Money Demand and Seigniorage-Maximizing Inflation

Money Demand and Seigniorage-Maximizing Inflation
Author(s): William R. Easterly, Paolo Mauro, Klaus Schmidt-Hebbel
Source: Journal of Money, Credit and Banking, Vol. 27, No. 2 (May, 1995), pp. 583-603
Published by: Blackwell Publishing
Stable URL: http://www.jstor.org/stable/2077885
Accessed: 18/08/2010 14:50
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=black.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
Blackwell Publishing and Ohio State University Press are collaborating with JSTOR to digitize, preserve and
extend access to Journal of Money, Credit and Banking.
http://www.jstor.org
WILLIAM R. EASTERLY
PAOLO MAURO
KLAUS SCHMIDT-HEBBEL
Money Demand and Seigniorage-Maximizing
Inflation
THEREIS WIDESPREAD
CONSENSUS
among economists that
high inflationis often caused by the government'sneed to raise seignioragein order
to finance high budget deficits (Sargent 1982; Dornbuschand Fischer 1986; Van
Wijnbergen1989; Buiter 1990; and Easterlyand Schmidt-Hebbel1994).1 Depending on the shape of the money demandfunction, steady-stateseigniorage may follow a Laffercurve, where seignioragefirstrises and then falls with higherinflation.
If this is the case, then there exists a rate of inflationthat maximizes steady-state
seigniorage, 1TmaX. Knowledge of 1TmaX may be of interestboth in orderto discriminate between existing theories of inflationand for policy purposes.
The literaturehas put forwardvarioushypothesesto explain high inflation.First,
the economy may be experiencinghigh inflation,but still be on the left-handside of
the Laffercurve. In this case, inflationmay be seen as a result of the government's
need to raise seigniorage. Second, the economy may be on the "wrong"side of the
Laffer curve. If inflationis above 1Tmczx and is fairly stable, then this may be interThe authorsare indebtedto RobertBarro, Alex Cukierman,Jose De Gregorio, Fernandode Holanda
Barbosa, IbrahimElbadawi, GrahamElliott, Alan Gelb, Miguel Kiguel, GregoryMankiw,Luis Serven,
RaimundoSoto, Luis Suarez, SalvadorValdes-Prieto,Steve Webb, JohnWelch, two anonymousreferees, and seminarparticipantsat HarvardUniversity,the XIth LatinAmericanMeetingsof the Econometric Society (Mexico) and the WorldBank for detailedcommentsand discussions. Many thanksgo also to
Jorge Canales, Mauricio Carrizosa,JanvierKporou-Litze,Daniel Oks, Jim Stephens, and Luis Suarez
for providing some of the data for this paper.
1. There is an unfortunatelack of standardlanguage in the literaturethat requiresus to define our
terms precisely: by seigniorage, we mean the total revenue from money creation, which includes two
components: (1) the "inflationtax" which is the inflation rate times real money balances, and (2) the
growth in real money balances. This terminologyis the same as thatfollowed by, for example, Blanchard
and Fischer (1990). Some authorsuse "seigniorage"to referto only the second component.
WILLIAM
R. EASTERLY
andKLAUS SCHMIDT-HEBBEL
are in thePolicyResearchDepartmentat the WorldBank.PAOLO MAURO is an economistat theInternational
Monetary
Fund.
Journalof Money,Credit,andBanking,Vol. 27, No. 2 (May 1995)
Copyright
1995
by The Ohio State University
Press
584
: MONEY, CREDIT,AND BANKING
preted as evidence in favor of the existence of a "high-inflationequilibrium."The
latter may be a consequence of the absence of a nominal anchor, as in Bruno and
Fischer (1990), or because of Barro-Gordon(1983) effects due to the inabilityof the
monetaryauthoritiesto undertakecrediblecommitments,as in Kiguel and Liviatan
(1991), or because of the authorities'high discount rate that biases policy against
stabilizationswith short-termcosts andlong-termbenefits. If inflationis above SmaX
and is accelerating,this may be seen as the consequence of the government'sneed
to raise seigniorage s' in excess of that which it can obtain by setting inflation at
Smax
S(XmaX)
51 in excess °f S(XmaX)
can only be collected by bringingabouteveracceleratinginflation, as emphasizedby Kiguel (1989).2 In fact, 1ThigherthanSmaX
has been suggested by Rodriguez(1994) as a definitionof a hyperinflation.
Estimatesof the seigniorage-maximizinginflationrate may help to decide among
such competingtheories. Conventionalestimatesof the seigniorage-maximizinginflation rate generally make use of the Cagan (1956) function, where the log of real
money is a linear function of inflation.The Caganfunction is appealingbecause of
its simplicity and its attractivealgebraic property:SmaX is given by one over the
coefficient on inflation. However, this simplicity is achieved at the expense of a restrictivefunctionalform, which assumes a constantsemielasticityof money demand
with respect to inflation. The estimates of SmaX using the Cagan form also usually
define the inflationrate affectingmoney demandas the percentchange in prices (or
sometimes the log change in prices), when theory implies that the correct opportunity cost of holding money per period is the inflationrate divided by one plus the
inflationrate. Ouraim is to test the sensitivityof estimates°f SmaX to the assumption
of constantsemielasticityin the Caganform and to the definitionof the opportunity
cost of money.
Section 1 develops a model of money demand, inflation, and seignioragebased
on an optimizingconsumer-investor-portfolio
allocator,who faces a cash-in-advance
constraint,forcing this agent to hold a combinationof money and bonds before incurring consumption expenditure.It will be shown that the existence of a Laffer
curve depends criticallyon how good substitutesmoney and bonds are in aggregate
financialassets held as "cash"-in-advance.
Section 2 presents both individual-countryand combined cross-countrytimeseries evidence that supportsthe notion that the semielasticity of money demand
with respect to inflationvaries with inflation.The empiricalevidence, collected for
all high-inflationcountries during the 1960-1990 period, is also used to provide
estimates of the seigniorage-maximizinginflationrate. It will be shown that both
these estimates and those for the semielasticity differ substantiallyfrom those obtained underthe conventionalCaganapproach.The results also have strikingimplications for the substitutabilityof bonds and money. The results will also show that
the semielasticity and the seigniorage-maximizinginflationrate, when based on the
correct measure of the opportunitycost of holding money, difter markedlyfrom
2. Bruno and Fischer (1990) also mention this possibility. With referenceto the hyperinflationof the
1920s, Barro (1972) notices that inflation tends to accelerate when the revenue-maximizingrate is
exceeded.
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL :
585
those obtainedwhen using conventionalbut incorrectmeasuresof inflation.Section
3 concludes.
1. THE MODEL
This section develops a simple model of money demand, inflation, and seigniorage. It shows that both the semielasticityof money demandwith respect to the opportunitycost of holding money and the inflationratethat maximizesseignioragein
the steady state depend on the degree of substitutabilitybetween money and bonds.
In addition, the inflation semielasticity of money demand is shown to vary with
inflation.
An infinitely lived optimizing representativeagent takes consumption, investment, and portfolio decisions in a closed economy. This agent holds money and
bonds for transaction purposes and maximizes a standard intertemporalutility
function:
cl-J
rX
max J
e-Pt
- 1
dt
(1)
where p is the discountrate, c is consumption,and 1/cris the intertemporalelasticity of substitution.
