Niehans, Jü g
A icle
Mone a y Policy wi h Full S ock Adjus men
Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Niehans, Jü g (1974) : Mone a y Policy wi h Full S ock Adjus men , Zei sch i ü
Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s-
und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783, Duncke & Humblo , Be lin, Vol.
94, Iss. 1, pp. 17-43,
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Mone a y Policy wi h Full S ock Adjus men
By Jii g Niehans
The e ec s o di e en ypes o mone a y policy on p ices, ou pu , em-
ploymen and in e es a es in a g owing economy a e examined unde he
assump ion o ull s ock/ low equilib ium. The in oduc ion o ime p e e -
ence pe mi s an in e p e a ion o "mone a ism".
I. A Classi ica ion o Mone a y Policies
The subjec o his pape a e he e ec s o changes in he money
supply on ou pu , employmen , he p ice le el and he a es o e u n
on bonds and capi al goods. The ea men goes beyond he amilia
analyses in he Hicks/Pa inkin/Tobin adi ion inasmuch as i conside s,
pe haps o he i s ime, si ua ions o ull s ock/ low equilib ium. I
will u n ou ha his leads o some s iking di e ences in esul s
which may equi e a pa ial e-examina ion o he e icacy o ce ain
mone a y policies. In gene al, he "mone a is " iews abou he e ec s
o mone a y policy a e no con i med, bu i will be shown ha an
impo an special case yields mos o he "mone a is " p oposi ions.
I will be assumed ha he e is no banking sys em, lea ing he go -
e nmen as he only supplie o money. The cen al bank is ega ded
as pa o he go e nmen . All money is oken money which may be
isualized in he o m o bankno es o o deposi s which p i a e i ms
and indi iduals main ain wi h he go e nmen . The go e nmen can
supply money in ou p incipal ways:
1. The money is issued in he o m o ans e paymen s o he p i a e
sec o , ha is, as a ee gi . This is he money "unexpec edly ound
in people's co e s" o "d opped om ai planes" so popula in he
olklo e o mone a y heo y. I will be called ans e money.
2. Money may be issued in paymen o goods and se ices, hus
inancing budge de ici s. This will be called expendi u e money.
3. The go e nmen can issue money by buying bonds om he p i a e
sec o , as in open ma ke ope a ions. In p inciple, he bonds can be
ei he p i a e bonds o go e nmen bonds al eady held by he
p i a e sec o . Such money will be called deb money.
2 Zei sch i Wi scha s- u. Sozialwissenscha en 1974/1
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18 Jii g Niehans
4. Finally, he money can be issued in paymen o in e na ional ese -
es like gold o o eign exchange. I his is done a a ixed p ice
o gold o a ixed exchange a es, we a e back in he commodi y
money wo ld.
The p esen analysis will concen a e on a closed economy, lea ing
h ee mechanisms o supplying money. They a e ela ed by he go -
e nmen budge cons ain 1
p ip
whe e
g low o go e nmen pu chases o goods and se ices om he p i a e sec-
o , in eal e ms,
axes ne o ans e s (including go e nmen in e es ), in eal e ms,
M money s ock, in dolla s,
B s ock o ou s anding go e nmen bonds, assumed o consis o pe pe ui-
ies (consols) paying $ 1 pe yea o e e *,
p p ice le el,
i
.
bond yield,
A ope a o deno ing he change in a s ock pe ime pe iod.
The h ee money supply mechanisms can be cha ac e ized as ollows:
pu e ans e money: — A M =
—
; g = A B = 0
P
pu e expendi u e money: — A M = g; = A B = 0
P
pu e deb money: — AM
—
—-- A B: = g = 0
p p
The e a e, in addi ion, h ee policies no in ol ing he money supply,
consis ing o a ious combina ions o g, and A B. Howe e , each o
he non-mone a y policies can be exp essed as a combina ion o wo
mone a y policies. Thus ax- inanced expendi u es a e equi alen o
expendi u es inanced by new money combined wi h a educ ion in
he money supply h ough axes. Simila ly, bond- inanced expendi u es
1 I is mainly Ca l Ch is (1968) who has d awn a en ion o he ole o
he go e nmen budge cons ain in mac oeconomic models.
2 Foley and Sid ausky iden i y hei "ibonds" wi h an in e es -bea ing de-
posi which can always be wi hd awn a ace alue (1971, p. 4). While his
simpli ies he exposi ion, i h ows ou he baby wi h he ba hwa e , be-
cause such deposi s would clea ly domina e money, and indi iduals would
hus ha e no eason e e o hold money.
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Mone a y Policy wi h Full S ock Adjus men 19
a e equi alen o money- inanced expendi u es combined wi h a con-
ac ion in he money supply h ough sales o bonds. In gene al, wi h
4 policy a iables linked by he go e nmen budge cons ain we can
de ine six policies, any h ee o which can be ega ded as combina ions
o he o he h ee. In he con ex o mone a y heo y i is na u al o
ega d he h ee mone a y policies as independen .
F om his poin o iew, he cen al p oblem o he heo y o oken
money supply a e he modus ope andi and he ela i e mac oeconomic
e ec s o a change in he money supply depending on he way i is
b ough abou . How does, say, ans e money a ec na ional income?
Does i ha e a s onge e ec han deb money o expendi u e money?
