On the Convergence of Beliefs and Policy to a Rational Expectations Equilibrium in a Dual Policy Problem

This paper considers the question of the convergence of expectations and policy in a model of monetary policy with asymmetric and imperfect information between the policy maker and the private sector. In this model the objective function facing the policy maker is non-quadratic because of the manner by which the optimal policy influences the private sector’s expectations. Certainty equivalence does not apply to the optimisation problem and the optimal policy reflects a dual control structure in which the policy maker must take into account both the effect of his policy action on the information set facing the private sector and also on his ability to affect how this information is used when the private sector forms its expectations. Despite this capacity for the policy maker to actively intervene in the expectation formation process of the private sector we show that there is a unique rational expectations equilibrium in the model to which both the expectations of the private sector and the optimal policy converge. In section 2 we introduce the policy problem which is solved analytically in section 3.