Objective Function and Constraints. We assume that the interest rate rule is chosen to solve the following optimization problem:

where Var(s) is the unconditional variance of variable s. The weight X e [0,1] indicates the policymaker^ relative preferences for minimizing output and inflation volatility. The policy rule f is a time-invariant linear function of a specified set of variables z (e.g., the output gap and the inflation rate) that comprise a subset of x, the set of all variables in the model. The disturbance vector e is assumed to be serially uncorrelated with mean zero and finite second moments. The transition matrices A(f) and B(f) describe the unique saddle-path solution to the model, and L signifies the lag operator. Finally, we use the constraint on the variance of the first-difference of the funds rate as a way of controlling for the different amounts of interest rate volatility generated by different rules. Each policy frontier shown in this paper is constructed using a specified value of the upper bound, k.

Objective Function and Constraints. We assume that the interest rate rule is chosen to solve the following optimization problem: where Var(s) is the unconditional variance of variable s. The weight X e [0,1] indicates the policymaker^ relative preferences for minimizing output and inflation volatility. The policy rule f is a time-invariant linear function of a specified set of variables z (e.g., the output gap and the inflation rate) that comprise a subset of x, the set of all variables in the model. The disturbance vector e is assumed to be serially uncorrelated with mean zero and finite second moments. The transition matrices A(f) and B(f) describe the unique saddle-path solution to the model, and L signifies the lag operator. Finally,