The design of feedback rules in linear stochastic rational expectations models (Q1092784)

This paper is concerned with optimal and suboptimal feedback rules for linear stochastic continuous time models with rational expectations. We consider four types of feedback rules: (1) the optimal but time- inconsistent rule which is available if the controller is able to commit himself or herself; (2) quasioptimal and time-inconsistent rules of the form \(w=Dy\) where w is the vector of instruments, y the state vector and D a matrix of constants possibly with constraints; (3) the optimal time- consistent rule which is also linear in y; (4) `over-stable' rules which have `too many' stable roots. We show that rules of type (1) can be expressed and implemented as a form of integral control, all except type (2) satisfy certainty equivalence and the rules of type (4) will always be inferior to the optimal rule (1). These results are demonstrated in two illustrative examples.