here. Models very close to ours have been studied extensively, without uncovering mul-
tiplicity under discretion. We explain why below, and we contrast the multiplicity here
with that found by Albanesi, Chari and Christiano [2002] in a different type of sticky
price model.
6.1 New Keynesian Models
There is an important recent literature that works out how the standard Kydland-
Prescott-Barro-Gordon (KPBG) model can be derived from a fully articulated New Key-
nesian framework. The key ingredients of the models in this literature are that output
is inefficiently low due to monopoly distortions; the monetary authority has temporary
leverage over the real economy because of staggered price setting; and the costs of ac-
tual inflation are welfare losses associated with relative price distortions. Analyses of
discretionary equilibrium in New Keynesian models has been conducted within linearized
versions of those models, and using a primal approach to policy (more on this below).
Just as in KPBG, there is a unique discretionary equilibrium, and it is characterized by
inflation bias.10
Our analysis takes the most basic fully articulated New Keynesian model, without
linearizing, and shows that there are multiple equilibria.11 Our model features costs of
stimulative policies — which bring about actual inflation — that stem from relative price
distortions across goods. It also features benefits from unexpected stimulative policies,
which lower monopoly markups and raise output toward the first best level. The model is
explicitly dynamic, with firms forecasting future inflation when setting nominal prices for
two periods. Multiple equilibria occur because of complementarity among price-setting
firms that is induced by the response of future policy to current prices.
It should be clear from figure 2 that nonlinearity is central to the multiplicity of
point-in-time equilibria we describe: the best response function of a price-setting firm is
10 For a textbook treatment, see the derivation in Wo odford [2002, chapter 3]. The inflation bias result
under discretion within such optimizing New Keynesian models has been popularized by Clarida, Gali
and Gertler [1999].
11 Much of the New Keynesian literature uses the Calvo assumption of a constant probability of price
adjustment. The Calvo assumption implies that a positive fraction of firms charge a price set arbitrarily
far in the past. However, for many purposes this formulation has the advantage of tractability. For our
purposes however the Calvo assumption is more complicated than two period staggered pricing, because
it would add a real state variable to the monetary authority’s problem. As we discuss below, adding a
real state variable leaves intact the fundamental mechanism generating multiplicity.
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