Of Mathematics And Sciences 2015, Yogyakarta State University, 17-19 May 2015
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autocorrelation, spatial structure, or spatial interaction Daniaty, 2012. These three elements are described in a matrix of size N x N. Matrix elements are the weights of the binary
interactions of two regions. 2.1.5. Spatial autocorrelation
Goodchild 1986 stated that the spatial autocorrelation focuses on the level of regional association on the surface of the earth that have similar patterns with objects that are
neighboring. SI 2013 defines the spatial autocorrelation as a representation of the regional association in general. Spatial autocorrelation is due to the interaction among the regions. This
interaction states that the value of the observation in a region affected by the value of the observations in the surrounding regions, so that the interaction is a form of interdependence
among regions.
2.2. Related Research
Research that discussed regional inequality have been done before. Research by Rey and Smith 2013 contained the derivation of Gini coefficient into a spatial Gini coefficient
considering neighborhood. The results of this research are a decomposition of Gini coefficient into two components – neighbor and non-neighbor components; and a spatial Gini test for
spatial autocorrelation. Rey and Janikas 2006 have developed an application for Spatial Gini, named STARS: Space-Time Analysis of Regional System. Devianingrum 2014 developed
application for calculating spatial Gini coefficient and testing a spatial autocorrelation. The spatial application has been tested to real data of per capita expenditure in Indonesia from 2008
until 2012. The conclusion was that there was a significant income inequality in Indonesia when viewed by the group of economic corridors. In this case, the group of economic corridors Java
provided the largest contribution to the inequality in Indonesia. 2.3. Framework
Framework of this research can be seen in Fig. 1.
III. Methodology
The methodology consists of data sources and tools, and research methods.
3.1. Data Source and Tools
Trial data used in this research is from Statistics Indonesia abbreviated as SI, based on the National Socioeconomic Survey SUSENAS 2007-2012. In Indonesia, data of income per
capita are not available, so that the data used are data of household expenditure which were obtained from Susenas. Data of household expenditure were processed, resulting in data of
average expenditure per capita of a regencycity, here in after referred to as the data of regional
Figure 1 . Framework of research
Problem: Java has a very high income
inequality compared to 5 other groups of economic corridor
Spatial Gini Decomposition
Application of spatial Gini for inequality and
spatial autocorrelation Implementation at the data
of regional expenditure of provinces in Java 2007 -
2012 Output:
- The level of regional
expenditure inequality of each province on the
island of Java -
The relationship between the regional expenditure
inequality of
each province and its spatial
autocorrelation regional
expenditure
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expenditure. We use this regional expenditure variable as an approach to the average income of a regencycity. Application used to perform calculations is WIRES 2.0.
3.2. Research Method
The method used in this research is based on a method developed by Rey and Smith 2013. To test the spatial autocorrelation, we use Monte-Carlo simulation. The Gini based test for
autocorrelation is defined as:
where: is the value for variable x observed at region i = 1, 2, …, n.
̅
= 1
∑ .
,
is an element of a binary spatial weights matrix expressing the neighbor relationship between region i and j.
=
∑ ∑
,
̅
+
∑ ∑
,
̅
. SG can be interpreted as the share of overall inequality that is associated with non-neighbor pair
of locations. Inference on this statistics relies on random spatial permutations of the data. More specifically, the value of 1 is first obtained from the original data. Next the values are spatially
permuted to simulate spatial randomness and the test statistic is calculated for this new map pattern. Additional permutations are carried out and the original value of the statistic is then
compared to the distribution of values obtained from the randomly permuted data. The pseudo p-value for the observed test statistic is then defined as:
where C is the number of the M = 499 permutation samples that generated SG values that were as extreme as the observed SG value for the original data. The definition of extreme depends on
whether one is conducting a one or two-tailed test. In the former a directional test holds in which case the alternative hypothesis is that there is positive negative autocorrelation and
values of the test statistic that exceed are less than the observed value from the original example contribute to C. Rey and Smith 2012
The algorithm for calculating the spatial Gini coefficient and for testing spatial autocorrelation, can be seen in the flowchart below
DATA START
END Cal cula te w eigh t
Gr ou p? Re calculat e w eigh t f or Gini Spat i al
Cal cula te Gin i Spa tia l Com po nent 1
Cal culat e p se udo p-value Cal cula te Gin i Spa tia l Com po nent 2
[Yes] [No]
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IV. Results and Discussion 4.1. Expenditure Inequalities
