of the interest rate, a point Woodford (1999b) highlights in his analysis of optimal interest
rate inertia. Further, as Giannoni and Woodford (2002b) stress, because the shocks are not
directly present, the timeless perspective targeting rule, as represented by equation (11), is
robust to misspecification of the shock processes.
3 A general approach
Researchers are often less interested in the timeless perspective targeting rule itself than they
are in the timeless perspective equilibrium. For example, if they are interested in impulse
responses, assessing the importance of particular shocks for business cycle volatility, or under-
standing the economic effects of particular nominal∕real rigidities, then the object of interest
is the timeless perspective equilibrium. Similarly, if they are interested in forecasting or in
system estimation of the model, then the object of interest is also the timeless perspective
equilibrium. This is certainly not to say that the timeless perspective targeting rule is never
of interest,6 and, to the extent that insight can be gained from both, the techniques described
in this section complement those in the previous section and those described in Giannoni and
Woodford (2002a) and Benigno and Woodford (2007).
For reasons that I explain below, timeless perspective equilibrium can be obtained from
the following three-step procedure.
1. Formulate and solve the period O optimal commitment problem.
2. Use the equilibrium relationships to derive expressions for the Lagrange multipliers
(shadow prices).
3. Assume that the expressions derived in step 2 hold in the initial period, thereby intro-
ducing the timeless perspective, and use these expressions to eliminate the shadow prices
from the system.
Notice that this three-step approach obtains the timeless perspective equilibrium directly
from the optimal commitment problem, without requiring modifications to either its objective
function or its constraints (c.f. Giannoni and Woodford, 2002a, and Benigno and Woodford,
2007).
6Indeed, timeless perspective policies are often analyzed for the purpose of establishing policy representations
that can implement uniquely the timeless perspective equilibrium.