This is one o he h ee main issues aised by he ecen deba es on
"mone a ism" in mac oeconomic policy making3. A "mone a is " would
end o a gue ha wha ma e s (a leas in a i s app oxima ion) is
he change in he money supply, while i makes li le di e ence which
way his change is b ough abou . The "non-mone a is ", on he o he
hand, would a gue ha i makes a conside able di e ence whe he
money is supplied agains bonds, o pay o expendi u es, o h ough
ans e s. An ex eme "non-mone a is ", a a e species oday, would
a gue ha his makes, in ac , all he di e ence, money being e ec i e
only i i is supplied, say, in paymen o go e nmen expendi u es o
h ough a educ ion in axes, while i would be impo en i supplied
agains bonds. Conside able con usion could ha e been a oided i he
pa icipan s in he "mone a is " deba e had s a ed hei p oposi ions
in he con ex o he go e nmen budge cons ain , ins ead o a guing
abou he po ency o indi idual policy a iables as i hey could be
a ied independen ly.
n. A Mac oeconomic Model o S ock/Flow Equilib ium
To de e mine he e ec s o al e na i e mone a y policies we ha e
o embed he mone a y policy a iables in a mac oeconomic model.
Following he spi i o Tobin's app oach, his will be a gene al equi-
lib ium model o ou pu and asse s, he la e including money, bonds
and capi al goods4. I will exclude p ocesses o con inuing in la ion.
The e is, o cou se, a as li e a u e on he mac oeconomic e ec s o
mone a y policy, and i is s ill p oli e a ing apidly. Fo he mos pa ,
3 Ano he issue is he ex en o which mac oeconomic luc ua ions a e
caused by mone a y policy, wha e e i s ype, and no by ac o s ou side he
go e nmen budge cons ain , like, say, p i a e in es men demand. The
hi d ques ion is whe he mone a y policy a ec s ou pu and p ices mainly
h ough in e es a es o also h ough o he channels.
4 Tobin
(1969);
see also Tobin and B aina d (1963).
2*
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20 Jii g Niehans
no ma e whe he i is mone a is o non-mone a is , i is basically
Keynesian in he sense ha in he guise o economic s a ics i o e s,
in ac , a lee ing pic u e o he economy in a ansi o y s a e o s ock
disequilib ium5. This is ue in, a leas , wo espec s. Fi s , he e is
posi i e sa ing and in es men , bu he es o he model is alid o
a gi en capi al s ock. We know, he e o e, ha he model mus
somehow shi om one pe iod o he nex , bu we do no know how.
Second, he e a e usually go e nmen expendi u es and axes, bu he
equilib ium esul ing om he model is alid o gi en s ocks o money
and bonds. We know om he go e nmen budge cons ain ha a
budge de ici has i s coun e pa in a change in he supply o money
and/o go e nmen bonds. Again i ollows ha he equilib ium de e -
mined by he model can only be empo a y. These models do no ell
us whe e he adjus men p ocess migh come o an end.
The p esen model is w i en om he complemen a y poin o iew
o comple e s ock/ low equilib ium, hus illing a gap le by he
IS/LM a ie y o mac oeconomic heo y. The dynamic analysis o he
adjus men p ocesses leading om one equilib ium o ano he will be
le o u u e esea ch. I may be conjec u ed ha om he poin o
iew o such a dynamic analysis he IS/LM models in he Hicks/Pa inkin
adi ion will appea in hei p ope ole as s ill pic u es o a mo ing
sys em6. While he p esen model, compa ed o he IS/LM models, mus
hus be ega ded as long- un, we can only guess wha his means in
e ms o calenda ime. I may well be ha , o mode a e dis u bances,
he adjus men o he capi al s ock is la gely comple ed wi hin h ee
yea s.
To econcile ull s ock/ low equilib ium wi h posi i e in es men and
unbalanced budge s, we shall use a balanced-g ow h amewo k. Fi s ,
we in e p e g, , M and B as pe capi a a iables wi h popula ion
measu ed by he numbe o people in he labo o ce. Second, we ex-
pand he e ms on he igh -hand side o he go e nmen budge con-
s ain
_ AM M , AB_ B_
9 * ~~ M p B ' ip '
Fo balanced g ow h wi h s able p ices, hus excluding con inuing in-
la ion, he p opo iona e g ow h o bo h money and bonds mus equal
he g ow h a e o he labo o ce d. We can w i e, he e o e,
6 Fo ep esen a i e examples see Hicks (1937) and Pa inkin (1956, 1965).
6 Fo an e o o sol e simila p oblems bo h o s ock/ low equilib ium
and ansi o y p ocesses see B unne and Mel ze (1972). I seems ha a sa -
is ac o y analysis o he ansi o y phases equi es mo e explici dynamics
han B unne and Mel ze p o ide.
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Mone a y Policy wi h Full S ock Adjus men 21
(1) *
p ip
whe e G =-yand T The exogenously gi en g ow h a e 5 hus
appea s as he a e a which he pe -capi a lows g and a e capi alized
o make hem dimensionally compa able o he pe -capi a s ocks o
money and bonds. Whene e on he ollowing pages changes in go -
e nmen expendi u es o ans e s a e men ioned, hey a e o be in e -
p e ed in he sense o he s ock a iables G and T.
The es o he model is also in pe capi a e ms. Le
(2) q = q (K, E)
be a mac oeconomic p oduc ion unc ion ela ing he low o ou pu o
he inpu s o eal capi al and employmen 7. I is assumed o be quasi-
conca e wi h qK > 0, qE > 0, qua < 0, qEE < 0, qek > 0. Each ac o
is paid i s ma ginal p oduc
(3) Qk =
w
<4> Qe = —
>
whe e is he a e o e u n on capi al and w is he money wage a e.
