Excess volatility of stock prices and knightian uncertainty

- - - -~--~~~~~~~~----..

.

.---~----:----~

N9

179

EXCESS VOLATILITY OF STOCK PRICES

AND KNIGHTIAN UNCERTAINTY

JAMES DOW

E

SERGIO RIBEIRO DA COSTA WERLANG

1991

Excess Volatility of Stock Prices and Knightian l:ncertainty

by

James DOW London Business School

Sussex P!ace. Regent's Park, London !\'Wl 4S.-\. CK

and

Sérgio Ribeiro da Costa WERLA!\G EPGE-Fundação Getúlio Vargas

IO-Andar, Praia de Botafogo 190. Botafogo CEP ~2250

Rio de Janeiro-RJ, Brazil

European Economic Association Cambridge

Introduction

This paper has two thc!mes, both of which have preoccupied economists for many years. The first is the volatility of stock prices. It has long hct:n suggc!sted thal the erratic movt!ments of stllCk prices art! incompatible with rational investor behaviÇlur. More recentJy. formal empirical tests have been devised which suggest that stock prices are excessively volatik. These tests show apparentJy systematic violations of a variance bounds inequality.

The second theme is the question of how a rarional person should behave under uncertainty. particularly when he or she has littJe information about the form of the uncertainty. Knight (1921) was a notable proponent of the view that this type of uncertainty is qualitativdy different from risl..-y situations where the parameters of the risk are well-kno\\n to the decision maker. However, the currentJy standard model in e conomics, due to Savage (\954), predicts that agents should have subjective probability distributions which do not make this distinction.

In this pape r , we show that mode1s which formalize Knightian un.:ertainty can hc used to

explain high stock price volatility. We provide an example in which the variance bound is violated. Since the future profitability of companies depends heavily on many long-term tàctors. including political fa.:tors, which are extremely difticult to predict. it is natural to think that the stock market is characterized by a high degree of Knightian uncertainty. Therefore. we suggest this type of behaviour under uncertainty as a possible explanation of the high volatility of stock market prices.

Excess Volatility

The variance bounds restricti0ns were deveJ0pcd hy LcRoy and Porte r ( 1981) and Shiller ( 198 I). Here we give only the briefest outiine

or

the réstri.:tions anJ the é\ij:::n.:e: the readér is reic:rreJ !t) l..çRt.)~ .!-\1989) survey and Shiller's (1989) book fJr further d=rails and rderen.::.'s. The ~:.artir.g

r-.

Jim b L'1-:

principIe that jf afents are risk-neutral an asset" s price ShllUld equal the expc.:tation ()f the diSCl\untéu \'alue oi tl-}e future di\·ij.~nds. Here Wé ~ill as~ume for simrlicity a .. ir.l20Cln where the a~s:.'t ray~ J

2

P = E(VI I)

The variance hounJs inequality is derived from lhe conJition Var(V)

=

VarlE(V; 1)) + EIVar(V; 1))

which is in rurn an immediate cOr\S(!quence of lhe relation E(V)

=

E(E(V: I)). Since variances art: non-nega tive and the price equals the expt!cted value.

Var(V) ~ Var(P). (1)

To test this requires some statistical assumptions. For example. if we had a large number of such assets whose Iiquidation values were iid. we c'ould simply compare lhe samplc! variance of the set of prices and the set of realized values. The empirical studies (Lc:Roy and Porte r (1980. Shiller (1981» used time series data on stock prices and dividend realizations. assuming a stationary dividend process (Iater studies. eg CampbelI and Shiller (1988), made weaker assumptions on lhe dividend process).

How do the variance oounds apply to a siruation of Knightian uncertaimy? Then the agem does nOI know the actual probability distribution 01' lhe value. A risk neutral agem who satisties the Savage axioms has a subjective probability distribution. This subjective distribution "ilI in general differ from the actual distributivn, and S0 the variance hound can be violated in a probabilistic sense (~cause the

expectation. under the actual distribution. l't" the .:'onditional expcctation under the suhjective àistribution. ",iH in general differ from t.'1e actual unconditional expectation l. Howevc:!r. it seems implausible to expIain the Iarge amoum of evidence that has bc:!en colIected by saying that agents svstematicallv have subjective distributions \\ith hillher variance lhan actual distributions (althouch

_..

