The paper is devoted to the assessment of living standards of population. Countries with emerging markets are characterized by significant transformations of the public sector in the context of European integration processes, which requires the adaptation of models for assessing the living standards of the population, allowing to analyze the effectiveness of public administration and ongoing reforms. The complex of models for assessing the living standards of the population as an assessment of the effectiveness of public administration is also interesting for countries with developed markets. The advantages and disadvantages of existing methods of predictive analytics for the study of standards of living are shown. It should be noted that the universal method of analysis and assessment of living standards contains the set of intangible components. Therefore, it is advisable to make a proposal on the need to improve a complex of models for assessing and analyzing living standards. The data set is built using of such key indicators that objectively reflect the real situation in EU and Ukraine. The proposed complex of models for assessing the living rating of the country has been provided by combination of multivariate exploratory analysis methods and predictive analysis methods (cluster and discriminant methods, the method of canonical correlations). The adaptation of models for assessing the quality of life of the population involves solving the problem of assessing the informativeness of indicators, the formation of a system of diagnostic indicators, the construction of an integral assessment and its scaling. The clustering and classification methods can be effectively used to solve these problems, which is shown in the paper. The provided complex of models can be used to make optimal decisions in developing of social and economic development strategy, transforming the public sector of government, smoothing the asymmetry of territorial development.
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In the context of the implemented processes of globalization and European integration of Ukraine, the assessment of the living standards of the population acquires special significance. It is classified as a key concept in defining the policy of socio-economic development of the country. Overcoming Ukraine's lag behind the European Union dictates the need for consistent implementation of the principles of a social market economy, characterized by developed market relations, high economic development, political democracy, guaranteed access to education and health care, and a well-developed social protection system.
The current economic situation in Ukraine confirms that the measures the government takes to improve the lives of its citizens (increase of minimum wage, living wage, etc.) are insufficient. To ensure a significant increase in the efficiency of all sectors of the economy, the reform of all spheres of public life in accordance with European standards should be completed. The standard of living of the population of Ukraine during the market reforms and by the influence of external and internal destabilizing factors has decreased, and it does not meet international standards. The most important direction of socio-economic transformations should be the achievement of sustainable positive dynamics of welfare of the population on the basis of increasing effective demand, in particular, increasing the wages of the working population.
The relevance of this work lies in the need to substantiate and improve models for assessing and analyzing the living standards of the population of Ukraine in terms of mathematical modelling and methods of predictive analytics. The need for this is due to the development of crisis phenomena and the decline of socio-economic development of Ukraine in the context of European integration processes, the existence of significant drawbacks in approaches to assessing the level of social development and analysis of living standards. This need to improve the existing tools and statistical processing of information to determine the living standards of the population of Ukraine is realized through the creation of a set of economic and mathematical models that can position the country on international indices of living standards and predict living standards for the future. 2
The conducted analysis of modern scientific literature has shown that many approaches
to determining the living standards of the population exist in world practice. A part of
scientific works [
A large of modern research [
Alhambra-Borrás, T., Doñate-Martínez, A. [
Thus, the methods described above do not allow creating a unified assessment system.
But, achieving a high standard of living, similar to the level in European countries is possible for Ukraine, subject to the study and adaptation of European social standards in their practice.
