<p>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.</p>

<p>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.</p>

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

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

CC BY-SA 4.0
2018-06-07T19:49:52.757Z
2018-06-07T19:49:52.757Z
Donald Lacombe
<p>Can someone explain how to solve the following problem in a spatial auoregressive model. 
The form is:</p>

<p><a href="https://i.sstatic.net/6EYwg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6EYwg.png" alt="enter image description here"></a></p>

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

<p>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:</p>

<p><a href="https://i.sstatic.net/cMTPs.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cMTPs.png" alt="enter image description here"></a></p>

<p>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!</p>

<autoregressive>
How do I apply the distance-weighting matrix in a spatial autoregressive model
Joe Stevens
# How do I apply the distance-weighting matrix in a spatial autoregressive model

(Asked by: username_0 on 2018-03-09)

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

[![enter image description here](https://i.sstatic.net/6EYwg.png)](https://i.sstatic.net/6EYwg.png)

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](https://i.sstatic.net/cMTPs.png)](https://i.sstatic.net/cMTPs.png)

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!

**Tags:** autoregressive


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## 1 answers

### Answer by username_1 on 2018-06-07. Score: 2

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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