Forecasting and control in nonlinear economic models with application to economic policy

Abstract

The complex irregular dynamics that arise in an economy can lead to instabilities and disruptions of an economic system. A system can be unstable not only due to the impact of external random shocks such as major bankruptcies, oil and currency shocks, floods, epidemics, but also by deterministic endogenous forces that are often hidden within the economic mechanism. In such cases, the system can go over to an irregular, including chaotic, mode. This creates difficulties for forecasting and controlling the behavior of the economic processes as well as for economic policy-making.

This dissertation is devoted to the development of effective analytical and numerical procedures based on nonlinear dynamics methods and control theory, including theory of hidden oscillations and chaos control, for forecasting, analysis, and control of complex dynamics in economic models, in order to help the design of economic policy rules.

The dissertation consists of three parts with nine journal publications that contain the obtained results. In the first part, we perform global stability analysis of the mid-size firm model and use the Pyragas control method to suppress chaotic behavior. Estimates and exact formula for characteristics based on Lyapunov exponents are obtained for the chaotic attractor in the model as a quantitative measure of irregular dynamics. These results could be used to forecast the model behavior and help decision-makers to control the behavior of the economic system. In the second part, we introduce New Keynesian models, which describe the dynamics of consumption, government bonds, inflation, and capital stock, where the interaction of monetary and fiscal policy rules could affect the emergence of complex dynamics, including complicated attracting sets of various nature. The government and the central bank can influence the dynamics of the system by controlling parameters of these policy rules. In the third part, we utilize the optimal control method to study analytically the problem of dynamical optimal allocation of resources in a three-sector balanced economy. For an unbalanced economy we obtained the optimal allocation of resources using a numerical optimization algorithm. These results can be applied to real-world economic problems for finding and fine-tuning of the optimal values of the resource distribution parameters.