nonlinear, and without nonlinearity there could not be multiple fixed points to that best
response function. Multiplicity of steady state equilibria could survive linearization, in
that one could approximate linearly around either of the two steady state discretionary
equilibria. Previous analyses of discretionary equilibrium in New Keynesian models have
not uncovered multiple steady states because they have used a “primal approach;” instead
of specifying a policymaker who chooses an instrument and must accept whatever equi-
libria correspond to the instrument setting, they have specified a planner who can choose
allocations (thus, prices), subject to those allocations being consistent with private-sector
equilibrium.
If the policymaker can commit to future actions, the distinction between planning
problem and policy problem is immaterial in New Keynesian models. However, absent
commitment the distinction becomes important; the planner’s formulation rules out the
steady state with lower welfare. To see this, consider a planner in the current period
who knows that the future will be characterized by the steady state with lower welfare
(higher p0 ). It is optimal for the planner to pick allocations that correspond to a low value
of p0 in the current period, and thus the low-welfare steady state is not an equilibrium
to the planning problem.12 In contrast, a policymaker — who can only choose m — must
respect private agents’ beliefs. If agents are pessimistic today and in the future, then
the current policymaker chooses an m such that the low-welfare steady state outcome is
realized today.
Without commitment, it is also important what the policy instrument is. If the
policy instrument is the nominal interest rate instead of the money supply, Dotsey and
Hornstein [2004] show that there is a unique Markov equilibrium, corresponding to the
low-p0 steady state of our model. This “Sargent and Wallace on their head” result is
somewhat misleading however: the focus on Markov equilibria rules out a continuum of
equilibria that would exist for exogenous fixed nominal interest rate policies.
6.2 Albanesi, Chari and Christiano
Third, our paper is closely related to recent work by Albanesi, Chari and Christiano
[2002]. They find multiple equilibria in an essentially static model where a portion of
monopolistically competitive firms must set prices before the monetary authority’s action
12 Wolman [2001] illustrates the exact discretionary solution to the planner’s problem in this model,
and Dotsey and Hornstein [2003] solve the discretionary planner’s problem of this model using an LQ
approximation. In neither case does multiplicity arise.
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