Federal Reserve Bank of St. Louis ; Inflation (Finance)

Edward C. Prescott

English

Research Papers in Economics

FE D E R A L RE S E RV E BA N K O F ST. LO U I S
MAY/ JU N E 1 9 9 6
Commentary
Edward C. Prescott
T
he ﬁrst question addressed in Robert
G. King and Alexander L. Wolman’s
article is, What is the optimal inﬂa-
tion rate in a world where prices are
“sticky”? (I will precisely deﬁne the term
sticky later.) The authors ﬁnd that for
their model world, the optimal inﬂation
rate is remarkably near the Friedman 
rule of deﬂating at the real interest rate
(that is, deﬂating at a rate that results in a
zero nominal interest rate). The second
question addressed is, What is the re-
sponse to a permanent technology shock
if monetary policy is such that the inﬂa-
tion rate is constant? King and Wolman
ﬁnd that the response is essentially the
same as that in a world with ﬂexible
prices. Thus, responses to permanent or
highly persistent technology shocks are
essentially optimal with inﬂation rate 
targeting. 
These ﬁndings suggest that even in
worlds with sticky prices, targeting inﬂa-
tion at a low or even a negative rate is a
good policy rule. An added advantage of a
policy that targets inﬂation rates is that
inﬂation rates are predictable: There are
no undesirable ﬂuctuations induced by
price surprises.
I ﬁrst review the abstraction King and
Wolman used in the study. Then I com-
ment on the reasonableness of this ab-
straction for the purpose it is used. Fi-
nally, I discuss the practicality of an
inﬂation rate targeting policy rule.
THE ABSTRACTION
Preferences in the model are standard
with a large number of type-identical
households. A representative household’s
utility function is the expected discounted
value of utility ﬂows that depend on con-
sumption and leisure ﬂows. The house-
hold allocates its time among leisure,
shopping activities, and market activities.
The motive for holding money is to econ-
omize on shopping time. Relying on the
results of Goodfriend and McCallum
(1987), King and Wolman assume that
shopping time is an increasing function of
the ratio of consumption to money hold-
ings. In particular, with more real money
holdings, less time is needed for shop-
ping. The household side of the model is
clearly speciﬁed.
The technology side of the model,
however, is not clearly speciﬁed. As a re-
sult, King and Wolman may not have
used the technology I describe. With this
caveat, I interpret the technology as fol-
lows. A large number of intermediate
technologies or ﬁrms exist. Each ﬁrm
produces a different intermediate good
using labor and ﬁrm-speciﬁc capital in-
puts. These technologies display constant
returns to scale. Each ﬁrm has an associ-
ated technology for producing its ﬁrm-
speciﬁc capital. A ﬁrm’s capital depreci-
ates in the usual way, namely, expo-
nentially. The increment to capital, how-
ever, is not new investment, as there are
adjustment costs. The increment-to-capi-
tal formation is homogeneous of degree
one in current ﬁrm-speciﬁc capital and a
ﬁrm’s current investment. A ﬁrm has mo-
nopoly power; however, because a ﬁrm is
small, its decisions have no general equi-
librium effects. The intermediate goods
are used to produce a composite good al-
located between consumption and invest-
ment uses. The technology to produce the
composite good is the usual one with
constant returns to scale.
So far, there are two features of King
and Wolman’s model that are not part of
the standard real business cycle model.
These features are a monopolistically
competitive intermediate goods sector and
a transaction role for real cash balances,
each of which previously has been intro-
Edward C. Prescott is professor of economics at the University of Minnesota and an adviser at the Federal Reserve Bank of Minneapolis.
The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal
Reserve System.MAY/ JU N E 1 9 9 6
FE D E R A L R E S E RV E BA N K O F ST. LO U I S
113
duced separately. Hornstein (1993) and
Devereux, Head, and Lapham (forthcom-
ing) have carried out quantitative analyses
with monopolistic competition. Cooley
and Hansen (1989) have introduced
money via a cash-in-advance constraint
that for all practical purposes is equiva-
lent to introducing money as a mecha-
nism to economize on shopping time. If
prices are ﬂexible, introducing either fea-
ture to the standard model does not alter
the conclusions of real business cycle the-
ory. I am sure that introducing both fea-
tures simultaneously would not alter the
conclusions of real business cycle theory,
given that I can think of no reason their
effects would not be additive.
In models with sticky prices, how-
