to VAR equations with lags of the output gap, inflation, the federal funds rate, and the
long-term interest rate included in each. Monetary policy is modeled using an estimated
Taylor (1993) rule with smoothing. Smoothing refers to the appearance of the lagged
funds rate in the policy rule. The lagged funds rate is often interpreted as capturing
smoothing behavior on the part of policymakers who may prefer to act gradually in the
presence of uncertainties about the structure of the economy. Gradualism may also reduce
financial market activity and increase economic responses to policy actions by magnifying
the response of other market interest rates to policy actions. See, for example, the discussion
in Amato and Laubach (1999) and English, Nelson, and Sack (2003). Empirical estimates of
Taylor rules with smoothing are provided in Kozicki (1999) and Sack and Wieland (2000).
The policy rule specifies that the deviation of the federal funds rate from its natural rate
is determined by policy responses to the output gap, the deviation of inflation over the
previous four quarters (πt,4) from the inflation target, a lagged funds rate deviation to
capture policy smoothing, and a transitory policy shock (ur,t):
rt = r + πp(t) + γy(yt - y) + γ∏(∏t,4 - πτ(t)) + ρ(rt-i - r - πp(t)) + Ur,t (1)
where πt4 ≡ P3 π ∏t-i.
Structural shocks to aggregate demand, aggregate supply, the funds rate (a transient
policy shock), and the term premium are identified by assuming a recursive causal ordering
with the output gap ordered first, followed by inflation, the federal funds rate, and the
long-term interest rate. Thus, the assumed causal ordering implies that long-term interest
rates respond contemporaneously to the aggregate demand, aggregate supply, transitory
policy, and term premium shocks. The residual in the output gap equation is identified as
an aggregate demand shock.
The inflation equation is a reduced-form Phillips curve. Inflation may respond
contemporaneously to the aggregate demand shock, explaining a possible correlation