y W y X N i i i i i ~ ( , ) 0 2

y is the dependent variable and X is a vector containing all the independent

variables and is a normally distributed error term. is called the autoregressive

parameter (even though there is no time dimensions in the equation) and W is the

weighting matrix that uses the location parameters to assign weights to counties next to

each other. This weighting matrix usually contains first-order contiguity relations

(counties only sharing a common border), although it can also contain other distance

functions. However, in this analysis I use only first-order contiguity relationship among

counties.^{7 }W is a nxn matrix (for the n number of counties), in which the rows contain

zeros if the counties are not next to each other, and one otherwise. Thus, the main

diagonal has zeros (implying that a county is not its’ own neighbor). Matlab identifies the

neighboring counties based on the values I assign to W using the latitude and longitude

data for each county.^{8 }

Spatial dependence could also arise if a shock to an omitted variable in the model

affects the dependent variable, in which case SEM can be used. The SEM takes the

following form:

y X u u Wu

N ~ ( , ) 0 2

7 Using different distance functions requires complicated spatial specifications, which is beyond the scope of this study.

8 Matlab uses the ‘Delaunay’ triangularization process, which identifies neighboring counties based on a set of lines connecting the points nearest to each other. The latitude and longitude values serve as the vertices of the triangles.

17