# Èkonomika i matematičeskie metody

Journal “Economics and Mathematical Methods” is an open ground for international communication and information exchange, for sharing the results of fundamental and applied research among the specialists of academic, analytical and expert communities. The Journal is aimed at the highest level in scientific discussion of the problems, methods of research and economic development, inviting the most expertized participants — researches and practitioners. Utmost goal of the Publishers is to provide conditions for free discussion and sharing ideas to advance creative propositions and results of theoretic researches into the real economy. Major mission of the Journal is to provide opportunity to publicize the results of scientific works as well as share the knowledge and experience for scientific researchers. The Editorial board of the Journal aims to make it the leading journal among the serious scientific and education publications, well known in the world economic community, informing about the last advances in economic sciences. The articles accepted for further publication are validated as actual by the reviewers — their problems and solutions, their novelty and relevance of results; these requisites being the necessary terms for publications.

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## Current Issue

### Vol 59, No 1 (2023)

**Year:**2023**Articles:**11**URL:**https://journals.rcsi.science/0424-7388/issue/view/6672

#### Articles

##### Production theory for constrained linear activity models

###### Abstract

The purpose of this paper is to generalize the framework of activity analysis discussed in the paper by Antonio Villar without requiring any dimensional requirements on the activity matrices and by introducing a model of activity analysis in which each activity may (or may not) have a capacity constraint. We follow the usual nomenclature of input-output analysis for “the quantity of a good supplied to the consumers outside the production (or manufacturing) sector” and refer it as “final demand”. We obtain results similar to those in Villar concerning solvability, non-substitution and existence of efficiency prices. We apply our analysis and results to the two-period multisector activity analysis model with capacity constraints. The activity matrix is the difference between a non-negative output coefficient matrix and a non-negative input coefficient matrix, with the coefficients being measured in money units for each activity. Almost all the results obtained thus far get replicated in this macroeconomic context. However, some reformulations are required for issues related to existence of equilibrium price vector and as a consequence, issues related to efficiency prices via the non-substitution theorems. The corresponding concepts in this application refer to “inflation rate” vectors.

**Èkonomika i matematičeskie metody**. 2023;59(1):5-15

##### About production functions that take into account simultaneously Hicks-, Harrod- and Solow-neutral technological progress

###### Abstract

In this article, the H.Uzawa problem about analytical form of dynamic aggregated production functions that take into account simultaneously Hicks, Harrod and Solow neutral technological progress is considered. All classes of aggregated dynamic production functions that take into account simultaneously Hicks, Harrod and Solow neutral technological progress are described.

**Èkonomika i matematičeskie metody**. 2023;59(1):16-21

##### Forecasting the sectoral structure of population employment

###### Abstract

All the labor market subjects that can influence the labor resources dynamics are interested in employment forecasts by labor market sectors. Such subjects are state employees and municipal employees, employers and workers. The statistical data aggregation degree affects the quality of the labor resources dynamics forecasting. Each labor market indicator combines a set of detailed indicators in a high degree of aggregation case. When building the trends it is impossibile to take into account information on the detailed indicators trends. The labor market indicators for each specific year don’t contain information about the interaction with each other. This fact also negatively affects the forecast quality. The article discusses the use of a balance mathematical model of the labor resources dynamics, which relates the labor market sectoral indicators, to define the intersectoral movements indicators. The authors consider a calculating labor market indicators method that uses only statistical data on sectoral employment and unemployment. Thus, the statistical data on the labor resources dynamics provided by the Federal State Statistics Service is a sufficient condition for the Russian Federation labor market detailing using intersectoral movements’ indicators. The paper shows how a set of intersectoral movements indicators allows building the forecast values of these indicators and using them to calculate the forecast values of labor market indicators. The article considers examples of building employment estimates by Russian Federation economy sectors for 2011–2016 and 2019. The entry into force of the All-Russian classifier of types of economic activity second edition in 2017 is the reason for choosing such research intervals. The purpose of these examples was to determine the impact of the detailed labor market indicators of the sectoral employment estimates reliability. The authors compared the forecast obtained directly from labor market indicators with the forecasts obtained from intersectoral movements indicators. Intersectoral movements indicators are the results of applying balance models with varying degrees of detail. The reliability tables presented in this work to assess the forecasting quality indicate that the detailing of the sectoral employment indicators by using the balance model can increase reliability of the forecast.

