Hellwig, Ma in F.
A icle
Wha do we know abou Cu ency Compe i ion?
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Sugges ed Ci a ion: Hellwig, Ma in F. (1985) : Wha do we know abou Cu ency Compe i ion?,
Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha
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Wha do we know abou Cu ency Compe i ion?
By Ma in F. Hellwig*
The pape p esen s a c i ical analysis o he p oposals o Hayek and Vau-
bel o un egula ed compe i ion among p i a e money supplie s. Because o
ex e nali ies, ime inconsis encies and mo al haza d, hese p oposals a e
de imen al o ou side money and, a bes , dubious o inside money.
I am skep ical abou he p ice heo e ical ounda ions o Vaubel's1
policy ecommenda ions. This skep icism ex ends o he wo k o on
Hayek (1976, 1977), which ini ia ed ou cu en conce n wi h he
op imal mone a y cons i u ion. Speci ically, I ha e he ollowing p o-
blems wi h he Hayek-Vaubel analysis.
A. Bo h, Hayek and Vaubel, neglec he dis inc ion be ween inside and
ou side money. Thei discussion o compe i ion among ou side monies
is based on an in alid p emise.
B. The e a e Pa e o- ele an ex e nali ies in money demand decisions
which jus i y he use o lumpsum axa ion o c ea e a eal e u n on
money.
C. In con as o he ma ke o an inside money, he ma ke o an
ou side money is des oyed by he coexis ence o mo e han one i m
in he ma ke .
D. Vaubel and Hayek ail o dis inguish be ween he dynamic p oblem
o ime inconsis ency and he s a ic p oblem o monopoly powe . In
he absence o binding money supply announcemen s, he ime in-
consis ency o p o i maximizing policies ules ou any un egula ed
p i a e o ganiza ion o he ma ke o ou side money.
E. The analysis o compe ing inside monies pays oo li le a en ion o
he p oblems o unce ain y, in o ma ion asymme ies, and ime in-
consis ency ha a e endemic o deb o -c edi o ela ions.
In he ollowing, I shall discuss hese poin s one by one.
* This pape was p esen ed as a commen on Vaubel (1985) a he May 1984
mee ing o he Ausschuß ü Geld heo ie und Geldpoli ik o he Ve ein ü
Socialpoli ik. I hank Michael Rey o esea ch assis ance and he Deu sche
Fo schungsgemeinscha o inancial suppo h ough Sonde o schungs-
be eiche 21 and 303.
1 Vaubel's analysis o ex e nal e ec s in he money ma ke is p esen ed in
Vaubel (1984). My commen s he e co e ha analysis as well because a he
May 1984 mee ing, i was p esen ed as an in eg al pa o he a gumen .
37*
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566 Ma in F. Hell wig
1. Inside e sus Ou side Money
We mus dis inguish be ween inside money, which gi es i s bea e a
legal claim agains he issue , and ou side money, which en ails no such
claim. Supplie s o inside money a e cons ained by he need o ul ill
hei obliga ions o else go bank up . Supplie s o ou side money a e
unde no such cons ain . P esumably hen, he beha iou o a money
supplie will depend on whe he he issues inside o ou side money.2
The dis inc ion be ween inside and ou side money will also a ec he
demand o money. My willingness o hold pape ou side money depends
only on he p ospec o selling his pape ou side money o somebody
else, who in u n is willing o pay a posi i e p ice only because he hopes
o esell i o a hi d agen , who ... In con as , he decision o pay a
posi i e p ice o inside money is a leas pa ly mo i a ed by he p o-
spec o calling he claim on he issue . The shopkeepe accep s my
check — no because he expec s o esell i o his wholesale , bu because
he will p esen i o my bank. Whe eas he eal alue o ou side money
is exclusi ely de e mined by esale conside a ions, i.e. by expec a ions
o i s eal alue in u u e ansac ions, he eal alue o inside money
will depend on he " undamen als" o he unde lying claim agains he
issue .
Any posi i e o no ma i e analysis o he mone a y cons i u ion mus
ake accoun o his di e ence. Hayek and Vaubel neglec i , appa en ly
because hey belie e ha he exis ence o ou side money i sel is me ely
a consequence o go e nmen in e e ence wi h he mone a y sys em.
Acco ding o his iew, un egula ed cu ency compe i ion would lead
o he disappea ance o ou side money and i s eplacemen by inside
money as a supe io asse .3
Howe e , as a as I can see, his poin emains o be p o ed. Mo e-
o e , i is no clea ha such an ou come is in ac desi able. Fo he
economy as a whole, he use o pape money may be ad an ageous
because i economizes on he holding o eal asse s. In a pu e inside
money economy, his ad an age is pa ly los because he supplie o
money mus hold a ese e agains he claims on him. In he absence o
ou side money, his ese e will consis o eal asse s such as gold,
2 In s essing his dis inc ion, I do no ake issue wi h Johnson's (1969)
p oposi ion ha " he eal heo e ical di e ence o be d awn is be ween
in e es -bea ing and nonin e es -bea ing money". Johnson was conce ned
wi h he de e mina ion o he economy's ne weal h a he han he beha-
iou o money supplie s. E en in he con ex o his analysis, he dis inc ion
be ween inside and ou side money is appa en in he inside money supplie s'
need o hold ese es agains wi hd awels.
3 This p oposi ion was explici y asse ed by Vaubel in he o al discussion
ollowing he p esen a ion o his pape and my commen s.
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Wha do we know abou Cu ency Compe i ion? 567
machines, sha es, e c. Qui e possibly hen, he pu e inside money eco-
nomy may be ine icien because i in ol es an oue accumula ion o eal
asse s.
