X hits on this document

# Poverty, Income Inequality and Economic Growth in U.S. Counties: - page 17 / 33

122 views

0 shares

17 / 33

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 Xu 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

 Document views 122 Page views 122 Page last viewed Fri Jan 20 18:29:22 UTC 2017 Pages 33 Paragraphs 888 Words 9215