NBER WORKING PAPER SERIES
MENU COSTS AND THE
NEUTRALITY OF MONEY
Andrew S. Caplin
Daniel F. Spulber
Working Paper No. 2311
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
July 1987
We thank Andrew Abel, Roland Benabou, Olivier Blanchard, Dennis Canton, Stan
Fischer, Ben Friedman, Barry Nalebuff, William Nordhaus, David Romer, Julio
Rotembeng, Eytan Sheshinski, John Veitch and an anonymous referee for valuable.
conffiients. Spulber's research was supported by the National Science Foundation
under Grant No. SES-82-19121. The paper was presented at the Fifth World Congress
of the Econometric Society, Cambridge, MA, 1985, and at the NBER Program in
Economic Fluctuations Conference, October 1985. The research reported here is
part of the NBER's research program in Economic Fluctuations. Any opinions
expressed are those of the authors and not those of the National Bureau of
Economic Research.
NBER Working Paper #2311
July 1987
Menu Costs and the Neutrality of Money
ABSTRACT
A
model of endogenous price adjustment under money growth is presented. Firma
follow (a, S) pricing policies and price revisions are imperfectly synchronized. In the
ag-
gregate, price stickiness disappears and money is neutral. The connection between firm
price adjustment and relative price variability in the presence of monetary growth is also
investigated. The results contrast with those obtained in models with exogenous fixed
timing of price adjustment.
Andrew
S. Caplin
Daniel F. Spulber
Department of Economics
Department Of Economics
Princeton University
University of Southern California
Princeton, NJ 08544
Los Angeles, CA 90089-0035
I. Introduction
Historically-determined nominal prices can lead to inertia
in the aggregate level of
prices, leaving room for monetary shocks to influence real
variables. Formal models con-
necting the microeconomic behavior of nominal prices with
aggregate price stickiness in-
clude models with staggered price and
wage decisions [Fischer, 1977; Taylor, 1980; Blan-
chard, 1983b; Parkin, 1986J, models with partial adjustment of
prices (e.g.,
Rotemberg
[19821), and the more recent menu cost" models of Akerlof and Yellen
[1985], Blanchard
and Kiyotaki [1985] and Mankiw [19851. We
present an alternative aggregate model with
microeconomic price stickiness which emphasizes the
importance of endogenous timing of
price adjustments. The model provides conditions under which
money shocks have no real
effects.
A number of macroeconomic models of price stickiness have
a common microeconomic
base: infrequent but large changes in nominal variables
are assumed to be more economical
then frequent small changes.' The models also share the
assumption that the time between
successive price revisions is pre-set, and hence unresponsive to shocks
to the economy. This
assumption is questionable both at the microeconomic level and in the
aggregate. Formal
microeconomic models (e.g.,
Sheshinski
and Weiss [1983]) strongl) suggest that more
rapid
inflation will shorten the time between price revisions.
Empirical evidence against the fixed
timing assumption is presented by Cecchetti [1986] and Liebermann and
Zilbefarb [i98s].
At the aggregate level, large monetary shocks
may increase the number of agents revising
their nominal prices in a given period. This in turn reduces the
extent of price level inertia.
An important open question remains: what
are the real effects of monetary shocks with
endogenous timing of price revisions?
The present paper assumes that individual firms adjust their
prices using (a, 5)
pricing
policies of Sheshinski and Weiss [1977, 1983]. To model
asynchronization, we make a
cross-sectional assumption on initial prices. The price level is derived
endogenously by
aggregating across firms. Aggregate price stickiness then vanishes despite the
presence of
1
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nominal price rigidity and imperfectly synchronized price revisions.
The presence of relative price variability as a
consequence of inflation is also observed
endogenously through aggregation of cross-sectional price data. A
simple formula is derived
linking nominal price adjustment by firms with cross-sectional
variability of inflation rates.
The basic model is outlined in section II. The
neutrality proposition is presented in
section III. In section IV, the model is applied to study relative
price variability. Section
V provides further discussion of the model and its
assumptions Conclusions are given in
section VI.
H. The Model
hA. The Aggregate Setting
We provide an aggregate model of price dynamics with individual
firms pursuing
asynchronous (a, S) pricing policies. The structure of the
aggregate model is kept as simple
as possible to highlight the distinction between our model and others with
asynchronous
price and wage decisions. These alternative models frequently
assume a staggered pattern
of timing (e.g., Akerlof 11969], Fischer 119771,
Taylor
f
1980]
and Blanchard [1983b]).
Money growth is subject to continuous shocks. The stochastic
process governing
monetary growth is taken as exogenous by all firms in the economy.2 Let M(t) denote the
logarithm of the money supply at time t, where time is measured
continuously. We assume
that the money supply process is increasing over time and does
not make discrete jumps.
ASSUMPTIoN 1. Monotonicity and Continuity. The
money supply does not decrease Over
time, M(t1) M(t2) for ij t2. Also, the money supply
process is continuous in the
time parameter t. Normalize such that M(0) =
0.
The monotonicity assumption will rule out periods of deflation. The
continuity assumption
allows a simple characterization of firm pricing policies. The
assumption also plays a role
in analysing the cross-sectional behavior of prices. This issue is taken
up below. The
monetary process is sufficiently general as to accommodate feedback rules. We will consider
2
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particular examples of monetary processes below.
There is a continuum of firms in the economy indexed by i E
10,11. All firms face
identical demand and cost conditions. The assumed microeconomic structure is based
on
the menu cost model of Sheshinski and Weiss 11977, 1983J. Let q(t) and
Q(t) represent
firm i's nominal price and the aggregate price index respectively, with p(t) and
P(t) their
respective logarithms. The aggregate price index, P(t), is derived endogenously below
from individual firm prices. It is convenient to express firm i's real price,
q(t)/Q(t), in log
form, r(t),
(1)
rt(t) 2
p1(t)
—
P(t)
=
ln[qj(t)/Q(t)j,
for all I E 10,11. We take r(0) as given.
The aggregate
price
index, Q(t), is determined endogenously by aggregating individual
firms' nominal prices, q(t). The index is assumed to depend only
on the frequency dis-
tribution over nominal prices. Because firms have menu costs of price adjustment,
prices
may remain dispersed in the long run. Thus, the set of observed prices at any date may
be described by a time-dependent frequency distribution function,
say Ct(q). The index
M assumed also to satisfy homogeneity; when nominal prices double,
so does the index.3
ASSUMPTIoN 2. Symmetric Price Index. The aggregate price index, Q(t), depends only
on the frequency distribution of nominal prices and satisfies homogeneity,
(2)
Q(t) =
Q(Gt(q)),
where C(q) is the proportion of firms i E 10,11
such that q(t) S q.
(3)
If G,(q) =
Gt3(Aq)
for all q, then AQ(t1) =
Q(t2),
for any t1,t3 0.
This condition is satisfied by a wide variety of common price indices.4 An example of
a
price index which satisfies assumption 2 is a simple average of nominal prices based on their
frequency distribution, Q(t) =
f
qdct(q). More generally, let Q(t) =
f
w(q, Cg(.))qdCt(q)
where w(q, C) represents weights as a function of prices q and the distribution of nominal
3
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