Unemploymen is he di e ence be ween he labo o ce (whose pe
capi a alue is 1) and employmen
(5) U = 1 - E.
The e a e h ee ypes o asse s, namely eal capi al, bonds and money.
Fo each asse , pe capi a demand o he p i a e sec o depends on he
same se o a iables8:
(6) K =
K(H,G, ,i,z) Kh >0 K. >0 K, <0 Kz <0
(7) B _
ip B (H, G, , i, 2) Bh> 0 B <0 B{ >0 B,
<0
(8) M _
T> L (H, G, , i, z) Ljî>0 Lgzc0 L <0 Li <0 L* >0
The expec ed signs o he pa ial de i a i es a e gi en on he igh .
The lowe case le e s deno e he in e es a es on capi al, bonds, and cash
balances, espec i ely. I will be assumed ha he di ec pa ial de i -
a i es domina e he c oss ela ionships in he sense ha K Bi > K* B ,
7 E is employmen pe uni o he labo o ce, which may be di e en
om uni y.
8 Fo bonds, his is p i a e demand ne o p i a e supply, all bonds being
assumed o consis o consols.
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22 Jii g Niehans
Bi Lz > Bz Li, and Lz K > L Kz. H = is human weal h, de ined as
E o
eal labo income capi alized a he a e o g ow h. The non-human
^ B M
componen s o weal h K, and — do no appea as a gumen s,
because hey a e no gi en o he p i a e sec o om he ou side. In
ac , he demand unc ions o asse s s a e ha he p i a e sec o
makes hese non-human componen s wha i wan s hem o be9.
By analogy wi h H, G could be called "public weal h". As an a gu-
men in (6) - (8) i exp esses he e ec o go e nmen expendi u es on
he p i a e demand o asse s. G, like H, is gi en o he p i a e sec o
om he ou side. Taxes T, on he o he hand, do no appea as an
a gumen , because by i ue o he go e nmen budge cons ain hey
B M
can always be exp essed in e ms o G, T^ and —I is no clea
a p io i in wha di ec ion G a ec s he asse demands. I public weal h
is ega ded as a supplemen o human weal h o as a complemen
o p i a e asse s, he pa ial de i a i es KG, BG and LQ will be posi i e.
This is a plausible assump ion i , o example, he go e nmen supplies
se ices o he p i a e sec o which o he wise would ha e abso bed
labo . I , on he o he hand, G is ega ded as an o se o human weal h
(was ed esou ces) o i i is a subs i u e o p i a e asse s (like public
u ili ies), he h ee pa ial de i a i es would be nega i e. I should be
no ed ha KG, BG and LG measu e he e ec o a change in G ac-
companied by an equal change in T; whene e one o he policy a i-
ables M, B o G is a ied a gi en le els o he o he s, his implies a
co esponding change in T. The Keynesism balanced budge mul iplie
seems o imply ha a leas some o he h ee pa ial de i a i es a e
• This means ha he e is no weal h cons ain o he amilia o m.
While such cons ain s a e essen ial aspec s o s ock/ low disequilib ia, hey
a e i ele an in s ock/ low equilib ium. This is one o he main di e ences
o he p esen model ela i e o hose o he Pa inkin-Tobin a ie y. In an
impo an sense, he place o he weal h cons ain is aken by he go e n-
men budge cons ain which links inancial asse s o go e nmen de ici s.
Suppose he demand unc ions a e ini ially w i en
K = K*(H,K, G, T, , i, z)
p %p
¿=B*(H,K,^, ® G, T, , i, z)
ip p ip
M . w M B _ _ . .
——
=
L* (H,
K, — , —,
G,
T,
, z,
z)
p pip
wi h G
—
T = — + I he condi ions o he implici unc ion heo em
p ip
hold, his can be sol ed o he demand unc ions (6) — (8).
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Mone a y Policy wi h Full S ock Adjus men 23
nega i e, since he e ec o a balanced budge inc ease on sa ing is
assumed o be nega i e. The p esen analysis shows ha he signs a e
ambiguous, p obably depending o a la ge ex en on he exac na u e
o go e nmen expendi u es11.
The asse demand unc ions can be ega ded as a desc ip ion o ob-
se ed beha io . Gene ally, we would hen expec asse s o be g oss
subs i u es, so ha hei c oss pa ial de i a i es a e nega i e. We shall
call his he gene al e sion o he model. I may be c i icized o he
ac ha he e is no explici ela ionship o in e es a es wi h he a e
o ime p e e ence o indi iduals. Al e na i ely, he asse demand
unc ions can be assumed o be de i ed om op imizing beha io o
indi iduals wi h a gi en a e o ime p e e ence This a e is de ined
as he one which is app op ia e o he capi aliza ion o u u e e enues
in he absence o any cos due o unce ain y o illiquidi y. To he
ex en ha he e may be no asse wi hou such a cos , i may be an
unobse able cons uc . In pa icula , & may be di e en om (and
p obably lowe han)
<3.
This will be called he ime-p e e ence e sion
o he model.
