+7 925 966 4690, 9am6pm (GMT+3), Monday – Friday
ИД «Финансы и кредит»






Regional Economics: Theory and Practice

A dynamic input-output model of the Tyumen Oblast south's development based on the von Neumann algorithm

Vol. 21, Iss. 5, MAY 2023

Received: 30 March 2023

Received in revised form: 11 April 2023

Accepted: 20 April 2023

Available online: 16 May 2023


JEL Classification: B16, B21, D57, H72, R13

Pages: 959–975


Vladimir R. TSIBUL'SKII Center for Ethno-Ecological and Technological Research of Siberia, Tyumen, Russian Federation


Il'ya G. SOLOV'EV Industrial University of Tyumen (IUT), Tyumen, Russian Federation


Denis A. GOVORKOV Industrial University of Tyumen (IUT), Tyumen, Russian Federation


Subject. This article deals with the problem of constructing a real trajectory of the region's development and comparing it with the stated one.
Objectives. The article aims to develop an algorithm for calculating and analyzing a dynamic input-output model of the south of the Tyumen Oblast, including social and infrastructural subsystems, and households as an endogenous variable-aggregate.
Methods. For the study, we used the methods of construction and analysis of dynamic models by W. Leontief and J. von Neumann. Indicators of balanced growth trajectories were estimated using the Perron–Frobenius theorem.
Results. The article proposes an algorithm for the formation of an investment variable. The matrix of direct costs for each year and on average for the periods 2017–2019 and 2017–2020 was identified. Based on the available statistical data, von Neumann highways and model development trajectories were constructed.
Conclusions. The shown mechanism for a possible comparison of actual and planned optimal development can help organize digital monitoring of the region's development and analyze deviations from the optimal forecast.

Keywords: input-output balance, dynamic von Neumann model, adjustment of model coefficients, development strategy, Tyumen Oblast, growth trajectory


  1. Miller R., Blair B. Input-Output Analysis. Foundations and Extensions. Cambridge, Cambridge University Press, 2009, 750 p. URL: Link
  2. Ibragimova N.M. [Modeling household income and expenditure multipliers in the SAM model: estimations for Uzbekistan]. Ekonomika i matematicheskie metody = Economics and Mathematical Methods, 2017, vol. 53, no. 4, pp. 75–88. URL: Link (In Russ.)
  3. Leontief W.W. Mezhotraslevaya ekonomika [Input-Output Economics]. Moscow, Ekonomika Publ., 1997, 479 p.
  4. Smirnov N.V., Smirnova T.E. [Prediction of macroeconomic trends and control of a multicommodity economy based on the dynamic input-output models]. Finansy i biznes = Finance and Business, 2015, no. 1, pp. 42–53. URL: Link (In Russ.)
  5. Shishkin A.A., Shishkin A.I. [Determining the trajectory of regional development]. Ekonomika i upravlenie = Economics and Management, 2017, no. 4, pp. 27–32. URL: Link (In Russ.)
  6. Mashunin Yu.K., Mashunin I.A. [Organization of management, modeling and forecasting of development of economy of the region]. Regional'naya ekonomika i upravlenie: elektronnyi nauchnyi zhurnal, 2016, no. 1, pp. 29–58. (In Russ.) URL: Link
  7. Dzhurka N.G. [Development trajectories of the Russian Far East: evaluation based on the dynamic model of economic interactions]. Problemy prognozirovaniya = Studies on Russian Economic Development, 2018, no. 2, pp. 49–59. URL: Link (In Russ.)
  8. Dyrkheev K.P. [Extended input-output model of the region based on Miyazawa's methodology]. Vestnik Buryatskogo gosudarstvennogo universiteta. Ekonomika i menedzhment = Bulletin of Buryat State University. Economics and Management, 2017, no. 3, pp. 65–71. URL: Link (In Russ.)
  9. Serebryakov G.R., Uzyakov M.N., Yantovsky A.A. [The Ivanovo Oblast economy: An IO model]. Problemy prognozirovaniya = Studies on Russian Economic Development, 2002, no. 5, pp. 64–74. URL: Link (In Russ.)
  10. Mikheeva N.N. [Long-term forecasts of regional development: analysis of results and the problem of development]. Problemy prognozirovaniya = Studies on Russian Economic Development, 2018, no. 5, pp. 24–38. URL: Link (In Russ.)
  11. Batey P.W.J., Weeks M.J. The Effects of Household Disaggregation in Extended Input-Output Models. In: Miller R.E., Polenske K.R., Rose A.Z. (eds) Frontiers of Input–Output Analysis. New York, Oxford University Press, 1989, pp. 119–133.
  12. Batey P.W.J., Madden M., Weeks M.J. Household Income and Expenditure in Extended Input-Output Models: A Comparative Theoretical and Empirical Analysis. Journal of Regional Science, 1987, vol. 27, iss. 3, pp. 341–356. URL: Link
  13. Uzava H. Optimum Technical Change in an Aggregative Model of Economic Growth. International Economic Review, 1965, vol. 6, no. 1, pp. 18–31. URL: Link
  14. Tsibulsky V.R., Vazhenina L.V., Solovyov I.G. et al. Assessment of the Leontiev Productive Matrix of the Economic Development Model for Tyumen Region (Russia). R-Economy, 2022, vol. 8, iss. 2, pp. 135–147. URL: Link
  15. Tsibul'skii V.R., Solov'ev I.G., Vazhenina L.V., Govorkov D.A. [Estimation of the input-output balance model for the south of the Tyumen Oblast]. Regional'naya ekonomika: teoriya i praktika = Regional Economics: Theory and Practice, 2022, vol. 20, iss. 8, pp. 1586–1604. (In Russ.) URL: Link

View all articles of issue


ISSN 2311-8733 (Online)
ISSN 2073-1477 (Print)

Journal current issue

Vol. 21, Iss. 5
May 2023