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:
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
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
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:
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
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