Permanent and Transitory Policy Shocks in an Empirical Macro Model with Asymmetric Information

such announcements need not be credible. Consequently, the private sector must form
beliefs about the inflation target. The model is augmented to capture learning behavior on
the part of the private sector and includes a time-varying perceived inflation target that
will tend to differ from the possibly time-varying inflation target.

The model includes expressions for the dynamics of four variables, the output gap (y_t),
inflation (π_t), the federal funds rate (r_t), and a long-term interest rate (R_t), and expressions
that describe the evolution of time-variation, if any, in natural rates. A long-term interest
rate has been included so that policy transmission issues associated with long-horizon
expectations can be better addressed. In particular, long-term interest rates depend on
private sector long-horizon forecasts of inflation, and those forecasts will be influenced in
the short-run by shifts in the perceived inflation target.

In model expressions, variables are expressed as deviations from natural rates. The
natural rate of the output gap is assumed to be constant (y) and equal to zero, although
empirical estimates may differ from zero over finite samples. The natural rate of inflation
equals the perceived inflation target (π^P (t)), which may be time varying. The natural
real rate is assumed to be constant (r). The perceived inflation target, π^p(t), appears in
the natural rates of both short-term and long-term nominal interest rates as it anchors
the expected inflation component of nominal interest rates. Thus, the natural rate of the
long-term nominal interest rate is equal to the sum of the natural real rate, the term
premium natural rate (θ) which is assumed to be constant, and the perceived inflation
target: r + θ + π^p(t). The natural rate of the federal funds rate is the sum of the natural
real rate and the perceived inflation target (r + π^p(t)). The policy equation also captures
the federal funds rate response to the deviation of recent inflation from the policy target
for inflation.

Expressions for the output gap, inflation, and the long-term interest rate are similar
employed by the private sector and policymakers.

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