Palgrave Handbook of Econometrics: Applied Econometrics

Sergio J. Rey and Julie Le Gallo 1275

class mobility within the distribution and, as such, it is subject to the criticisms
associated with the discretization of the income distribution to define the classes.
Chief among these is that moves that cross a class boundary are the only kind
recorded, while other moves of the same magnitude but remaining within the class
are not recorded. Since it is based on the classic Markov approach, the measure also
ignores any spatial dependence. However, one could construct a test statistic based
on values for this index taken from the specific conditional matrices of the spatial
Markov approach to explore whether mobility was affected by spatial context.
To incorporate a spatial dimension to the mobility analysis, Rey (2001) has sug-
gested analyzing the movement of a LISA statistic over a given time interval and
noting whether a particular LISA statistic remains in the same quadrant or tran-
sitions to a different quadrant. In any period there are four possible states for a
LISA – HH, LH, LL, HL, so between any two periods there are 16 different spatial
transitions that are possible. These can be summarized in a LISA Markov transition
matrix, as is done for the US case in Figure 27.4.
Applying the summary mobility index (27.23) to the traditional Markov tran-
sition matrix generates a value of 0.130, which is also found for the case of the
LISA Markov transitions, suggesting similar rates of mobility for the spatial versus
a-spatial transitions. However, a closer inspection of the two tables reveals some
subtle but important differences. In the classic Markov model, the probability of
remaining in an extreme (poorest or richest) class is lower than the probability of
remaining in the intermediate (2nd or 4th quintile) classes, reflecting a tendency
away from polarization in the extreme tails of the distribution. By contrast, for the

HH 0.929 0.037 0.004
LH 0.079 0.859 0.060
LL 0.005 0.020 0.947
HL 0.053 0.002 0.070

t HH LH LL

t + 1

1.602

Spatial Lag per 1929

1.337

1.073

0.809

0.544

0.441 0.799 1.157

per 1929

1.515 1.873

Figure 27.4 LISA Markov transitions