Economics and Mathematical Methods

This article examines the interaction between the world of economic systems and the world of their computer-mathematical models. The significance of this issue is growing with the expansion of digitalization and intellectualization of the domestic and global economies. The article consists of two parts. The proposed solution of the problem is based on the consistent typology of economic systems and their models that was developed in the first part of the article. The world of real economic systems was presented in accordance with the systems economic theory as a set of object (organizational), process (logistics), project (innovation) and environmental (infrastructure) systems operating in economic space-time. The world of the most well-known computer-mathematical models is currently represented by agent-based (agent-oriented), econometric, cognitive and equilibrium (optimization) models. In this situation, the relevant task is to develop methods for forming pairs “economic system — its mathematical model” that form the basis of computer-mathematical modeling of economic systems. The relationship between the subject and instrumental spheres of modeling is reflected in the concept of the systems modeling paradigm developed in this article. An in-depth study of the interactions between economic subsystems leads to an understanding of the role of subsystems not only in the processes of intra-system exchange of spatiotemporal and cognitive resources, but also in the integration and separation of these resources. Since each model type reflects one of the aspects of economic system functioning, there comes the task to aggregate models for their comprehensive and adequate reflection of economic system’s activities. The application of the proposed framework creates the prerequisites for improving the adequacy of modeling, expanding the possibilities for the effective use of models for forecasting and regulating the behavior of economic systems, and ensuring a higher level of user confidence in the modeling results. The methodology of the research is based on the principles of a systems paradigm, spatiotemporal, and cognitive-competence analysis.

The issue of strategic factors for providing national healthcare with human resources is a strategic task for all countries of the world without exception, including Russia. A significant shortage of medical personnel in our country is a strategic challenge that requires long-term measures based on established patterns of various levels. According to methodology of strategizing of V.L. Kvint, RAS Foreign member the authors identified patterns in the impact of healthcare workforce potential on its performance at various levels — global (particularly, intercountry) and national (particularly, interregional). Existing global trends indicate the importance of a high level of medical personnel for health care outcomes. It is shown that factors such as the healthcare system’s educational function, aimed at improving the population’s medical literacy, play an increasingly important role in healthcare workforce management. A study of the dynamics of the age distribution of physicians in Russia revealed that challenges to human resource potential primarily lie in creating conditions for retaining physicians in the profession, which is especially important after their starting years of work. A study of the dynamics of the age distribution of medical personnel in Russia revealed that the challenges to deficit in human resources primarily in creating conditions for the retention of doctors in the profession, which is especially important after the beginning years of work. This issue is also of strategic importance in terms of using the positive opportunities of state policy to increase the number of state-funded places in medical universities and expand the training of medical personnel. In general, on the basis of V.L. Kvint’s strategic methodology, a space of opportunities for increasing and improving the efficiency of the human resources of the national health care system was identified.

The growing uncertainty due to large-scale changes happening at the current stage of socioeconomic development increases the relevance of the problem of analyzing and shaping the future quality of life. The article suggests that in order to prevent possible negative consequences of the impact of major challenges, it is necessary to develop methodological foundations for predicting the quality of life indicators in the Russian regions. The innovative essence and complexity of the research problem led to the use of quality economics methodology and advanced computational methods, which involves the use of a supercomputer. The goal of the work is determined by the need to develop a theoretical and methodological basis for assessing quality of life as an instrument for reconciling strategic priorities and forecast indicators of socio-economic development of the region. The foundations established at the state and regional levels to ensure the economy's ability to withstand major challenges were considered. Prospects for further use of quality-of-life assessment indicators in quality-of-life modelling to account for significant changes taking place in the economy. The step was taken to create a prognostic model of quality of life. The quality assessment methodology developed in the IRES RAS was verified, with emphasis on its applied nature. In development of this methodology, a conceptual model is presented that describes three levels of contribution of exogenous and endogenous factors to the processes of formation of quality of life. In the future, it is proposed to direct research on specific quality of life issues towards a unified approach that combines the methodology of quality economics and the latest supercomputer technologies.

This article discusses ways to obtain convergence of calculation results obtained using before-tax and after-tax cash flow discounting models. Various ways of achieving this goal are proposed. Two concepts are considered — the concept of equivalence of post-tax and pre-tax bases of calculation, within which the theoretical equality of the results of calculations of the value of an asset, calculated based on post-tax or pre-tax cash flows, is implied, and the concept of non-equivalence of post-tax and pre-tax bases of calculation, within which the value of an asset generating cash flows is determined based on the required basis of the value of the asset itself. To align the results of estimates calculated in pre-tax and post-tax bases, the use of cash flow duration is considered. In the third part of the article, a recommendation is provided for the analysis and adjustment of the observed risk premium concerning post-tax and pre-tax cash flows of shareholders. In the fourth part of the article, a conclusion is drawn about the incorrect application of the results of calculations based on the CAPM model when assessing companies and investment projects, and recommendations are given on how to achieve more correct discounting of cash flows at the rates of alternative income calculated via the CAPM and WACC models. Suggestions are provided on the analysis and adjustment of the observed risk premium in relation to after-tax and before-tax capital cash flows. The appendices consider the theoretical impact of inflation on the amount of the observed risk premium and examples explaining recommendations for the correct accounting of the tax factor.

