Method and Criteria for Assessing Sustainable Development

The article is aimed at solving the urgent scientific task of creating new methods for an integrated assessment of the sustainable development of socio-economic objects, in particular, countries, regions and cities. A practical method of assessment is proposed, which allows to form ideas about the vector of sustainable development of objects. The construction of development models is based on the use of the principle of the corresponding states, according to which the positions of objects in multidimensional state spaces can be described by a single equation if an effective scale is constructed for comparing the states among themselves in a set of indicators. It is shown that the study of the features of sustainable development of countries, regions and cities can be performed by the method of cluster analysis of data with the subsequent construction of such scales. For comparison of objects it is suggested to use the reference vector of development, which is constructed for the control group of objects that are the most developed in terms of indicators of achieving the goals of sustainable development. Socio-econometric scales are proposed for assessing the development of regions, as well as criteria characterizing the stability of their development. As a realization of the method, a comparative analysis of the development of the regions of Russia on 13 indicators of sustainable development was carried out.


Introduction
The concept of Sustainable development has been improving for almost three decades. However, it should be noted that very little progress has been made in the area of theoretical approaches during this period. The theories and models used mainly involve the use of expert methods and simple complex estimates.
The generally accepted concept of sustainable development is set out in the UN General Assembly Declaration. Sustainable development refers to development that promotes prosperity and economic opportunity, well-being and environmental protection Since 1987, when the first formulation of sustainable development appeared, and to date, the concept of sustainable development remains a popular and beautiful idea. This concept is set out at a qualitative level without specific details, which would allow to create quantitative models of sustainable development of the analyzed objects.
The aim of this work is to develop a method and criteria for a comprehensive assessment of the development of countries, regions and cities, allowing to form ideas about the vector of sustainable development of both individual objects and groups of homogeneous objects.
In recent years there has been rapidly developing the field of systematic research, based on the application of natural and physical methods in the economic and social sciences. In these methods, data that determine the entire course of research and model (Barceló et al., 2015;Chakraborti et al., 2015).

Methodology of Complex Assessment of Complex Objects Development
We assume that the position of each socio-economic object is determined by a set of values of its indicators, which are formed at a certain time. To describe the position of the object relative to all other objects of the studied class, we will use the natural science concept of the state spacean abstract space formed by state variables. As the state variables, we will take for socio-econometric analysis indicators that are considered significant among experts and that characterize the studied objects in a certain aspect 1 , which will be considered as state variables. Let us form the n-dimensional state space in the form of a Cartesian coordinate system The main idea of the work is related to the study of the possibility of creating models that differ in the description of geometric points (States) and lines (processes) in multidimensional spaces of States of socio-economic objects on the basis of available statistical information. Modeling is based on the hypothesis of the existence of different measures of similarity of object States ,..., , 2 1  . This value is considered as a function of several variables (Crooks and Heppenstall, 2012).
The construction of models is based on the use of the principle of the corresponding States, according to which the positions of objects in the state space can be described by a single equation of state, if you build an effective scale for comparing States with each other and use some of the variables. Typically, the equation of state is represented as: the values of the indicators for the reference state. In this approach, the modeling object is the States of objects that can be characterized by a General equation that is valid for the entire multidimensional state space.
To construct the equation of state from a group of objects, a reference object or reference state is selected, and all other States are related to the selected point in the state space. The validity of the principle is verified on a caseby-case basis Tahavieva and Nigmatullina, 2017).
The principle of the corresponding States allows us to construct a scale for the relative comparison of the position of objects among themselves, in the form of an index  (Averin et al., 2016). In general, the content of the method is as follows (Fig. 1.). Select some linear reference process 0 l for some object and mark the reference state on it 0 M . On the line of this process, we note the second reference state 0 M  . The first reference state may correspond to the start time of statistical data collection, for example, as in the example below, 2012, and the second reference state to the last year of data collection, for example, 2015. The resulting segment is divided into a given number of identical intervals, for example, 100, and set the length of the obtained segments  , based on the measure of similarity of the States of objects W. Next, from the origin of the beam 0 OM and find the length of the segment 0 OM in the accepted system of measurement value W. The scale of measurements for the states of objects is formed in the form of an index  applied to the beam 0 OM with a unit of measurement  , the length of the segment 0 OM in this scale will be For certainty, we set the appropriate unit of measure  as a degree (°G), which is geometrically equal to the length  .
Using various measures of similarity W, the resulting scale can measure each state in degrees of the index  . Thus, the index  as a whole characterizes the state of objects and is an empirical measure for their measurement. This is the main criterion for determining the position of countries, regions and cities on a set of different socioeconomic indicators in a multidimensional space of States. The lengths of segments in the state space having Euclidean metric can be determined based on the Euclidean distance: where a and bthe beginning and the end of a certain segment ab . Now, to describe statistical data, we can search for a model of collective behavior of objects in the form of an equation of state.
(2) For different periods of time, using a common scale of econometric measurements, it is possible to obtain different values of the complex index  , as a function of time in the same state space of objects. This will allow you to study not only the state, but also the processes of development of objects (Averin and Zviagitrseva, 2017).