To make his poin p ecise, conside he p ecau iona y money holding
model o Bewley (1980, 1982) and mysel (1980, 1982). In his model,
agen s wi h unce ain commodi y endowmen s sa e and hold asse s
o sel -insu ance agains u u e endowmen luc ua ions. These agen s'
po olio choices be ween money and commodi y in en o ies depend on
hei expec a ions abou eal a es o e u n. Agen s will be indi e en
be ween money and in en o ies i bo h asse s ha e a ze o own a e o
e u n and i p ices a e non andom and cons an o e ime. A mone a y
a ional expec a ions equilib ium wi h non andom, cons an p ices does
in ac exis i he endowmen isks o di e en indi iduals cancel ou
so ha all economic agg ega es a e non andom.
In his equilib ium, he use o pape money as a s o e o alue
enables he sys em o economize on commodi y in en o ies. This sub-
s i u ion o money o in en o ies is use ul because commodi y in en-
o ies equi e a de e al o consump ion and he eby in ol e a eal cos .
Up o his poin , he a gumen does no depend on whe he we a e
dealing wi h an ou side money which happens o ha e a non andom,
cons an pu chasing powe o an inside money whose pu chasing powe
is suppo ed by an ins an epu chase p omise o he issue . In he ab-
sence o agg ega e luc ua ions, he inside money issue need no hold
any in en o ies because in each pe iod, he public's demand o his
money jus balances he a ailable supply.4
Howe e , i money does no bea in e es , he p i a e incen i es o
holding money a e oo small o Pa e o op imali y.5 In he p esen con-
ex , he use o non-in e es -bea ing money as a bu e s ock does no
yield pe ec insu ance o indi idual isks e en hough such pe ec
insu ance would be easible. I we a e dealing wi h a go e nmen
supplied ou side money, hen he alloca ion can be imp o ed by using
he go e nmen 's powe o ax in o de o c ea e a posi i e eal e u n
on money.6 This de ice is no a ailable o a p i a ely supplied inside
4 The subs i u ion o a money wi hou backing o a money wi h backing
is pe haps bes illus a ed in he s o y, old by Pe e Kenen, o he island
which used sa dine cans o money. A ou is once opened a can, ound he
sa dines inedible, and complained o he pe son who had gi en him he can.
The answe was: "The e is no hing o complain abou . I ga e you money
sa dines. I you wan ed ood sa dines, you should ha e gone o he supe -
ma ke !"
s F iedman (1969), Johnson (1969), (1970).
e Hellwig (1982).
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568 Ma in F. Hellwig
money. Such a non-in e es -bea ing inside money would in ac be dis-
placed by any go e nmen supplied ou side money which has a posi i e
eal e u n.7
Fu he mo e, e en wi hou in e es paymen s on money, he equi-
alence o inside and ou side money disappea s i he unde lying un-
ce ain y in ol es collec i e as well as indi idual isks. In his case, he
eal quan i y o money ha he economy wan s o hold will luc ua e
wi h he collec i e endowmen ealiza ion. The e o e, he supplie o
an inside money mus expec ha wi h posi i e p obabili y he claims
on him will be called. I he inside money ep esen s a claim o eal
commodi ies, he mus be p epa ed o ac ually deli e hese commodi ies.
I he wan s o be su e o a oid bank up cy — i.e. a de aul on his p o-
mise — hen he ypically needs o hold a 100
%>
ese e agains his
money issue.8 In equilib ium hen, inside money will ha e he same
e u n s uc u e as he unde lying eal asse o which i is a claim.
Whe he such an inside money can coexis wi h a non-in e es -bea ing
ou side money depends on (i) he ex en o collec i e isk and (ii) he
own a e o e u n and he ca ying cos o in en o ies. The non-in-
e es -bea ing ou side money is displaced by in en o ies o an inside
money backed by in en o ies i he own a e o e u n on in en o ies
is ze o; i is no so displaced i in en o ies ha e a high ca ying cos so
ha hei own a e o e u n is close o
—
100
%>.9
E en in hose in-
s ances in which a non-in e es -bea ing ou side money is displaced by
an inside money wi h a alue gua an ee o epu chase clause, his esul
is socially undesi able. In his case, he po olio choice be ween ou side
money and in en o y-backed inside money is biased agains he o -
me despi e he po en ial alloca ional ole o pape ou side money as a
socially cos less bu e s ock agains indi idual, i.e. insu able endow-
men isks. As in he case o pu ely indi idual isks, wel a e would be
inc eased by he in oduc ion o a ax- inanced eal e u n on ou side
money.
7 The a gumen in he ex is based on he assump ion ha commodi y
in en o ies wi h a ze o own a e o e u n a e he only asse in he model.
I we in oduce eal capi al wi h a neoclassical p oduc ion unc ion, he
a gumen mus be modi ied along he ollowing lines (due o T uman Bewley
in p i a e co espondence): Any non-in e es -bea ing money is displaced by
eal capi al o by an inside money which p omises he same eal e u n as
eal capi al and is backed by eal capi al. Howe e , because o he p ecau -
iona y demand o sa ing, he e would be an o e accumula ion o capi al o
a poin whe e he ne ma ginal p oduc o capi al is less han he a e o ime
p e e ence in consump ion. Again, wel a e can be inc eased by he in o-
duc ion o an in e es -bea ing ou side money which is backed by he go e n-
men 's powe o ax.
s The p oblem o de aul by an issue o inside money, which is neglec ed
by Hayek and Vaubel will be aken up in Sec ion 6 below.
» Hellwig (1980).