In international practice, the index of social (human) development was proposed by
the UN Research Institute for Social Development. It indicate the level of the country's
achievements in the most important socio-economic spheres and accumulates the
following indicators: life expectancy; literacy and learning coverage; GDP per capita at
currency parities, the ratio of prices to the "consumer basket", consisting of several
hundred goods and services. In 2010, the method of calculating the HDI was
significantly adjusted: the indicators of education and income were modified, the procedure
for their aggregation changed [
The standard of living is also determined by gross national product (GNP), using
indicators of purchasing power parity (PPS) per capita. There is also The Social
Progress Index, a combined measure of the international research project “The Social
Progress Imperative”, which measures the achievements of countries around the world in
terms of social well-being and social progress. Developed in 2013 under the direction
of Michael E. Porter [
The Global Innovation Index is a global study and the accompanying ranking of the
world's countries in terms of the level of innovation development [
The World Happiness Report is an international research project by The Earth
Institute, which measures the happiness of the world's population as part of the UN
Sustainable Development Solutions Network in order to show the achievements of countries
and individual regions in terms of their ability to provide their residents with a happy
life [
Among the attempts to comprehensively assess and analyze the level and quality of
life of the population the index of physical quality of life developed by D. Morris can
be named [
Quite common is the calculation of a generalized indicator in the form of a weighted average of partial indicators of living standards (groups of indicators). The weights are expert estimates, and the sum of the weights is 1. An example of such an indicator is the conjugation indicator. Its components are the degree of supply of consumer goods, the level of crime, the degree of dissatisfaction of the population with a set of unresolved social and political, and economic environmental problems.
Another way to reduce partial living standards to a single scale is to rank countries for each indicator. However, this method also has disadvantages: firstly, it is assumed that the comparison of objects on all indicators is in relation to a sample; secondly, that all indicators appear to be equivalent. Generalizations of the most famous techniques, their advantages and disadvantages are presented in table 1.
4 The method takes into account only the economic aspects of life, which determine the standard of living, which is only one of the criteria of quality of life Social indicators are not taken into account. The question of what meaning is attached to the concept of "physical quality of life" remains open.
Subjective indicators of quality of life are not taken into account, the social aspect is represented only by the level of education, there are no such sections as the degree of development of science, social tension, the state of the environment, etc.
large set of indicators, as well as the fact that the political and spiritual spheres are not taken into account
Analysis of foreign methods of assessing living standards in relation to the structure and indicators of living standards, found that this issue remains controversial. The following conclusions can be drawn:
foreign scientists are actively working in the development of methods for assessing the level and quality of life; the world community pays more and more attention to the living standards of the population every year; achieving and maintaining its high quality is the goal of all developed countries; existing methods differ significantly in the number and composition of indicators (the number of indicators varies from three to several dozen, and the composition includes indicators of economic, social and physiological components of quality of life);
most of the considered methods evaluate only objective indicators of quality of life and do not take into account subjective ones; all the considered methods allow to estimate only separate components of quality of life of the population and cannot claim universality. There is no universal method of analysis and assessment of living standards.
In our opinion, it is necessary to improve the assessment models, which include such assessment indicators that will more objectively reflect the living standards of the population. 3
The purpose of the study is to develop a set of models for assessing and analyzing the living standards of the population of Ukraine based on the use of tools of economic and mathematical modelling: canonical correlation analysis, cluster and discriminant analysis. This allows to assess Ukraine's position in the European space and to forecast the living standards of the population in the future. For a qualitative analysis of the living standards of the population of Ukraine and its assessment in the European space, as well as to solve these problems, the following conceptual scheme of modelling the living standards of the population is proposed (Fig. 1).
Let's consider in more detail the main stages of the constructed model, the methods applied at the corresponding stage and the selected indicators on the basis of which calculation was carried out. The first stage of the study is to form arrays of source data. The main method for information processing is the method of synthesis and analysis of information, based on the analysis of the categorical basis and analysis of modern approaches to assessing living standards.
The array of initial data was formed from such international indices as the ranking of countries in the world by happiness, the global index of innovation, the index of social progress, the index of human development, the global charity index, the index of global competitiveness. All the above indices define the standard of living as a complex set of characteristics, which includes indicators: a person's ability to work and live in normal conditions, to have a decent level of education, to receive high quality health care, to have access to cultural values, to live in a safe society.
The next stage of the study reveals the process of building models of living standards analysis based on methods of predictive analytics and data science. Therefore, in the second stage, to determine the significant groups of indicators that have an impact on the quality of life, a model of assessing the relationship between sets of groups of indicators of economic development and a group of international indices of socio-moral direction. The method of canonical analysis is used for this purpose.
