Palgrave Handbook of Econometrics: Applied Econometrics

1268 Spatial Analysis of Economic Convergence

Table 27.3 US state incomes: spatial Markov transition matrix

t+ 1

t 0.661 0.884 1.031 1.309 1.934

Lag class 0.661 0.661 0.985 0.015 0.000 0.000 0.000

0.884 0.032 0.871 0.097 0.000 0.000

1.031 0.000 0.222 0.778 0.000 0.000

1.309 0.000 0.000 0.000 0.000 0.000

1.934 0.000 0.000 0.000 0.000 0.000

Lag class 0.884 0.661 0.842 0.158 0.000 0.000 0.000

0.884 0.022 0.940 0.038 0.000 0.000

1.031 0.000 0.046 0.881 0.073 0.000

1.309 0.000 0.000 0.321 0.679 0.000

1.934 0.000 0.000 0.000 0.000 1.000

Lag class 1.031 0.661 0.857 0.143 0.000 0.000 0.000

0.884 0.007 0.916 0.077 0.000 0.000

1.031 0.000 0.056 0.873 0.071 0.000

1.309 0.000 0.000 0.060 0.936 0.004

1.934 0.000 0.000 0.000 0.231 0.769

Lag class 1.309 0.661 0.000 0.000 0.000 0.000 0.000

0.884 0.000 0.795 0.192 0.014 0.000

1.031 0.000 0.050 0.870 0.080 0.000

1.309 0.000 0.002 0.059 0.904 0.035

1.934 0.000 0.000 0.000 0.137 0.863

Lag class 1.934 0.661 0.000 0.000 0.000 0.000 0.000

0.884 0.000 0.000 0.000 0.000 0.000

1.031 0.000 0.000 0.889 0.111 0.000

1.309 0.000 0.000 0.024 0.929 0.048

1.934 0.000 0.000 0.000 0.048 0.952

classes are used to estimate transition matrices for subsets of the states at different
points in time. The sub-setting is based on the spatial lag of the incomes. For exam-
ple, focusing on the first matrix, we see that poor states that were surrounded by
poor states (i.e., those with incomes less than 66% of the national average) moved
out of the bottom class with a probability of 0.015. However, if this is contrasted
with other states in the lower class, but those who had neighbors that were slightly
better off (i.e., in the second class), the probability of moving out of the bottom
class now jumps to 0.158. The impact of the spatial context can also be seen for
the higher-income states, as the wealthiest states, when surrounded by similarly
wealthy states, have a probability of remaining in the upper class of 0.952. How-
ever, when a wealthy state is surrounded by states with average incomes in the
next lower class, the probability of remaining in the upper class of the distribution
drops to 0.863.
The spatial Markov approach has been applied by Le Gallo (2004) to a sample of
European regions and by Hammond (2004) to US labor markets. This approach has