Classical Linear-Control Analysis Applied to Business-Cycle Dynamics and Stability

Classical linear-control analysis provides a framework for studying dynamic systems involving random disturbances. This framework is used to develop a set of equations that, in historical perspective, combine traditional concepts about the dynamics of economic systems and about the effects of random economic disturbances. This set of equations provides relationships among well-known ideas in general macroeconomics and provides a means to interrelate and examine ideas about stabilization policies. In this study, linear-control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.