Environmental taxes in ensuring national security: A structural optimization model

The purpose of the article is to assess the optimal ratio of environmental taxes in the context of national security. National security is defined as a complex parameter of indicators of economic, environmental and energy security, sensitive to the impact of environmental taxation, according to the method of Kolmogorov-Gabor. The environmental taxes with the greatest impact on the three identified components of national security have been Received: April, 2020 1st Revision: March, 2021 Accepted: May, 2021 Journal of International Studies S ci en ti fi c P a pe rs © Foundation of International Studies, 2021 © CSR, 2021 Samusevych, Y. et al. Environmental taxes in ensuring national security: A structural optimization model 293 selected. The sample of the study consisted of six European countries (Belgium, France, Austria; Finland and United Kingdom). The study covers the time period between 1994-2019. The optimization model of the structure of environmental taxes, which provides maximization of the level of national security, is built using the simplex method and the method of the general reduced gradient. The calculations allowed determining the optimal structural ratios of environmental taxes within each country thatachieves the maximum level of integrated national security. Besides, the strategic guidelines for adjusting national environmental taxation systems were developed to ensure national security.


INTRODUCTION
Environmental sphere remains one of the crucial problems in the modern world community. The environmental sector requires sharp attention, as well as new and improved ways to ensure its effective functioning. The number of issues related to the need to be environmentally friendly is constantly growing due to the deteriorating impact of social processes and phenomena on the environment. Thus, environmental threats, such as depletion and destruction of available natural resources, pollution of the environment with artificial harmful substances, man-made disasters, environmental sabotage and others are very dangerous for further safe functioning of society (Chovancová, J., & Tej, J. 2020;Didenko et al., 2020;Dkhili, 2018). All this is exacerbated by political, legal, economic and social factors: imperfection of the legal framework for environmental law, insufficient efficiency of nature protection systems, improper organization of state control over the activities of entities that pollute or may adversely affect the environment, national economic situation, insufficient funding of the environmental sector, inefficient system of environmental taxation, unconscious environmental culture of society and others (Eddassi, H. 2020;Formankovaа, et al., 2018;He, 2019;Lyulyov et al., 2021). In turn, environmental threats significantly affect the general situation of the country, its safe functioning, the ability of public authorities to promptly intervene in emerging environmental problems, make necessary decisions and take appropriate action to address them effectively, determine the ability of people to consciously assess the importance of the environment. and the need to protect the environment (Masharsky et al., 2018;Sibanda & Ndlela, 2020;Starchenko et al., 2021;Vasylieva et al., 2021;Vysochyna et al., 2020b). Environmental security is closely linked to other types of national security, especially to the financial and economic sphere as one of the driving forces in ensuring overall national security and being able to provide adequate funding for the environmental protection through an effective system of measures, including environmental taxation. In turn, environmental taxes play a twofold role: on the one hand, a regulatory oneprovidings the ability to change the actions of those who harm the environment, and financially stimulate further rethinking and change of violators' behaviour, and on the other hand -a compensatory one, which will cover the damage and create a cushion of safety in case of possible economic and environmental losses. and on the other hand, to cover existing and possible losses from their unfair use or abuse. World experience demonstrates successful implementation of environmental taxes to achieve certain goals of national environmental policy (Miller, 2019).
The analysis of the existing literary achievements proves that the aspect of studying the field of ecology, and especially ecological taxation in terms of ensuring the security of the state, is still not sufficiently studied. This, in turn, does not allow to organize, formalize and sufficiently realize the existing financial potential of the environmental sector, as well as to ensure a sophisticated system of national security, which it directly affects. Synchronization of the goals of national policies of sustainable development and national security has led to an increase in the role of environmental taxes and the emergence of significant convergent trends in their dynamics (Vysochyna et al., 2020a). On the other hand, the process of transformation of tax policies of countries in the context of finding the most favorable operating conditions for national and international economic agents is incomplete (Boiko & Samusevych, 2017). This proves the importance of finding the optimal structure of the tax system that can maximize the effectiveness of tax policy. Accordingly, in the context of this study, the modeling of such a structure of environmental taxes, which maximizes the total effect of growth of the three components of national security (economic, environmental and energy).