Production(y) in the one-good economy is assumed to depend only on a broad
concept of capital (k), as in Barro(1990) and Rebelo (1991):3
y = Ak.
(2)
There are three assets availableto the consumer capital k, nonindexedmoney
(real value m), and indexed money (real value b, referredto as "bonds"for short).
Bonds pay no interest, but are fully indexed to the price level.4 We assume that
inflationcannotfall below-A. There is no uncertainty.Since capitalhas real return
A (net of depreciation),it always dominatesbonds and money. However, a cash-inadvance constraintrequires that some combinationof money and bonds must be
held in orderto purchaseconsumptiongoods:
f(m, b)-c-O
(3)
3. Populationis assumed fixed and normalizedat one, so all variablescan be interpretedin per capita
terms.
4. The classic example of this kind of asset in developing countriesis foreign currency,which maintains its value as the nominal exchange rate moves with the domestic price level. Otherkinds of highly
liquid financialassets often pay a nominalreturnadequateto compensatefor inflationbut little or no real
return. Formally inflation-indexedassets paying a zero real returnexist in some developing countries.
This was the case of selected bank deposits held by households in China between mid-1988 and late
1991. UPACdeposits held in Colombia'ssavings and loan associationsare highly liquiddeposits indexed
by consumerprices. Real assets are also often used as inflationhedges.
586 : MONEY,CREDIT,
ANDBANKING
wheref is linearly homogeneous in m and b, and satisfiestm > °, gb > °, gmm< °,
gm(°, b) = so andfb(m, O)= oo.SThe last two conditionsensure that there
are no cornersolutions;the consumeralways holds a positive amountof both money
and bonds, which in general are imperfectsubstitutes.
This cash-in-advanceconstraintsays that either money or bonds can be used for
transactions.6This approachis in the same spirit as the Lucas and Stokey (1987)
generalizationof cash-in-advancemodels to include "cash"and "credit"goods. The
intuitivejustification is also similar to the "shoppingcosts" approachof Arrauand
de Gregorio (1991).7 An alternativeapproachis to assumethatmoney providesutility. This option, followed by many studies, has been adoptedrecentlyby Calvo and
Leiderman(1992) in deriving a variable semielasticity of money demand with regard to the opportunitycost of holding money.
The consumerfaces the following budget constrainteach period:
gbb < °s
c = y + tr
lm
lb
lk
where tr are the real resourcestransferredfrom the governmentback to consumers
in lump-sum form, and lm lb, and Ik are real flows of resources devoted to accumulationof money, bonds, and capital, respectively.
Bonds b and money m are the liabilities of the government. The government
transfers exhaust the resources capturedfrom consumers by issuing money and
bonds:
tr = Im + Ib We assume the governmentdoes not hold any otherassets. Because our interestis in
the steady-stateequilibrium,we also rule out open marketoperationsby the government (exchange of b for m); changes in eithermoney or bonds are assumedto occur
onlyto finance transfers.
Asset accumulationis given by
m = lm - sTm
(6)
b = lb
(7)
k=
(8)
lk
where 1Tis the inflationrate. Dots denote time derivatives.
5. These conditions are all satisfiedby the CES function introducedbelow.
6. A similar cash-in-advanceconstraintappearsin Walsh(1984).
7. In high-inflationcountriesit is often necessaryto pay in foreign currencywhen purchasinga house,
though smaller transactionstypically requirethe use of local currency.[See Calvo and Vegh (1992) on
currency substitutionin developing countries.] This case is not fully capturedby this model with one
homogeneous good, but may help to develop intuitionfor the constraintin (3).
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 587
The consumer-producersolves the intertemporalproblem (1)-(4) and (6)-(8)
with perfect foresight. The first-orderconditions imply the following standardexpression (see Rebelo 1991 andBarro 1990) for the consumption(andoutput)growth
rate g 8
g=
(A-p)/cr.
(g)
Note that growth is not affectedby inflation, which is a standardresult when the
cash-in-advanceconstraintapplies only to consumptiongoods.
The first-ordercondition for the allocation of wealth between m and b is the
following:
tmlfb
=
(A
+ s)IA .
(10)
Consumerssubstitutebonds for money in transactionsas inflationrises. The determinationof the ratio of money to consumptionis given by (3), which can be rewrittenas
f(mic,bic) = 1 .
(11)
One convenient parameterizationoff for discussing the sensitivity of money demandto inflationis the ConstantElasticity of Substitution(CES) function:
f(m,
b) = @[+mn
+ (1-+)bn]l/n
(12)
where bonds and money have elasticity of substitutiong = lI(n-1) in transactions.
Combine (10) and (12) to obtain the following equilibriumratio of bonds to
money:
m
[(
+
) (
A
)]
(13)
From (11)-(13), demandfor money scaled to consumptionis given by
m
c
1 (+ + (1
(t)
-
I|l)¢n)-(l/n)
.
(14)
8. Rebelo (1991) and Barro(1990) show that the following restrictionon the parametersis needed to
make discountedlifetime utility finite:
P > (1-(X)A
Intuitively, momentaryutility U(c) = (c(l-ff)- 1)/(1-a)
must grow more slowly than the rate p at
which futureutility is discounted. Insertingthe growth of consumptionfrom (9), calculatingthe growth
of momentaryutility U(c), and comparingit to p yields the expression shown. Note that the restriction
can be compatible with positive growth. For example, a sufficientset of conditions (not necessary) for
positive growth with finite utility is p > O,A > p, and (s > 1.
588
: MONEY, CREDIT,AND BANKING
From (13) and (14), it can be seen that money demandis unambiguouslya negative function of inflation. The semielasticityof money demandwith respectto inflation, noted as >, is a function of the elasticity of substitutionbetween money and
bonds in transactions:
d :T
( 1 -n ) ( (+/(1-@)<D -n + 1 ) (A + 7r) *
( )
The absolutevalue of the semielasticitywith respectto inflationcould increaseor
fall with inflation:
ds
| | {(1-n)(1
-+)
x )-n [( 1 T fi) ¢
+ 1]
1) (A + 1r)
(16)
The sign of (16) will depend on that of the second right-handterm. Considering
(13), the sign condition is
dlel,
0
( 1 -+)I/(I-n)
(A +
7r)nl(n-1)
(2n-
1) ' 1
(17)
A sufficient(althoughnot necessary)conditionfor |e| to decreasewith inflationis
that the elasticity of substitutionbetween money and bonds be smallerthan two in
absolutevalue (|(| < 2, thatis, n C 1/2). A necessary(althoughnot sufficient)condition for |e| to increase with inflation is that |(| > 2 (that is, n > 1/2). The Cagan
constant semielasticity could be seen as a local approximationaroundthe inflation
rate that happenedto satisfy (17) with equality;however, the conditionfor constant
semielasticity would be violated at other rates of inflation.9
The necessary condition for the semielasticityto rise with inflationallows us to
draw a tight correspondencebetween empirical results on the functional form of
money demandand the deep parameter|g| which determinessubstitutabilityof money and bonds. A risingsemielasticity
indicatesa strikinglyhighelasticityof substi-
tutionbetweenmoneyandbonds.