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Wha do we know abou Cu ency Compe i ion? 569
In summa y, i we a e in e es ed in he impac o compe i ion on he
mone a y sys em, we mus conside bo h, ou side and inside monies,
and we mus be ca e ul o d aw he dis inc ion be ween hem.
2. Compe i ion among Ou side Monies
Bo h Hayek (1976) and Vaubel add ess he p oblem o compe i ion
among ou side monies when hey conside " he case o ee cu ency
compe i ion among cen al banks". They claim ha such compe i ion
"encou ages less in la iona y mone a y policies" because he cu ency
wi h he lowes in la ion a e will be he mos a ac i e o a public ha
is ee o choose among he di e en cu encies.
This claim es s on he implici assump ion ha each issuing bank can
a leas pa ially con ol he in la ion a e o i s own cu ency h ough
i s supply beha iou . This p emise is in alid.
To illus a e he basic p oblem, I conside an example o compe i ion
among wo "cu encies" ha is aken om he ecen pas . The i s
Table 1
Annual G ow h Ra es o e
P eceding Yea Rela i e
P ice
"Cu ency 1" "Cu ency 2"
1970 6,6 0,6 2
1971 9,5 1,8 2
1972 13,6 6,9 2
1973 5,3 - 1,2 2
1974 9,1 2,0 2
1975 9,1 3,5 2
1976 6,2 2,7 2
1977 12,0 6,0 2
1978 11,7 7,2 2
1979 5,0 2,0 2
1980 5,0 2,3 2
1981 0,1 - 0,7 2
Cumula i e
G ow h
1970 - 1981 128 °/o 38
o/o
Sou ce: S a is isches Jah buch ü die Bundes epublik Deu schland.
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570 Ma in F. Hellwig
wo columns o Table 1 show he e olu ion o he ou s anding quan i ies
o he wo "cu encies". O e he pe iod 1970 o 1981, "cu ency 1" g ew
by mo e han h ee imes as much as "cu ency 2". Ye he las column
shows ha he ela i e p ice o he wo "cu encies" did no change. In
each pe iod, wo uni s o "cu ency 2" we e ea ed as a pe ec sub-
s i u e o one uni o "cu ency 1". In acco dance wi h he Hicks-Leon-
ie agg ega ion heo em, bo h "cu encies" we e in ac ea ed as
pa s o a single composi e cu ency: In la ion conce ned his composi e
cu ency as a whole a he han i s indi idual componen s. The abo e
a e age g ow h a e o "cu ency 1" p obably aised he in la ion a e
o he composi e cu ency and hence he common in la ion a es o all
indi idual componen s; i did no induce an abo e a e age in la ion o
"cu ency 1".
In his example, "cu ency 1" a e blue pieces o pape on which he
Bundesbank has p in ed he numbe "100"; "cu ency 2" a e b own
pieces o pape on which he Bundesbank has p in ed he numbe "50".
We mus now see o wha ex en he analysis o his example can also
be applied o ou side monies ha a e issued by di e en agencies which
compe e wi h each o he .
Fi s we need o no e ha he ela i e p ice o wo DM 50,— bills o
one DM 100,— bill is in ac a ma ke p ice. One migh objec ha
DM 100,— is wice DM 50,— me ely as a ma e o a i hme ic. Howe e ,
he e we a e no conce ned wi h a i hme ic bu wi h he p ice a which
blue and b own pieces o pape , i.e. di e en physical objec s, a e ex-
changed in ac ual ansac ions. I you need o make an eme gency
phone call om a public phone boo h a nigh , you may ind you sel
willing o pa wi h a DM 10,— bill o much less han he en DM 1,—
coins ha would be indica ed by a i hme ic.10 Simila ly, he sca ci y o
I alian 5 and 10 li e pieces is due o he ac ha he cen al bank's
a i hme ic s ands in no ela ion o he alue o he nickel con ained in
hese coins.
Once he ela i e p ice o DM 100,— and DM 50,— bills is seen as a
ma ke p ice, we mus ask why he ma ke seems o con o m so well o
he Bundesbank's a i hme ic. The Bundesbank's eadiness o in e ene
in suppo o he exchange a e o wo DM 50,— bills o one DM 100,—
bill p o ides only pa o he explana ion o his phenomenon. A e
all, he e was a ime when he Bundesbank also s ood eady o suppo
an exchange a e o DM 4,— o 1,— US I was signi ican ly less suc-
io A he ime o he opening o he hen ul amode n Dallas-Fo Wo h
ai po , he ai po adminis a ion ied o cash in on his obse a ion by
ins alling money-change machines ha e u ned 90 c in coins o a 1 $ bill.
A e conside able public p o es , hey had o abandon he idea.
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Wha do we know abou Cu ency Compe i ion? 571
cess ull hen. Mo eo e , we obse e ha he Bundesbank ha dly e en
needs o in e ene in he ma ke o DM 50,— o DM 100,— bills. Wha
would happen, i i did no in e ene a all? I submi ha e en in he
absence o cu en o expec ed u u e in e en ions by he Bundesbank,
he ma ke migh clea a he cons an ela i e p ice o wo DM 50,—
bills o one DM 100,— bill. Fo conside any agen who expec s wo
pape ou side monies o ha e a ela i e p ice x in all u u e ansac ions.
This agen will ega d x uni s o one cu ency as a p e ec subs i u e o
one uni o he o he cu ency. I he cu en ela i e p ice o he wo
cu encies is also x, he will be indi e en be ween hem; i he cu en
ela i e p ice di e s om x he agen will ha e a s ic p e e ence o
one o he wo cu encies. I he expec ed p ice x is he same o all
agen s, he cu en equilib ium p ice mus also be x since o he wise no
agen would be willing o hold he cu ency ha is oo expensi e. I a
all imes all agen s expec wo DM 50,— bills o exchange o one
DM 100,— bill in all u u e ansac ions, hen wo DM 50,— bills will
exchange o one DM 100,— bill in all ac ual ansac ions e en i he
Bundesbank does no in e ene a all. Thus he ixed exchange a e o
wo DM 50,— bills o one DM 100,— bill will co espond o a a ional
expec a ions equilib ium.