METHODOLOGY
The methodology of building a multi-parameter model for optimizing the structure of environmental taxes in the context of national security involves the implementation of the following sequence of stages: 1 stage. Collection and processing of input statistical information in terms of optimizing the structure of environmental taxes in the context of national security. Substantiation of the indicators to be used to assess the components of national security (environmental, energy and economic security) was carried out in the works . The parameters of measurement national security were selected by testing their sensitivity to the impact of environmental taxes (using Granger Causality test).
Thus, environmental security indicators include: CO2 emissions, metric tons per capita; methane emissions, % change from 1990; nitrous oxide emissions, % change from 1990; fertilizer consumption, kilograms per hectare of arable land; total fisheries production growth, annual %; total greenhouse gas emissions, % change from 1990. Selected energy security indicators include: CO2 emissions from electricity and heat production, % of fuel combustion; CO2 intensity, kg per kg of oil equivalent energy use; electricity production from oil, gas and coal sources, % of total; energy imports, net % of energy use; combustible renewables and waste, % of total energy; energy use (kg of oil equivalent) per $1,000 GDP, constant 2011 PPP; fossil fuel energy consumption, % of total. Group of economic security indicators consists on: GDP growth, annual %;income share held by lowest 20%; industry (including construction) value added, annual % growth; current account balance, % of GDP.
The study included six countries (Belgium, Denmark, France, Austria, Finland and the United Kingdom) and covers 1994-2019. Analysis of the tax systems of each country allowed to select from two to nine environmental taxes that have the potential to simultaneously affect all three components of national security.
At this stage, in terms of interpolation of input statistics, gaps were processed using the method of average growth rate, in terms of extrapolation -forecasting the levels of time series by one of the methods of exponential smoothing by the Holt method: where ̂( ) -the predicted value of the level of the series for the time interval , defined for t first levels; 1, , 2, -initial parameters of the Holt model, calculated by the method of least squares on the basis of data of the first few levels of the studied time series; 1 , 2 -smoothing parameters (take possible values within [0; 1]), are calculated by applying the method of multidimensional numerical optimization; -remnants of the model.
Stage 2. Construction of integrated assessments of environmental, energy and economic safety based on the use of additive-multiplicative convolution by the Kolmogorov-Gabor method. This method is based on: 2.1 Normalization of input indicators by the method of natural normalization for indicatorsstimulators and Savage normalization for indicators-disincentives; 2.2 Taking into account the priority of component indicators in the formation of integrated assessments of environmental, energy and economic security based on the application of the method of analysis of hierarchies.
2.3 Carrying out nonlinear additive-multiplicative convolution of Kolmogorov-Gabor as integral indicators. This form of convolution allows to take into account the synergetic effect of interdependence of input indicators at their simultaneous influence as set. Additive-multiplicative convolution of Kolmogorov-Gabor takes the following form: where -Kolmogorov-Gabor integrated indicator of the ecological component of national security in terms of the i-th country for the t-th year; -weighting factor of the j-th indicator; ̃ -normalized value of the j-th indicator in terms of the i-th country for the t-th year.

Environmental taxes in ensuring national security:
A structural optimization model where -Kolmogorov -Gabor energy integral index component of national security in terms of the i-th country for the t-th year; where С -Kolmogorov -Gabor integral index of economic component of national security in terms of the i-th country for the t-th year Stage 3. Construction of the generalizing characteristic of the level of national security on the basis of application of additive-multiplicative convolution by the Kolmogorov -Gabor method: where -the level of national security of the country for the t-th year.
Stage 4. Construction of multiple linear and nonlinear ridge regression equations of dependence of the level of national security of six countries (Belgium, Denmark, France, Austria, Finland, Great Britain) on independent variables -shares of environmental tax revenues by types of total environmental taxes: де -the level of national security of Kolmogorov-Gabor for Belgium; Models of national security dependence from environmental taxation structure for the others 5 countries are presented in Annex A.
Stage 5. Formalization of the optimization model of the structure of environmental taxes, which maximizes the level of national security through the application of the simplex method and the method of the general reduced gradient.
where -the level of national security of the i-th country for the t-th year; -k-th variable, which takes values from 1 to n, and characterizes the share of the k-th type of tax in the total amount of environmental taxes; min =1÷ -the minimum possible value of the share of the k-th type of tax in the total amount of environmental taxes for the study period; max =1÷ -the maximum possible value of the share of the k-th type of tax in the total amount of environmental taxes for the study period; -the standard deviation of the share of the k-th type of tax in the total amount of environmental taxes for the study period.
Stage 6. Spectral analysis of environmental, energy and economic security assessment for the optimal level of national security.
-for Belgium: -for Denmark, France and Austria -for Finland: -for the United Kingdom:

EMPIRICAL RESULTS AND DISCUSSION
The construction of multiple linear and nonlinear ridge regression equations of dependence of the national security level of six countries on independent variables -shares of environmental tax revenues by type of the total amount of environmental taxes allowed to obtain results to assess the quantitative impact of individual environmental taxes and their combinations on national security. The evaluation was performed using the tools Statistica, Statistics / Multiple Regression for the case of linear models and Statistics / Advanced Linear / Nonlinear Models / Fixed Nonlinear Regression for the case of nonlinear models taking into account the Ridge Regression mark. The evaluation results obtained for Belgium are shown in Table 1. Table 1 The results of statistical analysis of the dependence of the integrated national security index Kolmogorov-Gabor on the share of revenues from environmental taxes by type of the total amount of environmental taxes for Belgium for the period 1994-2019 Source: own calculation The results presented in the table allow us to assess the separate impact of each of the studied environmental taxes on national security while operating in the country's environmental tax system, and take into account the synergistic effects arising from the interaction of their impact on the integrated level of national security.
Based on the data in Table 1 for the example of Belgium, the objective function of the problem of optimizing the structure of environmental taxes in the context of national security is as follows: = 0,523 + 29,657 • 1 + 7,938 • 2 − 807,159 • 1 • 2 де -the level of national security of Kolmogorov-Gabor for Belgium; 1 -the share of environmental charge in the total amount of environmental taxes; 2 -APETRA contribution share in the total amount of environmental taxes.
Generalizing models corresponding to equation (17) to describe the multiplex effect of combinations of environmental taxes on national security for other countries presented in Annex B. It should be noted that in systems with the simultaneous operation of more than two taxes, the impact of individual combinations of certain taxes, which are effective in assessing their separate impact, was also assessed. This allows maximizing their positive multiplex effects on the growth of national security and avoiding negative synergies through the simultaneous introduction of taxes, the combination of which poses a threat to national security.
Formalization of the optimization model of the structure of environmental taxes, which ensures the maximization of the level of national security was carried out using the simplex method (France, Finland) and the method of the general reduced gradient (Belgium, Denmark, Austria, Great Britain). For the example of Belgium, we will build an economic-mathematical multi-parameter model for optimizing the structure of environmental taxes in the context of national security: = 0,523 + 29,657 • 1 + 7,938 • 2 − 807,159 • 1 • 2 → { 1 , 2 ≥ 0 0,001024 ≤ 1 ≤ 0,003588 0,013219 ≤ 1 ≤ 0,050655 Solving the optimization task (23) using the method of the general reduced gradient allowed to obtain the following results (table 2). Table 2 The results of optimizing the structure of environmental taxes in the context of national security in Belgium Source: own calculation Therefore, it is determined that the structural optimization of the environmental tax system in Belgium should provide for a reduction in the level of APETRA contribution while increasing revenues Samusevych, Y. et al.

Environmental taxes in ensuring national security:
A structural optimization model 301 from environmental charge in the overall structure of environmental taxes. At the same time, a study conducted for Denmark (Table 3) showed that the structure of environmental taxes formed in the country is close to optimal in the context of national security. Thus, the obtained ratios provide only minor adjustments to maximize the multiplex effect of the estimated environmental taxes. Source: own calculation The next country for evaluation was France (Table 4). The results show that in order to optimize the multiplexed impact of environmental taxes on national security at the same time in terms of its environmental, economic and energy components, it is advisable to make significant structural adjustments to their levels. Table 4 The results of optimizing the structure of environmental taxes in the context of ensuring the national security of France Source: own calculation It should be noted that the existing approaches to the collection of environmental taxes in Austria need significant adjustments in terms of maximizing their regulatory capacity to ensure national security (Table 5). In particular, the role of recurrent car taxes should be significantly increased in order to achieve the optimal effect. At the same time, the rest of the taxes should be left in a balanced proportion. Table 5 The results of optimizing the structure of environmental taxes in the context of ensuring the national security of Austria

Source: own calculation
The results obtained for Finland (Table 6) also indicate that the predominance excise duty in the general structure will be optimal. Table 6 The results of optimizing the structure of environmental taxes in the context of ensuring the national security of Finland Source: own calculation At the same time, the system of environmental taxes formed in the United Kingdom can be considered close to optimal (Table 7). Spectral analysis of the assessment of environmental, energy and economic security for the optimal level of national security revealed the following interdependencies between the components of national security.