_{. . .}

-'

-loglcally. this argument is Juhil1US bc:!cause ir implies lha! th\! agem àfectiveÍ\ knows the true probability distriburion M" Ü1e stat\!S bu! with a k,s rr~:isé information Sétl. \\'~ ti"lc>r:::t"l1r\! turn tn

another éxpléinati0n: mat th.: ag::nts' Jé,isi,1~. in simati~)ns ut Knight:an un.:.::-taln~. :ir.: n·)1

to the forme r as ris/,; and the latter as

uncenainry,

or Knightian uncertainty. Synonyms lhat are used in the literaturt! in(lude:! wukttt! lottay. for risk, anJ horsi! lonery and amhiguity. fnr uncertainty. WC! now givC! a very brid t!XpOSitillO of lhe:! main aspc!cts of lhe! modd. The readc!r is retúred to tht! papc!rs by Schmeidler and Gilhoa cited above for.a compktt! dt!scription and for the underlying axioms, and to Dow and Werlang (1991) which contains an t!xample and an application to portfolio choicC!. Simonsen and Werlang (1991) also describe the implications for portfolio choice. Bewley (1986) presents a similar modd which is also designed to capture Knightian uncertainty. His model predict.'i Ihat uncertainty leads to inertia, a te!ndency to favour the! staTUS quo. while in SchmeidJer-Giltxla there is a tendency to choose acts where the age:!nt does not end up bearing uncertainty.

The Schmeidler-Gilboa model predicts that agents' behavior \\ill be represented by a utility function and a (subjective) non-additive probability distribution. A non-additive probability p retlecting aversion to un.:ertainty satisfies the condition

p(A) + p(B) ~ ptAUB) + ptAnBJ,

rather than the stronger condition satisfied hy (additive) probabilities:

1'(A) + 1'(B) = p(A l) B) ~ p(.A, n 8).

In particular. p(A) ~ p(N) may be less than I: the difference can tio.! thought of as a mc:!asure of the uncertainty attached by the agent to the event A.

The agent maximizes expected utility under a non-additive distribution. where the t!xpc!ctation af a nan-negative random variable X is defined as:

E( X)

=

f

K _ p( X

~

x, Jx.

Assodatcd v.ith a n.:m-additive probat-iliry p is a set ~ of additiVc:: prl1bahilitie:!s called the (Clre I'!" í'. which is ddined tarudogousiy t,) the core! in cUllpcrative game Ihe:!of) I as the Sét (H additivc! rrooahil;~

measures 7( su..:h ttat 1í~A) ~ p(Ai for ali évents A. If the nlm-adJitive pr(lhahiiity S4ti~ties in::.'quaii::,

- - -

---4

do nut necessarily know the true probability distribution. However, for the analysis ~Iow we will need some relationship ~~oeen the subjective non-additive distributions which rerre~ent agenL<;' hc!havi(lur. and the frequencies observed by the econometrician. We \\i1l thereiore assume thal the eCllnpme::trician observes realizations drawn from one element of the core.

When agents' prefere::nces satisfy Savage's axioms, it is natural to assume:: thal lhey upJate according to Bayes' role. Although this is not a consequence of Savage's mt)(Jel. many consideratlUns paint to Bayes' rule (the standard argument is given in Kreps (19881: Brown cl976) goes furlher. showing that il is optimal for agents to use Bayes' rule). Wilh non-adJitivl! probabilities. the Situati(lfl is nOI so ckar bUI the Dempster-Shafer rule is lhe natural generalizatian oi Bayes' Rule j Dempster.

1968 and Shafer, 1976). Dow, Madrigal and Werlang (1989) u~ lhe Dempster-Shaier rult:.

Schmeidler and Gilboa (1991) provide an axiomatic foundation for lhe Dempster-Shatá rule. Th~ updating rule is:

p(A:B)

=

[p(AUBC) - p(B")] / [1 - p(B")). (5) We now apply this model to an example af equilibrium in a stclck market with Knightian uncertainty o

An Example

There are three periods t = O.l.:!. There is one risky asset in posio\"e net suppl)" ("lhe assd' 1 and a safe asset (cash). The riskless rate of return is zero oro equivalent1y. all \Oaiues ma)" he interpreted a~ i're~nt values àiscou!1ted at the sate interest ra~.