Howe e , he same a gumen shows ha i he e is no Bundesbank
in e en ion, hen any o he ixed exchange a e beween DM 50,— and
DM 100,— bills will also co espond o a a ional expec a ions equili-
b ium. Mo e gene ally, any economy wi h mul iple ia monies whose
use in di e en ansac ions is no subjec o exogenous cons ain s will
ha e mul iple a ional expec a ions equilib ia (p o ided i has any
a ional expec a ions equilib ium a all). Fo any ec o o exchange
a es x > 0, such an economy will ha e an equilib ium in which all
ansac ions ake place a he ixed exchange a es x.11
This analysis is di ec ly applicable o he Hayek-Vaubel discussion
o cu ency compe i ion among cen al banks. A p esen o cou se, a
dolla bill and a DM coin canno be used side by side in all ansac ions.
Howe e , he Hayek-Vaubel p oposal aims p ecisely a li ing hose
es ic ions which limi he use o dolla s in Ge many and o ma ks in
he Uni ed S a es. I his p oposal is ealized, hen he wo cu encies
will ci cula e side by side and hei ela i e accep abili y in an in-
di idual ansac ion will depend only on he pa icipan s' expec a ions
abou hei ela i e esale alue in u u e ansac ions. In such a wo ld,
he e can be no sys ema ic di e ences in in la ion a es be ween ou side
monies: Any an icipa ion ha he ma k will be ela i ely wo hless in
he u u e mus make i ela i ely wo hless oday al eady.
11 Fo mal analyses o his p inciple a e p esen ed by Gi on / Rope (1981).
Hellwig (1976), Ka eken and Wallace (1981).
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572 Ma in F. Hellwig
3. Ex e nal E ec s in Money Demand12
I now conside he ques ion whe he money gi es ise o Pa e o-
ele an ex e nal e ec s. I will be con enien o dis inguish be ween
he ex e nal e ec s in money demand and he ex e nal e ec s in he
decision o use money a he han ba e .
Fi s , I mus ake issue wi h bo h F iedman's (1969) o mula ion and
Vaubel's c i icism o he p ice-le el ex e nali y o money demand. Bo h
au ho s use he language and he ools o s a ic equilib ium heo y o
wha is essen ially a non-s a ic, sequen ial p oblem. Unlike a e ige a-
o , money is no an asse ha one buys once in o de o hold i o e e
and o enjoy he "liquidi y se ices" ha i yields. Ins ead, money is
aded back and o h: one acqui es i , hen esells i , acqui es i again,
e c. "Liquidi y se ices" do no a ise om he possession o money as
such, bu om he ease wi h which money can be esold. I one expec s
ha wi h p obabili y one, one will ne e ac ually use his esale op-
po uni y, hen one has no eason o hold money in he i s place. The
use o money mus he e o e be analysed in a amewo k o sequen ial,
incomple e ma ke s a he han he usual se o simul aneous, comple e
ma ke s. In he sequen ial amewo k, he di e en pe iods and oc-
casions in which agen s ade money mus be ied oge he by he con-
cep o a a ional expec a ions equilib ium, i.e. an "equilib ium o plans,
p ices, and p ice expec a ions".n
In such a non-s a ic se ing, he e is no p esump ion ha pecunia y
ex e nali ies a e Pa e o-i ele an .14»15 Fo conside he e ec s o an
inc ease in some indi idual's demand o money in pe iod . F om he
pe spec i e o pe iod , his demand inc ease aises he alue o money
in ha pe iod, he eby con e ing a posi i e pecunia y ex e nali y on
all ne selle s and a nega i e pecunia y ex e nali y on all ne buye s o
money in money in pe iod . Ce e is pa ibus, Vaubel is igh in ob-
se ing — agains he o mula ion o F iedman (1969) — ha hese
pecunia y ex e nali ies a e Pa e o-i ele an .
Howe e , om he pe spec i e o pe iod
—
1, he inc ease in he
( eal) alue o (nominal) money in pe iod se es o aise he indi ec
expec ed u ili y associa ed wi h money holdings a he end o pe iod
—
1. In e ms o he empo a y equilib ium o pe iod
—
1, his e ec
is a non-pecunia y ex e nali y and is de ini ely Pa e o- ele an . I
ends o aise he equilib ium alue o money in pe iod
—
1, which in
12 See Foo no e 1.
13 Radne (1972).
14 See, e. g., Sci o sky (1954), 184 .
is Con a y o oo no e 14 in Vaubel (1984), a main poin o Sci o sky's
classic pape is he Pa e o- ele ance o pecunia y ex e nali ies ou side he
na ow amewo k o s a ic equilib ium heo y.
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Wha
do we
know abou Cu ency Compe i ion? 579
The ques ion is how he anchise is o be awa ded. I he e is no
con lic abou he anking o any wo bids {M],T}} and {M^, T?}, hen
he egula o y commission should simply awa d he anchise o he
bidde whose bid is (unanimously) anked highes . The bidde s a e hus
in ol ed in a ype o Be and game in which hey make "con ac "
o e s and " he public" chooses whiche e con ac maximizes i s u ili y.
The usual Be and a gumen shows ha in an equilib ium o his game,
he winning bid mus be he one ha is mos highly anked among all
hose ha a e echnically easible and do no impose a ne loss on he
bidde .