Unde he ime p e e ence e sion an indi idual is assumed o de-
mand each asse in such a quan i y ha he sum o he a e o e u n
and he ma ginal non-in e es o se ice yield is equal o he indi i-
dual's a e o ime p e e ence a ha le el o E. I he se ice yields
a e UK, UB and
UM,
he condi ions a e +
UK
= i +
UB —
z +
UM
— O.
UM
is likely o be posi i e, e lec ing he ansac ions se ices o money,
bu
UB
and
UK
a e p obably nega i e, ep esen ing he illiquidi y cos
o holding bonds and eal capi al, wi h (—
UK)
> (—
UB)
in mos cases.
The ma ginal se ice yields p esumably all as he quan i y o he
espec i e asse inc eases a gi en H. We hus ob ain a pic u e like
igu e 1. I H changes wi h gi en a es o e u n, he u-cu es shi
upwa d, because a a highe le el o economic ac i i y he same
amoun o an asse has a highe ma ginal se ice yield. This explains
why K , BH and LH a e posi i e.
The ime p e e ence e sion implies ha he c oss pa ial de i a i es
o he asse demand unc ions anish (K* = KZ = BR = BZ = LR = LI
= 0). In e ec , he ne e u n o each asse , which is ele an o he
c oss e ec s on he demand o o he s asse s, is always no ma e
11 The model needs no sepa a e sa ing and in es men unc ions. In es -
men is de e mined by he s ock demand o capi al goods and he g ow h
a e, i. e. I = 8 K. Sa ing is he change in non^human weal h, i. e. S = 8 (K +
BJip + M/p). The di e ence be ween p i a e sa ing and p i a e in es -
men co esponds o he go e nmen de ici (in a low sense): S — I =
8 (B /ip + M/p) = g — . This shows ha he model is consis en wi h he
usual accoun ing de ini ions.
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24 Jii gNiehans
% % %
K B_
¡P
M
P
Fig.
1
wha happens o i s g oss e u n. An inc ease in he own- a e o e u n,
on he o he hand, s ill has he usual posi i e e ec , he quan i y
demanded inc easing o he ex en necessa y o le he ma ginal u ili y
all jus by he amoun he a e o e u n has gone up. I will ha dly
come as a su p ise ha he use o he ime p e e ence e sion will
u n ou o ha e a - eaching consequences o he mac oeconomic
e ec s o money. Speci ically, i can be shown o p oduce mos o he
mone a is p oposi ions. Fo he sho un, he ime p e e ence e sion
would be ha d o de end heo e ically. Many empi ical s udies o asse
beha io also ha e ound nega i e c oss in e es elas ici ies o asse
demand unc ions. Howe e , as a long- un equilib ium in e p e a ion,
he ime p e e ence e sion equi es se ious conside a ion.
The model can be in e p e ed as a ull-employmen sys em by as-
suming U = 0, while conside ing p ices and wages as lexible. Al e -
na i ely, we can assume ha ei he p ices o wages a e igid and gi en
as a legacy o he pas . We hus ob ain an unde employmen sys em.
The ansi ion om unde employmen o ull employmen will no be
discussed. In ei he case, he model de e mines all a iables once he
policy a iables G, M and B and he yield on money z a e ixed. I is
di e en om he IS-LM amewo k inasmuch as i con ains h ee in-
dependen asse s ins ead o only wo, accoun s o he capaci y e ec s
o capi al, and o e s a consis en ea men o s ock/ low aspec s.
We now u n o he compa a i e s a ics o he model se ou in he
p e ious sec ion. Wha we wan o de e mine a e he e ec s o changes
in he money supply on p ices, ou pu , employmen , and in e es a es.
In he p esen sec ion, we shall conside he case o ull employmen ,
whe e he lexibili y o wages always sees o i ha employmen is
equal o he a ailable labo o ce. We hus ha e E = 1.
III. The E ec o Changes
in he Money Supply unde Full Employmen
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Mone a y Policy wi h Full S ock Adjus men 31
d
dB
I ollows ha an inc ease in he supply o deb money always lowe s
bo h in e es a es, he educ ion in bonds ein o cing he e ec o he
inc ease in money. As a consequence, he capi al s ock, he ou pu and he
eal alue o labo esou ces inc ease also. The clea -cu sign o he
in e es e ec is in con as o he somewha ambiguous p ice e ec .
While in he case o deb money, lowe in e es a es will usually be
associa ed wi h highe equilib ium p ices, he opposi e associa ion can-
no be en i ely uled ou . Open ma ke ope a ions which aise in e es
a es canno au oma ically be elied upon o lowe he p ice le el.
Unde he ime p e e ence e sion, he e ec o deb money on he
bond yield is he same as in he gene al case, since he exp ession o
di/dB con ains no c oss pa ial de i a i es. The e ec on capi al e-
u ns, howe e , anishes, and he e ec s on he capi al s ock and ou pu
anish wi h i . This ag ees well wi h he mone a is iew ha in ull-
employmen equilib ium an inc ease in he money supply has no " eal"
e ec s no ma e whe he i is b ough abou by ans e s o h ough
open ma ke ope a ions.
