Study the paper by Golpher , A. B., and P. R. Voss. How to Interpret the Coefficients of Spatial Models:
Spillovers, Direct and Indirect Effects. Spatial Demography (2016) 4:175-205.
Note: In this lab the terminology of the Golpher’s paper is used.
Assuming that we just deal with a simple bivariate base SLM model with with spatial observations and .
[a] How to interpret the entries in the derivatives matrix below with regards to changes in the
independent variable at location ?

[b] Explain, based on the derivative matrix , what the direct, indirect and total effects are as well as how
to interpret these effects?

[c] Why does the spatial error model SEM have only direct effect predictions ?

[d] The spatial error model SEM can be rewritten as (see page 179)

Argue why the estimates and of ordinary least squares and this general least squares model are the
same. Thus, the OLS estimates are unbiased, i.e., and .

[e] Discuss for Table 2 and the models SAR & SAC with and at how and why the spillover effects
distribute around the central region 7 and the peripheral region 3.
You may also use for your argument the property (see page 180). Note that consists of 2-steps links and
predominately of 3-steps links.