between the output gap equation residual and the inflation equation residual. Inflation
also responds to an aggregate supply (cost push) shock. A notable feature of the reduced
form Phillips curve specification is that the sum of coefficients on lags of inflation deviations
are not constrained to unity. However, because inflation only appears in the Phillips curve as
the deviation from the perceived target, the expression does not exhibit a long-run tradeoff
between inflation and the output gap.
A long-run tradeoff is absent because the policy rule in the model is such that positive
excess demand can persist only if the inflation target is allowed to increase. The learning
structure in the model is such that an increase in the target is eventually incorporated
into an increase in the perceived target, and consequently to inflation.4 The policy rule
structure assumes that monetary policy responds contemporaneously to the output gap
and inflation, and thus to the aggregate demand and aggregate supply shocks. The funds
rate also responds to the transitory policy shock (a liquidity supply shock).
The remaining equations of the model describe the evolution of the inflation target
series and the perceived target series. The inflation target follows a martingale process so
that changes in the inflation target series are not forecastable. The inflation target shifts
with policy accommodation (if any) of aggregate supply shocks (uS,t), with deterministic
regime change (in the early years of Volker’s chairmanship of the Federal Reserve), or with
exogenous permanent policy shocks (uT,t):
πT (t +1) =πT (t) + ηd79-82 + cST uS,t + uT,t. (2)
Regime change to bring inflation down following the appointment of Volker as chairman of
the Federal Reserve is captured deterministically through the dummy variable d79-82, set
to one for the period 1979Q4 through 1982Q4 and zero at other times. As captured by
4 Given the structure of the model, the monetary authority would be able to maintain permanent excess
demand (i.e., output above potential) by allowing the inflation target and inflation to continue to increase
without bound.
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