Sustainable development of Ukraine as a combination of social, economic and environmental components: structural econometric model of three-pillar approach

The combination of the economic, social and environmental issues of the country-level development in the case of Ukraine requires modernization of the national economic system and permanent deep institutional reforms. These measures should be aimed at forming a diverse, competitive and socially oriented post-industrial economy capable of ensuring sustainable development. To ensure the improvement of the management of Ukraine’s sustainable development strategy, structural (simultaneous) model is proposed, based on three endogenous (namely GDP as economic variable, income per household as social variable and the expenses for the environmental protection as environmental variable) and seven exogenous variables. Such an approach makes it possible to investigate the interdependence between variables. Model parameters estimates were calculated with the two-step least squares method. A forecast of the development of the main indicators characterizing the economic, social and environmental components of development at the country level was also estimated. For Ukraine in 2021, according to the forecast based on the structural model, the economic and environmental components will have positive dynamics and rapid growth, while the social component will develop, but more stably and without rapid growth.


Introduction
Before the start of the full-scale war in February, Ukraine was making steady progress in achieving 15 of the 17 Sustainable Development Goals (set of 17 Sustainable Development Goals (SDG) according to the "Transforming our world: the 2030 Agenda for Sustainable Development" [1]), and moreover, it achieved the greatest success precisely in reducing poverty.The first Voluntary National Review of progress towards achievement of the Sustainable Development Goals in Ukraine [2] showed that the main achievement is the reduction of poverty for more then 15 percent during 2015-2018.Now, when the discussions about the recovery of the country and the economy begin, the SDG are used as a reference point to ensure the most effective reconstruction of Ukraine.The war will require a review of development priorities to achieve the SDG.The interpretation of the 16th SDG -"Peace, justice and strong institutions" will change significantly.SDG 1 "Poverty" will now become a key task of social development.SDG 6 "Clean water and sanitation", which covers ensuring the availability and sustainable management of water resources and sanitation, is becoming urgent.Goal 8 "Decent work and economic growth" becomes of primary importance for the return of Ukrainian refugees.Undoubtedly, radical changes will have to be made to all state programs, because the focus on sustainable development in the "peaceful" version, where the main priorities are overcoming inequality and a green economy, is being revised even in wealthy democracies.The world is feeling the consequences of the energy crisis, including as a result of the sanctions imposed on Russia, and therefore the governments of the countries are not only postponing the green transition, but also resuming coal mining, taking care of the state of the industry.
Since the problems of sustainable development appear from new perspectives, a reasonable explanation of the dependencies between indicators of sustainable development with mathematical methods will help in making management decisions.
The concept of sustainable development has been spreading during the last decades, but the most popular definition was in the Brundtland report [3].And while its usefulness may still be questioned (e.g. in Beckerman article [4], it is one of the most popular concepts in terms of popularity.Salvia et al [5] investigated trends in sustainable development research in different levels of investigation.Chabay [6] believes that the greatest success in the implementation of the goals of sustainable development can be achieved by applying interdisciplinary complex systems approaches and trans-disciplinary research methods.Schoenmaker and Stegeman [7] think that the biggest problem in the practical implementation of the concept of sustainable development is the balancing of various goals, unlike, for example, economic concepts that consist in maximizing economic indicators.Vavoura and Vavouras [8] investigated COVID-19 impact on sustainable development and record a significant reduction in the social component of sustainable development in European Union, i.e. an actual return to the concept of economic growth, but on the basis of a green deal.
Regarding the investigation of the sustainable development of Ukraine, the researches of both domestic and foreign scientists are also devoted to this problem.In the article [17] the trends in sustainable development of Ukraine comparing to EU counties is described; in [18] it is considered from the position of the European integration of Ukraine as a strategic goal; Kuzior et al [19] study role of the innovative ecosystem of Ukraine and EU in sustainable development and Sokil et al [20] details innovation ecosystem to startups; Semenenko et al [21] investigate changes in sustainable development before and after the war.Also investigations of the sustainable development of Ukraine are devoted to different aeries, such as agriculture [22], transport [23], rural areas [24] and others.
A wide range of mathematical methods and models are used for quantitative analysis and modeling of sustainable development (table 1).The choice of method depends, among other things, on the purpose of the research.In order to reveal the interdependencies between various indicators that characterize the economic, social and environmental aspects of the country's sustainable development, it is advisable to apply structural modeling methods.

