Goodness of fit tests in spatial autoregressive stochastic frontier models

This article mainly considers goodness of fit tests for the inefficiency in spatial autoregressive stochastic frontier (SARSF) models by utilizing the characteristic function of the centralized composite error term. As a prerequisite of the tests, we propose easy-to-compute moment estimators for distributional parameters of such a term, showing the consistency based on spatial near-epoch dependent properties. Meanwhile, the asymptotic distribution of the estimators is derived by generalizing the central limit theorem (CLT) in Kelejian and Prucha (2001) from linear-quadratic forms to polynomial-trigonometric forms. Then, the cosine and sine tests, being simple to implement in SARSF analysis, are established to explore the distributional structure of the centered error. With the help of the generalized CLT, both trigonometry statistics are proved to follow an asymptotically chi-square distribution. Moreover, Monte Carlo simulation is conducted to investigate the finite sample performance of the moment estimators and trigonometry tests. Finally, in the efficiency analysis of Chinese A-shared listed companies in 2005, our tests reject the half-normal and exponential distributions and fail to reject the gamma one. This conforms to our subsequent calculation that the efficiency estimates based on the gamma model potentially lie within a more realistic range, but the other two models lead to significant distortions in efficiency estimates.