Ins ead o de e mining he change in in e es a es p oduced by an
exogenous change in deb money, we can e e se he ques ion and
conside he e ec s on he money supply and p ices o an exogenous
change in he bond yield. In his case, he go e nmen announces a
ce ain in e es a e and buys (o sells) all he bonds o e ed (o de-
manded) a ha a e. Wicksell a gued ha by se ing a bond yield
below he "na u al" a e he go e nmen would ini ia e a con inuing
in la iona y spi al. The p esen model does no con i m his iew. Fo
e e y bond yield, he e is a ini e quan i y o money and a ini e equi-
lib ium p ice le el, bo h in he gene al model and in he ime p e-
e ence e sion. In mos cases, a lowe bond yield will p obably esul
in highe p ices. In he ime p e e ence e sion, we can be su e abou
his, bu in he gene al model we canno exclude he possibili y ha
a lowe in e es a e ac ually esul s in lowe p ices. In a s a iona y
economy wi h s ock/ low equilib ium he e does no seem o be a
Wicksell p ocess15, and lowe in e es a es do no necessa ily lead o
highe p ices exep i we adop he ime p e e ence e sion.
15 On his ques ion also see Niehans (1965, sec ion II), whe e, howe e ,
he possibili y ha highe in e es a es may concei ably esul in highe
p ices was no ecognized. This was due o he neglec o inancial asse
ma ke s.
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32 Ju g Niehans
(c) Expendi u e Money
Money issued o pay o go e nmen expendi u es can be ega ded
as an inc ease in ans e money accompanied by an inc ease in ax-
inanced expendi u es. The o al e ec can hus be de e mined by
adding he e ec o a balanced-budge inc ease o he e ec o ans e
money. The main cha ac e is ic o he esul s is hei ambigui y. In-
spec ion o (10) - (12) e eals ha he sign o he e ec s o G on ,
i and p depends c ucially on he signs o KG, KB and KL, and li le
can be said abou hese signs a p io i.
The e ec o go e nmen expendi u es on he p ice le el can be
w i en as
% = n = - T {LGSI + BGS* +
whe e Si, S2 and S3 a e posi i e on he basis o p e ious assump ions
abou pa ial de i a i es and s abili y condi ions. I ollows ha
dp/dG > 0, i LG < 0, BG < 0, KG < 0. This means ha a balanced-
budge inc ease aises p ices i i s e ec s on he demands o p i a e
asse s a e nega i e. On he o he hand, i LG, BG and KG we e all po-
si i e, a balanced-budge inc ease would p oduce a all in p ices. This
is in ui i ely plausible. I go e nmen expendi u es aise he demand
o money and bonds in eal e ms, while hei nominal amoun s a e
ixed, a all in p ices is necessa y o keep supply and demand in bal-
ance. This all is b ough abou by he e o s o indi iduals o sell
goods o mo e money. Wi h espec o capi al goods, Kg > 0 means
ha go e nmen expendi u es s imula e he p i a e sec o o make
mo e capi al goods a ailable o p oduce s, which ends o lowe p ices.
In ac , he e ec o go e nmen expendi u es is he same as i he
go e nmen i sel had supplied ee capi al goods o indus y. I is con-
cei able, o cou se, ha he h ee pa ial de i a i es a e o di e en
sign, depending on he na u e o he go e nmen expendi u es. In his
case he ambigui y ge s wo se.
In iew o his ambigui y, he p ice e ec s o expendi u e money
may be ei he weake o s onge han hose o ans e money. The
way money is supplied may indeed ma e , bu we do no know which
way. The ime p e e ence e sion does no hing o emo e he am-
bigui y, excep o he ac ha BG becomes i ele an , being e e y-
whe e associa ed wi h c oss pa ial de i a i es. Mone a ism hus seems
o imply he iew ha he e ec s o go e nmen expendi u es on he
demand o p i a e asse s, wha e e hei sign, a e oo small o be
ele an .
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Mone a y Policy wi h Full S ock Adjus men 33
The si ua ion is he same o he e ec s o balanced budge expen-
di u es on in e es a es, ou pu and human capi al. In all hese cases,
he signs o KG, BG and LG a e o c ucial impo ance. I may be le
o he in e es ed eade o wo k ou he a ious cases.
In summa y, we ind ha in a ull-employmen economy i gene ally
ma e s a g ea deal whe he money is supplied h ough ans e s,
h ough he bond ma ke o o inance expendi u es. While mos o
he e ec s ha e he commonly expec ed di ec ion, i u ned ou ha
we canno ely on he de la iona y e ec o es ic i e open ma ke
ope a ions wi hou empi ical in o ma ion. Howe e , i we adop he
ime p e e ence iew and i , in addi ion, we ega d he asse demand
e ec s o balanced budge changes as negligible, he mone a is posi ion
seems o be jus i ied in all impo an poin s. We a e hen co ec in
asse ing ha wha ma e s is money and no he way i is c ea ed.
IV. The E ec o Changes
in he Money Supply wi h Fixed Wages
We now ein e p e he basic model o he case o unde - o o e -
employmen . In a s a ic amewo k wi h ull s ock/ low equilib ium
his can be done by assuming ei he igid p ices o igid wages. We
shall he e concen a e on wage igidi y, while commodi y p ices a e
assumed o be ma ke -clea ing. This seems o be a mo e ele an
idealiza ion o economic eali y han he e e se assump ion. On he
o he hand, employmen is now a iable, he di e ence be ween he
labo supply and employmen being unemploymen (possibly nega i e).
O cou se, he case o unemploymen wi h ixed wages, hough con-
side ed he e in a s a ic amewo k, is al eady a (Keynesian) way-
s a ion o dynamic analysis.