The concept of methods of canonical analysis is based on the nature of multiple
correlation, which, according to V. Hotteling, is the maximum correlation between the
chosen random result change and the linear function of the set of explanatory variables
[
At the 3rd stage of the research, models of formation of homogeneous groups of
countries are built according to the formed groups of indicators of living standards
assessment. For this purpose, agglomerative and iterative methods of cluster analysis are
used [
To eliminate the problem of heterogeneity of observation groups, z-transformation (standardization) of variable values was performed. Standardization reduces the values of all converted variables to a single range of values, namely the average of each is reduced to 0, and the mean deviation – to 1. Then all observations vary in the range of standard deviation from - 3 to +3.
At the 4th stage of the research a model of identification and forecasting of the living standard of the population of the European Union member states is built by methods of discriminant analysis, which allowed to determine the situation of our country and
Assessment of the degree of similarity between observations Hierarchical clustering and formation of the distribution hypothesis
further way of approaching one of the groups. Schematically, the algorithm for constructing the model is presented in Fig. 3.
Formation of the specification of the discriminant function Assessment of the quality and statistical significance of the discriminant model Positioning of observation classes in the space of discriminant roots and assessment of the country's forecast cluster for the quality of life of the population
In the case of one variable, the F-criterion is used as the final criterion of significance of whether the variable separates the two sets or not. When using discriminant analysis for multidimensional variables, the procedure is identical to the procedure of multiple analysis of variance. At each step, all variables are viewed and the one that contributes most to the difference between the populations is located. This variable must be included in the model in the current step, and there is a transition to the next step.
Thus, the proposed set of models of assessment and analysis of living standards based on methods of predictive analysis and analysis of multidimensional objects allows to comprehensively analyze the impact of key indicators on the quality of life, to assess the country's membership in one of the clusters and to find the forecast distribution and membership of certain clusters.
In accordance with the considered concept of the study, let’s consider the
implementation of models. According to stage 1 of the study, living standards were analyzed, which
can be divided into two sets: indices of the social and moral component (left set): Social
Progress Index (SPI) [
Estimation of mean (median) and scattering (quartiles and scope) for variables allowed to establish the symmetry of variable distribution. The results of building a model for assessing the relationship of two sets of indicators by canonical analysis are presented in Fig. 4.
Since the number of canonical roots is equal to the number of variables in the smaller set (2), both canonical roots explain 100% of the variance (variability) from the left set and 87.81% from the right. From Fig. 4 it follows that the canonical correlation R = 0.9039, that is the correlation between the first weighted sums corresponding to the first pair of canonical variables (root 1), is strong. Its value indicates a strong relationship between the indices of the social and moral component (left set) and the indices of the economic component (right set). This means that the growth of indices of countries by social and moral components leads to an increase in the rating of the country by indicators of economic development, and vice versa - the growth of the rating of the country by indicators of economic development causes the growth of indices of countries with social and moral orientation. High value SPI = 40,3476 and level of significance = 0,00, which is much less than 0,05, demonstrate the significance of R. The second row of the table shows the percentage of explained variances from the left and right sets of variables.
The value of the total redundancy of 69.25% means that the variables of the right set explain on average 69.25% of the variability of the variables of the left set. changes in the left set explain an average of 68.99% of the variability of variables in the right set. Thus, the left set is more redundant for a given right than the right for a given left set. Indicators of redundancy additionally confirm the strong relationship between indicators of social and moral orientation and economic orientation, while indicators of economic orientation are more informative than indicators of social and moral orientation.
The canonical value of R corresponds only to the first root - the most significant correlation. The obtained results according to chi-square statistics for canonical roots showed that only the first root is statistically significant and should be investigated in more detail in Fig. 5.
p
All correlations between the right variables are quite high, the highest correlation is observed between GCI (Global Competitiveness Index) and GII (Global Innovation Index), the lowest - between HDI (Human Development Index) and GCI (Global Competitiveness Index). The correlation between the variables of the left set is also positive, quite high, greater than 0.5 (Fig. 6).
