shocks, aggregate supply shocks and term premium shocks are similar.
The main difference between the policy rules in the two models is the estimated degree
of policy smoothing. In both models, the long-run response of policy to the output gap
and inflation is larger than the original Taylor rule response of 0.5. However, the estimate
of the policy smoothing parameter is 0.62 in the time-varying model, similar to estimates
obtained by English, Nelson, and Sack (2003), and considerably lower than the estimate of
0.91 obtained for the constant model. Estimates of transitory policy shocks are somewhat
smaller in the time-varying target model than in the constant target model, suggesting that
time-variation in the target and the funds rate natural rate explains some of the variation in
the funds rate. Replacing the time-varying target and perceived target series, the constant
model has a constant and credible inflation target, π, estimated to be 4 percent.
Some of the persistence of inflation and nominal interest rates in the constant model is
absorbed by low frequency fluctuations of the perceived inflation target in the natural rates
of the time-varying model. Comparing estimates of coefficients in β(L) in the time-varying
model in Table 2 to those for the constant model in Table 3, reveals that the sum of
coefficients on own lags is considerably lower in the time-varying model. The sum of
coefficients on lags of long-term interest rates in the long rate equation is 0.66, in the
time-varying model and 0.78 in the constant model; The sum of coefficients on lags of
inflation in the inflation equation is 0.53 in the time-varying model and 0.94 in the constant
model. The next section will show that estimates of lower persistence of devatiations of
economic variables from their natural rates in the time-varying model will show up as less
persistent impulse functions.
The lower sum of coefficients in the time-varying target model in conjunction with
the low frequency movements in the estimated perceived target series may help explain
time-variation in the persistence of inflation as found by Kozicki and Tinsley (2002) and
Cogley and Sargent (2003). In particular, the persistence of inflation incorporates the degree
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