The aSSl!t \\ill pay a liquidaong ài\"idend V at time t

=

2. Tha.: are three states i'i n:m.lre . o 2 and

3.

The value of V is different in each state and is, respecovely. 1. ;:: or

O.

Agente; are ali identkal. i:lnd are risk n~utral. In reril)(J t

=

I. ~~en:.s ~~..:;:i\"e f ;"luhlic)

~

necessary to spêcify these in aJdition tll th~ (nlm-aJditivt!) prohaoility oi ea(n !'tale, The l·"re. ~. IIr this measure is the (onvex hull ni the tlllklwing thret! (additive) prohahiiity mea~ures:

irJ = Jh. ir: = IA. ir~

=

J,~

~i = 1 .. 4. ;1":

=

li:. "Ir,

=

I~ SI

li!

=

14. ir· = \4. To, = rI: .

Let p! denote the price aI time t. Then ~in~'e the ass:::1 IS in positivt! nel suppiy. it illlhw,'s I Dom and Werlang. 1991) that P(I

=

E(Vlo P:

=

E(\, i Ilo and naturaily P:

= \',

Thus in the initial pêrioll.

p{J

=

E(V)

=

O ... (1.: - OI p:: - (I - 1:) P:

=

3'8,

IS impiied t"ly

me

D:::mp~ter-Sha!er ruk, i I f;,he~ receivt' r.aJ r.ews ! 5:<1le : ,lf :-; we Tir~t neel.l !.

:alculate the Cl?nditional prooahility lli state 2, By the Dempst:::r-Shatá rule lequation (4)) this is g1ven

;' : : - :-,,) (l - ",)

= ,':' -

~ I , I ' _{" I} 'o the price is P:

=

j 6, Tt1 summarize: S !.3tê ~ , ,

..

~ _{t. ~}

") =

\'1 ~

-

--- _ - ... :::~::' - i ' ~~ ..!..!Jj::\;,.- ~~:.1"'..:~!:::\ ....!; ... :!'"i~'-l:~·:-:. ....' --~;;:~\.!. ~l"":\ .. : ... '...1~ ... .:....:. : ! ' "'"

•

..

6

dear what rdatitln.<;hip 7 should hear to lhe suhjt=ctive non-adJitive distrihution p. For t=llamplt=. if lht=

agent were not uncertainty averse p wnuld he an aJJitive distrihution. hut since lhis is CIln.<;isknt wilh lhe! agent not knowing lhe Jistrihutilm. it wnulJ he 4uitc natural to have p ;= ::-. :\everlhelcss. !,'r lhe reasons outlined ahove. we will assume lh.at

1r

E ~. where! ~ is lhe core ot p.

For 7 E ~. lhe variance! oiP₁ rangt=s(wer Ih:! intervaI125í192. iOO.576)

=

10.1302.0.17361.

while lhe varian~e ofV range!s over lhe inte!rvaI18i_{64. 11/~1}

=

_{10.1250. 0.1719). ~(ltjce lhat txlth}

.~ endpoints of lhe interval of possihle variances are larger ror ;~.e price lhan t,\r lhe value. Thi!oo I~ a

stronger property lhan having an elcme!'nt oi ~ t'\.I[ which lhe \'alue has lower vananct= lhan lhe pnce. For lhe lhree prohahility Jistrihutions iisleQ anove. \\e haw:

In the case of (7). r! = l,~ .. ií":

= ''' ..

;r~

=

i:~ ..

Var(P₁)

=

0.1736. Var(V)

=

O.liI9. \'iolating the ..-ariance round.

In the case of(8) .. ii:

=

i~ .. ::-: = :. :7.":

=

t~ ..

VanP;)

=

0.1302. VanV\

=

0.1:50. ·;i'.liaung t.'1~ ·.anan.:c r.'un~.

Var(P.) = 0.130:. Var(VI = 0.171<). which dCl~s 0.'1 \inia!= ~hc vanancc nnunu.

