Likelihood functions of spatial autoregressive models with normal but heteroskedastic disturbances have been already derived [Anselin (1988, ch.6)]. But there is no implementation for maximum likelihood estimation of these likelihood functions in general (heteroskedastic disturbances) cases....

In proxy vector autoregressive models, the structural shocks of interest are identified by an instrument. Although heteroskedasticity is occasionally allowed for in inference, it is typically taken for granted that the impact effects of the structural shocks are time-invariant despite the change...