The decision to lend to individuals is associated with many factors, including expert opinions. Some factors are of uncertain nature, which cannot always be described mathematically, but affect the decision-making process. Among the various methods for assessing the risk of default, one can single out the scenario approach using the methods of fuzzy set theory to calculate the values of membership functions. The problem of ranking a set of default risk scenarios taking into account the mental properties of experts and borrowers was not sufficiently studied. The purpose of the study is to develop the new methods for assessing the risks of lending to individuals taking into account the temperament of the borrower and the preferences of experts based on logical and linguistic classification of images. To achieve this goal, an analysis is made of the influence of the experts' opinions with different temperaments on the decision on the lending risk by assigning borrowers scoring points selected randomly from a given set of membership functions. Based on the proposed method, an algorithm was developed for calculating the risk of default on the analyzed individual's loan with determination of his rating taking into account the experts' opinions. The results of computer modeling showed that with a spread of expert opinions establishing the coefficients of significance of borrowers' indicators at about 30%, individual experts can give a significantly different forecast of the lending risk from the average assessment of all experts, which affects the determination of the borrower's rating. Therefore, when assessing the risk of default on loan funds, it is advisable to use the opinion of at least five experts and rank the borrower by the average assessment. The research results can be used to shape recommendations for experts assessing the risks of loan default, as well as to design an expert system that can speed up the risk analysis of lending to individuals.

The development of urban agglomerations is impossible without long-term scientifically based forecasting of traffic flows, which should take into account not only the existing transport infrastructure and established travel routes, but also changes in both the technical and technological properties of vehicles and patterns of behavior of the population. At the same time, the overwhelming majority of models currently used to forecast traffic flows are based on the analysis of a relatively small number of variables that influence the choice of route. The purpose of this article is to demonstrate the capabilities of the agent-based approach to modeling traffic flows in comparison with currently used models based on the use of physical analogies, in particular, the gravity model. To implement this task, the authors developed a multifactor model of job selection by the population, taking into account the multiplicity of criteria for an individual to select a place of employment, as well as the different significance of these criteria for different groups of the population. The model assumes that the choice is made not only by potential employees, but also by employers, and the formation of paired combinations occurs on the basis of the Gale-Shapley algorithm. Comparative calculations carried out using multifactor and gravity models on the same conditional data showed that the roughening assumptions of the gravity model lead to significant deviations in the data obtained. At the same time, the multifactor model can be used for more accurate forecasting of traffic flows, provided that the results obtained are calibrated and adjusted based on statistical data.

The paper proposes a model for optimizing government support for research and development (R&D) prior to the implementation of an investment project in a real sector enterprise. Budget subsidies an enterprise for compensating part of R&D expenses, and deductions from the income tax base (with the certain coefficient) are considered as such support measures. After the R&D stage, an innovative project starts implementation only with some probability. The enterprise operates under uncertainty, its profits' flow is modeled by a stochastic process, and after the project implementation it changes to another stochastic process. The study of optimizing the support provided by the government to an enterprise for R&D is based on the principle of maximizing the expected integral budgetary effect from the operation of this enterprise. The control parameter is the index of government support for R&D, which characterizes the total direct and indirect budget expenditures (subsidies and lost tax revenue, respectively) per unit of R&D costs. The formula for the optimal government support index is explicitly derived. We analyze the dependence of this optimal index on the tax burden, the volatility of the enterprise profits, the probability of the project implementation, and the effectiveness of innovation project. The situations are described when the optimal budget effect will be achieved without any support from the state, as well as when the maximum possible state support for R&D is not optimal. The analysis considers situations where the optimal budgetary effect can be achieved without government support, as well as situations where maximum acceptable support for R&D may not be optimal.

The paper aims to develop a model that enables to construct density forecasts of inflation in Russia. The reason is that domestic researches are mainly concentrated on providing point forecasts for inflation with little attention paid to constructing confidence intervals. However, predicting the entire conditional distribution of inflation may provide insights into uncertainty and risks associated with future price level movements implying a point projection as well. Therefore ordinary quantile regression and quantile regression neural network are used as forecasting tools, with a large number of potentially informative indicators being considered. Several ways of imposing the L1-regularization term are employed to implement variable selection. Among them are standard quantile Lasso-regression, Bayesian quantile Lasso-regression and linear Lasso-regression. The performance of the first one turns out to be the most successful compared to benchmarks such as linear and quantile autoregressions. Ordinary quantile regression with selected predictors provides qualitative results when constructing both interval and point forecasts. In turn, the use of the neural network approach allows for improved inflation forecasting over longer time horizons. Additionally, we found that exchange rate volatility, housing starts, government debt and natural gas prices are variables that significantly enhance the predictive properties of the model when incorporated into equations for some quantiles. Taking into account the error correction mechanism has also proved its importance. The models proposed in this paper can be used for constructing point forecasts of inflation as well as evaluating inflation risks.