Ande sen, To ben M.
A icle
Recen De elopmen s in he Theo y o E icien Capi al
Ma ke s
K edi und Kapi al
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Ande sen, To ben M. (1985) : Recen De elopmen s in he Theo y o E icien
Capi al Ma ke s, K edi und Kapi al, ISSN 0023-4591, Duncke & Humblo , Be lin, Vol. 18, Iss. 3, pp.
347-371,
h ps://doi.o g/10.3790/ccm.18.3.347
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/293028
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Recen De elopmen s in he Theo y
o E icien Capi al Ma ke s*
By To ben M. Ande sen, Aa hus
I. In oduc ion
The hypo hesis ha p ices e lec all a ailable in o ma ion in inancial
ma ke s is p edominan in he inancial li e a u e. Acco ding o his socal-
led e icien capi al ma ke hypo hesis a "ma ke in which p ices ully
e lec a ailable in o ma ion is called e icien " {Fama, 1970, p. 383).
Despi e he popula i y o his hypo hesis and nume ous empi ical es s o i s
implica ions igo ous analysis o he unde lying p oblem o in o ma ion
agg ega ion and dissemina ion ha e un il ecen ly been
ew.
Fo his eason
su icien condi ions o ma ke
e iciency
ha e hi he o been conjec u ed o
be
(Fama,
1970) i) absence o ansac ions cos s, ii) all a ailable in o ma ion
is eely a ailable o all agen s, and iii) homogeneous expec a ions,
i. e.
all
agen s ag ee on he implica ions o he a ailable in o ma ion o cu en and
u u e asse p ices. These su icien condi ions imply essen ially ha he
in o ma ion p oblem is assumed away om he ou se , since by assuming all
in o ma ion o be eely a ailable o all agen s oge he wi h homogeneous
expec a ions is o assume ma ke
e iciency,
and hence o dep i e he no ion
o capi al ma ke e iciency o any meaning1. Ra he we shall analyse he
p oblem o capi al ma ke e iciency unde he assump ions i) ic ionless
(absence o ansac ions cos s) compe i i e inancial ma ke s, and ii) model
consis en o a ional expec a ions.
To unde s and he ma ke sys ems abili y o use all a ailable in o ma ion
e icien ly, and hence o e alua e he e icien capi al ma ke hypo hesis, a
igo ous analysis o in o ma ion agg ega ion and dissemina ion in decen-
alized ma ke s is indispensable. Recen ly a highly echnical li e a u e has
* Financial suppo om he "Danish Social Science Resea ch Council" is g a e ully
acknowledged.
1 In Ande sen (1984) i is, howe e , shown how e en unde hese assump ions he
no ion o ma ke e iciency may be unclea since he ele an in o ma ion se may no
be well-de ined, see sec ion 9.
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348 To ben
M.
Ande sen
de eloped in which p oblems o in o ma ion in compe i i e ma ke s is igo -
ously analysed, and whe e he issue o in o ma ional e iciency o inancial
ma ke s is explici ly add essed. The pu pose o his pape is o gi e a non-
echnical in oduc ion and e iew o his heo e ical li e a u e as i speci i-
cally ela es o he e icien capi al ma ke hypo hesis.
Agen s ading in inancial ma ke s will o nume ous easons ha e di e-
en opinions (in o ma ion/expec a ions) abou he e u ns on he asse s.
The ac ha agen s ade condi ional on di e en in o ma ion implies in a
compe i i e ma ke ha he equilib ium p ices e lec he in o ma ion o he
ade s since he compe i i e ma ke p ices depend on he demand o all
agen s, which in u n depends on he in o ma ion possessed by he agen s.
Hence, he ma ke p ice ec o embodies o some deg ee all in o ma ion cu -
en ly a ailable o he ade s, and he agen s should be able o in e some
o his in o ma ion om he p ices. Obse ed p ices cons i u e in his way
impo an in o ma ion sou ces since hey agg ega e he in o ma ion posses-
sed by di e en agen s and dissemina e his agg ega ed in o ma ion o all
ade s.
In o de o analyse he p oblem o how agen s can in e in o ma ion om
p ices i is necessa y o say some hing abou how agen s pe cei e p ices and
in o ma ion o be ela ed. Ob iously, he a ional expec a ions equilib ium
concep , c . Mu h (1961) and Lucas (1972), sugges s i sel by saying ha he
ela ion be ween p ices and in o ma ion pe cei ed by agen s is iden ical o
he objec i e ela ion be ween p ices and in o ma ion. The a ional expec a-
ions equilib ium concep has hus made a igo ous analysis o he p oblem
o in o ma ion and he p ice sys em possible, and mo i a ed by he pape s
by Kihls om and Mi mann (1975) and G ossman (1976) a mic oeconomic
li e a u e2 has been building up dealing wi h he p oblem o in o ma ion
dissemina ion and agg ega ion in compe i i e ma ke s. The opic o his
pape is es ic ed o his heo e ical li e a u e in ela ion o he e icien
capi al ma ke hypo hesis3.
Ma ke e iciency can be de ined wi h espec o di e en in o ma ion
se s, and commonly a dis inc ion is made be ween he ollowing o ms
(Fama, 1970)4: i) weak- o m e iciency, whe e only his o ical p ices a e
2 Simul aneously a mac oeconomic b anch o li e a u e has been building
up
whe e
he ole o p ices as dissemina e s o in o ma ion has been s essed. This li e a u e
was mo i a ed by he seminal pape by Lucas (1972), o a su ey and in oduc ion
see Ba o (1981) and
Taylo
(1983).
3 This su ey does no ea he ela ion be ween in o ma ion and specula ion (see
S igli z (1983) o a ecen discussion) no any empi ical wo k ela ed o he e icien
capi al ma ke hypo hesis.
