Method of stochastic optimal control by bayesian filtering techniques

Abstract

Application of optimal control, for planning a dynamic economy, calls for the specification and estimation of a proper econometric model. This estimation is based upon information available up to the current period. Future information, however, should be taken into consideration, in order to allow the policy maker to adjust his response by revising the model according to the new information. In this case, we may have at each time instant an updating process of the economic system and an analogous revision process of the plan. In the control literature this type of control may be called either a passive learning or active learning process. In the first method, we may take into consideration the parameter covariances, but we ignore the covariance between the state variables and the parameters of the system. In the second method we take into account the above covariances, as well as future covariances of the state and control variables. This consideration or the future perturbations allows the establishing of a more realistic control law, in order to achieve better results from the control exercise. The main purpose of this paper is to derive a method of updating the reduced form coefficients of an econometric model and their covariance matrix by mobilizing bayesian filtering techniques. The updating process can be used both with passive learning and active learning stochastic controls. We have implemented this method for a monetary model of the Indian economy and we have attempted to point out the essential differences in the results under the two abovementioned types of treatment of uncertainty, i.e. passive learning and active learning.