It is of interest to see how this affects the calculation of the seignioragemaximizing rate. Seigniorage is determinedby money growth, which is equal in
steady state to inflationplus growth, times money holdings (scaled to consumption):
(
+
) m
(18)
9. The model has been presentedhere in continuoustime for simplicity. The discrete-timeresultsrelevantfor empiricalimplementationin the following section are identicalexcept thatthe continuoustime inflationrate s should be replacedwith s/(1 + s), where s is the discrete-timeinflationrate.
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 589
The seigniorage-maximizinginflationrate (sT*)does not have a closed-formsolution. Its implicit equationis the following:l°
(
1
)
(g
+
t7T
)
_
1
=
(
+
)I/(l-n)
(
A
)n/(l-n)
(19)
sT*will be an interiormaximumfor seigniorage if money demandfalls off more
quickly than inflationrises, which requiresll
(
|el
) dir + 1 > O .
(20)
The implication of this section is that Cagan's constant semielastic money demand is inconsistent with fairly general conditions of intertemporalresource and
intratemporalportfolio allocation by an optimizing consumer-producerwho faces
cash-in-advanceconstraintsin consumption.At an intuitive level, the higher is the
elasticityof substitutionbetweenmoney and bonds, the lower will be the seignioragemaximizing inflation rate, and the higher will be the likelihood that the inflation
semielasticityof money demandincreaseswith inflation.
2. EMPIRICAL
RESULTS
This section presents empirical estimations of money demand functions and of
seigniorage-maximizinginflation consistent with the model derived in section 1.
The results show the importanceof allowing for a variablesemielasticity.
For our empirical estimates, we make use of the following money demand
function:
(
)
(21)
y
where y is output, sTis an appropriatemeasure of the opportunitycost of holding
money, and k, A, and y are parametersto be estimated.
Equation(21) differsfrom (14) by functionalform and includedvariables.Output
is included as the relevantscale variableinsteadof consumption.12Inflationis used
10. Derivedfromthestandard
first-order
conditionformaximumseignorage:
e(g + s) =-1.
11. Derivedfromthe standard
second-order
condition:d2slds2< O.
12. Althoughconsumption
is the scalefactorfor moneyin the modelof the precedingsection,we
choseoutputhereforvariousreasons.Outputis of generalized
use in Caganmoneydemandestimates.
Second,outputlacksmeasurement
noisetypicalof consumption
seriesandis morereadilyavailablethan
thelatter.Anyhow,consumption
andoutputmovetogetherin thepreviousmodel'ssteadystate.Unitary
consumption
(oroutput)elasticityis a featureof thecash-in-advance
specification
whichrelatesmoney
linearlyto consumption
(oroutput).However,mostempirical
moneydemandestimations
do notimpose
unitaryincomeelasticities.Preliminary
resultssuggestthatourmainconclusionsarenot alteredwhen
assumingnonunitary
outputelasticities.
ANDBANKING
590 : MONEY,CREDIT,
as the relevant opportunitycost of holding money ratherthan the nominal interest
rate.13
The nonlinearform of equation(21) has a numberof desirableproperties:(i) it is
simple and a straightforwardgeneralizationof the Cagan function, with a variable
Tr- 1;(ii) a necessarycondition
inflationsemielasticitygiven by a ln (mly)lATr= SyA
for the existence of a Laffer curve with a seigniorage maximum at a positive and
finite level of sTis A < O and y > O;14(iii) if y > 1 (^y= 1, Sy< 1), the absolute
value of the semielasticityrises (does not change, declines) with inflation;and (iv) it
can be shown to be equivalentto a nongeneralizedversion of the Box-Cox transformation.15
Three alternativemeasuresfor the opportunitycost of holding money have been
typically used in money demand estimations. (a) The conventionalmeasureof inflation, defined as the percentage rate of change of a given price index p for a
discrete period of time ((Pt-Pt- l )/Pt- l ) is often applied. (b) A second measureemployed by Cagan (1956) and many followers is the discrete-timechange in the
naturallogarithmof the price level (ln Pt-ln Pt- 1)-The two precedingmeasures
share the disadvantageof not representingthe true inflationcost of holding money
during a discrete period of time. (c) As suggested by Calvo and Leiderman(1992)
and others, the correctdiscrete-timemeasureof the alternativecost of holding money, equivalent to the capital loss due to inflation, is given by [(Pt-Pt-l)lPt-l]l
(or by it/(l + it), when the nominalinterestrate i constitutes
[1 + (Pt-Pt-l)/Pt-l]
the alternativecost to holding money).
Our estimationsbelow are based on the third,correctmeasureof the inflationcost
of holding money. However, we will also show comparativeresults with the incorrect measures to illustratethe sensitivity of the results to the choice of the inflation
measure.
Equation (21) is estimated for a sample of eleven high-inflationcountries the
universeof all countriesthathad inflationratesexceeding 100 percentp.a. in at least
one year duringthe 1960-1990 period.16We restrictedthe sample to high-inflation
countriesfor two reasons. First, the Caganmodel was originallyintendedas a model of high- or hyperinflation attemptingto explain money demandin low-inflation
countries as a sole function of the inflation rate is bound to be a ratherhopeless
13. Most of the sample countries defined below had extensive interestrate controls throughoutthe
1960s, some lifted them duringthe 1970s, and otherscontinuedwith interestcontrolsduringmost of the
1980s. Using inflationas the opportunitycost of holding money is relevantas long as people hold other
financialassets (foreign exchange) or real assets (gold, consumerdurables)with rates of returnstrongly
correlatedwith inflation. All these alternativeasset holdings were encompassedby holdings bonds in the
preceding section. Finally, using inflationoffers the advantageof a direct link to seigniorage.
14. A necessary condition for attaininga seigniorage optimum at a positive and finite level of 1Tis:
-(A) > 0. A necessary condition for that optimumto be a maximumis the one statedin the text. Note
that if A > 0 and z < 0, seigniorage reaches a minimum.
15. If the Box-Cox transformationis appliedto the independentvariable,thoughnot to the dependent
variable, we obtain ln m = a + b(rw-1)/e, which is equivalentto ln m = (a-ble) + (blw)sw,which
is in turnequivalentto our form. By estimatingour form it is possible to identify , b, and a.
16. They are eight LatinAmericaneconomies (Argentina,Bolivia, Brazil, Chile, Mexico, Nicaragua,
Peru, and Uruguay),two Africancountries(Ghanaand Zaire),and one Middle-Easterneconomy (Israel).
WILLIAM
R. EASTERLY,
PAOLO
MAURO,
ANDKLAUSSCHMIDT-HEBBEL
: 591
endeavor.17 Second, moderate-inflationcountriesconstitutea class of its own, with
behavioraland empiricalfeaturesquite differentfrom those found in high-inflation
economies.
18
Table 1 summarizesinflationpatternsin our eleven sample countries. The table's
taxonomy of inflation experiences bears resemblance to the distinction between
chronic inflationand hyperinflationcountries,made by Pazos (1972) and appliedby
Vegh (1992), among others. However, here the distinction,dictatedby the 1960-90
sample period, is between chronic and stable inflation, chronic and moderateinflation interruptedby high-inflationepisodes (including hyperinflation),and chronic
and explosive price rises. The categoriesof low, moderate,high, and hyperinflation
coincide roughly with inflationrates in the singleSlower double, triple, and quadruple (or more) digit levels the second category coinciding with Dornbusch and
Fischer's (1991) "moderateinflation"range.