4 On his see also Neumann and Klein (1982).
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 349
included in he in o ma ion se , ii) semi-s ong- o m e iciency, whe e all
public in o ma ion is included in he in o ma ion se , and iii) s ong- o m
e iciency, whe e all in o ma ion (public and p i a e) is included in he
in o ma ion se . Fo he p esen pu pose we shall p ima ily discuss he e i-
cien capi al ma ke hypo hesis in i s s ong- o m.
The pape is o ganized as ollows: Since he discussion depends c i ically
on he a ional expec a ions equilib ium concep we shall s a by gi ing a
sho discussion o he app op iabili y o his equilib ium concep in analys-
ing agg ega ion and dissemina ion o in o ma ion by p ices (sec ion II). The
ollowing discussion will be wi h e e ence o a simple illus a i e model
se -up in sec ion III, and he ole o p ices as agg ega o s and dissemina o s
o in o ma ion is analysed in sec ion IV. In sec ion V o IX we shall in o-
duce in o ma ion cos s, weal h dynamics, quan i y signals, exis ence o
ma ke s and sequen ial ading in o he analysis. Finally, sec ion X o e s
some concluding ema ks.
II. The Ra ional Expec a ions Equilib ium Concep
In analysing in o ma ional ques ions we shall make ex ensi e use o he
a ional expec a ions hypo hesis. Al hough i is a echnical a ac i e and
nice hypo hesis which a oids he p oblem o ad-hoc assump ions abou
expec a ions, is i also a easonable hypo hesis o use in analysing in o ma-
ional p oblems?
Le us s a by making clea wha he hypo hesis o a ional expec a ions
en ails. Mu h (1961) o mula ed he idea ha "Expec a ions, since hey a e
in o med p edic ions o u u e e en s, a e essen ially he same as he p edic-
ions o he ele an economic heo y.", o o pu i in ano he way, ha
agen s use all a ailable in o ma ion in a co ec way, i.e. consis en wi h
heo y.
I should be s essed ha he assump ion o a ional expec a ions is no
only a beha iou al pos ula e wi h espec o he agen s, bu also an equilib-
ium concep . Expec a ion o ma ion o endogenous a iables equi es ha
he agen s ha e a pe cep ion o how endogenous a iables a e ela ed o
s a e o exogenous a ables. This s uc u al dependence is de e mined by
he beha iou o all agen s in he economy. The a ional expec a ions
hypo hesis imposses he es ic ion ha he agen s pe cep ion o he educed
o m o he model is iden ical o he ue educed o m. In o he wo ds he
expec a ions o ma ion unde lying he beha iou o any agen is consis en
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350 To ben M. Ande sen
wi h he expec a ion o ma ion and hence beha iou o all o he agen s5,
i.
e.
he a ional expec a ions hypo hesis is an equilib ium concep .
I is essen ial ha gi en his de ini ion he app op ia eness o assuming
a ional expec a ions can no be seen independen ly o he model in which
i is pu o use. One should no , he e o e, necessa ily iden i y he a ional
expec a ions hypo hesis wi h he well known and con o e sial Lucas-Sa -
gen -Wallace p oposi ion saying ha sys ema ic mac oeconomic policy is
ine ec i e. This p oposi ion hinges equally on he s uc u al o m o he
model, and he expec a ion hypo hesis, and is no necessa ily implied by he
a ional expec a ions hypo hesis as such.
I is impo an o dis inguish be ween he way in which he a ional
expec a ions hypo hesis has been used in mac o models o he ISLM- a ie y
and he "mic o-models" discussed he e. In he o me he e m is used o
desc ibe equilib ia in a sequence o ma ke s unde unce ain y in which
ade s possessing homogeneous in o ma ion an icipa e he s ochas ic p o-
cess o he equilib ium p ices co ec ly, and in o ma ion p oblems a e only
ea ed in a e y udimen a y way. In he mic o- e sion he in o ma ion
p oblem is explici ly analysed and he e m desc ibes an equilib ium con-
cep o a ma ke in which ade s possessing di e en in o ma ion use he
equilib ium ma ke p ices as in o ma ional signals. I is he la e which is
he opic o his su ey.
The a ional expec a ions hypo hesis equi es ha agen s know he ue
educed o m and his can be in e p e ed in ei he o wo ways. In he i s »
in e p e a ion agen s a e assumed o lea n he s uc u e o he model o e
ime, and in he limi ( he long un) hey will know he ue s uc u e and
hence.ha e a ional expec a ions. Ob iously his in e p e a ion does no
apply o ma ke s which only a e open in equen ly o ma ke s wi h e-
quen s uc u al shi s6. Ano he in e p e a ion is o ega d he assump ion
o a ional expec a ions as an equilib ium concep o an economy whe e he
agen s posses pe ec knowledge on he s uc u e o he economy. In ei he
in e p e a ion i is seen ha he a ional expec a ions assump ion is he
limi o he mos which can be made o he idea ha in o ma ion is used
op imally and consis en wi h heo y.
All ad-hoc models o expec a ion o ma ion su e om he p oblem ha
any esul de i ed subjec o hem is liable o he c i ique ha all a ailable
in o ma ion is no used op imally. Hence, i he agen s in any way can
5 This does no necessa ily imply ha agen s ha e homogeneous expec a ions o
endogenous a iables in a a ional expec a ions equilib ium, c . below.
6 Fu he mo e he e is he p oblem o con e gence o he lea ning p ocess, see B ay
e al. (1982), Champsau (1983).
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 351
bene i om i hey will a emp o acqui e mo e in o ma ion and use i , and
his in u n changes he esul s.
