1272 Spatial Analysis of Economic Convergence
income levels between states from the same region are smaller (and the discordance
in rank changes over time greater) than is the case for states from different regions.
This form of spatial dependence weakens over time as the spatial rank mobility
statistic lessens in absolute value.
27.3.2 Exploratory space-time data analysis
The previous sets of ESDA methods can be seen as attempts to extend a-spatial
methods of exploratory convergence analysis to include a spatial component. A
second set of methods have been developed that extend exploratory spatial data
methods to the dynamic context.
27.3.2.1 Spatial transitions
Since full estimation of a square spatial Markov transition matrix is likely to be
infeasible in most data contexts, alternative approaches towards analyzing the
movements of the income level of an economy and that of its neighbors have been
suggested. These are based on the notion of a local indicator of spatial association
(LISA) statistic originally developed by Anselin (1995).
The LISA statistics can be visualized in a Moran scatterplot (Anselin, 1996),
depicted in the right-hand panel of Figure 27.2. In the first quadrant are
located relatively high-income economies that are neighbored by high-income
economies reflected in the spatial lag (HH). Quadrant two contains lower-income
(L) economies with wealthier neighbors (LH), while quadrant three might be con-
sidered spatial poverty zones since it contains poor economies with poor neighbors.
Finally, quadrant four has the “diamonds in the rough” economies – those with
high incomes and poor neighbors. These statistics have been extensively used to
analyze spatial distributions in several samples of European regions (López-Bazo
et al., 1999; Le Gallo and Ertur, 2003; Ertur and Koch, 2007) or other sub-sets of
regions (Ying, 2000; Mossiet al., 2004; Patacchini and Rice, 2007).
The spatial concentration of the low values is seen in the map on the left where
the user has selected a sub-set of the Southern states. In response, the positions
of those states in the scatterplot are indicated by solid black circles. The degree of
spatial association for this local cluster (dashed line) is contrasted against the global
pattern (solid line). The user can move the lasso around on the map to explore
the stability of the spatial clustering over regions of the map. Alternatively, the
scatterplot could serve as the origin view and the lasso moved over regions of the
plot to reveal the location of selected observations in geographical space, as shown
in Figure 27.3.
A number of summary measures of distributional mobility have appeared in the
literature. One such measure, due to Shorrocks (1978), is based on the estimates of
the classic Markov transition matrix:
SI=
k−∑
ipii
k− 1, (27.23)which is bounded on the interval[0,k/(k− 1 )], with the lower bound indicating a
complete lack of mobility and the upper bound maximum mobility.^6 This captures