Uruguay is the chronic-inflationcountrypar excellence. The unparalleledstability of its moderatelyhigh inflationrateputs it into a categoryof its own, with annual
rates which did not fall below 10 percentor surpass 140 percentduring 1960-90.
Uruguay does not even present the feature, common to all other countries, of increasing inflation after 1971-72; its three episodes of inflationexceeding 100 percent took place once each decade.
A second category is comprisedof six countriesof typically moderateinflation,
but which experienced bursts of high- or hyperinflationduringthe sample period.
They share a remarkablysimilar inflationpattern.Startingfrom low inflationlevels
in the (early) 1960s, these countriesslippedinto moderateinflationin the mid-1960s
to mid-1970s, subsequentlyjumping into high price instability,which was initiated
in the early 1970s (Chile) to early 1980s (Mexico). Only Bolivia experiencedhyperinflationas a final stage. All countries, except Zaire, successfully stabilizedduring
the last years, reachingsurprisinglysimilarand moderateinflationlevels in the 1530 percentrange.
Chronicand explosive inflationis observedin the last four countries.There inflation is not stationary,reachingfour- and five-digit levels in the late 1980s. Peru and
Nicaragua suffer the more extreme inflation explosion, startingwith low inflation
during the 1960s (when Argentinaand Brazil alreadyhad moderateinflation) and
ending with four-digitinflationlevels which double those of Argentinaand Brazil.
Testingthe Assumptionof ConstantSemielasticityof MoneyDemand
Ourcountrydatais annual,for 1960-90. The dependentvariableis definedas the
naturallogarithm of the ratio of real money balances (end-of-yearnominal Mll9
17. Preliminaryestimates for low-inflationcountriesyielded some positive A coefficients.
18. According to Dornbuschand Fischer (1993), moderateinflationcases seldom end in high inflation. Seigniorage plays at most a modest role in the persistenceof moderateinflation,and such inflation
can be reducedonly at a substantialshort-termcost to growth.
19. M1 is easily measuredbut often not the most relevantaggregatefor seignioragecollection. The
domestic creditcomponentof currencyplus requiredbankreserves(on demandandothernon-M1 deposits) could be more relevant,dependingon each country'smonetaryand financialinstitutionsand policies.
592 : MONEY,CREDIT,
ANDBANKING
TABLE
1
INFLATION
PATTERN
. Chronic
Stable
IN ELEVEN
HIGH-INFLATION
COUNTRIES
(ANNUAL
INFLATION
RATES,
%)
Inflation
ModeratelyHigh
(3)
Uruguay
2.
Chronic
56
(1960-90)
Moderate
Inflation
with
Low
(4)
Bolivia
Chile
(5)
(4)
Ghana
Israel
(7)
(2)
Mexico
Zaire
(3)
3. Chronic
and
Explosive
Peru
(7)
(6)
Bursts
High
Hyper
4,229
(1984-85)
Moderate
312
(1982-83)
8
(1960-61)
29
(1962-71)
294
(1972-76)
26
(1977-90)
5
(1960-62)
16
(1963-76)
77
(1977-83)
17
(1984-90)
5
(1960-69)
29
(1970-78)
170
(1979-85)
18
(1986-90)
3
(1960-72)
22
(1973-81)
91
(1982-87)
33
(1988-90)
7
(1964-65)
22
(1966-75)
61
(1976-90)
25
(1986-90)
Inflation
Moderate
High
Hyper
28
(1960-74)
234
(1975-88)
2,593
(1989-90)
40
(1960-80)
170
(1981-87)
1,435
(1988-90)
2
(1960-72)
23
(1973-84)
507
(1985-86)
5,760
(1987-90)
8
(1960-72)
52
(1973-82)
112
(1983-87)
3,337
(1988-90)
(9)
Nicaragua
Inflation
22
(1971-81)
Low
Brazil
(Hyper-)
Moderate
6
(1960-70)
(14)
Argentina
High-
NOTES:1. Annual inflationrates are geometric averagesof December-to-Decemberratesof change (conventionallymeasured)of the CPI.
2. Figures in parenthesesafter country names denote numberof years with annualinflation rates higher than 100 percent.
divided by the DecemberCPI) to real GDP. Inflationis measuredas the annualvariation of the CPI between the months of December of the currentand preceding
years,20and defined as consistent with the third(correct)measureof the alternative
cost of holding money, (c).
Both individual country and combined cross-countrytime-series (fixed-effects
panel) estimations were performed.2lTables2-3 reportcountryresults and Tables
4-5 presentpanel estimations. Table2 reportsthe resultsfor equation(21) in levels.
We use M l due to lack of readily available, bettermonetaryaggregates.As long as the measureof money
one uses is sufficiently highly correlatedwith relevantmoney, all we have is measurementerrorin the
dependentvariable.
20. This timing measure of inflation is consistent only with static inflation expectations. Forwardlooking timing measures such as the annualvariationof the CPI between the monthsof December of
the currentand futureyears yielded similarresults.
21. The sample period covers at most 1960-90 and is often somewhat shorter,depending on data
availabilityand estimationprocedure.
TABLE 2
COUNTRY
ESTIMATIONS
IN LEVELS
ln (-)
Country
k
A
w
=
k + Atrz
R2A
DW
ObS
(p-p_l
)
P-I
Argentina
Bolivia
-1.66
(0.04)
-1.32
(0.37)
- 2.63
(0.07)
-2.59
(0.09)
Brazil
-1.69
(0.12)
-2.06
(O. 10)
Chile
Ghana
-2.96
(0.17)
-2.97
(0.29)
-1.32
(0.15)
Israel
Mexico
- 1.21
(0.12)
-1.47
(0.13)
-1.60
(0.12)
-2.12
(0.05)
-2.16
(0.05)
Nicaragua
Peru
-3.53
(0.12)
-3.65
(0.08)
- 1.91
(0.13)
-2.08
Uruguay
- 1.83
(0.21)
1.99
Zaire
(66.25)
- 1.29
(O. 10)
-5.50
(106.8)
-1.69
(0.18)
- 1.93
(0.37)
-0.68
(0.14)
-0.69
(0.17)
-1.95
(0.22)
- 1.96
(0.14)
-0.16
(0.28)
-0.16
(0.27)
- 1.52
(0.56)
-1.35
(0.56)
-2.28
(0.21)
-2.55
(0.49)
-1.44
(0.27)
- 1.66
(0.52)
-1.58
_ s
0.77
0.83
30
145%
0.65
(0.26)
1
0.77
0.76
30
240%
0.36
0.29
30
0.81
(0.54)
0.33
0.29
30
0.76
0.38
30
105%
0.82
0.32
30
103%
-0.03
0.25
30
oo
-0.06
0.25
30
oo
0.23
0.25
31
0.68
(0.40)
1
0.21
0.26
31
0.69
0.23
31
78%
1.39
(0.51)
0.68
0.29
31
67%
0.58
0.33
31
227%
1.24
(0.55)
1
0.57
0.39
31
127%
0.49
0.41
31
172%
9.97
(2.12)
1
0.87
0.77
31
254%
0.60
0.47
30
294%
2.28
(0.12)
0.72
(0.54)
0.18
0.57
30
127%
0.26
31
278%
0.08
(1.31)
1
0.17
0.22
31
0.44
0.66
26
0.05
(0.67)
0.46
0.53
26
1
1
2.03
(0.67)
1
1.37
(9.42)
1
1
r
mnr
oo
oo
192%
oo
(0.55)
-2.75
(0.17)
-1.34
(0.30)
- 1.65
(0.11)
-1.36
(0.61)
-4.77
(65.72)
-1.57
(0.21)
-7.79
(106.6)
1
oo
175%
oo
Obs is the number of observations and srtXaris the implied steady-state seigniorage-maximizinginflation rate conventionally
measuredas in alternative(a) discussed in the text. Standarderrorsare in parentheses.