**Èkonomika i matematičeskie metody**. 2023;59(1):22-29

##### Evaluation of the effects from various ways of import substitution “input–output” method: Evidence from the Russian Federation

###### Abstract

The article is devoted to the issue of assessing the economic effects of import substitution to determine the consequences of investment decisions at the state level in the context of geopolitical risks. Due to a number of economic restrictions on the part of Western countries, the problem of replacing those types of products for which trade turnover were suspended particularly acute. In the conditions of a dramatic shock reduction of supply in the markets of many industries, with the level of demand remaining, there is a need for emergent reorientation of domestic production. Public investments should take into account the multiplier effect caused by the impact of each industry's output on each other. The paper proposes methodology for constructing a theoretical model of global interaction of countries based on input–output tables that take into account the production needs of each industry in the production of other industries and the multiplicative effect. Two experiments, the impact on the economies of all the countries of termination of trade between Russia and the European Union in a number of industries with subsequent measures: the replacement of European products with goods and services through China as well as its import substitution at the expense of Russia's own product facilities. The consequences of two scenarios of changes in output, tax charges, imports and exports of Russia and the EU are estimated; long-term effects are predicted. The practical significance of this work consists in helping to make managerial decisions at the state level in financing certain sectors of the Russian economy.

**Èkonomika i matematičeskie metody**. 2023;59(1):30-47

##### Oil in the age of coronavirus: Hysteria or appropriate fall?

###### Abstract

We look at the oil price fall in the beginning of 2020 and the effects of coronavirus and the attention towards it on these prices. Such a fall was observed at multiple markets simultaneously with the spread of coronavirus and the panic around it, and oil market wasn’t an exception. Using OLS time series models, we investigate — what was the main reason behind such a fall — the coronavirus pandemic itself or rather the attention towards it. We prove the absence of straight effects of the COVID-19 itself on oil prices. At the same time we find significant negative impact of the attention towards COVID-19 on the Internet search on the oil prices. We investigate the role of the OPEC in mitigating the negative impact of coronavirus and the attention towards it. We found that after the OPEC summit both the number of Covid cases and the attention towards the disease lost its influence on oil prices. Our paper is relevant for the behavioral finance researchers, as well as for those who look at the influence of informational shocks on different markets and particularly, on the oil market and at the effect of the COVID-19 on the economy.

**Èkonomika i matematičeskie metody**. 2023;59(1):48-64

##### On the impact of excessive document flow on the labor activity of a budgetary organization employee

###### Abstract

The causes and results of the formation of excessive workflow in budgetary organizations are analyzed with the help of mathematical modeling. The model was built taking into account the opinion of the former head of the Ministry of Economic Development of the Russian Federation Maxim Oreshkin, according to whom excessive reporting consumes a huge amount of resources, and therefore can be generated with a hostile intent to create an obstacle to achieving national goals. The model is based on the following assumptions: An agent (an employee of a budgetary organization) cannot refuse to carry out the reporting burden. An official (an employee of a higher ranking organization or a representative of government bodies) has an uncontrolled and unlimited opportunity to demand that the controlled organization draw up documents in the form proposed by him and provide them within the specified time. The utility of the official increases with receipt of these documents. It is shown that under such conditions the official benefits by unlimitedly increasing labor intensity of the reporting burden imposed on the agent. As a result of an increase in the amount of unpaid effort spent by an agent on reporting, his activity, which is determined by the part of paid efforts that exceed their minimum volume, drops to zero. The activity of two officials is compared: one of them has no hostile intentions and simply increases his work’s utility, while the other pursues a hostile goal to paralyze the work of the controlled organization. It is shown that there is only a quantitative difference in the results of their activities: the threshold value of the complexity of tasks, the achievement or exceeding of which destroys the activity of the agent, is lower in the case of a hostile official. Three possible ways of limiting the activity of an official are discussed: taxing the controlling organization with a corrective tax, full compensation for the costs of the controlled organization, and legislative restriction of document flow.

**Èkonomika i matematičeskie metody**. 2023;59(1):65-78

##### Empirical analysis of risks’ influence on the large mergers and acquisitions projects’ success in modern companies

###### Abstract

Mergers and acquisitions (M&A) are among the key strategies for stabilizing and strengthening a company's market position in an unstable economic environment and gaining a competitive advantage from inorganic growth. Doing so, big M&A deals show a higher risk of failing, being terminated, or being incomplete, which can lead to financial, reputational, and time losses. Due to these factors, prudent risk-management of such transactions is necessary, including the evaluation of the degree to which various risk groups influence M&A success. This paper evaluates big (those the value of which exceeds 10 billion euros) M&A projects risks influence on the success of the deal closure quantitatively and offers recommendations for managing significant risks using the project methodology. The analysis includes probit-regressions on a wide sample of 24 countries and 10 amalgamated industries. As a result, five risk groups appear significant: risk of transaction's hostile nature; cross-country risks; risk of misjudging the transaction value; risks associated with the size ratio of target and acquiring companies; risk of delaying the terms of the deal. Transnational mergers and acquisitions demonstrate a stronger influence of all significant risks on the transaction's success. The paper provides recommendations for managing significant risks using the project methodology.