This example thereT0re ~hows t.p,at agent' \\'no ..i.rC JVefSc ~I) un':crtatnt\ l i l :~c 'cr'~'c ..

Schmeidlcr and Gilboa may vioiate me vanan.:e [)< )una mec'Jautv.

elCampl~. E(~Xl

=

ÀE(X)for À ~ O whil~ - E( - X) ~ E(X). alsCl E(X + Yl ~ E(X) ... E(Y) hut with c:quality in ca~ X and Y S<ltisfy a ~llnJition ~alkd wmlmotnnicity.

An cx.ample of an arhitrage strategy I~ "Ir an agc:nt to buy an extra unlt in pt.'ri\ JJ O anJ ~(II it again in period 1. As~uming without Inss of generality thal the initial holding i!' \me unit. th.: eXf'é~ted utility from this stralegy is EIV(s) - PI) .... P:(sl! anJ from clIntinuing to h\)IJ the asset H I .. EIV(SII.

He:re random variables have been explicitly expresse:d as tunctions (lf the state llt nature:. ~. ror darity. We therefore require

ErV(s) - PIl - P:(s»)

:s

ErV(s»).

I.1r. by comonotl,"icity of V(s) and p;(SI. E[V(s)] - P,. - Erp1(s»)

:s

E[V(s)]

i;: PI) ~ E[Pl(SIJ. In the example. we have

EfP;IS1!

=

1.6 - lI-I '6H I~I = 3 8

=

p, ~Ll me arbitrage lS not prütitabie.

Equall~. the agent must nOI have an in-:enrive to sei! the assei and huy il had lmé rerilxl later:

;:~\"ISI - P - ?(Sl] :S EfV(sl].

; : - P. - i 6 = p" - 1 :: :lOd in SUle :. 0 - p - 1 6

=

p, - : 6. :-fén.:e U1e cf"'ltrage has

8

AcknowledJ,!ements: This r~s~arch was dant= whiJe DllW was visiting EPGE-Fundação Gt=tú1io Vargas under a grant fr,'m C:'\Pq. \VI! lhank Ailsa Rilell anti rarticirant<; at lhl! EEA c.mgrcss fllr ':Ilmrnc:n.l<;.

References

Bewley. Truman. 1986. Knightian d~cision lht=ory. part

1.

~wking pa~r. C. Jwks Fllunúatllln. Yak Llniversity .

Brov..n. Petl!r ~t. 1976. Conditionalization and I!xpected utility. Philosopny 11r" S~ien~e 43.415-411.).

Campbell. John Y and Rohert J Shilrer. 1988. The tli\'id~nJ-rri~e ratlll anti eXre;:tatiClr .. " nr" tUture dividenJs anti discount factors. Review of Financiai Srudies I. 195-~~8.

Dempster. .-\rtrmr P. 1968. A generalizatian tlr" Bayesian Inreren~e. ]'.Jurna:l \li lhe Ro\(!j Statisti~aj Socie~ \serit!s B) 30. 105-247.

oi portr',"\lio. E:onometri;:a. il1rth;:orning.

Dow. James, \'Í,'ente ~1adrjgal and Sergio R Werlang. 1989. Common knowleJge, j1reT-::n~nces and :-;p~cul:H:ve trade, working rapeL LmJon Bu~ine~s S.:hnol and FunJac3t) G~nili,-, \"an;as.

c,i ~1at..~=matical Economics 16. 65-88.

Gilhoa, Itzhak ~nj David S.:hmeidkr. !989. \1axrnin ex[';:>.:!~1i utijiry with á n,IO-Un!aUe ... 'r. JnurT1::l!

Savage. ~onard J. 1954. The foundati(\ns (lf statistics (Wiley. ~ew Yorkl. Selo'onu edition 197~

(Dover. :":ew York).

S~·hmeidkr. Da\'id. 1982. Suhk.:tive pwhahility with\lut aJditivity Itemp\lrary mieI. ·.\,\rkin~ rdfl<!r.

Foerdc::r Institute túr E.:onomic Research. Td Aviv rniversity.

Schmeidler. David. 1989. Subiective prohahility and expected utility withllut aJJitivity. E.:onllmetrtca 57.571-587.

