Hey everyone,

I'm puzzled about a recent result, and I'm wondering if anyone can help explain it.

I am currently estimating a growth model with many controls by OLS. Looking at the residual tests I find that the Breusch-Pagan test points the presence of heteroskedasticity.
Moreover, looking for spatial dependence in the residuals using the Moran's I test I find that with 3 definitions of spatial weight matrix I cannot reject
the null hp of no spatial dependence while with 3 different spatial weight matrices I can.

Here the results in details:

Breush-Pagan Test:
BP=66.3478, p-value=0

Moran'I test on regression residuals:

1) W1 is binary matrix with a cut-off=660.8 km (row-standardized):
     Observed Moran's I=-0.02938, p-value=/0.57547/

2) W2 is the first-order contiguity matrix(row-standardized):  
     Observed Moran's I=0.1389, p-value=_0.00021_

3)  W3 is the second-order contiguity matrix(row-standardized):  
     Observed Moran's I=0.0694 , p-value=_0.00724_

4)  W4 is the matrix s.t each region has at least one neighbour- max distance 1124.710 km -(row-standardized):  
     Observed Moran's I=-0.01286, p-value=/0.91883/

5)  W5 is the matrix where weights are 1/d_ij^2  with no cut-off(row-standardized):  
     Observed Moran's I=0.03239, p-value=_0.00350_

6)  W6 is the matrix where weights are 1/exp(2*d_ij)  with no cut-off(row-standardized):  
     Observed Moran's I=0.06847, p-value=/0.15462/


Therefore, my questions are:
- since I find evidence of heteroskedasticity shouldn't I look for aheteroskedasticity-robust version of the Moran's I? If yes, is there the possibility
   to implement it with the function "lm.morantest"?
- what should I conclude from such different results using different spatial weight matrices? It seems that the lower the number of neighbours is the higher is the
   probability of finding spatial effects. In this latter case how can I decide the "right" matrix? By looking at the AIC in the maximum likelihood?

Thank you very much!

Angela Parenti






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