Heteroskedasticity and autocorrelation consistent estimator

[Melisandre]

Good afternoon,

I have quite basic question however I would like to be sure about this.

I need to estimate a spatial econometric model with possible spatially autocorrelated and heteroscedastic error terms. Both spatial autocorrelation and heteroscedasticity is of an unknown form. If I use a heteroskedasticity and autocorrelation consistent (HAC) estimator of the variance-covariance (VC) matrix for a spatial econometric model, do I still need to test the residuals for spatial autocorrelation and heteroscedasticity using for example Moran's tests? (in particular I am using the HAC estimator based on Kelejian, H.H. and Prucha, I.R. (2007) HAC estimation in a spatial framework, Journal of Econometrics, 140, pages 131–154).

What if the residuals are spatially autocorrelated and (or) heteroscedastic? Can I still use this estimator with HAC estimate of VC matrix or shall I go for different estimator or specification? Do these estimates have required properties (are they unbiased, consistent, efficient) even if the residuals are autocorrelated according to Morans test?

I would be grateful for any reaction.