N=28 SPI WGI
SPI 1.0 0.69603
WGI 0.69603 1.0
N=28 WHR GII HDI GCI
The analysis of the relationship between the variables of the left and right sets is of particular interest, as it explains the structure of the relationship between the international indices of the level of development of the countries under analysis. The strong correlation between social and moral indices and economic development indices is explained by the strong correlations between such indicators of economic development countries as: GII (Global Innovation Index), HDI (Human Development Index) and SPI (Social Progress Index) of a moral aspect of the development level of the countries. The WGI (World Charity Index) also has close to strong correlations with economic development indices, but these relationships are less pronounced than the relationship between SPI and economic development indices. It should be noted that the GCI (Global Competitiveness Index) has the least impact on the ranking of countries (Fig. 7). Fig. 7. Correlations between variables of the left and right sets
The largest factor loads (correlations) of the left and right sets have with the canonical variables that correspond to the Root 1 (Fig. 8). This fact underlines once again the strong correlation between the indicators of social and moral indices and indices taking into account the economic development of the country.
GCI
Root 1 Root 2 -0.898585 0.182226 -0.972681 -0.026579 -0.928119 -0.246937 -0.871654 -0.207150
SPI WGI
Factor structure, left set Root 1 Root 2 -0.94754 -0.31963 -0.88902 0.45787
Analysis of canonical roots showed the following. Canonical Root 1 explains on average about 84% of the variance from the indicators of the economic component of the level of development and about 84% of the variance from the indicators of the sociomoral component of the level of development, that is it explains 84% of the variability of the rating of countries considering socio-moral aspect. In turn, the canonical Root 2 explains, respectively, about 15% and about 3% of the variability of the economic component of the level of development and the socio-moral component of the level of development (Fig. 9).
Root 1 Root 2
Variance Extracted (Proportions), left set Variance Extracted 0.844095 0.155905
right set Variance Extracted 0.843687 0.034450
According to the values of the first canonical root, the indicators of the right set indices of the economic aspect, explain about 69% of the variability in the indicators of the left set - the indices of the socio-moral aspect; the indicators of the left set also explain about 84% of the variability in the indicators of the right set. Thus, the indicators of both sets are almost identical in informativeness to predict each other.
Next, the coefficients of regression equations were calculated, in which the responses are canonical variables that correspond to both canonical roots, and the predicates are the indicators of the left and right sets, respectively (Fig. 10).
Fig. 10. Table of canonical weight coefficients of sets
Let us write the regression equations of the canonical variables of the left and right sets that correspond to the root 1: root 1right = − 0,25 – 0,72 – 0,28
+ 0,21 root 1left = −0,64 – 0,45
Let us write the regression equations of the canonical variables of the left and right sets that correspond to the root 2: root 2right = 1,81 + 1,19
− 1,64 root 2left = − 1,24 – 1,46 + 1,32
In terms of the value and sign of the coefficients (canonical weights) for variables in the regression equations, for the ranking of countries by social aspect, the largest contribution to Root 1left corresponds to SPI, slightly less than WGI. For the ranking of countries by economic aspect, the largest contribution to Root 1right corresponds to the GII, the smallest – GCI. Regression equations for each root represent the weighted sum. To calculate the canonical values (values of canonical variables) for each country, it is necessary to substitute standardized (normalized) values of the country's indicators in the linear regression models corresponding to each set.
The analysis of the scattering cloud of observations in the space of canonical roots has a shape characteristic of linear dependence. The correlation between the values of the canonical variables of the left (indicators of socio-moral orientation) and the right set (economic orientation) is equal to 0.9038. The horizontal axis (abscissa) corresponds to the indicators of the indices of the socio-moral aspect, and the vertical axis (ordinate) - to the indicators of the indices of the economic aspect (Fig. 11).
