time elapsed from the last adjustment. The discrete nature of price setting creates an incentive
to adjust prices by more the higher is the future inflation expected at time t.Theinflation
level is πt whereas the output gap is denoted by yt and captures the movements in marginal
costs associated with variations in excess demand. For analytical convenience, the aggregate
supply curve is assumed purely forward-looking. Gali' and Gertler (1999), Ireland (2001), Gali',
Gertler and Lopez-Salido (2003b), and Smets and Wouters (2003a) provide empirical support
for this choice as a good first approximation to the dynamics of US inflation.
Equation (2) is a standard Euler equation for consumption combined with the relevant
market clearing condition. It basically brings the notion of consumption smoothing into an
aggregate demand formulation by making the output gap a positive function of its future value
and a negative function of the real interest rate, it - Etπt+1. Lastly, εts and εtd are respectively
cost and demand disturbances that obey an autoregressive, mean reverting process.
2.2 An asymmetric specification of the loss function
The policy actions are taken before the realization of the economic shocks and thus the
central bank sets the interest rate at the beginning of period t on the basis of the information
available at the end of the previous period. This timing device is captured by the following
intertemporal criterion:
∞
Min Et-1 δτLt+τ (3)
{it} τ=0
where δ is the discount factor and L stands for the period loss function.
Our framework departures from the conventional quadratic set up in that policy makers are
allowed, but not required, to treat differently positive and negative deviations of inflation and
output from the target. Indeed, the quadratic form may approximate reasonably well a number
of different functions and in the absence of a rigorous theoretical foundation any specific
nonquadratic proposal is destined to be unsatisfactory against the wide range of plausible
alternatives. Nevertheless, a modeling choice is required and for the sake of concreteness we
specify Lt as follows:
e[α(πt-π*)] — α (∏t — ∏*) — 1
Lt = -------------2--+ λ
α2
e(γyt)
γyt
Y2
+ μ2(i,
i*)2
(4)
The coefficients λ and μ represent the central bank’s aversion towards output fluctuations
around potential and towards interest rate level fluctuations around the target i*. The pref-