Wi h he new se o assump ions, he o al di e en ial o he weal h
de ini ion becomes
w __ Ew _ H __ H _
dH = -T—dE -
-j—^
dp = — dE dp.
dp <5p2 * E p
Taking he di e en ial o he demand unc ion o capi al and subs i-
u ing o dH, we ob ain
dK = KH^-dE-KH^dp + KG dG + K d + K, du
JL
This can be subs i u ed in o he ma ginal condi ions o he capi al
and labo ma ke s, p ope ly di e en ia ed. Toge he wi h he demand
3 Zei sch i i Wi scha s- u. Sozialwissenscha en 1974/1
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34 Jii g Niehans
unc ions o bonds and money we hus ha e ou equa ions de e -
mining dE, d , di, and dp in e ms o dM, dB and dG:
(13) (qKK Kh~Y + q^dE + (qKK K -
1)
d + qKK K
di
- qKK KH ^ dp =
— QKK KG DG
(14) (qKE Kb^ + q^dE + qKE KR d + qKE KT
di
+ - qKE dP =
~~
Qke
kG dG
(15) BH§dE + B d + (Bi + di + ^ (l - B l dp =
— dB - Bg dG
ip u
(16) LhdE + L d + L(di + - LB ~^)dp = j- dM - LG dG
We now in oduce wo se s o addi ional es ic ions on he pa ame e s
o his sys em. The i s se ela es o he weal h elas ici ies o asse
demands. I will be assumed ha hey a e all equal o one. Thus
MiDH M/T H N *
TS
H ,
- - - 1 —BH ——— = — 1 - LH
———
= 0 and KU — = 1 .
ip2
u Blip J p2 a M/p) u K
The e is no gene al eason why a gi en indi idual should con o m o
his assump ion. Howe e , he e is also no gene al eason why he
de ia ions should be in one di ec ion a he han in he o he . We
would hus expec ha o he economy as a whole he de ia ions
would be ela i ely mino . Indeed, in he case o money, o which
empi ical esea ch is mos ex ensi e, scale elas ici ies ha e been ound
o be close o uni y.
Second, we shall assume ha he p oduc ion unc ion is o Cobb-
Douglas ype q = K* E1 -whence
qKE & _
QiEE
E _ i
Qkk k QKE k
I H K i H QKE E
T + qKE ) = + ^ k) = ° '
I H K ( H qEE E
+ ZEE ) = + — K j - 0 •
The jus i ica ion is again ha empi ical esul s suppo his assump ion
as a ough idealiza ion o eali y. To he ex en ha he esul s o he
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Mone a y Policy wi h Full S ock Adjus men 35
ollowing analysis a e quali a i e in na u e, ela ing o he signs o
compa a i e-s a ic e ec s, hese es ic ions a e no c ucial in he sense
ha he esul s would be alid e en i hey we e no p ecisely sa is ied.
Howe e , i he de ia ions become la ge , he e may come a poin a
which he esul s cease o hold.
Wi h hese es ic ions he ma ix o coe icien s on he le -hand
side o (13) - (16) becomes
dE
0
H E
d di
QKK
K —
1
QKK
QKEK
B
dp
- QKK KH
H
w ( „
H%>
QkeKÌ ¿Ï(I-<1KEKH—)
0
0
whe e
— QkekH P
p2
W
= —(l-o<)>0
Inspec ing his ma ix, we ind ha he addi ional assump ions a e
signi ican mainly in wo espec s. Fi s , hey imply ha changes in he
p ice le el, wi h in e es a es and employmen unchanged, do no
e ec excess demand in he money and bond ma ke s. O cou se, a all
in p ices will inc ease he supply o eal cash balances and bond
holdings, bu his is jus ma ched by he inc ease in demand due o
he inc ease in human weal h a gi en wages. Second, he equilib ium
be ween he ma ginal p oduc and he p ice o each ac o is no a -
ec ed by changes in employmen , hese changes being jus ma ched
by p opo ionally equal changes in capi al goods and hus lea ing
ma ginal p oduc s unchanged. Taking he de e minan o he abo e
ma ix o coe icien s, we ind ha A < 0 by i ue o he signs o
coe icien s16.
(a) T ans e Money
Wi hin his amewo k, he e ec o ans e money (dM > 0,
dB = dG = 0) on employmen is now de e mined as
This nega i e sign is consis en wi h s abili y o he sys em in he sense
ha he all in in e es a es which may be expec ed o esul om excess
demand in he bond ma ke ends o elimina e he la e .
3*
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36 Jii g Niehans
Fo se s o coe icien s consis en wi h ou assump ions, his exp ession
is posi i e. I ollows ha an inc ease in he money supply p oduces
an expansion o employmen . We a e no su p ised ha i is also ac-
companied by a all in bo h in e es a es:
d
dM
A M 11/ __ _ Hw
= = -¿^KKKiBH < 0 ,
= = __l_Lb jl
dM A A p H E
w
I
w __ H
QKK
K - {^-QKE^H —J
<0 .
