The state of art:

The first attempt to explain the cause of economic oscillations based on macroeconomics is found in the papers by Tinbergen (1930), and Frisch (1933). They tried to explain the cyclical behaviour of an economy through fluctuations of investments, using a special diference-differential equation. Later Kaldor (1940), and Goodwin (1951), developed further the endogenous concept of the business cycles. The approach of these authors is challenging because of the concept of nonlinearity in their models. This nonlinearity keeps the economy on a limit cycle, preventing the system from exploding, and the depression periods of the economy are always shorter than the boom ones. Chiarella (1990) proposed a model in which the nonlinear economic dynamics is explained. The nonlinear relationship in his model is embodied in the velocity of money circulation, where the velocity is a nonlinear function of expected inflation. The model was improved by Flaschel, Franke and Semmler (1997). These authors introduced a class of non-linear dynamism in which they examine monetary behaviour in the short-term, macroeconomic fluctuations and the interaction of product, labour, and the monetary sector. These models are able to encompass a more complex dynamic behaviour of economy.

Research objectives:

The research team will focus to the further development of the theory of the non-linear macro-economic deterministic systems including monetary sector. The research will be based on mentioned level of knowledge. The methodology will be based on the systems of non-linear ordinary differential equations and system of delay-differential equations. The equilibrium, stability and complex dynamics (nonlinear oscillations and chaos) will be examined. The members of the Working Group have published several papers in this field and shall push the research further within this Project.

In connection with the above mentioned, the empirical research in the field of the non-linear time series analysis will be conducted. In recent years, the regime switching models seem to be practically applicable and usable. The SETAR (Self-Exciting Threshold Autoregressive), STAR (Smooth Transition Autoregressive) and MSW (Markov-Switching) class of models will be used and developed, see Hamilton and Baldev (2002).

References

• Chiarella, C. (1990). The Elements of a Nonlinear Theory of Economic Dynamics. Springer Verlag, Berlin.
• Flaschel P., Franke R., and Semmler, W. (1997). Dynamic Macroeconomics. MIT Press, Cambridge (USA).
• Frisch, R. (1933). Propagation Problems and Impulse Problems in Dynamic Economics. Essays in Honor of Gustav Cassel. Allen and Unwin, London.
• Goodwin, R. M. (1951). The Nonlinear Accelerator and Persistence of Business Cycle. Econometrica 19 (1), 1–17.
• Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton.
• Hamilton, J. D. and Baldev, R. (eds.). (2002). Advances in Markov-Switching Models: Applications in Business Cycle Research and Finance (Studies in Empirical Economics). Physica Verlag, Berlin.
• Hillinger, C. (2005). Evidence and Ideology in Macroeconomics: The Case of Investment Cycle. Recent Developments in Macroeconomics, Eastern Economics Association.
• Kaldor, N. (1940). A Model of the Trade Cycle. Economic Journal 50, 78–92.