The a ional expec a ions hypo hesis elimina es his p oblem, al hough
ob iously a he cos o being an in o ma ionally demanding equilib ium
concep . Howe e , in he con ex o inancial ma ke s whe e ma ke s a e
well o ganized, he i ems aded a e s anda dized, and a la ge numbe o
agen s pa icipa e his "s ong" equilib ium concep may ep esen a
easonable i s -app oxima ion. This is ein o ced by he ac ha ansac-
ions cos s in inancial ma ke s ypically will be negligible and specialized
ade s o some deg ee will be able o coun e -ac he e ec s o 'i a ional'
ade s. Finally, i should be ema ked ha al hough he a ional expec a-
ions equilib ium concep is desc ip i ely oo s ong i is no de oid o any
sensible use in heo e ical models, since i is a benchma k which shows he
mos o be expec ed as ega d consis ency in expec a ions o ma ion.
The applicabili y o he a ional expec a ions hypo hesis is in ima ely
ela ed o he ma ke sys ems abili y o coo dina e economic ac i i ies. Gen-
e ally, economis s a e p ejudiced owa ds he iew ha he ma ke mecha-
nism succeeds qui e well in coo dina ing economic ac i i ies. Since he
a ional expec a ions hypo hesis implies ha all in o ma ion is used co -
ec ly i ends o il he esul owa ds well-beha ed esul s, and one should
hink ha he hypo hesis only seems easonable o hose who a e p ejudiced
owa ds he iew ha economic ac i i ies a e well coo dina ed7.
This is, howe e , no necessa ily he case since he a ional expec a ions
hypo hesis "pe mi s us o show ha e en in such a wo ld he in isible hand
may cease o guide be o e i has made ci izens as well o as, in he gi en
ci cums ances, hey could be". (Hahn, 1982, p. 11).
The ad an age o he a ional expec a ions equilib ium concep is ha i
allows a igo ous analysis o p oblems ela ed o in o ma ion and he p ice
sys em. The idea o employing his equilib ium concep is hus p ima ily
ha i is a use ul benchma k showing he mos o be expec ed om in o ma-
ion agg ega ion and dissemina ion in decen alized ma ke s a he han a
necessa ily ully ealis ic expec a ions hypo hesis.
III. An Illus a i e Model
As a benchma k o he ollowing discussion i is use ul o de elop a sim-
ple po olio model which allows us o discuss he basic issues in ol ed in
in o ma ion agg ega ion and dissemina ion by p ices.
7 Admi edly he e is a endency o his o be he case.
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352 To ben M. Ande sen
Conside a model wi h H weal h-maximizing households indexed by i,
i= 1, 2, ..H. Assume ha hey can in es in a iskless asse wi h ze o
e u n8 (money) and p ice no malized o one, and a isky asse wi h cu en
p ice p and which pays p a he end o he pe iod,
i. e.
he e u n on he isky
asse is gi en by he capi al gain p - p. All agen s a e assumed o be p ice-
ake s in he ma ke o he isky asse .
In es o i's budge cons ain is gi en as
(1)
TRi
+ pXj =
Wj
= 77lj + pXj
whe e
m^
and x{ a e he ini ial s ocks possessed by agen i o he iskless and
he isky asse . The ini ial weal h w{ o in es o i is gi en as he alue o he
ini ial s ocks. The budge cons ain in (1) equi es ha in es men s in he
iskless ( a^ and he isky asse (xj do no exceed he ini ial weal h. Gi en
in es men s we ind end-o -pe iod weal h o be
(2) wi = mi + px{
Combining (1) und (2) we ge
(3)
Wi
= w{ + (p-p)Xi
In es o s a e assumed o maximize he expec ed u ili y o end-o -pe iod
weal h condi ional on in o ma ion a ailable o he agen ( o be speci ied
below). Fo simplici y we assume he u ili y unc ion o all in es o s o be
a cons an absolu e isk-a e sion u ili y unc ion9. Hence, in es o i
maximizes
(4) ^[-expi-a^l/J
subjec o (3). a > 0 is he A ow-P a measu e o absolu e isk-a e sion o
agen z, assumed o be cons an .
The excess demand o agen i o he isky asse can now be ound o be
(5) zi (P> li) ~ =-: - X:
Vi VAR (p |
I{)
Le us assume ha each agen possess some p i a e in o ma ion, si} ele an
o p edic ing he end-o -pe iod alue o he isky asse (p). Since he
8 The assump ion o ze o e u n is no c i ical, bu simpli ies he exposi ion.
9 An impo an implica ion o his is ha he demand o he isky asse becomes
independen o weal h c . sec ion VI.
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 353
demand o he isky asse and hence he equilib ium p ice (p) depends on
he p i a e in o ma ion o he agen s, he p ice e eals some o his in o ma-
ion, and hence he p ice cons i u es an independen sou ce o in o ma ion
o he agen s. Tha is, he in o ma ion a ailable o agen i is gi en by p i a e
in o ma ion s and public in o ma ion om obse ing he ma ke p ice,
i.
e.
h = {Si> P}-
In he ollowing we shall dis inguish be ween a di e en ial in o ma ion
s uc u e and an asymme ic in o ma ion s uc u e. By a di e en ial in o -
ma ion s uc u e is unde s ood ha agen s ha e di e en ial ex-an e (p i-
a e) in o ma ion, bu no agen belie es any o he agen o be sys ema ically
be e in o med han himsel . By an asymme ic in o ma ion s uc u e is
unde s ood a sepa a ion o he agen s in o "in o med" and "unin o med"
agen s, whe e he la e g oup o agen s possess lesse in o ma ion han he
o me 10.
Le i = 1, 2,..., K deno e he g oup o 'in o med' agen s and i = K + 1,...,
H he g oup o 'unin o med' agen s hen he asymme ic in o ma ion s uc-
u e is cha ac e ized by
Ij
z
= 1,2,..K
ii =
I I i = K +
1, X +
2,..H
whe e I
c=
J7. Ob iously, he asymme ic in o ma ion s uc u e is a special
case o he di e en ial in o ma ion s uc u e.