CONCLUSION
The study aims to substantiate and confirm the hypothesis of the formation of the optimal structure of environmental taxes, which maximizes the integrated effect of their impact on national security. Empirical calculations have shown that environmental tax systems in European countries have different levels of their multiplex effectiveness in the context of national security. Construction of optimization models allowed to identify vectors of change in the structure of environmental taxes, which will increase their integrated regulatory efficiency. At the same time, the spectral analysis revealed the transmission effects that occur between the three components of national security -environmental, economic and energy. All this creates a basis for improving national tax policies in terms of achieving the strategic goals of national security, as well as its individual components.

ACKNOWLEDGEMENT
This work was supported by the Ministry of Education and Science of Ukraine and National Research Foundation of Ukraine and performed the results of the projects «Structural-functional multiplex model of ecological tax system building in Ukraine in the context of national security» (registration number 0119U100759); «Data-Mining for Countering Cyber Fraud and Money Laundering in the Context of Digitalization of the Financial Sector of the Ukrainian Economy» (registration number 0121U100467); «Stochastic modelling of road map for harmonizing national and European standards for energy market regulation in the transition to a circular and carbon-free economy» (0120U104807).

ANNEXES
where -the level of national security of Kolmogorov-Gabor for Denmark; 1 -the share of the duty on coal in the total amount of environmental taxes; 2 -the share of the duty on electricity in the total amount of environmental taxes; 3 -the share of pesticide duties in the total amount of environmental taxes; 4 -the share of the duty on tires in the total amount of environmental taxes; 5 -the share of sale of vehicle number plates in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for France; 1 -the share of the CO2-related malus system for vehicle registration in the total amount of environmental taxes; 2 -the share of the contribution to electricity generators for public services they provide in the total amount of environmental taxes; 3 -the share of the internal tax on final consumption of electricity in the total amount of environmental taxes; 4 -the share of the internal tax on natural gas in the total amount of environmental taxes; 5 -the share of production taxes in the total amount of environmental taxes; 6 -the share of special fuel tax in foreign communities in the total amount of environmental taxes; 7 -the share of the tax on electricity pylons in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for Austria; Samusevych, Y. et al. Environmental taxes in ensuring national security: A structural optimization model 1 -the share of duties on vehicles (based on fuel consumption) in the total amount of environmental taxes; 2 -the share of recurrent car taxes in the total amount of environmental taxes; 3 -the share of the tax on mineral oils in the total amount of environmental taxes; 4 -the share of road pricing for trucks for the use of highways in the total amount of environmental taxes; 5 -the share of the wastewater fee in the total amount of environmental taxes.
= 0 + ∑ • where -the level of national security of Kolmogorov-Gabor for Finland; 1 -the share of the fee for a fishing license in the total amount of environmental taxes; 2 -the share of excise duty on fuel and electricity in the total amount of environmental taxes; 3 -the share of the nuclear energy tax in the total amount of environmental taxes; 4 -the share of the fee for oil losses in the total amount of environmental taxes; 5 -the share of the registration fee for vehicles in the total amount of environmental taxes; 6 -the share of vehicle tax in the total amount of environmental taxes; 7 -the share of the fee for the collection / treatment of municipal waste in the total amount of environmental taxes; 8 -the share of the fee for nuclear waste in the total amount of environmental taxes; 9 -the share of fees for water use in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for Denmark; 1 -the share of the duty on coal in the total amount of environmental taxes; 2 -the share of the duty on electricity in the total amount of environmental taxes; 3 -the share of pesticide duties in the total amount of environmental taxes; 4 -the share of the duty on tires in the total amount of environmental taxes; 5 -the share of sale of vehicle number plates in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for France; 1 -the share of the CO2-related malus system for vehicle registration in the total amount of environmental taxes; 2 -the share of the contribution to electricity generators for public services they provide in the total amount of environmental taxes; 3 -the share of the internal tax on final consumption of electricity in the total amount of environmental taxes; 4 -the share of the internal tax on natural gas in the total amount of environmental taxes; 5 -the share of production taxes in the total amount of environmental taxes; 6 -the share of special fuel tax in foreign communities in the total amount of environmental taxes; 7 -the share of the tax on electricity pylons in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for Austria; 1 -the share of duties on vehicles (based on fuel consumption) in the total amount of environmental taxes; 2 -the share of recurrent car taxes in the total amount of environmental taxes; 3 -the share of the tax on mineral oils in the total amount of environmental taxes; 4 -the share of road pricing for trucks for the use of highways in the total amount of environmental taxes; 5 -the share of the wastewater fee in the total amount of environmental taxes.
where -the level of national security of Kolmogorov-Gabor for Finland;