NOTE:
TABLE 3
COUNTRY
ESTIMATIONS
IN FIRSTDIFFERENCES
ln (y)-ln
Country
Argentina
A
-
FY
-
-0.65
-
-
1
(y)
= A(sw-w1)
R2A
DW
Obs
0.17
2.07
29
X
0.19
2.17
29
X
0.23
1.53
29
X
0.20
1.53
29
X
0.68
0.66
29
109
0.82
1.35
29
117
0.12
1.70
29
X
1.65
29
X
0.36
1.43
30
X
0.40
1.78
30
102
0.65
1.41
30
313
0.64
1.43
30
202
0.26
0.82
30
X
0.24
0.80
30
X
0.01
1.32
30
X
0.72
1.53
30
167
0.34
2.13
29
333
0.68
1.59
29
376
0.11
2.55
30
X
0.10
2.49
30
X
0.26
2.13
25
X
0.23
2.10
25
X
-
-
-
(
p_ |
)
mw7r
ST,, - -t
(0.15)
Bolivia
-0.63
(0.13)
-0.36
0.80
(0.14)
1
(0.05)
Brazil
Chile
Ghana
-0.36
(0.06)
-1.92
(0.36)
-2.13
(0.10)
-0.56
(0.17)
- 1.09
(1,008)
-0.65
0.96
(0.32)
1
3.01
(0.44)
1
0.01
(6.39)
1
-0.02
(O. 10)
Israel
-7.28
(6.30)
-1.32
5.35
(1.59)
1
(0.15)
Mexico
- 1.34
(0.13)
-0.52
1.22
(0.24)
1
(0.09)
-0.57
(0.12)
Nicaragua
-0.68
1.38
(0.41)
1
(0.51)
Peru
-2.62
(0.2l)
- 1.30
5.80
(0.61)
1
(0.51)
Uruguay
Zaire
-2.34
(0.04)
-0.48
(0.17)
15.10
(0-34)
1
- 12.08
(1,236)
0.01
(11.04)
1
-0.58
(0.07)
-0.58
(0.l1)
0.63
(0.52)
Obs is the number of observations and ST is the implied steady-state seigniorage-maximizinginflation rate conventionally
measuredas in alternative(a) discussed in the text. Standardenors are in parentheses.
NOTE:
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 595
TABLE 4
PANEL ESTIMATIONS:
VARIOUSSPECIFICATIONS
Variable
Model
Estimated
Coefficient
Standard
Error
R2A
DW
Obs
(p-P-l
\
)
P - I
mat
Equation (a): ln(m/y) = ATroy
+ countrydummies
linear
ry
A
1
-1.420
nonlinear
ry
A
1.586
-1.526
Equation (b): (ln(m/y)-PD
linear
nonlinear
Equation
ry
A
ry
A
(c): ln(m/y)
linear
nonlinear
nonlinear
Equation
nonlinear
- ATrw
+ b ln(m/y)_l
0.40
33 1
238go
0.79
0.40
331
134go
1.66
320
1.75
320
252Go
oo
+ countrydummies
1
-0.643
0.816
0.062
0.031
ry
A
b
1.672
-0.704
0.809
0.269
0.081
0.030
0.95
1.82
321
°° (sr)
42<Yo
(lr)
0.96
1.88
321
lOlO<Yo(sr)
Sl<Yo(lr)
0.23
1.69
320
0.27
1.76
320
0.23
2.02
309
0.28
2.12
309
- ln(m/y)_ 1) = A(1TW-1TWI)
ry
A
ry
A
(e): [(ln(m/y)
linear
0.79
ln(m/y)_l) = A(sw-PD1TWI)
1
0.29
-0.760
0.105
2.275
0.477
0.33
-0.943
0.196
ry
A
b
Equation (d): (ln(m/y)
linear
0.124
0.234
0.152
1
-0.744
2.198
-0.917
n(m/y)_l)-PD
0.114
0.542
0.221
(ln(m/y)_l-ln(m/y)_2)]
A
1
-0.713
0.101
ry
A
2.016
-0.883
0.419
0.181
ry
=
oo
266Go
A[1TW-1TW
I-PD(1TW
I-1TW2)]
X
303Go
Obs is the number of observations and TrmaX
is the smplied steady-state seigniorage-maximizinginflation rate conventionally
measuredas in alternative(a) discussed sn the text.
NOTE.
Table 3 presentsthe results for equation(21) in first diSerences. Each table reports
results for the linear, Cagan-typespecification(imposing Py= 1) and our nonlinear,
variable-elasticityequation (21) (estimating Py).Tables 2-4 make use of (c), the
correct measure of the opportunitycost of holding money. We refer to this as w.
Standarderrors corrected for serial correlationusing the Newey-West procedure
and for heteroskedasticityusing the White methodare reportedin bracketsin Tables
2 and 3.22
Unit root tests showed that both the independentand the dependentvariableare
almost invariablyI(1).23 A glance at the Durbin-Watsonstatistics in Table2 shows
22. The reason why some of the standarderrorsof the individualcountrycoefficientsare enormous1S
simply that in those cases the estimates of the rycoefficient are very close to zero.
23. For the sake of brevity,the complete resultsof the unit root tests are not reported,thoughthey are
available from the authors. We performedDickey-Fullertests (with constant, and with constant and
S
TABLE
.1
ln
R2A
INFLATION
MEASURES
Obs
DW
{P
\
P-l j
P- l J max
m&t
Measure
Inflation
. Conventional
FOR ALTERNATIVE
Standard
Error
Estimated
Coefficient
Variable
Model
SPECIFICATIONS
VARIOUS
ESTIMATIONS:
PANEL
Levels:
(-)
=
A (P
1
ry
linear
0.0029
0.049
0.210
-0.00982
0.239
-0.827
A
ry
A
nonlinear
+ countrydummies
P-l )
0.66
0.54
323
10,183Go
0.78
0.44
323
88,310Go
1.2 First Differences:
| ln (y)
(y)
-ln
ry
A
ry
A
linear
nonlinear
A |(
]
P-l
1
-0.00248
0.233
-0.401
)
(
P-2
) ]
0.0005
0.044
0.131
0.07
1.63
306
40,323<Yo
0.26
1.71
306
2,620,919<Yo
0.042
0.79
0.42
33 1
725%
0.094
0.092
0.80
0.38
331
1 ,499So
2. Log-Difference Inflation
2.1 Levels:
/mi
ln t-J
= A(lnp-ln
linear
nonlinear
2.2
ry
A
ry
A
P- l )
1
-0.474
0.689
-0.719
First Differences:
(y)
| ln ( y ) -ln
linear
nonlinear
ry
A
ry
A
1 = A[(lnp-ln
p_ 1)-(ln
p_ l -ln p_2)w]
1
-0.242
0.056
0.30
1.74
320
6,132XYO
0.741
-0.378
0.113
0.063
0.31
1.69
320
26,149XYO
is the implied steady-state selgnlorage-maximizlngInflation rate conventionally
NOTE:Obs is the number of observations and srmaX
measuredas in alternative(a) discussed In the text.