**Èkonomika i matematičeskie metody**. 2023;59(1):79-92

##### The macroeconomic role of the collateral constraint in resource-rich countries

###### Abstract

In this paper, we consider DSGE model of a small open economy highly dependent on resource export. The aim of the study is to identify the role of the collateral constraint in the terms-of-trade (TOT) shock transmission. The model contains two non-linear constraints in the form of inequalities: the collateral constraint and the zero lower bound constraint. We have found that if the monetary policy is not inertial, then under a series of unidirectional TOT shocks, the response of the economy is highly skewed with respect to positive and negative shocks. Both inequalities bind and reduce the positive impact of the TOT shock. If the monetary policy is inertial or the central bank reacts poorly to inflation change, then only the collateral constraint binds, and the effect of asymmetry almost disappears

**Èkonomika i matematičeskie metody**. 2023;59(1):93-104

##### Approximation to portfolio liquidation value with calculation of its skewness

###### Abstract

A boundary problem for a homogeneous multidimensional diffusion process is considered under the assumption of small perturbations. Approximations to the mean, second and third central moments of the process at the moment of the first crossing a given plane in phase space are presented as a solution of ordinary differential equations with an additional transformation (“projection onto the boundary”). The quantile of a linear combination of coordinates is estimated by the second order expansion in powers of a small parameter determining the magnitude of perturbations. In the first approximation, this expansion corresponds to the Gaussian distribution, the next term contains skewness. The result is extended to a process with multiple boundaries, upon reaching each of them the equation of the process changes. Such a model describes the liquidation of a portfolio of financial instruments in which the closing rate of each of the positions is a random process. The result is illustrated by two examples. In the first example a portfolio consists of linear instruments (such as stocks, futures), prices are correlated Geometric Brownian Motions with zero drift. The closing rates are constant, but with random noise due to daily fluctuations in trading volume. In this particular case approximations for the mean, variance, skewness, VaR and CVaR of the financial result of portfolio liquidation are given explicitly. In the second example, the liquidation of an exchange-traded option position is considered under the assumption that the closing rate depends on the ratio of the underlying price to the strike of the option. Numerical calculations demonstrate that taking into account skewness significantly increases the accuracy of estimates.

**Èkonomika i matematičeskie metody**. 2023;59(1):105-118

##### Reducing the dynamic model of the software development market to a block problem of convex programming

###### Abstract

The authors propose to reduce a discrete dynamic model of the software development market to a block problem of convex programming, which can be solved by successive approximations based on contraction mapping, in case of abandoning the integer elements of the destination matrix. However, there are also peculiarities: equilibrium prices can be calculated directly and therefore a variational formulation of the internal problem of determining equilibrium prices based on Debreu's theorem is not required. The functions of phase coordinates’ change can be taken as convex, for example, the norm of the difference squared, and do not take into account the fixed costs for each control switch, which is excluded from the equations of system’s dynamics. The resulting block problem of convex programming allows decomposition by freezing the connection variables with neighboring blocks at the level of the previous iteration. It is shown that the operator on the right side of the resulting recurrent equation is compressive under fairly general conditions. This allows the authors to prove successive approximations for solving the resulting problem, based on the principle of contraction mapping. The authors give the model example of its use in the dynamic expansion of the transport problem according to the value.

**Èkonomika i matematičeskie metody**. 2023;59(1):119-130

##### Analysis of the influence of heterogeneous expectations of economic agents on the stability of general equilibrium models with an open economy

###### Abstract

The purpose of the publication is to study the influence of bounded rationality of agents on the ability of economic authorities to choose alternative policy rules that stabilize the dynamics of the relevant significant macroeconomic variables by simultaneously analyzing the entire range of model parameters. The scientific novelty lies in the fact that models with an open economy are analyzed, in which economic agents interact with the outside world. The article evaluates and compares behavioral neo-Keynesian models obtained with two alternative ways of introducing heterogeneous expectations. It is assumed that agents can be either short-sighted with a short-term forecast, or far-sighted forecasters. The difference does not matter when the agents have rational expectations, but it does matter when some of them form beliefs about the future according to some heuristics. Bayesian estimates based on the data of the Russian economy show that the behavioral model based on short-term forecasts is better in agreement with empirical data than the model based on long-term forecasts and even compared to the model with rational expectations of agents. Stability and stability analysis was carried out using a numerical procedure — Monte Carlo Filtration Mapping (MCF). This procedure generalizes and supplements the results obtained for a more limited set of parameters of low-dimensional models in which agents do not interact with the outside world. MCF-analysis shows that incorporating heterogeneous expectations reduces the stability and robustness of models. At the same time, a model based on predictors of long-term forecasting is less stable compared to models of short-term forecasting and with rational expectations of agents. An important result is a significant proportion of areas with unstable behavior of the studied models with heterogeneous expectations of agents, in which solutions are characterized by an explosive nature. With the help of Smirnov–Kolmogorov statistics, significant parameters were identified that determine the deterministic behavior of all analyzed models. An interesting result is: the response of the interest rate to changes in the output gap and changes in the real effective exchange rate does not affect the deterministic behavior of the models under study. All obtained results are confirmed by a posteriori Bayesian estimates for these parameters. The findings provide guidance to economists who study the processes of expectation formation with the help of microdata.

**Èkonomika i matematičeskie metody**. 2023;59(1):131-144