Optimization of structural dynamics of the economy in the framework of the “input-output” methodology

Publication type Article
Status Published
Occupation: professor
Affiliation: North Caucasus Federal University
Address: Stavropol, 355042, Stavropol, 50-letiya VLKSM, 67/3, ap. 8
Affiliation: Center for Sustainable Development, Kabardino-Balkar State University
Address: Russia
Affiliation: Scientific and educational mathematical center "North-Caucasus Center for Mathematical Re-search"
Address: Russia
Journal nameEkonomika i matematicheskie metody
EditionVolume 59 No. 2

The dynamic input-output balance model in the form of a system of differential equations, being digitized by the already published author's methodology, allows solving a wide range of problems of static structural stability of economic systems. Structural dynamics can be optimized by including any variable parameters in the vector and the limit of all model elements. In this paper, inter-sectoral inertias are chosen, and a method is proposed that uses a vector of parameters of an arbitrary (allowed by the model itself) length at the step of the search process. This distinguishes the proposed method from existing ones, making it unique. The uniqueness specified here lies in the removal of the so-called “curse of dimensionality” inherent in the classical optimization problems (numerical search problems) using methods from the coordinate-wise descent to the rich Newtonian-type tools. In this sense, the method is a competitor to machine learning-based optimization of artificial neural networks. At the same time, it does not matter how exactly the task is formalized: it should highlight the target indicators and the vector of variable parameters. It is possible to define and solve many optimization problems by changing the content of the vector of variable parameters according to the corresponding plan of the computational experiment. The paper presents only one example and one optimization stage. The limiting and functional conditions for the operation of the method preserve a linear relationship between the desired increments of the fundamental parts of the eigenvalues of the model state matrix and their sensitivities to control parameters. Such “small” optimization steps are separate and independent problems, the numerical solution of which can be repeated.

Keywordsdynamic input-output balance, digitization, optimization, sensitivities, singular value decomposition of a matrix.
Publication date30.06.2023
Number of characters31621
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1. Almon Cl., Grassini M. (2010). The changing structure of employment in Italy 1980–2010: Can investment affect the outcome? INFORUM Working Papers.

2. Almon K. (2021). The Art of economic modeling. Moscow: INP RAS, MAX Press (in Russian).

3. Andrukovich P.F. (2020). Notes on the principles of constructing models for forecasting economic indicators (on the example of the forecast system “prorosec”). Economics and Mathematical Methods, 56, 2, 66–76 (in Russian).

4. Ashimov A.A., Aisakova B.A., Alshanov R.A. (2014). Parametric regulation of economic growth based on non-autonomous computable general equilibrium models. Automation and Remote Control, 6, 69–85 (in Russian).

5. Baranov A.O. (2017). Recovery from the crisis and prospects for economic growth in Russia in 2018–2019. ECO Journal, 12, 5–17 (in Russian).

6. Baranov A.O., Kvaktun M.I. (2020). Forecasting accelerated renewal of fixed capital in Russia using a dynamic intersectoral model. Studies on Russian Economic Development, 2, 48–59 (in Russian).

7. Baranov A.O., Shirov A.A. (2020). Economic policy of Russia in the intersectoral and spatial di-mension: Materials of the 2nd conference of INP RAS and IEPP SB RAS on intersectoral and regional analysis and forecasting. Novosibirsk: Publishing House of IEOPP SB RAS (in Russian).

8. Baranov E.F., Elsakova A.V., Korneva E.S. (2015). Decomposition analysis based on input-output tables from the WIOD database. Moscow: Publishing House of the Higher School of Economics (in Russian).

9. Bertsekas D. (1982). Constrained optimization and multiplier methods. New York, London: Aca-demic Press, Inc.

10. Bertsekas D. (1987). Constrained optimization and lagrange multiplier methods. Transl. from the English. Moscow: Radio i Svjaz'. 400 p. (in Russian).Originally published by Academic Press, 1982.

11. Brunet F. (2011). Basics on Continuous Optimization. Available at: https://www.brnt.eu/phd/node10.html

12. Chen X., Guo J., Yang C. (2004). Chinese economic development and input-output extension. In-ternational Journal of Applied Economics and Econometrics, 12, 1, 43–88.

13. Dennis J.E., Schnabel R.B. (1988). Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, 1983). Moscow: Mir (in Russian).

14. Dennis J.E., Schnabel R.B. (1983). Numerical methods for unconstrained optimization and nonli-near equations. New Jersey: Prentice Hall Inc.

15. Dotsenko E.Yu. (2019). Structural inertia as a methodological tool for the study of structural shifts in the economy. Economics and Innovation Management. Scientific & Practical Journal, 1, 4–17 (in Russian).

16. Duszynski R.R., Toroptsev E.L., Marakhovsky A.S. (2018). Integration of information and ana-lytical opportunities of equilibrium and dynamic input-output models. Economic Analysis: Theory and Practice, 17, 4, 736–753. DOI: 10.24891/ea.17.4.736 (in Russian).

17. Duszynski R.R., Toroptsev E.L., Marakhovsky A.S. (2017). Systemic problems of economic growth in modern Russia. Economic Analysis: Theory and Practice, 16, 2, 204–220 (in Rus-sian).

18. Forsythe J., Malcolm M., Mouler K. (1980). Machine methods of mathematical calculations. Moscow: Mir (in Russian).

19. Glazyev S.Yu. (2012). The modern theory of long waves in the development of the economy. Eco-nomics of Contemporary Russia, 2 (57), 8–27 (in Russian).

