthermore, we extend this test to the panel SARSF data model, accounting for both individual and time fixed-effects. Additionally, Monte Carlo simulations demonstrate the robustness of our test against non-normal disturbances and its satisfactory performance with different one-sided distributions for inefficiency. Finally, we provide an empirical application using data from 137 dairy farms in Northern Spain to illustrate the presence of technical inefficiency in production according to our test.