In con as o he un egula ed monopoly, he app oach would always
lead o he second bes mone a y policy, i.e. he one ha is bes among
all policies ha do no ely on he go e nmen 's powe o ax. Mo e-
o e , in his app oach e en he seignio age would no s ay wi h he
winning bidde bu would be channelled back o he economy h ough
he seignio age axes T .
The p eceding analysis has i s weak spo in he assump ion o una-
nimi y among he use s o money. In gene al, he e is no eason o
expec such unanimi y. Di e en people wi h di e en as es will ha e
di e en iews abou mone a y policies and he dis ibu ion o seign-
io age. In his case, he c i e ia o he egula o y commission become
p oblema ic. Howe e , he dis ibu ional con lic s ha a ise a e no di -
e en han he dis ibu ional con lic s a ising in any o he a ea o collec-
i e choice, o , mo e na owly, in any o he egula o y p oblem. The
p oblem o egula ing he supply o ou side money no longe is a p ob-
lem sui gene is, bu i has been b ough in o he con ines o adi ional
public choice and wel a e analysis. E en i one is pessimis ic abou he
possibili y o esol ing he dis ibu ional issues ha a ise, one may s ill
expec ha a commission o he so ha is sugges ed will pay a he
mo e a en ion o he public's a e sion o in la ion and less a en ion
o he money supplie s' desi e o seignio age han an en i ely un-
egula ed monopoly.
5. The P oblem o Time Inconsis ency
I now u n o wha is p obably he mos impo an p oblem o any
mone a y cons i u ion. Up o now, I assumed ha he sequence o money
supplies is announced be o e he i s pe iod and ha his announce-
men canno be e oked in any la e pe iod. In p ac ice he e is no
eason why such ini ial announcemen s should be binding a la e da es.
The ques ion hen is how he money ma ke beha es in he absence o
binding announcemen s o u u e money supplies.
38 Zei sch i Wi scha s- und Sozialwissenscha en 1985/5
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580 Ma in F. Hellwig
I ini ial announcemen s a e no binding, he op imal policy p ecom-
mi men {M } o an un egula ed p i a e monopoly ha was discussed in
Sec ion 4.1 no longe is an equilib ium. This conclusion is ob ious in
hose cases in which he money supplies M a e cons an and ¡u = 0 o
all . Wi h ze o money g ow h, he monopolis ea ns he e enue
zq
Mo
in pe iod ze o and no hing he ea e . F om he pe spec i e o pe iod 0,
his may be a good policy because ze o money g ow h and ze o in la-
ion in la e pe iods enhance he eal e enue m
Mo
in pe iod 0. F om
he pe spec i e o pe iod 1, he e enue coMo o pe iod 0 is o e e
bygone and does no en e in o he monopolis 's conside a ions any
mo e. F om he pe spec i e o pe iod 1 he ze o money g ow h policy
con inua ion wi h ze o e enues in all pe iods = 1 is domina ed by a
policy o posi i e money g ow h and posi i e e enues in some pe iods.
Mo e gene ally, le {M } be he op imal policy p ecommi men o he
p i a e monopolis , and ecall ha his policy yields he eal e enues
So in pe iod 0 and-^—S in pe iod ¡> 1, whe e
pn
= (M — M -i)/M -i
1 + a
is he money g ow h a e and So, Si, ... a e he economy's eal money
demands in pe iods 0,1, ... a he gi en a es o e u n. Fo a gi en
quan i y o money Mo in pe iod 0 and gi en money g ow h a es pn o
^ 2, he quan i y o money Mi in pe iod 1 a ec s only he eal money
U
demand So in pe iod 0 and he seignio age income — Si in pe iod 1.
1 + iu
The seignio age income is an inc easing unc ion o ¡x and hence, o
gi en M0, o Mi. Ne e heless, om he pe spec i e o pe iod ze o, i is
no desi able o se ju = oo because a la ge alue o Mi en ails a low
eal alue o money 7i = Si/Mi a da e 1, and unde a ional expec a-
ions, a low eal alue o money no a da e 0. (I in en o ies ha e no
ca ying cos s, a bi age be ween in en o ies and money ensu es o = ;
i a bi age conside a ions impose no bound on he a e o in la ion,
in e empo al subs i u ion will educe So.) Howe e , om he pe spec-
i e o pe iod 1, his conside a ion plays no ole, and he e enue
"maximizing" policy equi es an in ini e money g ow h a e.
The basic a ionale o he a gumen is e y simple: A any da e , a
ixed pa e n o money g ow h a es
jLi + i,
pi •
• •
induces a ce ain pa -
e n o expec ed in la ion a es, which de e mines he eal esou ces S
ha he economy is willing o spend on i s money holdings a he end
o pe iod . These eal esou ces S a e sha ed be ween he monopolis
LL 1
and he p e ious holde s o money in p opo ions and . By
1 +
1
+
*
making pn inde ini ely Za ge, he monopolis can disp op ia e he p e-
ious money holde s and aise his po ion o he quan i y S ha goes
in o money.
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Wha do we know abou Cu ency Compe i ion? 581
In gene al hen, he monopolis 's e enue-maximizing policy is ime-
inconsis en 25 because in la e pe iods, he monopolis wan s o de ia e
om his policy. I ollows ha he monopolis 's ini ial announcemen
will no ac ually be c edible unless he can de ise an ins i u ion ha
makes his announcemen binding.