P2 ^A/i- yp2
We may be somewha su p ised, howe e , o ind ha p ices will all:
dp _ V _ 1 1 H
The eason is easy o ind. The all in in e es a es calls o h an in-
c ease in capi al pe uni o labo and hus an inc ease in he ma ginal
p oduc i i y o labo . A ixed money wages, his implies a educ ion
in he ma ginal cos o p oduc ion which, unde he p essu e o com-
pe i ion, will be e lec ed in lowe p ices. The c ucial link in his causal
chain is, o cou se, he igidi y o wages. Once wages begin o gi e
way, as hey can ha dly ail o do soone o la e , we app oach he ull
employmen case, conside ed abo e, wi h i s ising p ices. A p esen ,
i is impo an o ealize ha as long as wages a e indeed igid, he e
is no eason o expec ha an inc ease in he money supply will lead
o highe equilib ium p ices. By he same oken, a es ic ion o he
money supply canno be expec ed o be e ec i e agains in la ion. The
expe iences in he ini ial phases o expansiona y policies, as o ex-
ample in he ea ly 'six ies, and in he ea ly phases o es ic i e pe-
iods, as in he la e 'six ies and ea ly 'se en ies, seem o be consis en
wi h he heo e ical analysis.
Wi h hese esul s we now compa e hose o he ime p e e ence
e sion. I u ns ou ha employmen , capi al and ou pu all expand
a he same a e as he money supply, while he a e o e u n ^ on
capi al and he p ice le el emain unchanged. The la e s a emen
ollows immedia ely om ARU and ApM o KI = 0. To pe mi he eade
o check he i s s a emen mo e easily, we w i e he de e minan A as
modi ied o he ime p e e ence e sion:
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Mone a y Policy wi h Full S ock Adjus men 37
w (w __ H
QkR-z^ - ~2 ~ —J
<0
p2 yp2
Wi h co esponding modi ica ions o he nume a o s, we ob ain
dE aem 1 E 1 = E
dM A* H M ' H M '
dK 1 d Qke dE K dE _ K
dM ~ qKK dM qKK dM ~ E dM M 9
dq _ dK _ g
dM ~ K dM
~~
M '
These esul s amoun o a quan i y heo y o ou pu and money
income. I should be no ed ha he cons ancy o p ices is no assumed,
bu de i ed om he model. Unde he ime p e e ence e sion, mone-
a is s a e hus jus i ied in using he quan i y heo y bo h o un-
employmen wi h igid wages and o ull employmen . Bond yields,
howe e , a e s ill in e sely ela ed o he money supply:
H Ji_
= Bg 1 BnWp 1
dM A LH'Bi + B/i2p H ' ,B _ , B
n~M/p i^p
This means ha he bond yield alls jus enough o inc ease he eal
alue o bond holdings o he ex en necessa y o sa is y he inc eased
demand o bonds due o highe human weal h. The impo an poin
is ha unde he ime p e e ence e sion lowe bond yields ha e no
epe cussions in he ma ke o eal capi al goods. I is s ill ue ha
a highe money supply is associa ed bo h wi h an inc eased demand
o eal capi al and a lowe bond yield, bu he " ansmission mech-
anism" in ol es no causal e ec o he la e on he o me . This ag ees
well wi h he equen asse ion o mone a is s ha wha hey call
he adi ional Keynesian model o e emphasizes he e ec o bond
yields on eal capi al demand a he expense o o he (o en ill-de ined)
elemen s o he ansmission mechanism.
(b) Deb Money
We now e u n o he gene al model o analyze he e ec s o deb
money, assuming (1/ p) dB =
—
(1/p) dM and dG = 0. Again his can
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38 Jü g Niehans
be done mos e icien ly by conside ing he e ec s o ans e bonds
( ha is, dB > 0, dM = dG = 0) and sub ac ing hem om he e ec s
o ans e money. Fo ans e bonds, he employmen e ec is
posi i e:
dE = aEB = 1 1
dB A A ip
w i w H
QKK~2 <KiL ~ KRLI) + - QkeKh
— j
L{
>0.
A ee gi o bonds in an economy wi h ixed wages inc eases employ-
men . Sub ac ing his (a e mul iplica ion by i) om he employmen
e ec o ans e money, we ob ain he employmen e ec o open
ma ke ope a ions:
dE
dM (dB = - idM) = -i-I {qKE K ( i¿ + " KiB + K L{- K,L
The sign o his exp ession is ambiguous, depending on he size o he
e ms in ol ing c oss pa ial de i a i es ela i e o hose in ol ing
di ec e ec s only. Mo e in o ma ion abou he coe icien s han was
con ained in ou assump ions is necessa y o make su e ha open
ma ke ope a ions ha e he "no mal" e ec s on employmen . I by
mone a y policy we mean open ma ke ope a ions, we do no need
"liquidi y aps" and he like o make i look ine ec i e as a means
o s imula e employmen . We do no ha e o be Keynesians o ollow
Keynes in doub ing he e ec i eness o mone a y policy.
Fo in e es a es, on he o he hand, he e ec s o open ma ke
ope a ions a e clea : T ans e bonds aise bo h a es. Deb money hus
lowe s bo h a es e en mo e han ans e money. I is in e es ing o
no e ha he e ec o open ma ke ope a ions on in e es a es is no
a eliable indica o o i s employmen e ec ; lowe in e es a es may
concei ably be accompanied by lowe employmen .
The p ice e ec o open ma ke ope a ions is equally clea . Fo he
same eason ha ans e money, wi h igid wages, lowe s p ices,
ans e bonds make hem ise: The ise in in e es a es calls o h a
lowe capi al in ensi y o p oduc ion, hus lowe ing he ma ginal p o-
duc o labo and aising p ices. Wi h open ma ke ope a ions, he e-
duc ion in bonds hus ein o ces he p ice decline due o he inc ease
in he money supply. Wi h ixed wages, he e is indeed li le hope ha
es ic i e open ma ke ope a ions will esul in lowe p ices once ull
equilib ium is eached again.
