The literature in this part treats the question of optimal monetary policy as one of constrained optimization in an uncertain environment. The policymaker minimizes a given loss function. In the chapters in this part, the loss function will simply be posited to be a social welfare function, the arguments of which are various macroeconomic goals (such as high employment and price stability). Later we will consider the derivation of the loss function and extensions of it to a multi-period time horizon. The constraints facing the policymaker are the equations of the model that characterizes the economy. These equations specify relationships among the variables that the policymaker controls, the instruments, those he wishes to inﬂuence, the goals (or targets), as well as other endogenous and exogenous variables. Uncertainty enters because we assume these equations are stochastic. Adding these stochastic elements to the model is a representation of the fact that in the real world the goal variables will be aﬀected by numerous factors about which the policymaker has only limited knowledge. In this chapter we set out the equations for one type of model that has been widely used in the optimal monetary policy literature. Next we consider several possible loss functions that have been employed. We then consider optimal policy questions within a simpliﬁed model that was used by Poole (1970). Poole’s model illustrates the basic nature of the relationship between the optimal monetary policy and the types of the uncertainty that confront the policymaker – a relationship...
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