The C(alpha)-type gradient test for spatial dependence in spatial autoregressive models

This paper proposes the C(alpha)-type test in the GMM framework to test the possible presence of spatial correlation through the spatial lag in the spatial autoregressive (SAR) model. This test statistics is especially useful for the SAR model with disturbances under unknown heteroskedasticity. We provide analytical justification of its asymptotic distribution and also investigate its performance via various Monte Carlo simulations. We show that the C(alpha) test is computationally simple and has satisfactory finite sample performance.