Economics and Mathematical Methods

In modern scientific literature the category of «capital» is beginning to be applied to a wide range of company assets that can bring economic benefits over a long period of time. Various researchers distinguish human, intellectual, social, network and other types of capital. This makes it urgent to develop new approaches to assessing various types of capital, taking into account their complementary specificity. Within the framework of this article the task is to propose a new approach to measure company’s network capital. Existing methods for estimating company’s value are often based on summing up the costs of individual types of capital. However, such an additive approach does not consider the complementary nature of different types of capital. The work proposes to use a multiplicative approach based on the modified Cobb–Douglas function, which takes into account property and network capital as well as the economic efficiency of the company. This approach takes into account the complementarity of different types of capital and their combined impact on the value of а company. Seven leading global companies in the IT industry (Microsoft, Apple, Oracle Corp., Alphabet, Baidu, Meta, Twitter) were chosen as the empirical basis for the study. The proposed approach made possible to compare the network capital of different companies and identify the factors influencing its accumulation.

Effective management of national science and research is on the constant rise, so the task of revealing how economic “return” from the research and development sector can be maximized is becoming more and more relevant. The article examines the mutual influence of the development of science and the funding of research and development in 97 countries around the world, on the one hand, and their national per capita incomes, on the other hand. A wide range of indicators is used, including patent activity, research and development expenditures, the number of researchers and the number of Scopus-indexed publications by subject area (relative to the population of countries). Among all the subject areas studied, the number of publications in economics is most closely related to the level of GDP per capita (PPP). We then use linear multiple regression to study the relation between the number of Scopus-indexed publications in economics and expenditures on research and development. A comparison of simulated data with real data shows that oil and gas producing countries (including Russia) demonstrate an economic level higher than expected. The leading world economies (USA, China, Japan, Germany, France, Great Britain) are well described by our resulting model. Ensuring high expenditure on research and development is of paramount importance for modern economic growth. In addition, an overall high level of publication activity is important, with particular attention to the development of research in economics.

The purpose of the study is to develop analytical tools and methodological support for assessing the stability and vulnerability of sectors of the national economy to the effects of external sanctions. The study of the problem was based on the general scientific methods of generalization, analysis and classification. Methods of logical, economic, content, statistical, investment and expert analysis were used, as well as methods of econometric and mathematical modeling to achieve the research goal. A system of indicators for assessing the operational (technological and commercial) and investment dependence of the economic sector on imports is proposed. Methodological methods for assessing the sanctions dependence of the industry in the formation of production and investment development programs are substantiated. Examples of calculations of dependence indicators by levels and aspects of the industry description in the operating and investment areas are given. Recommendations are given on the use of the proposed indicators in the process of strategic and programming development in the conditions of ensuring technological independence and structural adaptation of the Russian economy.

It is often difficult to choose the necessary variables when we are forecasting the economic dynamics. On the one hand, vector autoregression (VAR) models can solve this problem by taking into account a sufficiently large number of variables. However, on the other hand, excessive parametrization of such models is not always justified, because it is often possible to choose such a small combination of variables the predictive power of which will be no worse than unlimited VARs with a large number of variables and lags. Bayesian methods help to solve this problem by introducing a priori restrictions on the VAR coefficients. The main goal of this work is to build a Large quarterly Bayesian vector autoregression (QBVAR) for the modern Russian economy. The hypotheses of the study: 1) BVAR(p) models reveal their maximum potential with a small number of variables, but with a large number of lags, 2) The Minnesota prior distribution is not always the best option for the modern Russian economy in the BVAR(p) model. As a result of the analysis, it turned out that for a number of the most important macroeconomic variables (GDP, inflation, key rate, unemployment, wages), Normal-Flat / Wishart-type priors turned out to be the optimal. In case of 29 input variables and two lags, the predictive power of the QBVAR(2) model is worse than the equivalent frequency VAR(2) or VECM(2). However, when it was possible to find the optimal combinations of variables, QBVAR(p) turned to be several times more accurate than its analogous frequency VAR(p) for all important macro indicators. In addition, the stiffness parameters of the considered a priori distributions decreases with increasing lags entering the model, i. e. the higher the order of the model with the minimum optimal set of variables, the tighter the distribution is necessary to obtain more accurate predictions. For the Russian realities, it is necessary to use very tight priors, 6–8 variables and 9–12 lags in a quarterly representation.

