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Chapter4. Typology of theSubjects
of the RussianFederation

4.1. Building economic indicators

As it was mentioned above, the majorinconvenience in the use of cluster analysis is that appearance of new datarequires a recalculation of the total>1 used as teaching samples fordiscriminative analysis. In this study, as discriminant functions we useindicators of the qualities under research (the methods to built theseindicators were described in section 2.3). An advantage of this choice ofdiscriminant functions is the fact that indicators are substantive – the higher is the value of anindicator, the better is the situation of the region in terms of the analyzedquality. Shortcomings of this approach include the ambiguity of thecorrespondence between the results of cluster analysis and the>

The indicators built in the course of thestudy may be used similarly to discriminant functions. In case there isobtained additional information (for instance, for regions, where suchinformation had been unavailable, or for some other year) it is not necessaryto carry out a new clusterization of regions. It suffices to calculate thevalues of the indicator basing on the data related to each new unit and toclassify the unit into the appropriate >

In order to test the proposed methods to buildthe indicators we will build indicators measuring three properties of Russianregions: interregional differentiation of living standards, investment activityin different regions, and potential of economic growth. Each property shall becharacterized by three indicators.

Interregional differentiation of livingstandards (IDS):

  • The share of population with incomes below the subsistence level(SPSL);
  • Ratio between per capita incomes and the subsistence level (PCISL);
  • Ratio between per capita expenditures and the subsistence level(PCESL).
  • Investment activity (IA):
  • The share of investment in fixed assets in the GRP (SI);
  • Relative rates of growth in investment in fixed assets as comparedto the all-Russian average level (RGI);
  • Ratio between foreign investment and GRP (FI).
  • Economic potential (EP):
  • Ratio between the rates of growth in GRP and GDP (GRP);
  • Unemployment level (as at the end of the year; in per cent ofeconomically active population (UL);
  • The share of fuel industries in the regional volume of industrialoutput (FI).

As it was mentioned above, the indicatorscharacterizing the properties under observation are not homogenous in terms ofdimensionality and the scale of values. Therefore, in this section we will alsonormalize indicators and build indicators of these properties in accordancewith adjusted indicators.

4.1.1. Indicator of interregionaldifferentiation of living standards

The information collected across the regionsof Russia (excluding the Chechen Republic, autonomous entities and data fromthe Ingush Republic for years 1995 and 1996) in 1995 through 1999 was used asinitial data.

Therefore, we have 383 objects, which interms of the degree of interregional differentiation of living standards arecharacterized by three indicators, i.e. N = 383, n = 3.Let us once present the sequence of actions in the course of buildingindicators in accordance with the algorithm described above. The whole set ofobjects shall be > and. As the indicatorof preference relation across the set of clusters two functions shall bereviewed:

and.

1, if i = 1 2, if i = 1

2, if i = 2 1, if i = 2

Let us introduce for each object X(j) variables

and

.

In other words, in the first case we assumethat the value of variable is equal to 1 if the j-th object belongs to the first cluster,and 2 in case it belongs to the second cluster. In the second case we, to thecontrary, assume that the value of variable is equal to1 in case the j-th objectbelongs to the second>

Let us build regressions of variables SPSL,PCISL, and PCESL on variables y(1) and y(2)respectively. The result is: y(1) = 0,7245 + 0,0180SPSL + 0,0015PCISL +0,0005PCESL and y(2) = 2,2755 - 0,0181SPSL - 0,0016PCISL - 0,0005PCESL. In both cases the value ofF-statistics is equal to299,7141, while the values of t-statistics are 14,2172 (44,6499), 23,8291, 0,5552, 0,1935.Multiple coefficient of correlation R is equal to 0,8387 (adjusted R2 = 0,7011).Let us assume that clusters rank in accordance with function f2. Thenapproximated value of the index of interregional differentiation of livingstandards shall be calculated as

φ2 = - 3,0789 +1,0224 SPSL + 0,0878PCISL + 0,0281PCESL.

Let us to>,, and.It turns out that cluster is divided in two: and, while. In accordance with the algorithm,let us review as the indicator of a linear preference relationship within a setof clusters two functions:

and.

In this case variables and look as follows:

.

In other words, let us assume that the valueof variable is equal to 1, in case the j-th object belongs to the first cluster,3 in case it belongs to the second cluster, and 2 in case it belongs to thethird cluster. The value of variable is equal to 2 incase the j-th object belongsto the first cluster, 3 in case it belongs to the second cluster, and 1 in caseit belongs to the third cluster.