Shafer. Glenn. 1976. A mathemati.:al theory ot eviJence (Prinl.:ctnn L" niversity Press. Princetnn. :\t'\\ Jersey I.

Shilkr. Rohcrt 1. J 981. Do ~ttI.:k rnú~s move ti 1,1 mu.:n til f'\;: iustJtieJ

r. ...

"'u~~euuent .:nanges ':1

Jividends? American E.:onllmic Revi.:w i I. 4~ 1-~36.

Shiller. R<.I~rt J. 1989. ~tarket volatility (~tJT Press. C.tm11ridge. \1assa~husett..".

1

_!

ENSAIOS ECONÔMICOS DA EPGE

(a partir do n

Q

₁₀₀₎

100. JUROS, PREÇOS E DíVIDA PÚ3LICA

VOLU~lE

I: ASPECTOS TEÓRICOS

- Marco Antonio

C. Martins

e

Clovis de Faro - 19a7 (esgotaao)

101. JUROS, PREÇOS E DíVID.C, PÚBLICA VOLUr-:E

11: p~

ECO:.JOf':IA

8~.4SILGRA

-

::'71'65 :

_ Antonio Salazar P. 8ra.ndão, Clóvis

~

r2I'O

e

f'-·\-1IDJP ..

C. i'artirs - 1%7 '~~:?"-Jta_-u) . 102. M~. C R O E C O ~; Otn A K:; L E C K I P. : ~ A - R u b e n 5 P P. ÍI h a C y s n e - 1 9 8 7

103. O

PR~MIO

DO DÓLAR NO MERCADO PARALELO. O

SUBFATURA~ENTO

DE

EXPORTAÇbES E O

S~PERFATUR;~~~TO

DE

IMPO~TAÇbES

- Fernando

de Halarda

Barbosa -

Rube~s

Penha CysGe e Marcos CQsta rloland3 - 1987 (esgctado)

104. BRAZILIAN EXPERIENCE WITH EX7ERNAL DEBT AND PROSPECTS FOR

GRC~TH-Fernarldo

d~

hai.anda Ba:-bosa and

r'~anljel

S8:1CreZ de.La Cal - 1987

(es9'J~ÕlÓ)

105. KEYNES

~jA

SEDIÇÃO DA E5COU-iA

PÚBLICA '- Ar,tonio r·r.da Süveira-1987(as;:::'6':o)

106. O TEORH1A

DE

FROBENIUS-PERRGN - Carlos

Iva~l

Simonsen Leal - 1S87

1ú7. POPULAÇÃO BRASILEIRA - JessÉ

~1ontel1o-1987

(esGoteda)

108. MACROECO:',:O~lI,Q.

- CAPíTL:LO 'JI: "DEf'-1.lHWA PDR i'tOEDA

~

A CURVP

U-ilf

_ Mario Henrique Simonsen e Rubens Penha Cysne-1987 (e3gotsua)

109. MACROECONi:HUA - CAPíTULO VII: "DEivi':.NDA PGREGADA E A CURVl\

IS':

_ Mario Henrique Sir.ionsen e .Rubens Penha Cysne - 1967 - (e3gotaco)

110. MACROECONOMIA - MODELOS DE EQUILíaRIO AGREGATIVO

A

CURTO

F2~:~

_ Mario Henrique Simonsen e

R~bens

Penha Cysne-1987

(esgota~a)

111. THE BAYESIAN FOUNDATIONS DF SOLUTION CONCEPTS

DF

GAMES -

S~raio

Ribeiro da Costa W2rlang

e

Tonmy Chir.-Chiu Tan - 1987 (esgotado)

-112.

~REÇOS

LíqUIDOS (PREÇCS DE VALOR

ADICION~DO)

E SEUS DETERM!MANTES;

DE PRODUTOS SELECIONADOS, NO PERíODO 1960/1

Q

_{Semestre/1986}

-- Raul Ekerman -- 1987

113.