Re u ning o he illus a i e model we shall assume ha he end-o -pe iod
alue o he isky asse is de e mined exogenously as11
(6) P= +e
whe e / ~N
( ,
o% e~ N( 0,
a2
e)
and E e = 0.
I is use ul o s a by conside ing his model unde an asymme ic in o -
ma ion s uc u e. Assume ha he in o ma ion se o in o med agen s is
gi en as I7 = {/, p} and he in o ma ion se o unin o med agen s as I =
{p}12, i.e. in o med agen s can obse e he/-pa o he end-o -pe iod alue
o he isky asse whe eas unin o med agen s only ecei e he in o ma ion
which hey can in e om he equilib ium p ice. No ice, ha he in es men
10 This is common knowledge o all agen s.
11 No ice ha his implies a posi i e p obabili y o a nega i e end-o -pe iod alue
o he isky asse . We shall neglec his p oblem o ake ad an age o he analy ical
simplici y o e ed by no mally dis ibu ed andom a iables.
12 Tha is, S/ = {/} and s = {0}.
23 K edi und Kapi al 3/1985
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354 To ben
M.
Ande sen
in he isky asse is unce ain o he in o med agen s since he e-pa o he
u u e spo p ice is unobse able o he in o med agen s, mo eo e he
in o med agen s do no gain any u he in o ma ion om obse ing he
equilib ium p ice since hey al eady know all ele an p i a e in o ma ion
in he ma ke .
I ollows ha he ma ke demand o any in o med agen can be w i en zl
(P>
/)13> i-e. as a unc ion o he p ice and he in o ma ion a ailable o he
in o med agen s. To de e mine he demand o an unin o med agen is mo e
di icul since hese agen s only ecei e he in o ma ion which hey can in e
om he equilib ium p ice. To in e in o ma ion om he p ice i is neces-
sa y - ha he unin o med agen s conjec u e how he p ice depends on he
in o ma ion (o he in o med agen s). Assume ha he unin o med agen s
conjec u e he equilib ium p ice o be ela ed o in o ma ion possessed by
in o med agen s as ollows
(7) • P = h' (/; •)
Condi ional on his conjec u e he unin o med agen s in e in o ma ion on
/ om he p ice signal, and hence he (excess) demand o an unin o med
agen can be w i en zu (p). No ice, ha p appea s bo h o i s alloca ional
ole and o i s in o ma ional ole in he demand o he unin o med agen s.
Le he o al (pe capi a) exogenous supply o he isky asse be deno ed
z8i and he ac ion o agen s being in o med A (= K/H) be cons an and
exogenously gi en (see sec ion V). The equilib ium condi ion can be w i en
(8) Az,(p,/) + (1 - A)z (p) = zs
The equilib ium p ice can now be w i en
(9) p = h (/;
A,
zs)
No e ha e en i
A
and zs a e cons an hey ha e been s a ed explici ly in
he p ice unc ion o s ess ha he equilib ium p ice depends signi ican ly
on hese wo pa ame e s, c . below.
The esul ing equilib ium p ice (9) depends on he conjec u e made by he
agen s on he ela ion be ween he p ice and in o ma ion (7). We shall
employ he a ional expec a ions equilib ium concep acco ding o which
he agen s conjec u e o he ela ion be ween he equilib ium p ice and
in o ma ion (7) is iden ical o he objec i e ela ion be ween he equilib ium
p ice and in o ma ion (c . sec ion II), i.e.14
13 See G ossman (1976) and G ossman and S igli z (1980).
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 361
ma es a ull in o ma ion e icien ma ke a bi a y closely, and s ill he
e u n o being in o med is bounded away om ze o, c . Hellwig (1982).
VI. Weal h Dynamics
We ha e hus a been looking upon in o ma ion e iciency as been
b ough abou i p ices pe ec ly agg ega e and dissemina e in o ma ion.
Ano he ou e by which in o ma ion e iciency may be ob ained is h ough
a p ocess o weal h ealloca ion, ini ia ed by he ac ha be e in o med
agen s make a posi i e p o i . We should expec his o imply an inc ease in
hei weal h and hence an inc ease in he weigh o hei in o ma ion in he
ma ke p ice, whe eas wo se in o med agen s loose money and e en ually
a e d i en ou o he ma ke . This p ocess is caused by he ac ha ma ke s
weigh a ade s in o ma ion no by i s quali y, bu by he amoun o money
behind i ("dolla o es"). Hence, in o ma ion e iciency is achie ed in he
long un by a p ocess whe e weal h is edis ibu ed om wo se in o med
agen s o be e in o med agen s, "I his p ocess wo ked well enough, he
p esen p ice would e lec he bes in o ma ion abou he u u e ..."
Coo ne (1964, p. 80). Tha is, he wo se in o med agen s a e squeezed ou o
he ma ke , and only well in o med agen s emain in he ma ke wi h he
p ice pe ec ly e lec ing hei in o ma ion.
Implici ly we ha e so a been assuming his impo an weal h dynamic
p ocess o be absen by ha ing es ic ed a en ion o cons an absolu e isk-
a e sion u ili y unc ions implying ha asse demand is independen o
weal h. We shall in his sec ion discuss his weal h dynamics in some de ail.
Feige (1978) discusses his p oblem in a simple wo pe iod model wi h
spo ma ke s a da e and + 1, and a o wa d ma ke a da e o deli e y
a da e + 1. In o med agen s ha e some in o ma ion on he pe iod 4-1
spo p ice, which o ms he basis o hei ade in he o wa d ma ke . I
can now be shown ha i he in o med agen s domina e he ma ke he o -
wa d p ice will e lec hei in o ma ion, and consequen ly unin o med
agen s ha e access o he in o ma ion o he in o med agen s. Gi en ha he
p ice is e ealing all ha e he same in o ma ion, hence he e will be no
weal h edis ibu ion.