Structural equations method for sustainable development modelling
A system of simultaneous equations is a statistical model in the form of a set of simultaneous linear equations.They differ from ordinary regression models in that there are two or more dependent variables.
Variables that are explained by the functioning of the system and whose values are determined by the simultaneous interaction of the links in the model are endogenous variables or jointly determined variables.
Variables that help provide explanations for endogenous variables and whose values are determined outside the model are exogenous variables or predetermined variables.Exogenous variables help explain variations in endogenous variables.
Table 1.Methods and models of sustainable development investigation and modelling.

Authors Method
Taghvaee et al [25] vector autoregressive model Udemba and Keleş [26] ARDL Liu et al [27] ARIMA de Armas et al [28] operations research Wu et al [29] graph neural networks Chai et al [30] fuzzy logic Moreta et al [31] text analysis Zomchak and Starchevska [32] logistic regression Holloway and Mengersen [33] machine learning Alharbi et al [34] hierarchical framework Bielinskyi et al [35] econophysics Chen et al [36] data envelopment analysis Sutthichaimethee and Ariyasajjakorn [37] structural equation model Izonin et al [38] Wiener polynomial approximation Horoshkova et al [39] Kuznets curve Matviychuk et al [40] fractal analysis Valaskova et al [41] regression analysis Determining from the data sample those variables which are endogenous and which are exogenous belongs to the model developer himself, that is, in essence, it is partially based on the expert method.
A structural simultaneous model is used to describe the structure of relationships between endogenous and exogenous variables.In general, it can be written like this: Certain macroeconomic models built with a system of simultaneous equations can be a powerful econometric tool as a result, which will make it possible to investigate complex relationships in various kinds of socio-economic systems, in particular, relationships in ecologicalsocio-economic systems, in conditions of certain uncertainty, high risks and rapid changes in the economic environment.
Simultaneous models can be both quite detailed and quite compact, so they can be used not only for in-depth analysis considering various scenarios of system development, but also for preliminary diagnosis of the system state or display of the behavior of certain of its components in different situations.
Structural equations are used for sustainable development modeling in the investigations of urbanisation [42], green buildings [43], business environment [44], machine-building enterprises [45] and others.
For modeling sustainable development, simultaneous models can also be considered quite effective, as they make it possible to analyze and forecast the development of environmental, social and economic components both separately and to consider their interrelationships.Also, such modeling makes it possible to assess the overall impact on sustainable development of the changes implemented in each of its components and, if necessary, to change the further strategy.To describe the economic component, we will use the following variables: 1) Endogenous variable -gross domestic product (million UAH), y 1 .
To describe the social component: 1) Endogenous variable -disposable income per household, UAH, y 2 .
To describe the ecological component: 1) Endogenous variable -expenses for the protection of the natural environment, thousand UAH, y 3 .2) Exogenous variables: • volume of emissions of polluting substances into the air by stationary sources, thousand tons, x 6 ; • capital investments for the protection of the natural environment, UAH, x 7 .
In general terms, the model looks like this: The dependence equations will have the following form: 1. Gross domestic product depends on available income per person, costs for environmental protection, retail trade turnover, export of goods, consumer price index, average monthly real wages: 2. The disposable income per household depends on the gross domestic product, the number of employed people, and the average monthly real wage: 3. Costs for environmental protection depend on the gross domestic product, the amount of pollutants emitted into the air by stationary sources, capital investments for environmental protection: So, the simultaneous model will look like this: Let's check whether the model is identified, for this we will first write it down in tabular form (table 2).
Table 2. Tabular form of the simultaneous model.
Let us now check the order condition and rank condition for each equation of the constructed simultaneous model (table 3).Since the order and rank conditions are fulfilled for all equations of the model, we conclude that all of them are over identified, and therefore the model as a whole can be considered as over identified.
Since the equations of the model are over-identified, we cannot use the least-squares method to estimate the parameters, that's is why we used the two-step least-squares method.We will estimate the parameters based on the statistical data of the described variables from 2000 to 2020, which were collected from the website of the State Statistics Service of Ukraine.