Canonical Variables: Var. 1 (left set) by 1 (right set) -2,0-2,0 -1,5 -1,0 -0,5 0,0
0,5 Left set 1,0 1,5 2,0
2,5
The scattering diagram of the values of the canonical variables corresponding to the Root 2 has a cloud shape that is less characteristic of the linear relationship. This is due to the fact that the correlation between the values of the canonical variables of the left and right sets takes a small value equal to 0.1366.
35 30 25 ce tan20 s i eD ikag15 Ln 10 5
Thus, the analysis of the model of the relationship between the sets of indicators for assessing the quality of life of the population revealed the presence of strong relationships between all components of the sets. The results of the modelling, namely the construction of a scattering diagram of canonical values, gave the opportunity for further detailed analysis - the development of a model for the formation of clusters of EU member states according to international indices of living standards.
Hierarchical (tree-like) methods of cluster analysis were used to determine the current standard of living of the population of Ukraine in comparison with the EU countries. In the work to determine the number of clusters of regions of the EU countries a dendrogram of classification was constructed according to the method of Ward, depending on the values of international iTnreedDiiacgraemsforo28fCalsievsing standards (Fig. 12).
Ward`s method
Euclidean distances 0 C_2C2_1C9_2C6_2C5_1C5_8C_C6_1C2_C5_2C4_2C1_1C7_1C6_1C3_C4_2C3_C3_2C7_C9_2C8_1C4_2C0_1C1_C7_1C0_C2_1C8_1
Dendrogram analysis allows to recognize three groups (clusters) of homogeneous states in the observed data set. Based on the data of the dendrogram, the hypothesis of the existence of three clusters, which are divided into EU countries depending on the values of international indices of living standards is accepted in advance. An iterative method of clustering of k-means was used to divide the regions of the country into three clusters depending on the value of the components of the living standards of the population. The graph of average values for clusters of countries is given in Fig.13.
Plot of Means for Each Cluster 2,0 1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5 -2,0
WWHHR2R016 SSPIP2I016 GGII I2I0V1a6riabHleDHsI 2D01I6GCI 20G1C6-2I017WGWI20G17I
Fig. 13. Graph the means of each cluster
Cluster 1 Cluster 2 Cluster 3
Cluster 1 Cluster2 Cluster3
As can be seen from Fig. 13, clusters differ in all respects and you can see clearly defined boundaries between groups of objects. This corresponds to the initial assumption of the division of countries by living standards into three groups: countries with very high living standards; countries with a high standard of living; countries with an average standard of living. Thus, with the help of the obtained results of the classification model the countries are distributed by clusters (Table 3).
The results of analysis of variance: evaluation of the F-criterion, the values of intergroup and intragroup variances, showed the statistical significance of all selected indicators for clustering at 99 % (Fig. 14).
HDI GCI WGI
Between
Group Variation 19.50747 21.08796 23.44965 20.10858 23.15670 17.43817 df 2 2 2 2 2 2
Thus, the cluster No. 1 includes 11 countries with the highest ratings according to international indices of living standards compared to other countries. Therefore, it can be described as a cluster with countries with a very high level of development. Countries with a high level of development belong to the cluster № 2, namely 8 countries have average values of indicators of the level of development of regions in all studied areas. Paying attention to the fact that according to the Index of Social Progress, countries are closer to the countries of the first cluster, and according to the Index of Global Competitiveness - on the contrary, they fall to the indicators of the countries of the third cluster. The member states of the European Union - Bulgaria, Croatia, Greece, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia were included in the cluster No. 3. These are the countries with an average level of development, which have the lowest level of population development among the countries of the European Union. Particular attention should be paid to the rather low indicators of the Social Progress Index and the Global Innovation Index, which indicate significant problems in the social and educational aspects.