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 597
that none of the above is a cointegratingregression.24As pointedout by Arrauand
De Gregorio (1991), this may be the consequence of financialinnovation, that is,
systematic shifts in the demandfor money due to the introductionof monetarysubstitutes. The use of dummy variablesto represent"regimechanges," often caused
by financial innovation, may help towards obtaining cointegration. In Easterly,
Schmidt-Hebbel,and Mauro (1992), we reportthe results obtainedby introducing
such dummies for periods that we selected on the basis of institutionalchanges and
other importantevents that are known to have occurredin the countriesin the sample. Nevertheless, introducingdummies in order to capture financial innovation
does not substantiallyalterthe results.25
Given the difficultyinvolved in obtainingcointegratingequationsfor money demand, we estimate our equation in first-differencedform.26The results, shown in
Table 3, suggest more robust time-series propertiesthan those of Table 2, as reflected by the Durbin-Watsonstatistics.
The results suggest both the diversityof the differentcountryexperiencesand the
strengthof our variable-elasticityapproach.The importanceof relaxingthe constant
semielasticityassumptionis vindicatedby the findingthatthe PysdiSer significantly
from one in four countries(Brazil, Ghana,Nicaragua,and Peru).Massive improvements in overall fit are observedunderthe nonlinearform as comparedto the Cagan
specification.The estimatedPysare very large, exceeding significantlyone, both statistically and numerically.Thereforethe semielasticity of money demand with respect to inflationincreaseswith the rateof inflationin these countries.Recallingthe
results of section 1, we inferthatthe elasticityof substitution
betweenmoneyand
nonmonetary
financialassets is strikinglyhigh (largerthantwo) in this country
group.
In the remainingcountries the results for the nonlinearspecificationdo not improve upon those correspondingto the Cagan form. The w coefficients are not significantly different from one (but significantly larger than zero) in Argentina,
Bolivia, Israel, and Mexico, althoughtheir numericalvalues differby up to 38 percent (Mexico) from the unit value assumed by the linear form. In the remaining
three countries(Chile, Uruguay,andZaire), the estimatedcoefficientsturnout to be
nonsignificantunderthe nonlinearform, while the A coefficientsare significantunder the Cagan form.
trend)using the S percentcritical value. The opportunitycost of holding money, Tr,was found to be I(O)
in Ghana and Zaire. We could not reject the null hypothesis that the first differenceof the dependent
variableis nonstationaryin Israel and Mexico.
24. This was confirmedby formal Dickey-Fullerand augmentedDickey-Fullertests on the series of
residuals. Complete results are availableupon request.
25. Arrau and De Gregorio (1991) obtain cointegrationby applying a methodology introducedby
Cooley and Prescott(1976). They let the interceptterm in their money demandregressionsbe a random
walk, and define
any changes in the interceptas "financialinnovation."If the dependentand independent
variablesare I(1), it can be shown that this procedurenecessarilyyields stationaryresiduals.
26. First-differencingis admittedlynot adequatefor the datagenerationprocess when individualvariables are nonstationaryin levels (Engle and Granger1987). In our case, however, it is highly likely that
the test results were influenced not only by structuralshifts (as addressedabove) but also by the small
sample.
598 : MONEY,CREDIT,
ANDBANKING
The last column of Table 3 reports seigniorage-maximizinglevels of inflation
conventionally measured),derived from the estimated coefficients.27In six
of the countries, no Laffercurve exists; that is, seignioragealways rises with inflation. In five other countries, however, positive maximum-seigniorageinflationrates
are observed, which vary between 102 percent(Ghana)and 376 percent(Peru).The
1TmaX estimates change dramaticallyin two countries(Ghanaand Nicaragua)when
lifting the restrictivez = 1 assumption.It is also noteworthythat in the two other
countries where the ws exceed significantly one (Brazil and Peru), the 1TmaX estimates do not differ much from those obtainedunderthe Caganform. But for Israel,
with a w estimate that does not differ significantly from 1, 1TmaX falls drastically,
from 313 percent underthe Cagan form to 202 percentunderour nonlinearspecification. This implies that even if the nonlinearspecificationresultsdo not differ significantlyfrom the linearcase, the numerical1TmaX estimatescan differsubstantially.
Thereforethese countryresults suggest how sensitive seigniorage-maximizinginflation estimates are not only to sample choice, but, most important,to specification
selection.
Our next step is to perform a number of panel regressions in order to infer
more generally about the specificationof money demand and related seignioragemaximizing inflation rates in high-inflationcountries. The panel estimationsallow
for fixed effects by introducingcountry-specificdummiesand are performedfor the
sample of eleven high-inflationcountriesduring 1960-1990. Country-specificfeatures, such as financial structure,are assumed to be entirely capturedby country
fixed effects. Hence the constantterm k in equation (21) is allowed to vary across
countries, while A and w are held invariant.
Estimates are reportedin Table 4 for the level and first-differencedversion of
equation(21). Equation(a) is an ordinaryleast squaresregressionon the levels of ln
(m/y) and Tr,which shows very high serial correlation.28As a way of dealing with
nonstationarity,we estimate the equation in its first-differencedform, as equation
(d). As in the case of most countryestimationsin Table 2, this procedurereduced
significantly the incidence of residual correlation.Equation(b) corrects for serial
correlationby running an AR1 for panel data, following the Bhargava, Franzini,
and Narendranathan
(1982) methodology.29Equation(c) is a partialadjustmentversion of equation(21), for which we reportboththe short-runSmaX (sr, corresponding
to the short-runsemielasticity)and the long-run1TmaX (lr, correspondingto the longrun semielasticity). Equation (e) applies the Bhargavaet al. (1982) correctionto
equation (d).
(1TmaXS
27.
with inflation conventionally measured (s = (p -p_l)lp_l),
is obtained from the
first-ordercondition for seigniorage maximum,
(-A^y)-(').
Hence,
(-oyA)-(')/[l-(-oyA)-('t)].
There exists a finite
only if-A^y > 1. Otherwise, seigniorage increases monotonicalywith s and no Laffercurve exists, hence
28. It seems clear that the null hypothesis that the residualsfrom equation(a) are white noise would
be rejectedby the formaltest describedin Bhargavaet al. (1982).
We did not constructtables appropriate
to our own sample size. Also, it should be noted that the calculationof the Durbin-Watsonstatistics in
Tables 3 and 4 treats appropriatelyresidualcorrelationin the time dimension of the panels.