EMPR~STIMOS

BANCARIOS

E

SALDO-M~DIO:

O CASO DE PRESTAÇnE3

- Clovis de Faro - 19B8 (esgotaQo)

114. A DINAMICA DA INFLAÇAo - Mario Henrique Simonsen - 1988 (es;ctado)

115. UNCERTAINTY AVERSION ANO THE OPTIMAL CHOISE

DF

PORTFOLIO

-James - Dow e Sérgio Ribeiro da Costa Wer1ang-1988 (esgotaoG)

116. O CICLO ECONÔMICO - Mario Henrioue Simonsen - 19B8 (esgotada)

117. FOREIGN CAPITAL ANO ECONOMI: GROWTH - THE BRAZILIAN CASE

ST~JV­

Mario Henrique Simonsen - 1988

118. C O

m~

O

N K

~J

O

W

L

E D G E - 5

é

r

9 i

o R i

b

e

i

r o d a C o s

t

a We r 1 a n

9 -

1

9

e

gk~pt.a.:i.J)

119. OS FUNDAMENTOS

D~ A~ALISE ~ACROECONÔMICA-Prof.Mario Henriq~e

Simonsen e Prof. Rubens Penha

Sy~ne

- 1988 (esgotada)

120. CAPíTULO XII - EXPECTATIVASS

RACIO~AIS

- Mario Henrique

Simonsen - 1988

(esgotado)

121.

A

OFERTA AGREGADA E

O

MERCADO DE TRABALHO - Prof. Mario Henriqu2

Simonsen e Prof. Rubens

?en~a

Cysne - 1988 (esgotada)

122.

HJ~RCIA IN::-LPCIO~!:\:;I;:'

E

HIFLAÇAo r:-;Er<CIAL. - Prof.

~1ario He'l:-:

:'J'?

Simonen -

1968

(esgotado)

123. r-1ODELOS DO , ..

FJi-iEí·1:

ECC;;Ci'~IA

[ PD:J:I.iaSTR!,çÃtJ -

;'\ntonio

:-:éJl-i~

ri:

5 i 1 \/ 8 i r .3 - 1 J ;.1 S

124.

lJ

~J:J

r-::

n

HJ I}

r.

I

r:

I f:

L~

C F [J: P CJ R -; S I 8 V E R I rJ Ij O I c: I Nr; [] F HW [1 R T 5 I

Ar-:

D T H [

úCLU,\f(

Pf;E;-:IU:: Q~J T:ir:- :~LP.CK i-P.P.KCT - rrClf. Fo::mclndo dr: fieL"',:] L; ::':"1:;.1,

A 11 t o fi j o 5 LI 1 LI Z v r P t:: ~ S CJ tJ [j r d n C ~ o c

C

1 (l v

i

s d e F êJ r O - 1;0 O S (e

s

9 t: t u d o

12G.

PLfd~ú

CRUlf\DCJ:

cor;~.[pç:\ü

[

o

ERRO

DE

POLi11CA FISCAL - Ruben::; .

PcnhLl

~y5np -

1988

127. TAXA

DE

JU~D~ rLU1U~~lE

VERSUS

CORREÇ~O MO~[llRJA ~AS PR~STAÇ~E5

UH H C

['d.;

P A R {,

ç. :..

C

rw

C

fi

S O DOS

fi

C [

JfJ

F L A

ç

Tt

O C O

f';

5 T

h

N T [ - C

J

o

v

i

~

de-128.

129.

130.

131.

132.

133.

FaTO -

198fJ

CAPiTULO II -

MO~ETARY

CORREC1ION ANO REAL IN1[RESl

ACCOUNTl~G

-

.Rub~ns P~nh2

Cysne - 1988

CAPi1ULO

)~1 - l~CO~E

ANDDEMAND POLICIES IN BRAZIL -

Rubcn~

Pcnh~

CyEne - 1988

CAP11ULO IV -

BRAZILIA~ ECO~OMY

IN lHE EIGHTIE& AND lHE DE81

CRIS!S -

Ruber.~

Penha Cysne - 1908

lHE 8RAZ!LIAN

AGRICULTU~AL

POLICY EXPERJENCE:

RATID~ALE

AND

F U 1 U R [ O I R [C 11

O!