We consider the next stage of modelling the living standards of the population - the implementation of the model of identification and forecasting the living standards of the population. The task is to use the International Indices for Assessing the Living Standards of the European Union (the Social Progress Index, the Global Innovation Index, the Human Development Index, the Global Happiness Report Index, the Global Competitiveness Index and the World Charitable Index) for classifying Ukraine into one of the three clusters identified by cluster analysis. The main characteristics of the model of recognizing the living standards of the population of the EU countries are shown in Fig. 15.
N=28 GII GCI SPI WGI
Discriminant Function Analysis Summary Step 4, N of vars in model: 4; Grouping: Claster (3grps) Wilks’ Lambda: 0.04509 approx. F (8,44)=20.401 p<0.0000 Wilks’ Partial F-remove p-value Toler.
Lambda Lambda (2,22) 0.053644 0.840575 2.086278 0.148027 0.081887 0.550653 8.976275 0.001411 0.064797 0.695889 4.807120 0.018533 0.052473 0.859328 1.811704 0.188689
The value of Wilk's Lambda is close to zero (Wilk's Lambda = 0.045), which characterizes the excellent quality of discrimination. According to the analysis, it is seen that the GCI and SPI indices give the most significant contribution to the discriminant function, which was also noted when using the hierarchical method of clustering of kmeans. The coefficients of discriminant functions for each of the indices of living standards assessment are calculated. Discriminant functions have the form:
+ 5,70 ∙ 2 = 0,59 ∙ 3 = −4,73 ∙ − 4,12 ∙ − 3,31 ∙ + 2,23 ∙ + 1,2 ∙ + 2,47 ∙ − 0,71 ∙ – 7,97; – 2,42; − 3,78 ∙ − 2,39 ∙ – 8,68,
Estimated values of classification functions for Ukraine: Cluster1 = −30,4757, Cluster2 = −0,56229, Cluster3 = 17,15047. Thus, Ukraine in terms of development of living standards of population can be attributed to cluster 3, namely the countries with average living standards, as the classification value for this function is maximum. The graph of the scattering of countries in the space of discriminant roots shows that the objects in the three classes are grouped quite densely, and the distances between the classes are large enough (Fig. 16). This will allow us to prove with greater certainty that the recognition of countries by the three levels of life of the population has been done correctly.
Root 1 vs. Root 2 4 3 2 1 2 to 0 o R -1 -2 -3 -4-6 -4 -2 0 2 4
6 Root 1
The case, namely Ukraine, belongs to a group to which the distance of Mahalanobis is at least 16,458 – this is a group of countries with an average standard of living. The recognition of living standard of the population on the basis of the international indices and forecasting of its level both for the investigated period and for the future is carried out by the constructed discriminant functions. Given the results, we can once again make a statement that Ukraine in terms of living standards falls into the cluster № 3 countries with average living standards. 5
According to the research results it can be concluded that the analysis of modern approaches to the assessment of living standards shows that this issue remains controversial. It needs refinement and improvement due to a number of related problems, such as the lack of a universal method of analysis and assessment of the level, the difficulty of determining the optimal categorical basis, the measurement of which with objective indicators is almost impossible. Therefore, it is fair to make a proposal on the need to create a new system of analysis and assessment of living standards, which will include indicators that more objectively reflect the real situation not only in Ukraine, but it will be suitable for assessing living standards in Europe. The paper develops an adapted methodological approach to the rating of the European Union and Ukraine, which, in contrast to existing ones, is based on a combination of multidimensional analysis methods, namely the method of canonical correlations, cluster and discriminant methods, which allows to classify EU countries by living standards taking into account the differentiation of international indices of living standards for such groups of countries (with a very high level, high, average) and to refer our country to the third cluster of countries. This allows to ensure the objectification of the evaluation results and to form a system of recommendations for further development of the country.
Prospects for further research include the possibility of developing separate strategies and trajectories of social development of the country and of a significant increase in living standards on the basis of the proposed set of models. The set of models can be expanded with additional modules for assessing the asymmetry of living standards by regions of the country and individual territories. This will build a decision-making system to equalize social asymmetry in general.