On he o he hand i he unin o med agen s wi h homogeneous, bu
e oneous in o ma ion domina e he ma ke hey will make he p ice, and
his p e en s he p ice om e ealing he in o ma ion a ailable o in o med
agen s. Hence, impe ec in o ma ion pe sis s in equilib ium implying a
ans e o weal h om unin o med o in o med agen s. This weal h eallo-
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362 To ben M. Ande sen
ca ion inc eases, howe e , he impo ance o he in o med agen s and an
uppe limi o his p ocess is se by he poin whe e hey come o domina e
he ma ke , since in his case he p ice e lec s he in o ma ion o he
in o med agen s. Hence, s a ing om a posi ion whe e unin o med agen s
domina e he ma ke se s in o mo ion a weal h ealloca ion p ocess which
uns un il he in o med agen s come o domina e he ma ke , i.e. hei
weal h has inc eased so as o make hem domina e he ma ke .
Simila ly Figlewski (1979) analyses he weal h dynamics esul ing om
di e ences in in o ma ion. Using a model wi h an asymme ic in o ma ion
s uc u e wi h agen s pa ioned in o wo g oups he in o ma ional e iciency
o a inancial ma ke is analysed. The cen al poin is ha he p ice agg e-
ga es agen s in o ma ion, bu he weigh s in agg ega ion a e gi en by weal h
and no by he quali y o in o ma ion. I is shown ha agen s wi h in o ma-
ion o e alued in he p ice ends o loose money and ice e sa.
In e es ingly i is shown ha agen s wi h in e io in o ma ion a e no d i-
en ou o he ma ke by he be e in o med agen s, bu end o lose money
as long as hei in o ma ion is o e alued. Hence he wo se in o med agen s
will lose money as long as hei in o ma ion is o e alued by he p ice, and
gene ally he adjus men o weal h s ops be o e he agen is d i en ou o he
ma ke .
The dis ibu ion o weal h will in his way in he sho un end owa ds
he dis ibu ion o weal h consis en wi h ma ke e iciency. This con-
e gence is, howe e , in expec ed alue since we ha e a s ochas ic equilib-
ium,
i. e.
he ma ke will be in o ma ionally e icien in he mean. O o pu
i in ano he way he long un equilib ium can wi h a posi i e p obabili y
be a away om he in o ma ionally e icien equilib ium. Thus ma ke s
should no always be expec ed o be in o ma ionally e icien , i can, how-
e e , be shown ha i is close o in o ma ion e iciency i ei he all agen s
ha e a high isk a e sion o i he ade s ha e homogeneous in o ma ion,
c . Figlewski (1979).
VII. Quan i y Signals
We ha e seen how p ices play a ole as in o ma ional signals in inancial
ma ke s, bu i his is a co ec desc ip ion o he eal wo ld, how can i be
ha eco ds om inancial ma ke s o en alongside p ices p o ide in o ma-
ion on he amoun s aded o he asse s23?
23 Al e na i e i such quan i y in o ma ion is no made a ailable o he ade s one
could, o he ex en ha quan i y signals e eal ele an in o ma ion no con ained in
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 363
Conside he model o sec ion III unde an asymme ic in o ma ion s uc-
u e. I he supply o he isky asse is andom (M = 2) we ha e seen ha he
p ice becomes a noisy signal on he in o ma ion a ailable o he in o med
agen s. The o al quan i y aded in he ma ke s depends, howe e , on he
in o ma ion o he in o med agen s and he andom supply as does he
equilib ium p ice. In Ande sen (1983) i has been shown ha he quan i y
signal ac ually e eals in o ma ion on he in o ma ion o he in o med
agen s and he andom supply in a quali a i ely di e en way han he p ice
signal, al hough he quan i y signal as he p ice signal is a noisy signal on
he in o ma ion a ailable o he in o med agen s.
I u ns ou ha he quan i y signal may be a mo e eliable signal~on he
in o ma ion a ailable o he in o med agen s han he p ice. Whe he he
p ice o he quan i y signal is he mos eliable signal depends on he ela-
i e slope o he agg ega e demand and supply cu es, c . Ande sen (1983).
This con adic s he adi ional p esump ion ha p ice signals alone play an
in o ma ional ole, c . Hayek (1945).
Since he p ice signal and he quan i y signal e eal di e en in o ma ion
i ollows ha he unin o med agen s can gain in o ma ion by combining he
wo signals. In he case e e ed o abo e he combined use o he p ice and
he quan i y signal implies ha he unin o med agen s can in e he in o -
ma ion a ailable o he in o med agen s. Tha is, e en hough he dimension
o he p ice ec o (N = 1) is less han he dimension o he s a e ec o
(M = 2), he inclusion o he quan i y signal inc eases he dimension o he
ec o o obse ed signals o be equal o he dimension o he s a e ec o ,
and hence in o ma ion e iciency is ob ained. Bo h p ice and quan i y sig-
nals a e in his way ele an o he alloca ion o economic esou ces and
capi al ma ke e iciency is no a ained solely h ough he in o ma ional
ole o he p ice signal, bu equi es he inclusion o he quan i y signal as
an in o ma ion signal. O cou se he combined p ice and quan i y signal can
be made a noisy signal on he in o ma ion possessed by in o med agen s (c .
sec ion III) by inc easing he dimension o he s a e ec o , bu he conclu-
sion emains ha he quan i y signal con inues o be an impo an indepen-
den in o ma ion signal.
