Back
 AM  Vol.9 No.5 , May 2018
Nonlinear Differential Equation of Macroeconomic Dynamics for Long-Term Forecasting of Economic Development
Abstract:
In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investment. A scheme is proposed for obtaining approximate solutions of nonlinear differential equation by splitting solution into the rapidly oscillating business cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging. Simplest modes of the economic system are described. Characteristics of the bifurcation point are found and bifurcation phenomenon is interpreted as loss of stability making the economic system available to structural change and accepting innovations. System being in a nonequilibrium state has a dynamics with self-sustained undamped oscillations. The model is verified with economic development of the US during the fifth Kondratieff cycle (1982-2010). Model adequately describes real process of economic growth in both quantitative and qualitative aspects. It is one of major results that the model gives a rough estimation of critical points of system stability loss and falling into a crisis recession. The model is used to forecast the macroeconomic dynamics of the US during the sixth Kondratieff cycle (2018-2050). For this forecast we use fixed production capital functional dependence on a long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles. More accurate estimations of the time of crisis and recession are based on the model of accelerating log-periodic oscillations. The explosive growth of the prices of highly liquid commodities such as gold and oil is taken as real predictors of the global financial crisis. The second wave of crisis is expected to come in June 2011.
Cite this paper: Akaev, A. (2018) Nonlinear Differential Equation of Macroeconomic Dynamics for Long-Term Forecasting of Economic Development. Applied Mathematics, 9, 512-535. doi: 10.4236/am.2018.95037.
References

[1]   Allen, R.G.D. (1960) Mathematical Economics. Macmillan and Co. Ltd., London, St. Martin’s Press, New York.

[2]   Solow, R. (1956) A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics, 70, 65-94.
https://doi.org/10.2307/1884513

[3]   Schumpeter, J.A. (1934) The Theory of Economic Development. Harvard University Press, Cambridge.

[4]   Schumpeter, J.A. (1939) Business Cycles. McGraw-Hill, New York.

[5]   Kydland, F. and Prescott, E. (1982) Time to Build and Aggregate Fluctuations. Econometrica, 50, 1345-1370.
https://doi.org/10.2307/1913386

[6]   Akaev, A.A. (2007) Derivation of the General Macroeconomic Dynamics Equation Describing the Joint Interaction of Long-Term Growth and Business Cycles. Doklady Mathematics, 76, 879-881.
https://doi.org/10.1134/S1064562407060191

[7]   Stoleru, L. (1967) L’equilibre et la croissance economiques: Principes de macroeconomie. Dunod, Paris.

[8]   Okun, A.M. (1970) The Political Economy of Prosperity. Norton, New York.

[9]   Sachs, J. and Larrian, F. (1993) Macroeconomics in the Global Economy. Prentice Hall, New York.

[10]   Bogolyubov, N.N. and Mitropol’skii, Yu.A. (1962) Asymptotic Methods in the Theory on Nonlinear Oscillations. Gordon & Breach, New York.

[11]   Akaev, A.A. (2008) Influence of Business Cycles on Long-Term Economic Growth. Doklady Mathematics, 78, 1-5.
https://doi.org/10.1134/S106456240804039X

[12]   Pantin, V.I. and Lapkin, V.V. (2006) Philosophy of Historical Forecasting: Rhythms of History and Perspectives of World Development. Fenix +, Dubna.

[13]   Akaev, A.A. (2008) An Analysis of Solutions of General Equation of Macroeconomic Dynamics. Economics and Mathematical Methods, 44, с62-c78.

[14]   Akaev, A.A., Galileev, M.M. and Mikhailushkin, A.I. (2011) Computer Analysis of the Model of Long-Term Economic Development. Future Projects and Risks. М: KRASAND, 130-137.

[15]   Hansen, A. (1951) Business Cycles and National Income. W. W. Norten, New York.

[16]   Hirooka, М. (2006) Innovation Dynamism and Economic Growth. A Nonlinear Perspective. Edward Elgar, Cheltenham, Northampton.

[17]   United Nations Database.

[18]   Kaldor, N. (1961) Capital Accumulation and Economic Growth. The Theory of Economic Growth. St. Martin’s Press, New York, 177-222.
https://doi.org/10.1007/978-1-349-08452-4_10

[19]   Hall, R.E. (1978) Stohastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence. Journal of Political Economy, 86, 971-987.
https://doi.org/10.1086/260724

[20]   Artamonov, N.V. (2008) Theory of Random Processes. М: “MGIMO University” Publishing House.

[21]   Wilson, D. and Parashothaman, R. (2003) Dreaming with BRICs: The Path to 2050. Goldman Sachs; New York, Global Economics Paper 99.

[22]   Sornette, D. and Johansen, A. (2001) Significance of Log-Periodic Precursors to Financial Crashes. Quantitative Finance, 1, 452-471.
https://doi.org/10.1088/1469-7688/1/4/305

[23]   Akaev, A., Fomin, A., Tsirel, S. and Korotayev, A. (2011) Log-Periodic Oscillation Analysis Forecasts the Burst of the “Gold Bubble” in April-June 2011. Structure & Dynamics, 5, 3-18.

[24]   Marchetti, C. and Naricenovic, N. (1979) The Dynamics of Energy Systems and the Logistic Substitution Model. International Institute for Applied Systems Analysis, Laxenburg.

[25]   Korotayev, A. and Tsirel, S. (2010) A Spectral Analysis of World GDP Dynamics: Kondratieff Waves, Kuznets Swings, Juglar and Kitchin Cycles in Global Economic Development, and the 2008-2009 Economic Crisis. Structure and Dynamics, 4, 3-57.
http://www.escholarship.org/uc/item/9jv108xp

[26]   Akaev, A., Sadovnichy, V. and Korotayev, A. (2012) On the Dynamics of the World Demographic Transition and Financial-Economic Crises Forecasts. The European Physical Journal Special Topics, 205, 355-373.
https://doi.org/10.1140/epjst/e2012-01578-2

 
 
Top