29. We discuss the details of the methodologyin Easterlyet al. (1992).
snlax7
smavc
/
(l
+
smav>)
=
sma>
sma>
iS
oo.
smat
=
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 599
For both levels and first-differencespecifications,the y coefficientestimatesobtained in the nonlinear versions are significantly higher than one, validating our
variablesemielasticitymodel. In fact, the resultsconstitutestrongevidence-robust
to various specificationalternatives-that the inflationsemielasticityof money demand increaseswith inflationacross high-inflationcountries.The estimatedA and y
coefficientsare quite similaracross estimationsandreachvery high significancelevels in all of them. The overall fit is systematicallyimprovedby estimatingthe nonlinear form. Under the Cagan form, Laffer-curvemaxima vary widely (between
42 percent and infinite rates of inflation);in fact, there is no Laffercurve in three
of the five equations. Under our nonlinearspecification,however, there is always a
Laffer-curvemaximumat finite inflationrates. In fact, the estimatesof seignioragemaximizing inflationrates are systematicallylower in the nonlinearresults as compared to the Cagan estimates. Allowing for a variable inflation semielasticity
changes drasticallythe shape of the money demandand associatedLaffercurves in
high-inflationcountries. We may infer that in a large samplerepresentativeof highinflationcountries encompassingboth low and high semielasticitycases-higher
inflationincreases on averagethe flight away from money and towardfinancialassets that provide protectionfrom inflation.
Ourpreferredresultsarethe first-differencedformspresentedin equations(d) and
(e) (with and without the Bhargavaet al. correction,respectively). While their results are quite similar, we will focus on equation (d) to ensure comparabilitywith
the countryresults in Table2.
As in other equations, the estimate of the seigniorage-maximizinginflationrate
changes drastically in equation (d) when lifting the y = 1 restriction.While no
Laffer curve exists under the linear (Cagan) specification, the Laffer-curvemaximum is reached at an inflationrate of 266 percentwhen y is freely estimated. The
estimatedcoefficients (A =-0.917, y = 2.198), at a 100 percentrate of inflation,
imply a point estimate of 0.88 for the absolutevalue of the semielasticityof money
to inflation(|e|). This value increases to 1.38 when the seigniorage-maximizinginflation rate of 266 percent is reached. Beyond the Laffer-curvemaximum-when
the representativehigh-inflation economy reaches the wrong side of the Laffer
curve the semielasticity continues to rise with inflation, convergingto a value of
2.01 when inflation tends to infinity. Seigniorage collection reaches a maximum
of 4.0 percentof GDP at an inflationof 266 percent, falling off toward3.6 percent
of GDP when inflationtends to infinity.30
The central implication of these results is that the linear Cagan form misrepresents money demandin high-inflationcountries.Insteadof being constant,inflation
semielasticities of money demandon average increase with inflation. While under
the Cagan form there is no seignioargeLaffercurve, the variablesemielasticityapproachrendersa seigniorage-maximizinglevel of inflationof reasonablemagnitude.
30. Seignioragecollection levels are calculatedfrom the definitionof seigniorage:S = (s/(1 + s)) *
exp[k + A * (w/(1 + s))**^y]. The constantk, which is not availablefrom the first-differenceestimations, is calculatedas [ln(m/y)]a-A * [s/(1 + s)]a**#Y wherethe a-subindexedvariablesdenote simple
estimationsample averages.
600
: MONEY, CREDIT,AND BANKING
As in the earlier country results, the finding of rising semielasticity implies a
strikingly high-greater than 2 elasticity of substitutionbetween monetary and
nonmonetaryassets.
Alternativelnf ation Measures
In orderto put the resultsof Table4 in a broaderperspective,we reportin Table5
panel estimations, based on the same datasample, for two alternativeinflationmeasures. The firstalternativeuses the conventionalinflationmeasure((p-P-l)/P-l),
while the second is based on the first difference of the logarithmof p. Both are
wrong measuresof the inflationarycost of holding money for a discretetime period,
as discussed above.
While the patternof preferredresultsfor each set of estimationsis similarto those
of Tables 2-4 based on the correct inflation measure (first differences better than
level estimations, nonlinearspecificationssuperiorto linearmodel results),the estimated coefficients and correspondingseigniorage-maximizinginflation estimates
differ dramaticallyfrom those of Table4. This should not come as a surprise,as the
three inflationmeasuresdiverge substantiallyfor high inflationlevels.
The conventionalinflationmeasurerendersa point estimate for y-0.233
that
is significantlylower thanone. The correspondingLaffercurve peak reachesan implausibly high level at an inflationof 2,620,919 percentp.a. ! The implicationthat
the semielasticityof money demandwith respectto inflationdeclines with the latter
and that no countryin the sample has been on the wrong side of the Laffercurve is
empirically implausibleand technically wrong, due to the flawed inflationmeasure
used in obtainingthese results.
The second incorrect inflation measure the first-differencedlogarithm of the
price level used by many researcherssince Cagan (1956) also yields results with
implausiblyhigh Laffercurve maxima. The y is higher than that from the conventional inflationmeasurebut still is significantlysmaller than one and thereforeimplies a falling semielasticity.
The conclusion from these resultsis thatinferencesfor the inflationsemielasticity
of money demandand Laffercurve maximafor high-inflationcountriesare also very
sensitive to the choice of the inflation measure-and there is only one that accurately describes the inflationtax in discretetime.
A numberof assumptionswe made might be relaxedin furtherresearch,if one is
willing to go beyond some of the featuresof our model and, in particular,if more
country data and higher-frequencyinformationbecomes available. In addition to
lifting the assumptionof unitaryincome elasticity both in the long and short run,
one could relax the homogeneityof degree one of real money demandin prices, and
add alternativereturnssuch as the nominalinterestrate, the expected returnon foreign assets, or the expected returnon the stock market. Furthermore,it would be
interestingto test the variable-elasticitymodel using more refinedmonetaryaggregates ratherthan M1. However, it is by no means unambiguouswhat the relevant
measure of money is for the government'scollection of seigniorage. It might also
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 601
prove useful to use real consumptionratherthanreal GDP as a scale variable.Finally, higher-frequencydata could be used when sufficiently long quarterlyGDP or
consumptionseries become available.
3. CONCLUSIONS
We have developed a model of money demand, inflation, and seignioragebased
on an optimizing agent who faces cash-in-advanceconstraintsin consumption.Her
behaviorgives rise to a money demandthat exhibits a variable semielasticity with
regardto inflation, as opposed to the constant-elasticityform of Cagan (1956) used
by a plethoraof followers. We showed that the higher is the degree of substitution
between money and bonds in the consumer portfolio, the higher is the likelihood
that the inflation semielasticity increases with inflation and that a seignioragemaximizing level of inflationexists.
The empirical applicationof the model to a 1960-1990 sample of eleven highinflationdeveloping countries(definedas those with 100 percentinflationin at least
one year of the sample period) led to rejectingthe constant-elasticityhypothesis in
four countries and, in the case of the panel estimations, for the sample as a whole.
The panel results imply an absolute value of the semielasticitythat increases with
inflation, which implies a strikinglyhigh degree of substitutionbetween money and
financialassets in high-inflationcountries. While underthe Caganform there is no
seigniorage Laffercurve, the variable semielasticity approachrendersa reasonable
seigniorage-maximizinginflationrate:266 percentp.a. These results, based on the
correctmeasureof the opportunitycost of holding money, also differmarkedlyfrom
those obtainedwhen using conventionalbut incorrectmeasuresof inflation.