VIII. Exis ence o Ma ke s
We ha e p e iously aken he numbe o ma ke s o be exogenously gi en,
and i was shown ha he p ice sys em is no in o ma ionally e icien i he
he p ice signals, jus i y he incu ence o cos s o collec and elease such quan i y
in o ma ion.
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364 To ben
M.
Ande sen
dimension o he p ice ec o is less han he dimension o he ec o o s a e
a iables (N < M). We shall a gue ha he numbe o ma ke s (N)24 depends
c ucially on he in o ma ion dissemina ed by p ices and ansac ion- and
in o ma ion cos s.
I he numbe o ma ke s is educed wo hings will gene ally happen: i)
he dimension o he p ice ec o is educed, and he e o e p ices e eal less
in o ma ion, ii) he dimension o he s a e ec o is inc eased as a esul o
s ocks o non- aded goods, and his ends o educe he amoun o in o ma-
ion dissemina ed by p ices, G ossman (1977, 1978).
Hence, he amoun o in o ma ion dissemina ed by p ices is an inc easing
unc ion in he numbe o ma ke s. We should he e o e expec ha , i gi en
a ma ke s uc u e whe e he p ices dissemina e a small amoun o in o ma-
ion (N < M), he e will be a endency o he numbe o ma ke s o inc ease,
and in he limi app oach he numbe o s a e a iables.
Conside he ollowing wo-pe iod model (due o G ossman (1977)) o a
single commodi y, wi h a spo ma ke a da e 0 and 1. Supply is exogenously
gi en a ime 0 and no supply is a ailable a ime 1, hence esou ces can only
be ans e ed o pe iod 1 by means o in en o ies. I u u e demand is
unce ain, bu in o med agen s possess some in o ma ion on u u e demand
he pe iod 0 spo p ice will e lec his in o ma ion (N = M = 1). The e o e
he unin o med agen s can in e his in o ma ion om he pe iod 0 spo
p ice.
I , howe e , bo h pe iod 0 and 1 demands a e unce ain (M = 2) he pe iod
0 spo p ice is no longe a su icien s a is ic o he a ailable in o ma ion,
ha is, he e is an in o ma ional di e ence be ween in o med and unin-
o med agen s. This implies ha hey do no hold he same expec a ions as
o he pe iod 1 spo p ice. Since he ans e o esou ces o pe iod 1 is a
specula i e ac i i y his di e ence in expec a ions imply di e ences in he
specula i e commi men s o in o med and unin o med agen s.
This di e ence in in o ma ion and consequen ly expec a ions gi es an
incen i e o se up a u u es ma ke . Tha is, a new ma ke o ading a
da e 0 is se up, and he dimension o he p ice ec o is inc eased. In his
case he pe iod 0 spo p ice and he o wa d p ice pe ec ly e eal he a ail-
able in o ma ion {N = M = 2).
The exis ence o his new ma ke depends on he in o ma ional e i-
ciency o he pe iod 0 spo ma ke . When his ma ke is in o ma ionally e i-
24 S ic ly speaking he dimension o he p ice ec o is equal o he numbe o ma -
ke s less one, since he p ice ec o can be no malized o lie on he uni ci cle wi hou
loss o gene ali y.
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 365
cien (M = N = 1) he e a e no di e ences in in o ma ion and no incen i e
o se up new ma ke s, bu i he ma ke is in o ma ionally ine icien
(M = 2, N = 1) he e is an incen i e o expand he numbe o ma ke s.
Gene alizing his esul we can conclude ha whene e he p ice sys em
is in o ma ionally ine icien (N < M) he e will be a endency o he
numbe o ma ke s o inc ease. Does his imply ha one should expec he
numbe o ma ke s o inc ease such as o ensu e in o ma ionally e iciency?
Qui e ob iously he answe is no, since we ha e le ou in o ma ion and
ansac ion cos s.
T ade is caused by di e ences in endowmen s, p e e ences and in o ma-
ion. I endowmen s and p e e ences a e iden ical o all agen s, ade will
only ake place i in o ma ion di e s be ween agen s. I he numbe o ma -
ke s inc eases o make he p ice sys em in o ma ional e icien we will ind
ha no ade is aking place. I he e o ins ance a e ixed cos s in se ing
up and ope a ing ma ke s, he e will no be enough ade o pay he ixed
cos s. Hence we should no expec he numbe o ma ke s o inc ease o
make he p ice sys em in o ma ionally e icien unless ansac ion cos s a e
absen .
In he same way in o ma ion cos s p eclude he expansion o he numbe
o ma ke s o es ablish in o ma ionally e iciency. I he e a e in o ma ion
cos s and he numbe o ma ke s is expanded so as o imply in o ma ional
e iciency we un in o he non-exis ence p oblem discussed in sec ion V. I
is seen ha his is in con as o he adi ional iew ha i only he se o
ma ke s is comple e he adi ional A ow-Deb eu esul s hold. Gi en in o -
ma ion cos s an inc ease in he numbe o ma ke s dec ease he incen i e o
acqui e in o ma ion. O o pu i in ano he way he e is a ade-o be ween
he alloca i e gain ha adi ionally is seen o a ise om an expanded se o
ma ke s and he disincen i e e ec s on in o ma ion acquisi ion o expand-
ing he numbe o ma ke s. Hence, he e is an op imum numbe o ma ke s
(sho o a comple e se ) de e mined by in o ma ion and ansac ion cos s.
IX. Sequen ial T ading
Up o now we ha e only been conside ing one-sho ma ke s, ha is, agen s
ade oday in a ma ke o a isky asse which has an exogenously gi en
end-o -pe iod alue. This u ns ou o be a c i ical assump ion since he
e u n on isky asse s depends on he ma ke 's alua ion o he asse omo -
ow, i is he e o e necessa y o conside he p oblem o sequen ial ading.