Mo eo e , i is now easy o see ha in he absence o binding p e-
commi men s abou u u e money supplies, he e canno be any equilib-
ium in which he alue o money is posi i e. The p eceding a gumen s
show ha no ma e wha si ua ion we a e conside ing, as o pe iod ,
he monopolis has an incen i e o make M and
JLi
a bi a ily la ge (and
hence n a bi a ily close o ze o). Unde a ional expec a ions, his
u u e beha iou o he monopolis is an icipa ed by he ma ke . Wi h
his an icipa ion, he ma ke se s S = nx = 0 o < because nobody
wan s o spend eal esou ces on an asse ha will be made wo hless
by he monopolis 's u u e beha iou . In gene al S = n = 0 o all is
he only possible equilib ium.
In summa y, an un egula ed p i a e monopoly wi hou binding com-
mi men s des oys he use o ou side pape money jus as su ely (and
by almos he same a gumen ) as he coexis ence o se e al compe ing
ou side money supplies.26 I conjec u e ha his conclusion does in ac
hold o any un egula ed p i a e o ganiza ion o a ma ke o ou side
pape money.
I also belie e ha he p oblem o ime inconsis ency bede ils any
go e nmen un o egula ed mone a y sys em. This is ob ious i he
go e nmen i sel beha es like a e enue-maximizing monopolis . Mos
o on Hayek's (1977) his o ical o e iew illus a es he e y con lic
be ween he mone a y s abili y ha is p omised o make money accep -
able and he money g ow h ha is gene a ed la e o aise e enues.
Howe e , ime inconsis ency would p obably be a p oblem e en i
he go e nmen we e un by wel a e economis s who do no y o
maximize seignio age e enue pe se. Fo conside again he model o
Be and compe i ion among po en ial money supplie s ha was dis-
cussed in Sec ion 4.3. Suppose ha he egula o y commission has
awa ded he anchise o a i m wi h a bid {M , . In pe iod 0,
25 This ime-inconsis ency was i s discussed by Cal o (1978). Fo he
gene al p oblem o ime-inconsis ency o monopoly in a du able goods ma -
ke , see
Coase
(1972) and S okey (1981).
20 See Coase (1972) on he analogy be ween he du able goods monopoly
and pe ec compe i ion. Because o he peculia i y o money, he conclusion
he e is e en s onge han Coase's, which holds only i he ime span be ween
subsequen ma ke da es is small, see S okey (1981).
38»
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582 Ma in F. Hellwig
he ini ial money supply Mo and seignio age ax To a e implemen ed.
Now in pe iod 1, he winning i m (o some o he i m) p esen s a new
bid {M , T*)~=0 o he egula o y commission, which i inds p e e able
because he ne seignio age e enues n (M
—
T ) unde he new policy
a e highe han he ne seignio age e enues n (M
—
T ) unde he old
policy. How will he egula o y commission eac o his new bid?
A his poin , he e is going o be an impo an dis ibu ional con lic
in he economy: Those who ha e held money om pe iod 0 will objec
o any inc ease in he quan i y o money Mi because i educes he alue
o hei own money holdings; hose who do no hold any money will no
objec unless he new p oposal also aises he in la ion a e om pe iod
1 o pe iod 2 and he eby wo sens he in e empo al p ice a io wi h
which hey a e aced. The la e agen s will ac ually a ou he p o-
posed policy change i hey can sha e in he spoils by ob aining a la ge
po ion o he seignio age ax Ti.
The egula o y commission's eac ion o he p oposed change in
mone a y policy will he e o e depend on he commission's composi ion
and on i s ules o p ocedu e. Speci ically he ques ion is how he com-
mission's ules o p ocedu e adjudica e he dis ibu ional con lic be-
ween money-holde s and non-money-holde s.27 The mos conse a i e
ule would equi e unanimi y o any changes in policy and would
he eby gi e ei he g oup an e ec i e e o. A unanimi y equi emen
would p obably elimina e he p oblem o ime inconsis ency by making
i impossible o change mone a y policy.
On he o he hand, a unanimi y equi emen will make i ha d o
ag ee on a winning bid in he i s place. Mo eo e , i .migh be desi able
o discipline he i m ha has been awa ded he money supply anchise
by h ea ening o gi e he anchise o ano he bank i i ails o comply
wi h he e ms o he con ac . I such a mo e equi es an unanimous
ag eemen by all membe s o he commission, hen he h ea is no
e y e ec i e, and he exis ing supplie o ou side money can y o
iola e he e ms o he winning bid wi hou much ea o epe cus-
sions.
Howe e , o any o ing ule ha does no equi e unanimi y o
decisions abou mone a y policy, ime inconsis ency is likely o be a
p oblem. I suspec ha ime inconsis ency is indeed he deepes and
leas sol able p oblem o he mone a y cons i u ion.
27 In Sec ion 4.3, his dis ibu ional con lic played no ule because p io
o he de e mina ion o he winning bid he e we e no ye any money
holde s.
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Wha do we know abou Cu ency Compe i ion? 583
6. Compe i ion among Inside Monies
To conclude he discussion, I b ie ly conside compe i ion among in-
side monies, i.e. among monies whose issue s gi e hei clien s a claim
o some so o o he . In he simples case, he holde o an inside
money has he igh o ob ain a ce ain speci ied quan i y o a eal
good, an asse , o ano he money upon demand o a some p especi ied
da e. The Hayek-Vaubel no ion o a " alue gua an ee" is a bi mo e
complica ed because i does no seem o in ol e a legal claim o he
money holde on he money issue . Ins ead, he alue gua an ee is
publicly announced as he guiding p inciple o u u e policy.28 How-
e e , as long as he money issue ul ils his obliga ion, i does no
ma e whe he he obliga ion a ises om a policy announcemen o
om a legal claim. The dis inc ion ma e s only when he money issue
de aul s on his p omise and he ques ion is how one can make him pay.