20. Glazyev S.Yu. (2016). Applied results of the theory of world economic patterns. Economics and Mathematical Methods, 52, 3, 3–21 (in Russian).

21. Golub J., Lone C.W. (1999). Matrix calculations. Moscow: Mir (in Russian).

22. Grinberg R.S. (2015). The economy of modern Russia: Status, problems, prospects. Overall results of the system transformation. Journal of Globalization Studies, 1 (15), 166–182 (in Russian).

23. Grinberg R.S., Rubinstein A.Ya. (2008). The foundations of a mixed economy. Economic soci-odynamics. Moscow: IE RAS (in Russian).

24. Hemdi A.T. (2005). Introduction to operations research. 6th ed. Trans. from the English. Moscow: Williams (in Russian).

25. Ivanter V.V. (2017). Structural and investment policy for sustainable growth and modernization of the economy. Moscow: INP RAS (in Russian).

26. Kantorovich L.V. (2011). Selected works. Economic and mathematical works. S.L. Sobolev Insti-tute of Mathematics, SB RAS (in Russian).

27. Kasimov A.A., Bogatyrev A.V. (2009). Optimization of the resource policy of the enterprise. Rus-sian Journal of Entrepreneurship, 10, 4, 46–50 (in Russian).

28. Kleiner G.B. (2020). The intellectual economy of the digital age. Economics and Mathematical Methods, 56, 1, 18–33 (in Russian).

29. Kolemaev V.A. (2005). Economic and mathematical modeling. Modeling of macroeconomic processes and systems. Moscow: UNITY-DANA (in Russian).

30. Kondratiev N.D., Yakovets Yu. V., Abalkin L.I. (2002). Large cycles of conjuncture and the theory of foresight. Selected works. Moscow: Ekonomika (in Russian).

31. Krutko P.D., Maksimov A.I., Skvortsov L.M. (1988). Algorithms and programs for designing automatic systems. Moscow: Radio i Svjaz' (in Russian).

32. Kryukov V.A., Baranov A.O., Pavlov V.N., Suslov V.I., Suslov N.I. (2020). Problems of devel-opment of a single set of tools for macroeconomic interregional intersectoral analysis and forecasting. Economy of Region, 16, 4, 1072–1086 (in Russian).

33. Ksenofontov M.Yu., Shirov A.A., Polzikov D.A., Yantovsky A.A. (2018). Estimation of multip-licative effects in the Russian economy based on input-output tables. Studies on Russian Economic Development, 2 (167), 3–13 (in Russian).

34. Leontiev V.V. (1990). Economic essays. Theory, research, facts and policies. Moscow: Politi-cheskaja literatura (in Russian).

35. Madsen K., Nielsen H.B., Tingleff O. (2004). Methods for non-linear least squares problems. 2nd ed. Informatics and Mathematical Modelling (IMM), Technical University of Denmark (DTU), Lyngby.

36. Mirolyubova T.V., Karlina T.V., Nikolaev R.S. (2020). Digital economy: Problems of identifica-tion and measurement in the regional economy. Economics of Region, 16, 2, 377–390 (in Russian).

37. Mohajan H.K. (2012). Aspects of mathematical economics, social choice and game theory. PhD Dissertation, Lambert Academic Publishing, Germany.

38. Mohajan H.K. (2017). Optimization models in mathematical economics. Journal of Scientific Achievements, 2 (5), 30–42.

39. Mohajan H.K., Islam J.N., Moolio P. (2013). Optimization and social welfare in economics. Saarbrücken: Lambert Academic Publishing, Germany.

40. Petrikova E.M. (2011). Interrelation of indicators of payment and intersectoral balances. Voprosy Statistiki, 7, 59–68 (in Russian).

41. Pozamantir E.I. (2014). Computable general equilibrium of the economy and transport (transport in a dynamic intersectoral balance). Moscow: Poli Print Servis (in Russian).

42. Shirov A.A., Yantovsky A.A. (2017). Inter-industry macroeconomic model of RIM — develop-ment of tools in modern Russian conditions. Studies on Russian Economic Development, 162, 3, 3–19 (in Russian).

43. Smirnov V.I., Krylov V.I., Kantorovich L.V. (1933). Calculus of variations. Leningrad: Kubuch (in Russian).

44. Suvorov N.V., Crack S.V., Beletsky Yu. V. (2017). Balance and factor models as a tool for ana-lyzing and forecasting the structure of the economy. Moscow: MAKS Press (in Russian).

45. Svetunkov S.G., Abdullaev I.S. (2009). Economic dynamics and production functions. Vestnik of the Orenburg State University, 5 (99), 110–114 (in Russian).

46. Toroptsev E.L., Marakhovsky A.S. (2022a). Analysis of macrostructural dynamics within the framework of the input-output methodology. Journal of the New Economic Association, 1 (53), 12–30 (in Russian).

47. Toroptsev E.L., Marakhovsky A.S. (2022b). Structural inertia of economic systems. Economics and Mathematical Methods, 1, 58, 38–47 (in Russian).

48. Vojvodina V.V. (1968). Rounding errors in algebraic processes. Moscow: VC MSU (in Russian).

49. Wilkinson J. (1970). Algebraic problem of eigenvalues. Moscow: Nauka (in Russian).

50. Zaruk N.F., Galkin M.S., Svetlov N.M. (2019). Methodology of investment attractiveness analy-sis using economic and mathematical methods: Intersectoral aspect. Economy, Labor, Man-agement in Agriculture, 11, 63–76 (in Russian).

51. Zhang H., Chen X. (2008). An extended input-output model on education and the shortfall of hu-man capital in China. Economic Systems Research, 20, 2, 205–221.

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