As above, let us build two regressions ofvariables SPSL, PCISL, and PCESL on variables y(1) andy(2) respectively. The result is: y(1) = 0,2001 +0,0384SPSL + 0,0073PCISL + 0,0072PCESL and y(2) = 1,9735 +0,0158SPSL - 0,0026PCISL- 0,0058PCESL. In the firstcase the value of F-statistics is equal to 297,3517, in the second case it is equal to317.4733; while the values of t-statistics in the first (second) case are 1,9595 (37,6677),25,2798 (20,2598), 1,2978 (-0,9094), 1,4093 (-2,1822). Multiple coefficient ofcorrelation R is equal to0,8377 (adjusted R2 = 0,6995) and 0.8458 (0,7131),respectively. Therefore, in this case the clusters rank in accordance withfunction. Then approximated value of the index ofinterregional differentiation of living standards shall be calculated as

φ3 = 33,5549 + 0,6667 SPSL - 0,1103PCISL - 0,2433PCESL;

Acting similarly (using the algorithmdescribed above) let us build the function of the index of interregionaldifferentiation of living standards meeting the>

φ4 = 12,3332 + 0,8587SPSL + 0,2656PCISL - 0,4122PCESL;

φ5 = 27,9509 + 0,7264SPSL - 0,2945PCISL -0,0047PCESL;

φ6 = 22,4781 + 0,7783SPSL - 0,1542PCISL -0,0916PCESL;

φ7 = 23,3005 + 0,7711SPSL - 0,2044PCISL -0,0494PCESL;

φ8 = 23,8965 + 0,7681SPSL - 0,3538PCISL + 0,0941PCESL;

φ9 = 20,1597 + 0,8053SPSL - 0,3431PCISL + 0,1198PCESL;

φ10 = 25,6281 + 0,7516SPSL - 0,3951PCISL + 0,1185PCESL;

φ11 = 19,9712 + 0,8056SPSL - 0,2654PCISL + 0,0440PCESL;

φ12 = 22,8666 + 0,7774SPSL - 0,3042PCISL + 0,0545PCESL;

φ13 = 19,7484 + 0,8069SPSL - 0,2178PCISL -0,0015PCESL;

φ14 = 21,5683 + 0,7895SPSL - 0,2574PCISL + 0,0204PCESL;

φ15 = 22,9486 + 0,7765SPSL - 0,3014PCISL + 0,0510PCESL;

φ16 = 23,8546 + 0,7678SPSL - 0,3185PCISL + 0,0592PCESL;

φ17 = 27,2100 + 0,7351SPSL - 0,3594PCISL + 0,0674PCESL;

φ18 = 25,0285 + 0,7563SPSL - 0,3291PCISL + 0,0584PCESL;

φ19 = 22,5783 + 0,7799SPSL - 0,2858PCISL + 0,0389PCESL;

φ20 = 21,7283 + 0,7880SPSL - 0,2635PCISL + 0,0249PCESL;

φ21 = 19,2000 + 0,8124SPSL - 0,2212PCISL + 0,0072PCESL;

φ22 = 17,2662 + 0,8337SPSL - 0,1828PCISL -0,0087PCESL;

φ23 = 17,0732 + 0,8336SPSL - 0,2160PCISL + 0,0228PCESL;

φ24 = 18,2074 + 0,8228SPSL - 0,2453PCISL + 0,0411PCESL;

φ25 = 20,1069 + 0,8047SPSL - 0,2866PCISL + 0,0638PCESL;

For statistical characteristics of respectiveregressions see Table 4.1.

Table 4.1.

Number of clusters

Multiple R

Adjusted R2

F-statistics

t-statistics

1

SPSL

PCISL

PCESL

2

0,8387

0,7011

299,7141

14,2172

23,8291

0,5552

0,1935

3

0,8458

0,7131

317,4733

37,6677

20,2598

-0,9094

-2,1822

4

0,9152

0,8363

651,4862

27,0305

33,2517

2,7918

-4,7107

5

0,9395

0,8817

950,1661

30,7197

35,5755

-3,9140

-0,0673

6

0,9616

0,9240

1549,5493

32,4956

47,4104

-2,5487

-1,6475

7

0,9038

0,8155

563,7977

19,1145

28,3399

-2,0387

-0,5363

8

0,8668

0,7494

381,6798

17,0449

22,8779

-2,8603

0,8276

9

0,8909

0,7920

485,8912

15,1417

26,2962

-3,0411

1,1546

10

0,8751

0,7639

413,0471

16,8547

23,4831

-3,3500

1,0927

11

0,9076

0,8224

590,7623

15,8493

29,2656

-2,6169

0,4714

12

0,8835

0,7788

449,2029

13,9736

25,0802

-2,6631

0,5190

13

0,9032

0,8143

559,1951

13,5608

28,6444

-2,0982

-0,0156

14

0,9001

0,8087

539,1986

12,7070

27,7844

-2,4590

0,2123

15

0,8779

0,7689

424,7212

11,6373

24,3849

-2,5690

0,4725

16

0,8718

0,7582

400,2099

10,9437

23,5236

-2,6480

0,5353

17

0,8715

0,7576

398,8886

13,2761

22,9778

-3,0486

0,6219

18

0,8841

0,7799

452,2930

12,5298

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