Control of a linear regression process with unknown parameters

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Abstract
IntroductionApplications of forms of control theory to economic policy making have been studied by Theil (1958), Chow (1975, 1981), and Prescott (1972). Many of the applications are approximations to the optimal policy – suggestions of how to improve existing practice using quantitative methods rather than development of fully optimal policies. Chow (1975) obtains the fully optimal feedback control policy for linear systems with known coefficients for a quadratic loss function and a finite time horizon. Chow (1981) argues that the use of control technique for the evaluation of economic policies is possible and essential under rational expectations. The use of optimal control for microeconomic planning is fully established. An early analysis with many practical suggestions is Theil (1958). Optimal control theory has also been useful in economic theory, in analyzing the growth of economies as well as the behavior over time of economic agents.The problem of control of a stochastic economic system with unknown parameters is far less well studied. Zellner (1971, Chapter 11) studied the two–period control problem for a normal regression process with a conjugate prior and quadratic loss function.

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