Sustainable Development Indicators
Today, 247 indicators recommended by the UN, 47 indicators proposed by the world Bank, and 35 national indicators recommended for use by the state statistics Service of Russia are used for sustainable development (Tan, 2007).
For example, 13 indicators were selected from the list of 35 national indicators for integrated assessment of sustainable development of Russian regions, which were grouped into two groups. The group that characterizes the socio-economic stability of the development of the regions include:  gross regional product per capita, RUB/person, s z 1 ; This group in relation to the regions was based on the principle "the higher the value of the indicator, the better".
The group that characterizes the environmental sustainability of the regions include:  investments in fixed capital aimed at environmental protection, RUB/person, s z 8 ;  emissions of air pollutants from stationary and mobile sources, kg/person, s z 9 ;  water intake from natural water bodies, m3/person, s z 10 ;  discharge of contaminated wastewater into surface water bodies, m3/person, s z 11 ;  the energy intensity of the GRP, kg of standard fuel/10 thousand RUB, s z 12 ; infant mortality, the number of children who died before the age of 1 year per 1,000 births, s z 13 .
The group of indicators of environmental sustainability of regional development was organized according to the principle "the lower the value of the indicator, the better".
Data on the above indicators were collected for the period 2012-2015 for 80 regions of Russia. The study of the features of sustainable development of regions was carried out by the method of cluster data analysis, followed by the construction of socio-econometric scales for comparing the States of objects. Clustering was carried out by the kmeans method using the Statistica program separately for groups of indicators characterizing the socio-economic and environmental sustainability of regional development. The clustering technique involved the use of the nearest neighbor method, where Euclidean distance was used as a clustering measure. The studied indicators were previously standardized by bringing them to the form: , for the analysis of environmental sustainability. The number of clusters was determined by the method of hierarchical clustering in the Statistical software product by building dendrograms.
Clustering of regions according to the observations of the values of socio-economic stability indicators allowed to identify three groups of regions. The characteristics of the clustering areas by standardized indicators are given in table 1.  Table 1 shows that for the regions of the first cluster, there are high indicators of socio-economic stability, since six of the seven clustering indicators have the highest average. These regions, in the context of the country as a whole, can be seen as examples of sustainable socio-economic development.
Clustering of regions according to observations of the values of environmental sustainability indicators also allowed us to identify three groups of regions: the first cluster (12 regions  Thus, on the basis of the results of cluster data analysis, two control groups of regions were formed, which are distinguished by indicators of socio-economic and environmental sustainability. The vectors of sustainability defined for the selected small control groups of regions, which will be considered as examples of sustainable development in the context of the whole country, can be used to form criteria for integrated assessment. The value of the vector module will be used as one of these criteria. On its basis, we will create an appropriate socio-econometric school. Measurements on this scale allow you to compare the regions of Russia with each other.

Integrat Assessment Criteria
The index  , as a measure of similarity of States, will be along the length of the vector characterizing the development of each region in a certain period of time, for example, in 2012-2015. This index determines the level of sustainable development of the region in relation to the reference vector, which characterizes the most developed group of regions in this respect.
It should be noted that the vector s F  can be characterized not only by the length, but also by the direction of development in the space of object States. Therefore, the second criterion for sustainable development of the region in relation to the most developed group of regions can be the angle  between the reference vector and the vector of development of the region.
The smaller the angle  , the more the direction of development of the analyzed region corresponds to the indicators of sustainability priority development of the most developed control group.

Comparison of Russian Ergions in Terms of Sustainable Development
We will carry out a comprehensive assessment of the socio-economic and environmental sustainability of the regions according to the above indicators of achieving sustainable development goals. We will use the method of integrated assessment of the development of socio-economic objects, given earlier. Table 3 presents a comparison of Russian regions by a set of indicators based on the created scales of socio-economic and environmental sustainability. The value of θ is taken for the reference vectors equal to 100.
As can be seen from the data obtained, the five regions that have a high level of socio-economic stability in terms of specific indicators (related to the population) include the Sakhalin, Belgorod, Kaliningrad regions, the Republic of Altai, the Tyumen region.
In turn, the five regions that have a high level of environmental sustainability in terms of specific indicators include the Krasnodar territory, Nizhny Novgorod region, Moscow, Sverdlovsk region and the Kabardian-Balkar Republic. The presence of Moscow in this group is explained by a significant number of the population (12.3 million people) and the fact that the integrated assessment considered specific indicators of environmental sustainability (related to the number of the population).

Conclusions and Prospects
The above example shows that the study of the features of sustainable development of countries, regions and cities can be performed by cluster analysis of data, followed by the construction of econometric scales to compare the States of objects among themselves on a set of indicators. For comparison of objects it is offered to use a basic vector of development which is under construction for control group of objects which are the most developed on indicators of achievement of the purposes of sustainable development.
The article proposes socio-econometric scales for assessing the development of regions, as well as criteria characterizing their sustainability, which are based on a relative comparison of the vector of development of each region with the reference vector of development of the control group of regions.