ever, the interaction between monopolistic
competition and a transaction technology
could well alter the conclusions drawn
from ﬂexible price models. The way King
and Wolman introduce sticky prices is to
assume that at each point in time, with
some probability, the agent operating an
intermediate goods technology has the
opportunity to change the price of the
good being produced. The opportunities
to change prices are identically and inde-
pendently distributed across the interme-
diate goods technologies and over time.
All households own equal shares of all
the technologies and there are equal
lump-sum taxes or transfers to the type-
identical households. 
Before I proceed with substantive
comments, I must address one technical
problem. The state of a monopolistic
competitive ﬁrm must specify:
• Whether its nominal price can be
changed in the current period
• Its previously charged price if it can-
not change its nominal price for the
current period
• Its beginning-of-period, ﬁrm-speciﬁc
capital
The state of the economy must spec-
ify the entire distribution of the monopo-
listic, competitive ﬁrms’ states, as well 
as the aggregate capital stock, the stock 
of money, and the current value of the
technology shock. Computing the equilib-
rium of model economies with both ag-
gregate uncertainty and a distribution as
part of the state variable has proved difﬁ-
cult. If corners are not a problem and
functions are reasonably smooth, we can
use recursive competitive equilibrium
model economies that are linear-quadratic
and have the desired steady states and 
desired substitution elasticities at the
steady-state values.1 When this is not the
case, other methods are needed. The only
method I know of is the one in Krusell
and Smith (1995). King and Wolman ap-
pear to be implicitly assuming that a par-
ticular low-dimensional element sufﬁces
to summarize the relevant aspects of the
distribution to an adequate degree of pre-
cision. This is a feature of the Krusell-
Smith approach as well. Krusell and
Smith carry out some tests to determine
whether the statistics used are sufﬁcient
for all practical purposes. I think King
and Wolman should have carried out
such tests. 
THE REASONABLENESS
OF THE ABSTRACTION
I turn now to the substantive com-
ments. How effective is the transaction-
based model of money used by King and
Wolman for evaluating an inﬂation rate
targeting policy? An implication of
transaction-based models is an empirical
demand-for-money relationship. There
are, in fact, large and persistent deviations
from the demand-for-money relationship.2
If these deviations were not present, I
would have more conﬁdence in the
authors’ conclusions. 
Another deviation I ﬁnd bothersome
is the counterfactual prediction of the
theory for the difference between the av-
erage returns on capital and the return on
short-term government debt. King and
Wolman’s model implies that the return
on government debt should be almost as
1 See Hansen and Prescott
(1995) and Ríos-Rull (1995).
2 See Lucas (1993).MAY/ JU N E 1 9 9 6
FE D E R A L RE S E RV E BA N K O F ST.  LO U I S
114
high as the average return on capital in
the economy. This is not the case. Look-
ing at the results of Kravis (1959), I note
that the average return on capital (com-
puted as the total capital income divided
by the current value of the capital stock)
is a little under 5 percent. The average
real return on liquid government debt is
much lower—about 1 percent. I see this
difference as a big and bothersome dis-
crepancy for representative household
models used to evaluate monetary
policy.
Another problem is that the monetary
aggregate King and Wolman use does not
correspond well to their theory. The the-
ory has households holding non–interest-
bearing money, while the monetary aggre-
gate used in the demand-for-money
function is M1. Most of M1 is not non–
interest-bearing debt held by households.
Only a third of M1 is currency and half of
that is probably held abroad. Another
third is demand deposits held by busi-
nesses, which often earn interest de facto.
Households do not use these demand de-
posits to economize on shopping time.
The ﬁnal third is demand deposits held
by households that, at least in recent
years, can pay interest.
One feature of reality from which the
authors deviate is that households enter
into explicit and implicit contracts based
on expectations of future relative prices.
Sometimes realizations greatly vary with
expectations, and some parties to the
contracts are unable to fulﬁll them. These
defaults in turn lead to additional de-
faults. In such situations, with no inﬂa-
