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Chapter3. Multidimensionalclassification of regions of the Russian Federation

As noted above, at the first stage we will beconsidering multidimensional (three-dimensional) >

In this work we prefer the analysis thetotality of regional data accumulated over several years to the analysis ofannual distributions, what permits to detect more general types of regionaleconomic behavior in 1995 through 1999, including the dynamics of observedcharacteristics across years. The analysis of the results of the clusteranalysis for individual years may play the auxiliary role and be used toexplain the inclusion of a region into a certain >

3.1. Classification of regions by theirpopulation’s
livingstandards

The distinctive feature of the Russian economyover the period of market reforms is an extremely high level of interregionaldifferentiation of living standards1. In 1995 through 1997, the percapita household incomes in the most reach and poorest regions differed byseveral times. Although this inequality has somewhat smoothened recently, thedifferentiation of living standards across certain Russia’s regions remains very high incomparison with developed countries and economies in transition. Unfortunately,it is difficult to analyze this situation due to incomplete official statisticsrelated to various aspects of living standards. Although the results of surveyspermit to study this problem in more detail, these data are not alwayscollected on the regular basis and therefore do not present uninterruptedseries of observations. In the framework of>

As it was stated in the introduction, weassume that inter-regional living standards differentiation can becharacterized by thee indicators:

  1. The share of the population with their income belowsubsistence minimum, as%
  2. The ratio of average income per capita to subsistence minimum, as%; and
  3. The ratio of average spending per capita to subsistence minimum, as%.

Let us conduct clusterization ofRussia’s regions (77regions) in the respective three-dimensional space by the noted indicatorsusing the data over 1995-99 by seven cluster analysis methods using seven different distances.

The analysis of the whole integrity of theregions through all the noted years by all the methods and distances allowsselection of method and distance that ensure the most even>

In order to choose the formally bestclassification method, let us determine the enthropy obtained in the course ofclassification by each method at different distances. The best>

Original data.Considering all the methods and distances until the 364th iteration, the distance betweenthe united clusters does not exceed 10% of maximal one on average, while untilthe 340th – 5%. While neglecting clearlyoutstanding results of Average Linkage (Within Groups) method with distances,as follows: Euclidean Distance, Chebychev Distance,City Block Distance, and Minkowski Distance, then the distance between unitedclusters does not exceed on average 5% of maximal one until the 367th iteration, and 10%- until the375th.

The stop of clusterization methods after the367th iteration allowsclassification of Russian regions over the 5 years considered into 16 clusters.The results of such a clusterization for the >

Maximal entropy (3,243 bit) matches theclassification built using Ward Linkage with the use of Squared Euclidean Distance. Hence, thisparticular method of >

The comparison of the results of thisclassification related to 1995 with the>

Table 3.1.1. The number of regions inclusters over different years
under theclusterization according to Ward Linkage based
onthe data over 1995-99

Cluster

1995

1996

1997

1998

1999

1

25

20

14

14

16

2

14

11

9

18

8

3

9

13

9

10

4

4

1

1

2

1

1

5

8

6

4

8

20

6

6

11

22

11

3

7

1

0

0

1

0

8

3

1

0

2

8

9

2

4

4

3

3

10

2

3

2

4

8

11

2

1

1

2

4

12

3

1

5

1

1

13

0

1

1

0

0

14

0

2

3

1

0

15

0

1

1

1

0

16

0

0

0

0

1

Total

76

76

77

77

77

Adjusted data. Theindices characterizing inter-regional differentiation of thepopulation’s livingstandards used for clusterization are non-homogenous. That is why let us adjustthem by the way of linear transformation so all variables acquire values withinthe interval [0, 100] (0 is the minimal value, 100 is the maximal value of eachvariable) and built >

Distances between united clusters grow moreevenly: 5% of maximal distance on average matches >

Table 3.1.2. The number of regions inclusters over different
years with clusterizationaccording to Ward Linkage
based on adjusted dataover 1995-99

Cluster

1995

1996

1997

1998

1999

1

14

22

9

8

0

2

12

17

2

0

0

3

1

1

1

1

1

4

11

7

8

11

8

5

6

3

3

6

7

6

9

4

3

5

1

7

3

2

16

14

13

8

1

1

1

1

1

9

6

5

19

12

11

10

2

4

2

3

2

11

3

3

1

3

2

12

2

4

7

6

6

13

2

2

2

3

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