I we accep he usual ea men o demand deposi s as "money", we
see ha mos coun ies al eady ha e some compe i ion among inside
monies. Howe e , his compe i ion is igidly egula ed by he go e n-
men . The Hayek-Vaubel p oposal amoun s o an ou igh aboli ion o
all go e nmen egula ion o his sec o . In pa icula , hey wan o
abolish he ollowing egula ions:
a) The ban on he issue o p i a e bank no es ha can ci cula e as
money.
b) The equi emen o hold (minimum) ese es in cen al bank money.
c) The equi emen o denomina e he p i a e money issue 's obliga ion
in uni s o cen al bank money.
I should wholehea edly suppo hese p oposals i we li ed in a
wo ld in which all agen s a e comple ely in o med abou e e y hing
and all con ac s and p omises a e always honou ed. Un o una ely, he
e y use o money has o do wi h he ac ha we do no li e in such a
wo ld. Gi en he impe ec ions and unce ain ies o ac ual ma ke s, I
see no conclusi e e idence ei he agains o o go e nmen egula ion
o he banking sys em and he ma ke o inside money. Economic
heo y simply has oo li le o say on hese ma e s o wa an any i m
conclusions o he so Hayek and Vaubel wan o d aw.
The ela ion be ween he holde and he issue o an inside money
is akin o ha be ween a c edi o and a deb o . This ela ion is p o-
blema ic because when he con ac is made he c edi o su ende s a
eal asse and ge s no mo e han a piece o pape wi h a epaymen
p omise o he u u e. The whole c edi o -deb o ela ion hinges on
28 Hayek (1977), 31,
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584 Ma in F. Hellwig
he ques ion wha his p omise is going o be wo h. In conside ing his
ques ion one mus deal wi h a whole spec um o di icul ies a ising
om unce ain y, mo al haza d, asymme ic in o ma ion, and again
ime inconsis ency. These di icul ies which bese he heo y o c edi
ma ke s a e jus as impo an in he ma ke o inside monies.
6.1 Unce ain y and P oduc He e ogenei y
The e u ns ha he bank ea ns on i s own in es men s a e ypically
unce ain. The e o e, i s own abili y o ul il i s obliga ions o he hol-
de s o i s money is unce ain. The e u ns on inside money will gene -
ally be unce ain and will depend on he bank's own in es men policy.
In consequence he inside monies issued by di e en banks will be less
han pe ec subs i u es o each o he . Inside monies mus be ega ded
as a se o di e en ia ed p oduc s a he han a single homogeneous
p oduc . Compe i ion among inside monies hen mus be analysed as
monopolis ic compe i ion in he sense o Chambe lin a he han pe ec
compe i ion. In a wo ld o Chambe linian monopolis ic compe i ion,
he e is no p esump ion ha he ma ke ou come has any nice wel a e
p ope ies.29
Bo h Vaubel and Hayek a e awa e ha he ma ke o inside monies
mus be analysed in e ms o di e en ia ed a he han homogeneous
p oduc s. They do no seem o be awa e ha he wel a e p ope ies o
monopolis ic compe i ion in a di e en ia ed p oduc s ma ke a e qui e
unclea .
6.2 Mo al Haza d and Bank up cy
The e u n ha an inside money holde e en ually ge s depends on
he beha iou o he issue o he money. I he issue selec s poo in-
es men s, he holde o he inside money ge s a poo e u n — like
hose deposi o s who su e ed om He s a 's bad cu ency specula ions.
I he issue embezzles he company's unds, he holde o he inside
money ge s a poo e u n — like hose IOS ce i ica e holde s who su -
e ed om M . Vesco's deple ing he und's asse s. In p inciple, he con-
ac be ween he issue and holde o an inside money migh p esc ibe
he mos ca e ul beha iou on he side o he bank; in p ac ice, he
holde has no way o en o cing such a clause.
The ecen li e a u e on c edi a ioning and c edi con ac s shows
ha many ins i u ional peculia i ies in capi al ma ke s may be in e -
p e ed as de ices ha elimina e o educe such ins ances o mo al
29 See, e. g. Ha (1983).
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Wha do we know abou Cu ency Compe i ion? 585
haza d. Thus, he s anda d deb con ac wi h a ixed epaymen obliga-
ion and bank up cy i and only i he epaymen obliga ion canno be
me may be in e p e ed as he ma ke 's esponse o he mo al haza d
ha a ises i he deb o (he e he bank), bu no he c edi o (he e he
money holde ) can cos lessly obse e he ealized e u n on he deb o 's
in es men .30 In he same se ing, banks as in e media ies may se e o
educe he agency cos s o inancing inal eal in es men .31 C edi
a ioning wi h bounds on bo h loan sizes and in e es a es may se e
o induce less isky in es men policies by deb o s and banks.32
Such de ices educe, bu do no elimina e he p oblem o mo al
haza d in inancial ela ions. The cen al issue is ha he beha iou o
a deb o , in pa icula he issue o an inside money, exe s an ex e nal
e ec on he c edi o , in pa icula he holde o he inside money.
Because o his ex e nal e ec , ma ke alloca ions will gene ally no
be mo e han n- h bes , and i is unclea whe he go e nmen in e -
en ion is ha m ul o use ul.
To some ex en , Vaubel seems o see ha mo al haza d migh be a
p oblem. He sugges s ha he dange o "p o i sna ching" can be elim-
ina ed h ough alue gua an ees ((1985), 554).33 Howe e , he does no see
ha such gua an ees hemsel es migh be subjec o mo al haza d and
he e o e migh no be c edible. A alue gua an ee, deb obliga ion and
he like may elimina e mo al haza d i he penal ies o non-compliance
wi h one's obliga ion a e e y la ge. I as in he Vesco-IOS case, he
penal ies a e small in compa ison o he gains om noncompliance,
hen such obliga ions may simply be i ele an .