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366 To ben M. Ande sen
Sequen ial ading in oduces some p oblems which did no a ise in he
models conside ed so a . To see his conside a simple specula i e ma ke
o a single isky asse whe e he cu en p ice in pe iod depends on he
expec a ions o he spo p ice which will p e ail in pe iod + 1, since he
e u n on he isky asse is gi en by he capi al gain on he asse . Gi en
a ional expec a ions agen s will ealize ha he pe iod + 1 p ice depends
on he expec a ion o he pe iod + 2 p ice as o da e + 1, and ha he
pe iod + 2 p ice in u n depends on he expec a ion o he pe iod + 3
p ice and so on. Hence, in a sequence o ma ke s25 he ac ha agen s o m
expec a ions a ionally in oduces a dynamic elemen in o he model, which
did no appea in he models conside ed so a .
I is well-known om mac omodels wi h a ional expec a ions ha a
sequence s uc u e implies, e en unde homogeneous expec a ions, ha
spu ious a iables o sunspo s may in luence he solu ion. I is hus possible
ha o ally i ele an a iables may in luence he equilib ium, and con-
sequen ly an in ini y o equilib ia exis s, c . .i. Gou ieoux e al. (1982). This
shows ha pu ely specula i e manias o bubbles a e consis en wi h he
assump ion o a ional expec a ions, c . Blancha d (1979) and Flood and
Ga be (19 80)26. Mo eo e i is consis en wi h a ional expec a ions ha he
bubble "bu s s" and he ma ke goes back o "no mal" (ma ke undamen-
als)27.
In a ic ionless ma ke in es o s will be conce ned wi h he sho - un
gain o be made by in es ing in a gi en isky asse ,
i. e.
hey beha e myop-
ically. In Ande sen (1984) i is shown, wi hin a model simila o he model o
sec ion III, ha i he ma ke is in o ma ionally e icien , he expec a ions
o u u e asse p ices become inde e mina e. Since p ices depend on p ice
expec a ions i ollows ha asse p ices a e inde e mina e, and hence hey
become de e mined in an a bi a y way simila o Keynes' analogy be ween
a beau y con es and he ope a ion o inancial ma ke s. Keynes' iew on
s ock ma ke s is he e o e no necessa ily inconsis en wi h he assump ions
o he e icien capi al ma ke hypo hesis, c . sec ion I. The inde e minancy
o asse p ices implies in u n ha i becomes impossible o de ine he in o -
25 Mos mac oeconomic models wi h a ional expec a ions ha e a sequence s uc-
u e, bu he p oblem discussed he e is pa ly a oided by assuming homogeneous
in o ma ion.
26 Flood and Ga be (1980) s udy he Ge man hype in la ion in he 1920's, and hey
a e unable o disp o e he hypo hesis ha specula i e bubbles we e absen in he
pe iod.
27 See Azia idis (1982) o an in e es ing analysis o how ex aneous in o ma ion
a iables may come o in luence he equilib ium in an o e lapping-gene a ions model
wi h a ional expec a ions.
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 367
ma ion ele an o he p icing o inancial asse s in any p ecise way, ha
is, any in o ma ion which agen s conjec u e o be ele an o asse p ices
comes in a sel - ul illing way o be e lec ed in he equilib ium p ices o he
asse s, c . Ande sen (1984).
Finally, impo an wo k by Fu ia (1981) on a sequence o ma ke s unde
di e en ial in o ma ion should be men ioned. In a simple model wi h a di -
e en ial in o ma ion s uc u e Fu ia (1981) shows ha he a ional expec-
a ions equilib ium no gene ically will be e ealing, and in ac i u ns ou
ha i) he e exis s non- e ealing a ional expec a ions equilib ia,
i. e.
agen s
in o ma ion and he e o e expec a ions will di e in equilib ium, and ii) a
a ional expec a ions equilib ium needs no e en exis .
A u he in e es ing implica ion is ha some a ional expec a ions
equilib ia may possess he p ope y ha ade s a e ully in o med, i.e.
know all he in o ma ion a ailable o he economy, when hey combine he
in o ma ion e ealed by he p ice wi h hei p i a e in o ma ion. In his case
he p ice only e eals pa o he o al in o ma ion se , ha is, e en i he
a ional expec a ions equilib ium is e ealing he p i a e in o ma ion is no
supe lous, i.e. he p ice alone does no e eal all in o ma ion. In his case
he pa adox o p i a e in o ma ion men ioned in sec ion IV is a oided.
X. Conclusion
Acco ding o he e icien capi al ma ke hypo hesis inancial ma ke s a e
highly e icien in he sense o being a bi aged and ha ing all a ailable
in o ma ion ully e lec ed in cu en asse p ices. The no ma i e appeal o
his hypo hesis is qui e ob ious; e icien ma ke p ices gi e he igh incen-
i es o he i ms' p oduc ion-in es men decisions and in es o s po olio
decisions.
In he p esen pape he ecen heo e ical de elopmen on he p oblem o
in o ma ion agg ega ion and in o ma ion in inancial ma ke s has been
e iewed and discussed. I is clea om his wo k how es ic i e he
e icien capi al ma ke hypo hesis is in i s s ong- o m; capi al ma ke e i-
ciency should no in gene al be expec ed o p e ail. This conclusion is sup-
po ed by he ac ha he dimension o he ec o o s a e- a iables is
g ea e han he dimension o he obse ed ma ke signals (p ices), sec-
ion IV, and ha cos s o acqui ing in o ma ion p ecludes in o ma ional
e iciency, sec ion V.
In e alua ing his ecen heo e ical li e a u e on ma ke e iciency i is
impo an o keep in mind ha al hough pa s o he e icien capi al ma ke
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368 To ben
M.
Ande sen
hypo hesis ha e been challenged some o i s basic insigh s emain in ac .