tion, there might be a ﬁnancial crisis and
large economic disruptions. Because it has
a representative household, the King and
Wolman model cannot have ﬁnancial
crises of this type. Whether inﬂation rate
targeting is a good policy in worlds with
heterogeneous households and credit sys-
tems playing a crucial role in the opera-
tion of the economy is an interesting
open question. At a minimum, I suspect
that good policy would be characterized
by relatively stable interest rates, as well
as stable inﬂation rates.
THE PRACTICALITY
OF INFLATION
TARGETING POLICY
I turn now to the question, How can the
monetary authorities target the price level?
King and Wolman do not address this ques-
tion, but it must be addressed if an inﬂation
rate targeting policy rule is to be followed.
The experience of New Zealand, a country
that follows an inﬂation rate targeting policy
rule, is relevant to this question. The Re-
serve Bank of New Zealand Act of 1989,
pursuant to the 1992 Policy Target Agree-
ment Document, speciﬁes an inﬂation rate
target of zero to 2 percent consumer price
index inﬂation. The 1989 legislation made
the pursuit of price stability the primary
(and only macroeconomic) objective of the
New Zealand Reserve Bank. Subsequent to
the 1992 agreement, which incidentally
speciﬁed that the governor of the Reserve
Bank would be ﬁred if he failed to keep the
inﬂation rate within the target range, the 
inﬂation rate has been within the zero to 
2 percent range.
New Zealand’s experience suggests that
a central bank can maintain price stability
if no ﬁnancial crises arise. Basically, the
rule that the New Zealand government fol-
lows is to set the short-term interest rate
above the long-term rate if the recent inﬂa-
tion rate has been near the maximum of
the targeted range. Similarly, if the recent
inﬂation rate is near the minimum of the
targeted range, the short-term interest rate
is set below the long-term rate. Subsequent
to the signing of the agreement, price sta-
bility has characterized the New Zealand
economy. However, the New Zealand gov-
ernment has maintained a budgetary sur-
plus during this period. Whether the 
New Zealand Reserve Bank could have suc-
cessfully targeted the inﬂation rate if there
were government deﬁcits of a signiﬁcant
magnitude remains unanswered.
REFERENCES
Cooley, Thomas F., and Gary D. Hansen. “The Inﬂation Tax in a Real
Business Cycle Model,” The American Economic Review (September
1989), pp. 733–48.Devereux, Michael B.; Allen C. Head; and Beverly J. Lapham. “Aggregate
Fluctuations with Increasing Returns to Specialization and Scale,”
Journal of Economic Dynamics and Control (forthcoming).
Goodfriend, Marvin S., and Bennett T. McCallum. “Theoretical Studies of
the Demand for Money.” In The New Palgrave: A Dictionary of
Economics; John Eatwell, Murray Milgate, and Peter Newman, eds.
Stockton Press, 1987, pp. 775–81.
Hansen, Gary D., and Edward C. Prescott. “Recursive Methods for
Computing Equilibria of Business Cycle Models.” In Frontiers of
Business Cycle Research, T. F. Cooley, ed. Princeton University Press,
1995, pp. 39–64.
Hornstein, Andreas. “Monopolistic Competition, Increasing Returns to
Scale, and the Importance of Productivity Shocks,” Journal of
Monetary Economics (Vol. 31, 1993), pp. 299–316.
Kravis, Irving B. “Relative Income Shares in Fact and Theory,” The
American Economic Review (December 1959), pp. 917–49.
Krusell, Per, and Anthony A. Smith, Jr. “Income and Wealth
Heterogeneity in the Macroeconomy.” Manuscript, University of
Rochester, 1995.
Lucas, Robert E. Jr. “On the Welfare Cost of Inﬂation.” Manuscript pre-
pared for the Hitotsubashi International Symposium on Financial
Markets and the Changing World, 1993.
Ríos-Rull, José-Víctor. “Models with Heterogeneous Agents.” In Frontiers
of Business Cycle Research, T. F. Cooley, ed. Princeton University Press,
1995, pp. 98–125.
MAY/ JU N E 1 9 9 6
FE D E R A L RE S E RV E BA N K O F ST. LO U I S
115

Models with Heterogeneous Agents.” In Frontiers of Business Cycle Research,

Monopolistic Competition, Increasing Returns to Scale, and the Importance of Productivity Shocks,”

On the Welfare Cost of Inﬂation.” Manuscript prepared for the Hitotsubashi International

Recursive Methods for Computing Equilibria of Business Cycle Models.”

Relative Income Shares in Fact and Theory,”

The Inﬂation Tax in a Real Business Cycle Model,” The American Economic Review

Inflation targeting in a St. Louis model of the 21st century - commentary

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Inflation targeting in a St. Louis model of the 21st century - commentary

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