INTEREST-RATE RULES: Rules that Involve a Lagged Inter est-Rate

We achieve improvements in household welfare if we generalize the family of simple Taylor rules to allow the funds rate to respond also to lagged values of itself. We thus consider generalized Taylor rules of the form
where we now allow с to be greater than zero. This allows for interest rate smoothing, so that sustained changes in output and inflation lead to only gradual changes in interest rates. Actual policy in the United States and elsewhere seems to involve some degree of interest rate smoothing, though academic commentators have often questioned why this should be so. read more
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INTEREST-RATE RULES: Consequences of Simple Policy Rules 6

Making a big contributes to stabilization because it ensures that interest rates rise a lot when either G rises or Ys falls. This ensures that inflation does not rise much in either case and that, at least after the demand for output adjusts to changes in real rates, output does not rise in the former case while it declines substantially in the latter.
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As Figure 7 indicates, the rule that minimizes L by setting a equal to 20 leads to very variable interest rates. This is in part due to the delays in the response of output to interest rates. These delays imply that changes in Gt that become known at t — 1 inevitably change output at t since Ct is predetermined. This leads firms to raise their prices at t unless long term real interest rates rise unexpectedly. With с equal to zero, this means that prices can only be stabilized if the nominal interest rate at t rises a great deal.
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INTEREST-RATE RULES: Consequences of Simple Policy Rules 5

The real interest rate would then fall (because the nominal interest rate responds little) and the resulting increase in output means that expected future inflation is lower than current inflation. Thus the change in the expected future path of inflation that is required to justify the initial change in inflation is consistent with expected future inflation converging back to the target inflation rate ix*. In this case, a stationary rational expectations equilibrium is possible in which such fluctuations occur simply because they are expected to. there
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