Simultaneous equations of Ukrainian sustainable development
All the input data about exogenous and endogenous variables are collected from the official web-page of the State Statistics Service of Ukraine [46] for the period 2000-2020 years.
The first step is to construct three regression models of the dependence of each endogenous variable on all exogenous variables.
After the actions taken, we have three models for calculating the theoretical values of endogenous variables, which will be used in the second step as auxiliary variables to obtain estimates of the parameters of simultaneous model: 1) for gross domestic product: 2) for disposable income per household: y 2t = −1707.95+ 0.001x 1t + 0.09x 2t + 2.32x 3t + 0.07x 4t + 0.94x 5t + 0.014x 6t + 0.00007x 7t .
3) for environmental protection expenses: The three equations have high coefficients of determination, which indicates that the obtained equations of the simultaneous model perfectly explain the variance of the endogenous variables.For the equation of the economic component, this indicator is 99.58 percent, for the equation of the social component -99.57percent, and for the equation of the ecological component -98.96 percent.
We will also check the statistical significance of model parameter estimates.As mentioned earlier, we will do this using the Student's test with a confidence probability of 90 percent.
Tabular values of the Student's criterion at a probability of 0.1 and 14 degrees of freedom is 1.761, and at 17 degrees of freedom -1.739.
The obtained empirical values of the Student's test were also calculated as a proportion of the obtained variable parameters and their standard error.The results are described in table 4. Since the empirical values are greater than the critical values, we can reject the null hypothesis and conclude that all parameters of the obtained simultaneous model of sustainable development of Ukraine are statistically significant.That is, we can use the model to further build a forecast.

Forecasting three-pillar approach indicators of sustainable development
Based on the model, we will forecast the dynamics of each selected component of Ukraine's sustainable development.We will use the data for 2021, which is on the website of the State Statistics Office of Ukraine [46], as well as their forecasts of the development of some indicators.
First, let's calculate the theoretical values of all our endogenous variables for 2021.As a result, we have that the GDP is UAH 6433133.192million; available income per household -UAH 13,518.51,expenses for environmental protection -UAH 2,276,465.42thousand.
Next, we substitute all these values and get that in 2021 GDP will be UAH 6,433,133.192million, disposable income per household is UAH 17,381.18,027,and costs for environmental protection are UAH 3,872,110.64thousand.
Figures 1-3 show the dynamics of our selected endogenous variables from 2000 to 2020, the obtained forecast for 2021, as well as the forecast of the State Administration of Statistics of Ukraine and Forecast.

Conclusions
The proposed and implemented structural model of sustainable development of Ukraine based on the three-pillar approach.The economic component of development is represented by GDP as a function of wages, trade turnover, exports and inflation.The social component is described in terms of income per person as a function of GDP, average wages and the number of employed population.Environmental protection costs, which depend on GDP, emissions from stationary sources of pollution, etc., and capital investments in the environment, were used as an ecological characteristic.Since GDP is both the dependent variable in the first equation and the independent variable in the next two equations, the interaction between the three pillars of sustainable development can be explored.In this way, it was found that the growth of household income is not accompanied by the growth of GDP, that is, incomes grow faster than the economy, which is quite unexpected.Simultaneously with the growth of the GDP of Ukraine, the income of households increases, which can be seen from the equation that describes the social component.If we talk about the environmental component, the growth of environmental protection costs is accompanied by GDP growth, and vice versa, GDP growth increases environmental protection costs.Forecasts of three exogenous variables were also obtained, which differs from the official forecasts, but also confirmed the correct selection of variables and the description of the dependencies between them.
Unfortunately, the State Statistics Service has suspended the publication of statistical information for the period of martial law or the state of war, as well as for three months after its termination, and for the occupied territories, even the collection of statistics is not possible.It is obvious that with the beginning of a full-scale invasion, statistical economic, social and environmental indicators have undergone catastrophic changes (which have not yet acquired a clear quantitative dimension) and the assessment of the scale of losses is still ahead.Catastrophic changes took place in various areas, including those that describe the social, economic and ecological components of sustainable development, goals and priorities changed dramatically, so the correctness of forecasts for the following periods will require additional clarification.
The deepest decline of the Ukrainian economy in the entire history of the state took place, household incomes experienced a significant reduction and often large changes in the structure, the environmental consequences of the war also cause significant concern.Obviously, the classical econometric model could not take into account such changes, but it allows to investigate the structure of dependencies between economic, social and environmental indicators and provides tools for its explanation.
We also note that the reconstruction of Ukraine will take place on the basis of the concept of sustainable development and require adequate justification of decisions, and econometric approaches can be used for this purpose.

4 3 .
Structural model of sustainable development of Ukraine on three-pillar approach A simultaneous model of three equations, each of which describes one of the three components of sustainable development (ecological, economic, and social) is proposed for investigation and forecasting the sustainable development of Ukraine.

Figure 1 .
Figure 1.Dynamics and forecast of the gross domestic product.

Figure 2 .
Figure 2. Dynamics and forecast of disposable income per household.

Figure 3 .
Figure 3. Dynamics and forecast of the expenses for the environment protection.

Table 3 .
Order condition and rank condition.

Table 4 .
Empirical and critical values of Student's criterion.