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**Authors : **1. Mikhail I. Geraskin,
Doctor of Economics, Professor, Head of the Department of Mathematical Methods in Economics

*Samara National Research University named after academician S.P. Korolev*

2. Polina V. Porubova,
post-graduate student of the Department of Mathematical Methods in Economics

*Samara National Research University named after academician S.P. Korolev*

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Differential model of macroeconomic growth with endogenic cyclicity

**Objective:** to elaborate a mathematical model of economic growth, taking into account the cyclical nature of macroeconomic dynamics, with the model parameters based on the Russian economy statistics.

**Methods:** economic and mathematical modeling, system analysis, regression factor analysis, econometric time series analysis.

**Results:** the article states that, under unstable economic growth in Russia, forecasting of strategic prospects of the Russian economy is one of the topical directions of scientific studies. Furthermore, construction of predictive models should be based on multiple factors, taking into account such basic concepts as the neo-Keynesian Harrod-Domar model, Ramsey – Cass – Koopmans model, S. V. Dubovskiy’s concept, as well as the neoclassical growth model by R. Solow. They served as the basis for developing a multi-factor differential economic growth model, which is a modification of the neoclassical growth model by R. Solow, taking into account the labor-saving and capital-saving forms of scientific-technical progress and the Keynesian concept of investment. The model parameters are determined based on the dynamics of actual GDP, employment,

fixed assets and investments in fixed assets for 1965-2016 in Russia, on the basis of official statistics. The generalized model showed the presence of long-wave fluctuations that are not detected during the individual periods modeling. The cyclical nature of macroeconomic dynamics with a period of 54 years was found, which corresponds to the parameters of long waves by N. D. Kondratiev. Basing on the model, the macroeconomic growth forecast was generated, which shows that after 2020, the increase of scientific-technical progress will be negative.

**Scientific novelty:** a model is proposed of the scientific-technical progress indicator showing the growth rate of the capital productivity ratio to the saving rate; a differential model of macroeconomic growth is obtained, which endogenously takes cyclicity into account.

**Practical significance:** the differential growth model can be used to predict the macroeconomic dynamics, including economic crises, for the strategic regulation of the economy and elaboration of state programs of economic development.

**Keywords : **
Mathematical and instrumental methods in Economics; Economic growth; Cyclicality; Differential model of economic dynamics; Macroeconomic dynamics in Russia

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**Citation : **
Geraskin M. I., Porubova P. V. Differential model of macroeconomic growth with endogenic cyclicity, Actual Problems of Economics and Law, 2017, vol. 11, No. 3, pp. 43–55 (in Russ.). DOI: http://dx.doi.org/10.21202/1993-047X.11.2017.3.43-55

**Type of article : **The scientific article

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Date of receipt of the article : *

19.05.2017

Date of adoption of the print :

27.06.2017

Date of online accommodation :

25.09.2017