This applies in pa icula o capi al ma ke e iciency in i s weak and semi-
s ong o m which has been amply suppo ed by empi ical esea ch; none o
he ecen con ibu ions lea e any possibili y ha ade s can make a p o i
in inancial ma ke s by exploi ing public in o ma ion.
I should be kep in mind ha al hough good heo e ical easons ha e
been ound why capi al ma ke s a e no e icien in he s ong- o m, his
so o ine iciency does no lea e open an ob ious ole o any ac i e policy,
i. e.
i is no clea whe he he e exis s a sui able and implemen able policy
o cope wi h hese ine iciencies28. Mo e esea ch is needed o cla i y his
poin . Fu he mo e, hese ine iciencies do no necessa ily indica e any
social subop imali y o he ma ke alloca ion. To ake an example, cos s o
acqui ing in o ma ion which p e en capi al ma ke e iciency a e as much
a ac o li e as a e he cos s o p oducing commodi ies.
Finally, le us commen sho ly on he me hodology, iz. he a ional
expec a ions equilib ium concep . Al hough, as no ed, he a ional expec a-
ions equilib ium concep is e y es ic i e i has p o ed o be pa o a
ui ul esea ch s a egy. One should no , howe e , be sa is ied wi h he
a ional expec a ions equilib ium concep in i s p esen o m, and he
impo an wo k on he p oblems o lea ning, lea ning adjus men cos s mus
e en ually lead o mo e desc ip i ely ealis ic expec a ions models. The
majo ad an age o he a ional expec a ions equilib ium concep ela i e
o o he expec a ions models is ha i allows an explici modelling o in o -
ma ion dissemina ion in decen alized ma ke s, and in his way i has been
aluable in analysing he e icien capi al ma ke hypo hesis. The a ional
expec a ions equilib ium concep is a benchma k showing he mos o be
expec ed ega ding in o ma ion dissemina ion in decen alized ma ke s,
and when i u ns ou ha e en he mos is a om being pe ec i is a eli-
able indica o o he ac ha eal-wo ld ma ke s a e ine icien .
Re e ences
Allen, B. (1982): S ic Ra ional Expec a ions Equilib ia wi h Di useness, Jou nal
o Economic Theo y, 27, 20 - 46. — Ande sen, T. M. (1982): Specula ion, Op imism
and Di e en ial In o ma ion (unpublished). — Ande sen, T. M. (1983): P ice and
Quan i y Signals in Financial Ma ke s, Zei sch i ü Na ionalökonomie, 43, 109 -
129. — Ande sen, T. M. (1984): Some Implica ions o he E icien Capi al Ma ke
Hypo hesis, Jou nal o Pos Keynesian Economics, Win e 1983 - 84, VI, 281 - 294. —
Azia idis, C. (1982): Sel - ul illing P ophecies, Jou nal o Economic Theo y, 25, 380 -
28 See, howe e , Weiss (1982) o an example o a wo kable policy.
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Recen De elopmen s in he Theo y o E icien Capi al Ma ke s 369
396. — Ba o, R. J. (1981): The Equilib ium App oach o Business Cycles, in Ba o,
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Zusammen assung
Neue En wicklungen de Theo ie e izien e Kapi almä k e
In de Finanzli e a u he sch die Hypo hese o , daß die P eise in Mä k en ü
Finanzak i a säm lich e ügba e In o ma ion e lek ie en. Ungeach e ih e Belieb -
hei un e lieg de Hypo hese eines e izien en Kapi alma k es keine igo ose heo e-
ische Fundie ung. Neue dings is eine seh echnische Li e a u en wickel wo den,
die die In o ma ionsp obleme au We bewe bsmä k en igo os analysie und die
F age de In o ma ionse izienz on Finanzmä k en ausd ücklich behandel . Diese
Au sa z soll einen un echnischen, ein üh enden Übe blick übe diese heo e ische
Li e a u geben und zwa speziell im Hinblick au die Hypo hese e izien e Kapi al-
mä k e.
Da diese Li e a u aus üh lich au das Konzep eines Ma k gleichgewich s bei
a ionalen E wa ungen zu ückg ei , beginnen wi mi eine eingehende en Diskus-
sion diese Me hodologie. Anschließend wi d zu Illus a ion ein Modell en wickel ,
das es uns e laub , die olgenden In o ma ionsp obleme in Finanzmä k en zu behan-
deln: die Ve b ei ung on In o ma ion du ch P eise, In o ma ionskos en, In o ma ions-
und Ve mögensdynamik, Ve b ei ung on In o ma ion du ch Mengensignale, die
Exis enz on Mä k en und sequen ielle Handel.
Summa y
Recen De elopmen s in he Theo y o E icien Capi al Ma ke s
The hypo hesis ha p ices e lec all a ailable in o ma ion in inancial ma ke s is
p edominan in he inancial li e a u e. Despi e he popula i y o he e icien capi al
ma ke hypo hesis i has no been based on a igou ous heo e ical ounda ion.
Recen ly a highly echnical li e a u e has de eloped in which p oblems o in o ma ion
in compe i i e ma ke s a e igou ously analysed, and whe e he issue o in o ma ional
e iciency o inancial ma ke s is explici ly add essed. The pu pose o his pape is o
gi e a non- echnical in oduc ion and e iew o his heo e ical li e a u e as i
speci ically ela es o he e icien capi al ma ke hypo hesis.
Since he li e a u e elies hea ily on he a ional expec a ions equilib ium concep
ma ke hypo hesis we shall s a ou by discussing his me hodology in some de ail.
Subsequen o his an illus a i e model is de eloped which allows us o add ess he
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DOI h ps://doi.o g/10.3790/ccm.18.3.347 | Gene a ed on 2023-01-16 12:51:50