p.1387

Analytical Policy Design under Rational Expectations

Charles H. Whiteman

Abstract

The formulation of optimal policy in linear rational expectations models is studied using methods analogous to the classical design techniques utilized in linear systems engineering. Specifically, the policy-maker's present-value-like objective function is converted, using the convolution transform, to an equivalent frequency domain, "spectral utility" function. Then the residue calculus and Wiener-Hopf methods are used to maximize spectral utility through the choice of a complex function which represents a sequence of distributed lag coefficients to be applied to current and past values of instrument variables. The solution to this problem is a closed form expression for the decision rule of the dominant player in a particular type of linear-quadratic dynamic game.