When drawing policy conclusions, it is importantto recognize that the KeynesOlivera-Tanziand bracket-creepeffects of inflationon tax revenue and nonindexation of government expenditure make it necessary to distinguish between the
seigniorage-maximizingand the revenue-maximizinginflationrates.3l If higher ineffect, higher
flationimplies lower real tax revenuedue to the Keynes-Olivera-Tanzi
tax revenuedue to bracketcreep or lower governmentexpendituredue to lack of full
indexationof governmentexpenditure,the inflationrate that maximizes total revenue to the governmentwill diverge from that which maximizes seigniorage. As a
consequence, estimates of 1TmaX will differ from the revenue-maximizinginflation
rate, whetherthe specificationof money demandis linearor nonlinear.
Our empirical results on the variable semielasticity might need to be qualified
with respect to the difficultyof distinguishingbetween nonlinearitiesand shifts of
the money demand schedule. One could conceive of an extreme case in which the
true money demand function is linear (in the sense of a constant semielasticity),
while it keeps shifting due to financial innovation. Dornbusch, Sturzenegger,and
Wolf (1990) provide some evidence of hysteresisin money demand:they show that,
31. See Easterly and Schmidt-Hebbel (1994) for recent evidence on Keynes-Olivera-Tanziand
bracket-creepeffects of inflationon tax revenue in developing countries.
602
: MONEY, CREDIT,AND BANKING
as a consequence of high inflation, new institutionsarise thatallow people to economize on money holdings. This constitutesa permanentshift in the money demand
function, which persists even when inflation falls back to low levels. Arrauet al.
(1991) provide evidence that shifts in the money demandfunctionoccur to a greater
extent in countries that experience higher (and more variable) inflation. Finally,
policy-induced financial innovation could cause shifts in the demand for money.
However, we found that dummies for obvious financialreformevents did not alter
our results.
LITERATURECITED
Arrau, Patricio, and Jose De Gregorio. "FinancialInnovationand Money Demand:Theory
and Empirical Implementation."The World Bank, Workingpaper series 585, January
1991.
Arrau, Patricio, Jose De Gregorio, CarmenReinhart,and Peter Wickham."TheDemand for
Money in Developing Countries:Assessing the Role of FinancialInnovation."The World
Bank, Workingpaper series 721, July 1991.
Barro, RobertJ. "InflationaryFinanceand the WelfareCost of Inflation."Journalof Political
Economy 80 (1972).
. "GovernmentSpendingin a Simple Model of EndogenousGrowth."Journal of Political Economy 98 (1990), S 103-S 125.
Barro, Robert J., and David Gordon. "A Positive Theory of MonetaryPolicy in a Natural
Rate Model." Journal of Political Economy91 ( 1983), 353-74.
Bhargava,A., L. Franzini,and W. Narendranathan.
"SerialCorrelationand the Fixed Effects
Model." Review of Economic Studies 49 (1982), 533-49.
Blanchard, Olivier, and Stanley Fischer. Lectures on Macroeconomics. Cambridge:MIT
Press, 1990.
Bruno, Michael, and Stanley Fischer. "Seigniorage,OperatingRules and the High-Inflation
Trap."The QuarterlyJournal of Economics (May 1990).
Buiter, Willem. Principles of Financial and BudgetaryPolicy. Cambridge:MIT Press, 1990.
Cagan, Phillip. "TheMonetaryDynamics of Hyperinflation."In Studiesin the QuantityTheory of Money, edited by M. Friedman.Chicago: Universityof Chicago Press, 1956.
Calvo, Guillermo, and Leo Leiderman."OptimalInflationTax underPrecommitment:Theory and Evidence."AmericanEconomicReview 82 (March 1992), 179-95.
Calvo, Guillermo, and Carlos Vegh. "CurrencySubstitutionin Developing Countries:An Introduction."Revista de Analisis Economico 7 (June 1992), 3-27.
Cooley, Thomas F., and EdwardC. Prescott. "Estimationin the Presence of Stochastic ParameterVariation."Econometrica44 (1976), 167-84.
Dornbusch, Rudiger, and Stanley Fischer. "StoppingHyperinflationPast and Present."WeltwirtschaftlichesArchiv. 122 (1986), 1-47.
. "ModerateInflation."WorldBank EconomicReview 7 (January1993), 1-44.
Dornbusch,Rudiger,FedericoSturzenegger,and Holger Wolf. "ExtremeInflation:Dynamics
and Stabilization."BrookingsPapers on EconomicActivity (1990), 1-84.
Easterly,William, and Klaus Schmidt-Hebbel."FiscalAdjustmentand MacroeconomicPerformance:A Synthesis." In Public Sector Def eits and MacroeconomicPerformance,edited by William Easterly, Carlos Alfredo Rodriquez, and Klaus Schmidt-Hebbel.Oxford
University Press, 1994.
WILLIAMR. EASTERLY,PAOLOMAURO,AND KLAUS SCHMIDT-HEBBEL : 603
Easterly,Wiliam, Klaus Schmidt-Hebbel,and Paolo Mauro."MoneyDemandand SeignorageMaximizing Inflation."The WorldBank, Workingpaperseries 1049, November 1992.
Engle, RobertF., and Clive W.J. Granger."Co-IntegrationandError-Correction:
Representation, Estimationand Testing."Econometrica55 (1987), 251-76.
Kiguel, Miguel. "BudgetDeficits, Stability and the MonetaryDynamics of Hyperinflation."
Journal of Money, Credit, and Banking21 (May 1989), 61-80.
Kiguel, Miguel, and Nissan Liviatan. "A Policy-GameApproachto the High InflationEquilibrium."The WorldBank, Manuscript,April 1991.
Lucas, Robert E., and Nancy L. Stokey. "Money and Interestin a Cash-in-AdvanceEconomy." Econometrica55 (1987), 491-513.
Pazos, Felipe. ChronicInJqationin Latin America. New York:PraegerPublishers, 1972.
Rebelo, Sergio. "Long-RunPolicy Analysis and Long-Run Growth."Journal of Political
Economy 99 ( June 1991), 500-21.
Rodriguez, Carlos A. "Argentina:Fiscal DisequilibriaLeadingto Hyperinflation."In Public
Sector Deficits and MacroeconomicPerformance,edited by William Easterly,Carlos Alfredo Rodriquez, and Klaus Schmidt-Hebbel.OxfordUniversityPress, 1994.
Sargent,Thomas J. "TheEnd of FourBig Hyperinflations."In InJqation,edited by RobertE.
Hall. Chicago: University of Chicago Press, 1982.
Vegh, Carlos A. "StoppingHigh Inflation:An AnalyticalOverview."InternationalMonetary
FundStaffPapers 39 (September1992), 626-95.
Walsh,CarlE. "OptimalTaxationby the MonetaryAuthority."National Bureauof Economic
Research Workingpaper 1375, June 1984.
Van Wijnbergen, Sweder. "ExternalDebt, Inflation, and the Public Sector:TowardsFiscal
Policy for SustainableGrowth."WorldBank EconomicReview 3 (September1989), 297320.