Optimal Policies for Economic Stabilization

Abstract

SOME FIFTEEN YEARS have passed since Phillips [15] first showed that the application of certain types of stabilization policies to multiplier-accelerator macroeconomic models could result in undesired oscillations or instabilities. It has become clear from this and other analyses of macroeconomic policy [1, 3, 5, 16] that, because of the dynamic structure of the economy, well-intentioned policies may have unexpected and counterintuitive results. In recent years a number of economists have demonstrated the potential application of the mathematical techniques of optimal control theory to economic policy formulation for stabilization [6, 20, 22] as well as long-run growth and development [7, 8, 12, 13, 21]. While much of this work has been successful in showing how optimal control could be applied to policy problems, there has been little attempt made to actually apply it to a realistic policy problem, particularly in the area of short-run stabilization. A goal of this paper is to show that if one is willing to work with a linear or linearized economic model and quadratic cost criteria, optimal control theory can provide a viable tool for both analyzing and understanding the dynamic properties of the model, and for formulating stabilization policies based on the model. In this paper economic stabilization will be approached as a dual tracking problem in optimal control. The problem that is defined and solved involves tracking nominal state and nominal policy trajectories, subject to a quadratic cost function and the constraint of a linear system. This is actually quite general and will enable us to penalize for variations in, as well as the levels of, the state variables and control variables. Moreover, this lets us structure the problem as one without absolute limitations on the sets of allowable controls and allowable states; any restrictions that are to be imposed on the motion of control or state variables are expressed by assigning higher costs to their deviations. We will also