The quality and timeliness of medicinesʼ supply to the healthcare system through public procurement is an urgent task of public policy in all countries of the world, including Russia. Failure to close (failure of tenders, termination of already concluded contracts) procurement procedures in such a socially significant area carries risks for the population, provokes the emergence of hidden transaction costs for the budget system to eliminate the consequences of procurement failures. In their previous works, the authors identified the factors that lead to the failure to close tenders for the purchase of remedies, and initially assessed the consequences of their influence on procurement procedures. The purpose of this article is to present a mathematical model of the probability of non-closure tenders based on the obtained results. To achieve this goal, through processing more than 1 million notifications of public procurement of remedies for 2022–2023, collected from the open sources, the tasks with no methodological solutions were completed. Thus, a set of features accompanying the failure to close procedures for the purchase of remedies was compiled. The composition of identified features was analyzed; their influence on non-closure of the procedure was assessed. A model of the probability of non-closure of the procedure was constructed, and the results were interpreted. Unlike previously published studies, the forecast model was implemented on the ensembles of decision trees using gradient boosting. This made possible to significantly improve the quality of the forecast for each factor affecting the probability of non-closure of the bidding. The results obtained in the article are not only scientifically novel, but can also be used by regulatory and control bodies in public procurement to develop methodological recommendations for customers on establishing optimal conditions for concluding and fulfilling contracts, which will reduce procurement risks and damage to the state budget.

Currently, all three components of sustainable development at all levels are becoming increasingly important to ensure the existence and development of states. This article is devoted to green finance, linking economic and environmental aspects of development. Green financing is a policy direction to reduce negative environmental externalities and attract investment in new technologies, which has become widespread in recent years; green bonds are one of its most important instruments. To assess the impact of issuing green bonds on the environmental component, represented by the equivalent of carbon monoxide emissions, the article was the first to apply a matching procedure to evaluate company data obtained using the Refinitiv database. The authors showed a model specification that supports the hypothesis that the issuance of green bonds has an impact on reducing carbon monoxide equivalent emissions in the long term, but the results of the logarithmic specification of this model turned out to be unstable. From the calculations presented in the article it follows, that despite the fact that the effect of issuing green bonds does not have an immediate impact on the company’s environmental performance, but in the long run it can improve their performance. It helps to raise environmental rating of companies and, in turn, can help attract investments for the development of technologies and infrastructure that ensure technological independence, the use of promising energy sources, the best available technologies, and the transport greening.

In the context of the development of scientific and technological progress and the growth of the capital stock, an important task is modeling and optimization of the terms of operation of production funds. The development of technologies and automation of production lead to a reduction in the workforce employed in production. In the article, for the previously developed single-product dynamic model of the replacement of production assets, taking into account the inertial properties of the funds being introduced, the case of a reduction in labor resources under the condition of an increase in output and capital investment is investigated. A solution was obtained that allows to determine the optimal strategy for the withdrawal of obsolete funds and the introduction of the new ones in case of decrease in labor resources. As the optimization criterion the principle of differential optimization is used. The theorem of equivalence of a trajectory satisfying the principle of differential optimization, the obtained solution is given. A system of functional differential equations is presented, which should be satisfied by variable models both in terms of growth and reduction of labor resources. Numerical methods are used to solve such a system. The variants of the system development are considered under various assumptions regarding changes in the total amount of labor resources. The results of numerical implementation of the model are presented.

In this paper we develop a method for constructing a paired regression model in the class of piecewise linear continuous functions with fixed nodes. The concept of linear division of the correlation field, its partial sections and its nodes is introduced into consideration. Using the linear division of the correlation field, a class of piecewise linear functions with fixed nodes is determined. The linear division is revealed during the visual analysis of the correlation field. Using the least squares method, a system of linear equations is compiled to find point estimates of the parameters of the approximating function. With the exception of two unknown angular coefficients (unknown) this system is reduced to a tridiagonal system of equations, the unknowns of which are the nodal values of the approximating function. The tridiagonal system is solved by the run-through method. An algorithm was constructed to demonstrate the operation of the developed method. Its initial data is arrays of the corresponding values of the explanatory and dependent variables, as well as an array of numbers of the right ends of the intervals defining the nodes. An array of fixed nodes is constructed from an array of values of the explanatory variable and an array of numbers of the right ends of the intervals. Next, an array of point estimates of the parameters of the approximating function is constructed. This algorithm is implemented in Python in the form of user-defined functions.