The name is absent

generates the best performance, with the optimal commitment policy delivering a 4.3 percent
improvement in performance relative to discretion. Also by construction, since y_i is not a
state variable in either the discretionary equilibrium or the optimal commitment equilibrium,
the performances associated with these policies are invariant to this variable.

Now consider the performances associated with the timeless perspective policy. For the
timeless perspective, performance is maximized when y_ = 0 and rises symmetrically for
absolute deviations in y_i about 0. In fact, when y_i = 0, the timeless perspective policy
performs identically to the optimal commitment policy. Most obviously, Figure IA reveals
that as y_i becomes larger in magnitude, loss for the timeless perspective policy increases to
become larger than the loss for discretion. Clearly there exist states (here a lagged output gap
greater than about 0.5 percent) for which discretion is superior, delivering a better performance
than the timeless perspective policy. This is an issue for a central bank pursuing a timeless
perspective policy because in states where discretion is superior it is not clear that the central
bank would continue to implement the inferior policy, highlighting the time inconsistency of the
timeless perspective policy. Timeless perspective policies perform poorly when the output
gap is large because the timeless perspective assumes that it is the stationary asymptotic
equilibrium—and not initial expectations or transition dynamics—that govern outcomes.

With policies evaluated according to equation (14), it is not difficult to see that it will al-
ways be possible to find states where discretion is superior to timeless perspective policymaking
for any model in which there is a time-consistency problem.⁹ An alternative to evaluating
policy according to equation (14), hinted at in the discussion above, is to use unconditional
loss. By using the unconditional expectation of equation (14), the equation’s dependence on
the initial state is eliminated. Figure 1B displays unconditional loss for each policy, where
the initial state has been integrated out using the (unconditional) probability density implied
by the model.¹⁰ Since policies are now being evaluated according to the characteristics of
their asymptotic equilibrium, and the optimal commitment policy and the timeless perspective
policy share the same asymptotic equilibrium, these policies deliver the same unconditional
loss. Clearly, if unconditional loss is the appropriate measure of performance, then discretion
is the inferior policy.

⁹To the extent that timeless perspective commitments are untenable in such states, this consideration pro-
vides motivation for the “quasi-commitment” equilibrium analyzed by Schaumburg and Tambalotti (2007) and
the “loose commitment” equilibrium studied by Debartoli and Nunes (2006).

¹⁰Importantly, to the extent that observed data are not well explained by the model, very different results
might be obtained if the integration used the observed frequency distribution for the state variables rather than
using the model-implied density function.

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