Mo e e , e en i he penal ies a e la ge enough o elimina e ou igh
dishones y, hey may s ill no be la ge enough o ensu e an app op ia e
in es men policy ex an e.34 Could i be he case ha minimum ese e
equi emen s o banks o in es men egula ions o insu ance com-
panies a e jus one admi edly coa se way o "in e nalize" he e ec s
ha hese companies' decisions ha e on hei inancie s h ough he
isk o bank up cy?
30 Gale / Hellwig (1983).
31 Diamond (1984).
32
Ja ee / Russell (1976), S igli z / Weiss (1981).
33 Vaubel himsel dismisses he Klein-Tullock a gumen ha mo al haza d
is less o a p oblem in a epea ed-game se ing in which banks ca e abou
hei long un p ospec s. This a gumen equi es ha agen s do no dis-
coun he u u e so ha no ma e how la ge he sho u n gains om dis-
hones o negligen beha iou may be, hey a e always ou weighed by he
in ini e ail o con inued u u e ela ions wi h one's c edi o s. A leas M .
Vesco does seem o ha e had a posi i e discoun a e.
34 See, e. g. S igli z / Weiss (1981).
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586 Ma in
F.
Hellwig
6.3 Mo al Haza d and Time Inconsis ency
I a deb o ells his c edi o ha he canno pay, does he c edi o call
a bank up cy o does he wai in he hope o sha ing in he deb o 's
be e luck in he u u e? Gi en he mo al haza d p oblems discussed
abo e, i seems desi able ab ini io o h ea en bank up cy ai ly quickly
in o de o induce he deb o o ake ca e o a oid bank up cy. How-
e e , a e i has been de e mined ha he deb o canno pay, a leas
a p esen , he c edi o may p e e o keep him ali e. I bank up cy is
called immedia ely, he c edi o has o w i e o his claims on he
deb o . I bank up cy is no called, he e migh be a ime in he u u e
when hese claims could be collec ed. The decision o call a bank up cy
is hus subjec o ime inconsis ency jus like he op imal supply o
ou side money.35 Conc e e examples o hese conside a ions ha e been
obse ed in ecen p oceedings conce ning he Ci y o New Yo k as well
as he so-called "In e na ional Deb C isis".
In hose cases whe e he deb o is a la ge bank and he deb s a e
inside money held by he public, he eluc ance o call a bank up cy
seems o be especially g ea . In he case o he Con inen al Illinois
Bank, i was made clea ha because o ad e se e ec s on he mone a y
sys em, a la ge bank would no be allowed o go bank up no ma e
how many bad loans i migh ha e made. The p oblem is, o cou se,
ha i he banks know his, hen hey ha e no eason o a oid making
bad loans. Mo e gene ally, deb o s who know ha hey will no be pu
in o bank up cy ha e only weak incen i es o manage hei means
ca e ully so as o make su e ha hey can ul il hei obliga ions.
In summa y, I belie e ha he ma ke s o inside monies and he
la ge se o capi al ma ke s o which hey o m pa a e so eple e wi h
ma ke impe ec ions, in o ma ion asymme ies and p oblems o mo al
haza d ha we canno make any i m assessmen abou he wel a e
p ope ies o he ou comes in such ma ke s. Whe he go e nmen e-
gula ion in hese ma ke s is wa an ed a all, whe he i should ake
he o m i does ake, is some hing ha a p esen we do no know —
unless o cou se we s a om he axiom ha e e y hing would be o
he bes in he bes o all possible wo lds i only he go e nmen
ceased in e e ing. I we do no accep his axiom, we mus admi ha
we simply do no know e y much abou how compe i ion among inside
monies wo ks.
35 Hellwig (1977).
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Wha do we know abou Cu ency Compe i ion? 587
Summa y
The pape s udies he p oposals o Hayek and Vaubel o un egula ed
p i a e compe i ion in he money ma ke . These p oposals a e shown o es
on an insu icien dis inc ion be ween inside and ou side money. The exis -
ence o an ou side money wi hou a backing is desi able on wel a e g ounds.
Howe e , any p i a e supply o ou side money in pe ec compe i ion, Cou -
no oligopoly o monopoly would ac ually des oy he use o ou side money.
The main p oblem is ha o ime inconsis ency o he op imal money supply
policy. P oblems o ime inconsis ency and o mo al haza d a ise also in he
ma ke o inside money. Because o hese p oblems, he app op ia eness
o un egula ed compe i ion in he ma ke o inside money mus also be
doub ed.
Zusammen assung
Die A bei be aß sich mi den Vo schlägen Hayeks und Vaubels zu Ein-
üh ung des We bewe bs im Geldwesen. Es wi d gezeig , daß diese Vo -
schläge au eine unzu eichenden Un e scheidung zwischen Außengeld und
Innengeld be uhen. Die Exis enz eines Außengeldes ohne Deckung is aus
wohl ah s heo e ischen E wägungen wünschenswe . Ein p i a es Angebo
an Außengeld im We bewe b, Cou no -Oligopol ode Monopol wü de abe
die Funk ions ähigkei des Ma k es ü Außengeld ze s ö en. Zen ales P o-
blem is die Zei inkonsis enz jegliche Geldangebo spoli ik. Zei inkonsis enz-
p obleme in Ve bindung mi „mo al haza d" e en auch im Ma k ü Innen-
geld au und lassen auch hie die Angemessenhei de Vo schläge on Hayek
und Vaubel als zwei elha e scheinen.
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