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Mone a y Policy wi h Full S ock Adjus men 39
The ime p e e ence e sion p o ides a adical simpli ica ion o he
pic u e. Wi h anishing c oss e ec s in he demand unc ions, he ma-
ix o coe icien s looks as ollows
dE dR di dp
0 X 0 X
0 X 0 X
X 0 X 0
X 0 0 0
whe e x deno es a non-ze o en y. I can easily be checked ha ans e
bonds now ha e no e ec s on E, , and p17. I ollows ha wi h espec
o employmen , capi al e u ns, and he p ice le el, he mone a is
posi ion is alida ed: I makes no di e ence whe he money is c ea ed
h ough ans e s o by open ma ke ope a ions. The only di e ence
is o bond yields, whe e he e ec o open ma ke ope a ions emains
s onge han ha o ans e money. Howe e , in he ime p e e ence
iew o he wo ld he bond ma ke is a side show wi h no signi icance
o he eal a iables.
(c) Expendi u e Money
We inally conside he e ec s o money issued o pay o public
expendi u es. We emembe ha we can ega d i as ans e money
combined wi h an inc ease in expendi u es balanced by axes. Fo he
balanced-budge e ec on employmen wi h ixed wages, he pic u e
is e y simila o ha o p ices unde ull employmen . The c ucial
exp ession is A
EG,
which is ob ained by eplacing he column o coe -
icien s o
dE
by ha o dG. I is clea ha he signs o
KG, BG
and
LG
again play a decisi e ole. I hey a e all posi i e, a balanced-budge
inc ease, wi h he usual assump ions abou coe icien s, is su e o
educe employmen . I hey a e all nega i e, employmen will expand.
Nega i e signs o Lg and
BG
mean ha an inc ease in employmen is
necessa y o compensa e o he all in he demand o money and
bonds caused by go e nmen expendi u es. Fo capi al goods, a neg-
a i e sign means ha less capi al will be a ailable o p oduce s, who
will hus employ mo e labo . I ollows ha he expansi e e ec o
expendi u e money on employmen may be ei he s onge o weake
han ha o ans e money wi h ha dly a de ini e p esump ion one
way o he o he . Unde he ime p e e ence e sion, KG and
BG
d op
ou o he solu ion, being associa ed wi h c oss pa ial de i a i es o
" Fo he e ec o B on E, he hi d en y in he i s column becomes x,
while he es o he column consis s o ze os. In he case o , he same is
ue o he second, and in he case o p, o he ou h column. In each
case, he de e minan is ze o.
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40 Mone a y Policy wi h Full S ock Adjus men
he demand unc ion.
LG
emains as he only ele an expendi u e
coe icien . The mone a is p oposi ion ha , wi h ixed wages, he e ec
o money on employmen is he same no ma e how i is c ea ed, is
hus shown o low logically om he double p oposi ion ha (1) he
ime p e e ence e sion is alid, and (2) balanced go e nmen ex-
pendi u es ha e no e ec on he demand o eal cash balances.
V. Concluding Rema ks
In summa y, i has been shown ha he mac oeconomic e ec s o
mone a y policy, once we wai o he ees ablishmen o s ock/ low
equilib ium, may be qui e di e en om wha we a e used o expec .
In gene al, wi hou special assump ions abou ime p e e ence, he e
is li le suppo o he mone a is iew ha he money supply is
p ac ically all ha ma e s; indeed i seems o ma e conside ably
how a change in he money supply is b ough abou . Wi h ull
employmen , i he e is a go e nmen deb , new money used o in-
c ease ans e s o o lowe axes will aise p ices, lowe bond yields
and s imula e capi al o ma ion and ou pu . In he absence o go e n-
men bonds, o cou se, he quan i y heo y applies. Money c ea ed
h ough expansiona y open ma ke ope a ions a ec s bond yields,
capi al o ma ion and ou pu in he same di ec ion as ans e money,
bu mo e so. I s e ec on he p ice le el, howe e , is weake , and we
canno logically exclude he possibili y ha p ices may ac ually all.
This implies ha a es ic i e open ma ke policy, hough esul ing in
highe in e es a es, may ha e disappoin ing p ice e ec s. I he new
money is used o pay o go e nmen expendi u es, he e ec s a e
again di e en om ans e money, bu he di ec ion o he di e ence
depends on whe he he expendi u es s imula e o discou age he
p i a e demand o asse s. This implies ha he mac oeconomic e ec
o a balanced-budge change is heo e ically ambiguous; wi h ull s ock
adjus men he Keynesian balanced-budge mul iplie canno be elied
upon.
Applying he gene al model o unde employmen wi h igid wages,
we will no be su p ised o ind ha ans e money inc eases employ-
men and lowe s he yields on bonds and capi al goods, bu we also
ind ha he p ice le el will a he all han ise. Con e sely, as long
as wages a e indeed igid, which may no be o long, a con ac i e
mone a y policy will ail o ha e de la iona y esul s. Wi h unemploy-
men and igid wages, ans e money ends o p oduce ei he he bes
o he wo s o bo h wo lds. Expansiona y open ma ke ope a ions
would ha e he expec ed e ec s on asse yields, bu hei e ec on
employmen is ne e heless unce ain; lowe in e es a es may well
OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/
DOI h ps://doi.o g/10.3790/schm.94.1.17 | Gene a ed on 2023-04-04 11:51:20