Can someone explain how to solve the following problem in a spatial auoregressive model. The form is:

enter image description here

where p is the SAR coefficient and W is a distance-weighting matrix with a 0-diagonal.

The world only consists of Poland, Germany, and Austria. The weighting matrix is such that a country with a land border receives a w=1 and 0 otherwise. So the Matrix looks as follows:

enter image description here

p = 0.5 and there is a shock to FDI in Poland of size 10. How much would FDI increase in Germany? I cannot make a hold how to make use of W. Thanks!


The weight matrix that you have illustrated needs to be row-normalized, i.e. the row-sum must be one in order for the rho parameter to have the proper parameter bounds, i.e. between (-1/lambda,1), where lambda is the smallest real eigenvalue of the W matrix.

When the weight matrix is row normalized and there is a change in the dependent variable, the shock in that other country will be an average of the surrounding values.

I'm not sure if this helps but a good resource is the LeSage and Pace text, Introduction to Spatial Econometrics, CRC Press 2009.

You can also visit www.spatial-econometrics.com to download free PDF books on spatial econometrics as well.

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