Optimal Forward-Looking Monetary Policy under Rational Expectations

Peter Zadrozny

Standard methods of optimal control were developed for causal physical systems and have been used to optimize dynamic economic systems. "Causal" means past events affect current and future events, but expected future events do not affect current or past events. Until the advent of rational expectations, dynamic economic models were casual. The present paper extends linear-quadratic optimal control to noncausal, linear, discrete- time, rational expectations models. The setting is a standard, two- equation, demand-supply model of optimal monetary policy. The monetary authority, i.e., the "Fed", sets coefficients of expected future and realized past variables in a money-supply equation in order to minimize weighted covariances of equilibrium money and prices. A second equation represents aggregate demanded money holdings of a multitude of agents. In similar past discussions, the Fed only optimized linear feedback terms, i.e., coefficients of realized current and past variables. The innovation here is to determine when and how the Fed should also optimize feedforward terms, i.e., coefficients of expected future variables. First-order conditions are derived for a general statement of the optimization problem, the conditions are restated in the form of a block Gauss-Seidel algorithm, and the algorithm is illustrated with the monetary control problem.

Additional Key Words: Optimal Noncausal Linear Dynamic Systems, Stackelberg Dynamic Games

Scheduled for Session 5.3 Techniques In Economic Dynamics