~

S - A n·i o

r.

i

o 5

2

1

õ

z a r P e

5 S

o a 8 r a n dão - 1 9 8 8

r·~OF\i',í6;::IA

lrnERt\h, D1vIDA PÚBLICA E JUROS RUnS - '-'.ariõ Silvi2

Basto~

n ....

rques e SÉ:-gio Ribeiro d2 Costa

l~er1õng

- 1985

CAPiTULO IX - TEORIA DO CRESCIMENTO

ECON6~ICO

- Mario

Henri~u2

Sirrton~er:

- 1988

CoI~GEu\r'~U:TO cor·j J'.801JO

SALARIAL GERANDO EXCESSO DE

DEMAr~DA

-13l; •

_ Joaquim Vieira Ferreira Levy e SÉrgio Ribeiro da Coste werlé:ng - 19>

135. AS ORIGENS E CONSEQUtNCIAS DA INFLAÇAo NA AMERICA

LAT!~A

-Fernando de Holand2 Barbosa - 1988

136.

A CONTA-CORRENTE DO GOVERNO - 1970-1988 - Mario Henrique

Simonsen - 1ge9

137. A REVIElJ

or~

THE THEORY DF

COr·~l-ior~

KNOWLEQGE

-

5~rgio

Ribeiro da Costa Werlang - 1989

138.

~ACROECO~O~lA

- Fernando de Ho12nd2 Bérbosa - 1989 (esgotédu)

139. TEoRIP DO

EhLAr~cO

DE F'AGAf"ENlOS:

U!'~A

ABORDAGEf-1

SIMPLIFIC~DA­

- João Luiz Tenreiro Barroso - 1989

l~O. CO~TAEILfDADE

ceM

JUROS REAIS -

RUBE~S

PENHA CYSNE -

1989

1111. "CF:EDIi RATIONING At~D THE PERr·~At~[ln It:CO~~E HYPOTHESISII

- Vicente P.adriç:Jl,"

Tom~y Tan,

Daniel Vicent.

S~rgio

Ribeiro da Costa Wer1ang - 1989

1~2. liA

AMAZONIA BRASILEIRA" -

Ney Coe· de 01iveirél -

1939

143. DE:SÁG!O D!~S LFTs E r". ?ROBI-.BILIDJ..DE n';PLICITA DE MORP.l(:!\IA

~~ria

Silvia Bastos

~arques

e Sirgio Ribeiro da Costa

1C.~

-

..

1~4.

THE

LDC

OEBT PROBLEM: A GAME-THEORETICAL ANALYSIS

Mario Henrique Simonsen e Sérgio

~ibeiro

da Costa Werlang -

1989

.

145. ANALISE CONVEXA NO R

n

- Mario Henrique Simonsen -

1989

146. A CONTROVrRSIA MONETARISTA NO

HEMISF~RIO NORTE

Fernando de Holanda Barbosa -

1989

147.

FISCAL

REFOR.~ r,ND STJ\gillZATIO~I:

THE

BRI\ZlllUJ

EXPERIENCE -

Fernando

de

Hnl.,;)(Ll

148. RETúR~~OS Ei,j EDCC;,çAo NO BRASIL: 1976-1986

Car-los IVéln Simor,3\.">n Leal e Sérgio Ribeiro da Costa t\'edang - 1983

149. PREFERE~CES, CO~~O~ KNOWLEDGE, A~D SPSCULATIVE TRADE - James Dü~,

Vicente Madrigal, S~rgio Ribeiro da Costa Wcrlang - 1990

150. EDUCAC~O E DISTRI9UIÇ~O DE RENDA

Carlo; Ivan Simons0n-Leal e S~rgio Ribeiro da Costa - 1990

151. OBSERVAÇOES À MARGEN DO TRABALHO "A AMAZONIA BRASILEIRA" Ney

Coe de Oliveira - 1990

152. PLANO COLLOR: UM GOLPE DE MESTRE CONTRA A INFLAÇ~O?

- Fernando de Holanda Barbosa - 1990

153. O EFEITO DA TAXA DE JUROS E DA It-"!CERTE?1l SOBRE A CURVA DE PHH.LIPS

DA ECON0rUA 6R~.SILEIRA - Ricardo de Oliveica Cavalcanti - 1990

154. PLANO COLLOR: CO~TRA FACTUALIDADE E SUGESTOES SOBRE À CONDUÇ~O

DA POLíTICA ~ONETÁRIA-FISCAL - Rubens Penha Cysne - 1990

155. DEPÓSITOS ~O TESOURO! NO BANCO CENTRAL OU NOS BANCOS COMERCI~IS?

Ruben~ Penha Cysne - 1990

156. SISTEMA FINA~CEIRO DE HABITAÇAo: A QUESTÃO DO DESEQUILíBRIO DO

FCVS - Clovis de Faro - 199b

157. CONPLEr1E~~TO DO FAScíCULO N2151 DOS "ENSAIOS ECO~~OMICOS" (A 1' ..

1'11\-ZONIA BRASILEIRA) - Ney Coe de Oliveira - 1990

158. POLíTICA MCNETÂRIA ÓTIMA NO COMBATE À INFLAÇÃO

- Fernando de H81anda Barbosa - 1990

159. TEORIA DOS JOGOS - CONCEITOS BÂSICOS - Mario Henrique SiMon~0n - '

- 1990

]60. O MERCADO ABERTO BRASILEIRO: ANÂLISE DOS PROCSDIMENTOS OPCRACIO, ;-:,1),1 S - ,Fe rna ndo dE Hol anda Ba rbosa - 1990

16]. A RELAÇ~O ARBITRAGEM ENTRE A ORTN CAMBIAL E A CRTN ~O~lETÂRIA

-- Luiz Guilherme Schymura de Oliveira - 1990

162. SUBADDITIV8 Plwar..BILITIES Atm PORTFOLIO INERTIA - [·tario llellri"JL!<:'

simons€n 0 S~rgio Ribeiro d~ Costa Werlang - 1990

163. i'l!.CKO:::CC':C!:;U-I c(r-i :14 - Céldo:3 IVdn Simo:1scn LG-al e Sérgio Ribd !~o d,' Cr

.'(".:1

Wl?rlang - 1990

Cr PIT'r r,,),_!!..~\·!"·mc

. \ . . . . ~ • .J I~_ ... u " L . t l . .. --, 19~1O

','

lGG. TlIE nern.IC Cl!OICS PERSi'ECTIVE N..JD y'l'HC!I':"S H1S'l'I'T'U'T'IO'\Tl'LlS'T li!:!!','

- l\ntol1.1o :1,i1.' i..l Jd Sih·,'jl.-.:'-t - J 9()O

168. JAPANESE DIRECT INVESTMENT IN BRAZIL - Neantro Saavedra Riva

no - 1990

169. A CARTEIRA DE AÇOES DA CORRETORA: UMA ANÂLISE ECONOMICA-Luiz

Guilherme Schymura de Oliveira - 1991

170. PLANO COLLOR: OS PRIMEIROS NOVE MESES - Clovis de Faro -1991

171. PERCALÇOS DA INDEXAÇAo-EX-ANTE - Clovis de Faro - 1991

172. NOVE PONTOS SOBRE O PLANO COLLOR 11 - Rubens Penha cys~l~l

173. A DINAMICA DA HIPERINFLAÇAo - Fernando de H. Barbosa, Waldyr

Muniz Oliva e E1via Mureb Sa11um - 1991

174. LOCAL CONCAVIFIABILITY OF PREFERENCES AND DETERMINACY OF

EQUILIBRIUM

~

Mario Rui Pascoa e Sirgio Ribeiro da Costa Wer

lang - Maio de 1991

175. A CONTABILIDADE DOS AGREGADOS MONETÂRIOS NO BRASIL - Carlos Ivan Simonsen Leal e Sirgio Ribeiro da. Costa Wer1ang

de 1991.

maio 176. HOMOTHETIC PREFERENCES - James Dow e Sirgio Ribeiro da Costa

Wer1ang - 1991

177. ~ARREIRAS Ã ENTRADA NAS INDÚSTRIAS: O PAPEL DA FIRMA PIONEIRA Luiz Guilherme Schymura de Oliveira -_, 1991.

178. POUPANÇA E CRESCIMENTO ECONÔMICO - O CASO BRASILEIRO - Mario Henrique Simonsen ~ agosto de 1991.

179~ EXCESS VOLATILITY OF STOCK PRICES AND KNIGHTIAN UNCERTAINTY -James Dow e Sérgio Ribeiro da Costa Werlang - 1991 •

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